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106.813 279.382 106.813 280.335 c 106.813 281.24 106.179 281.874 105.284 281.874 c 104.79 281.874 104.402 281.703 104.137 281.373 c 104.143 282.556 104.541 283.213 105.261 283.213 c 105.702 283.213 106.006 282.969 106.106 282.544 c 106.729 282.544 l h 105.313 281.373 m 105.925 281.373 106.31 280.956 106.31 280.286 c 106.31 279.657 105.876 279.199 105.291 279.199 c 104.698 279.199 104.25 279.679 104.25 280.321 c 104.25 280.942 104.683 281.373 105.313 281.373 c f 109.069 283.715 m 108.616 283.715 108.206 283.527 107.951 283.213 c 107.636 282.783 107.479 282.13 107.479 281.225 c 107.479 279.575 108.026 278.697 109.069 278.697 c 110.095 278.697 110.656 279.574 110.656 281.181 c 110.656 282.135 110.506 282.77 110.186 283.213 c 109.931 283.534 109.528 283.715 109.069 283.715 c h 109.069 283.213 m 109.796 283.213 110.155 282.548 110.155 281.235 c 110.155 279.848 109.802 279.199 109.052 279.199 c 108.341 279.199 107.98 279.877 107.98 281.216 c 107.98 282.556 108.341 283.213 109.069 283.213 c f 139.104 281.411 m 139.594 281.713 139.755 281.961 139.755 282.419 c 139.755 283.18 139.174 283.715 138.334 283.715 c 137.5 283.715 136.911 283.18 136.911 282.419 c 136.911 281.965 137.06 281.72 137.5 281.411 c 136.995 281.144 136.746 280.739 136.746 280.205 c 136.746 279.314 137.398 278.697 138.334 278.697 c 139.27 278.697 139.922 279.314 139.922 280.198 c 139.922 280.739 139.656 281.144 139.104 281.41 c 139.104 281.411 l h 138.334 282.966 m 138.894 282.966 139.254 282.669 139.254 282.204 c 139.254 281.759 138.887 281.461 138.334 281.461 c 137.78 281.461 137.414 281.759 137.414 282.211 c 137.414 282.669 137.78 282.966 138.334 282.966 c h 138.334 281.206 m 138.98 281.206 139.42 280.803 139.42 280.205 c 139.42 279.602 138.98 279.199 138.318 279.199 c 137.689 279.199 137.247 279.609 137.247 280.205 c 137.247 280.803 137.689 281.206 138.334 281.206 c f 142.179 283.715 m 141.729 283.715 141.318 283.527 141.064 283.213 c 140.749 282.783 140.592 282.13 140.592 281.225 c 140.592 279.575 141.138 278.697 142.179 278.697 c 143.206 278.697 143.768 279.574 143.768 281.181 c 143.768 282.135 143.619 282.77 143.297 283.213 c 143.043 283.534 142.641 283.715 142.179 283.715 c h 142.179 283.213 m 142.907 283.213 143.268 282.548 143.268 281.235 c 143.268 279.848 142.915 279.199 142.165 279.199 c 141.454 279.199 141.092 279.877 141.092 281.216 c 141.092 282.556 141.454 283.213 142.179 283.213 c f 169.21 282.318 m 169.21 278.864 l 169.712 278.864 l 169.712 283.715 l 169.324 283.715 l 169.117 282.969 168.983 282.865 168.072 282.75 c 168.072 282.32 l f 173.141 283.715 m 172.688 283.715 172.277 283.527 172.023 283.213 c 171.708 282.783 171.552 282.13 171.552 281.225 c 171.552 279.575 172.097 278.697 173.141 278.697 c 174.167 278.697 174.729 279.574 174.729 281.181 c 174.729 282.135 174.578 282.77 174.256 283.213 c 174.002 283.534 173.6 283.715 173.141 283.715 c h 173.141 283.213 m 173.866 283.213 174.227 282.548 174.227 281.235 c 174.227 279.848 173.874 279.199 173.126 279.199 c 172.413 279.199 172.053 279.877 172.053 281.216 c 172.053 282.556 172.413 283.213 173.141 283.213 c f 176.986 283.715 m 176.536 283.715 176.124 283.527 175.871 283.213 c 175.554 282.783 175.398 282.13 175.398 281.225 c 175.398 279.575 175.944 278.697 176.986 278.697 c 178.013 278.697 178.574 279.574 178.574 281.181 c 178.574 282.135 178.425 282.77 178.104 283.213 c 177.849 283.534 177.446 283.715 176.986 283.715 c h 176.986 283.213 m 177.713 283.213 178.074 282.548 178.074 281.235 c 178.074 279.848 177.721 279.199 176.971 279.199 c 176.259 279.199 175.899 279.877 175.899 281.216 c 175.899 282.556 176.259 283.213 176.986 283.213 c f 202.322 282.318 m 202.322 278.864 l 202.825 278.864 l 202.825 283.715 l 202.436 283.715 l 202.229 282.969 202.096 282.865 201.185 282.75 c 201.185 282.32 l f 207.807 279.367 m 205.244 279.367 l 205.305 279.773 205.525 280.031 206.123 280.386 c 206.81 280.764 l 207.492 281.142 207.841 281.652 207.841 282.262 c 207.841 282.671 207.676 283.059 207.388 283.323 c 207.099 283.59 206.743 283.715 206.282 283.715 c 205.664 283.715 205.204 283.499 204.936 283.093 c 204.763 282.838 204.689 282.544 204.676 282.056 c 205.308 282.056 l 205.33 282.384 205.373 282.583 205.458 282.74 c 205.623 283.035 205.953 283.212 206.334 283.212 c 206.91 283.212 207.34 282.819 207.34 282.296 c 207.34 281.912 207.104 281.58 206.652 281.335 c 205.991 280.976 l 204.93 280.397 204.622 279.937 204.564 278.863 c 207.808 278.863 l f 210.1 283.715 m 209.647 283.715 209.236 283.527 208.982 283.213 c 208.667 282.783 208.509 282.13 208.509 281.225 c 208.509 279.575 209.057 278.697 210.1 278.697 c 211.126 278.697 211.688 279.574 211.688 281.181 c 211.688 282.135 211.536 282.77 211.215 283.213 c 210.96 283.534 210.559 283.715 210.1 283.715 c h 210.1 283.213 m 210.825 283.213 211.187 282.548 211.187 281.235 c 211.187 279.848 210.834 279.199 210.084 279.199 c 209.372 279.199 209.011 279.877 209.011 281.216 c 209.011 282.556 209.372 283.213 210.1 283.213 c f 235.435 282.318 m 235.435 278.864 l 235.936 278.864 l 235.936 283.715 l 235.548 283.715 l 235.34 282.969 235.208 282.865 234.299 282.75 c 234.299 282.32 l f 239.783 280.036 m 239.783 278.864 l 240.285 278.864 l 240.285 280.036 l 241.025 280.036 l 241.025 280.538 l 240.285 280.538 l 240.285 283.715 l 239.841 283.715 l 237.636 280.671 l 237.636 280.036 l 239.783 280.036 l h 239.783 280.538 m 238.167 280.538 l 239.783 282.718 l f 243.21 283.715 m 242.761 283.715 242.348 283.527 242.093 283.213 c 241.781 282.783 241.623 282.13 241.623 281.225 c 241.623 279.575 242.171 278.697 243.21 278.697 c 244.237 278.697 244.8 279.574 244.8 281.181 c 244.8 282.135 244.648 282.77 244.328 283.213 c 244.074 283.534 243.67 283.715 243.21 283.715 c h 243.21 283.213 m 243.938 283.213 244.296 282.548 244.296 281.235 c 244.296 279.848 243.945 279.199 243.197 279.199 c 242.484 279.199 242.125 279.877 242.125 281.216 c 242.125 282.556 242.484 283.213 243.21 283.213 c f 4.9663 289.503 m 4.5151 289.503 4.1035 289.316 3.8486 289.003 c 3.5361 288.571 3.3784 287.919 3.3784 287.014 c 3.3784 285.364 3.9243 284.486 4.9663 284.486 c 5.9932 284.486 6.5542 285.362 6.5542 286.971 c 6.5542 287.924 6.4053 288.558 6.0835 289.003 c 5.8296 289.323 5.4268 289.503 4.9663 289.503 c h 4.9663 289.003 m 5.6943 289.003 6.0532 288.337 6.0532 287.025 c 6.0532 285.638 5.7007 284.988 4.9507 284.988 c 4.2388 284.988 3.8794 285.665 3.8794 287.006 c 3.8794 288.344 4.2388 289.003 4.9663 289.003 c f 1.5679 304.372 m 1.5679 300.919 l 2.0688 300.919 l 2.0688 305.769 l 1.6816 305.769 l 1.4736 305.023 1.3403 304.919 0.42969 304.804 c 0.42969 304.374 l f 5.4976 305.769 m 5.0464 305.769 4.6343 305.581 4.3794 305.268 c 4.0674 304.838 3.9097 304.183 3.9097 303.278 c 3.9097 301.629 4.4556 300.753 5.4976 300.753 c 6.5239 300.753 7.0854 301.628 7.0854 303.237 c 7.0854 304.19 6.936 304.824 6.6143 305.268 c 6.3604 305.589 5.958 305.769 5.4976 305.769 c h 5.4976 305.268 m 6.2251 305.268 6.5845 304.604 6.5845 303.291 c 6.5845 301.902 6.2315 301.255 5.4819 301.255 c 4.77 301.255 4.4107 301.931 4.4107 303.272 c 4.4107 304.611 4.77 305.268 5.4976 305.268 c f 3.2749 317.803 m 0.71338 317.803 l 0.77539 318.21 0.99463 318.468 1.5918 318.822 c 2.2798 319.2 l 2.9614 319.58 3.3105 320.089 3.3105 320.697 c 3.3105 321.11 3.1465 321.495 2.8565 321.76 c 2.5674 322.025 2.2119 322.151 1.752 322.151 c 1.1328 322.151 0.67383 321.936 0.40479 321.53 c 0.2334 321.275 0.15723 320.979 0.14502 320.491 c 0.77734 320.491 l 0.7998 320.82 0.84082 321.02 0.92675 321.176 c 1.0928 321.47 1.4238 321.648 1.8042 321.648 c 2.3789 321.648 2.8105 321.255 2.8105 320.733 c 2.8105 320.349 2.5732 320.018 2.1221 319.77 c 1.4609 319.412 l 0.40087 318.834 0.091309 318.374 0.03418 317.299 c 3.2769 317.299 l f 5.5679 322.151 m 5.1172 322.151 4.7051 321.965 4.4502 321.649 c 4.1377 321.218 3.9805 320.566 3.9805 319.662 c 3.9805 318.012 4.5259 317.133 5.5679 317.133 c 6.5947 317.133 7.1558 318.011 7.1558 319.619 c 7.1558 320.573 7.0068 321.206 6.6851 321.649 c 6.4312 321.97 6.0283 322.151 5.5679 322.151 c h 5.5679 321.649 m 6.2959 321.649 6.6553 320.985 6.6553 319.672 c 6.6553 318.285 6.3027 317.635 5.5527 317.635 c 4.8403 317.635 4.481 318.314 4.481 319.653 c 4.481 320.992 4.8403 321.649 5.5679 321.649 c f 1.3252 335.74 m 1.6489 335.74 l 2.3076 335.74 2.6426 335.441 2.6426 334.865 c 2.6426 334.263 2.2676 333.902 1.6411 333.902 c 0.98486 333.902 0.66454 334.246 0.62256 334.987 c 0.021973 334.987 l 0.049309 334.591 0.11376 334.336 0.22655 334.113 c 0.46239 333.643 0.92529 333.4 1.562 333.4 c 2.5254 333.4 3.1455 333.997 3.1455 334.915 c 3.1455 335.53 2.9443 335.873 2.4619 336.071 c 2.9189 336.25 3.1455 336.593 3.1455 337.079 c 3.1455 337.916 2.5889 338.417 1.6602 338.417 c 0.67919 338.417 0.15576 337.891 0.13477 336.874 c 0.63671 336.874 l 0.64404 337.169 0.67626 337.333 0.75976 337.484 c 0.91553 337.749 1.2539 337.916 1.6787 337.916 c 2.2803 337.916 2.6426 337.585 2.6426 337.043 c 2.6426 336.682 2.5063 336.467 2.2114 336.351 c 2.0283 336.279 1.792 336.249 1.3252 336.242 c f q 0 354.78 244.8 -354.78 re W n 5.5703 338.417 m 5.1196 338.417 4.7075 338.229 4.4526 337.916 c 4.1401 337.484 3.9824 336.83 3.9824 335.925 c 3.9824 334.278 4.5283 333.4 5.5703 333.4 c 6.5972 333.4 7.1582 334.277 7.1582 335.884 c 7.1582 336.839 7.0093 337.472 6.6875 337.916 c 6.4336 338.236 6.0308 338.417 5.5703 338.417 c h 5.5703 337.916 m 6.2983 337.916 6.6577 337.251 6.6577 335.938 c 6.6577 334.55 6.3052 333.902 5.5552 333.902 c 4.8428 333.902 4.4834 334.579 4.4834 335.917 c 4.4834 337.258 4.8428 337.916 5.5703 337.916 c f 2.146 351.12 m 2.146 349.95 l 2.647 349.95 l 2.647 351.12 l 3.3892 351.12 l 3.3892 351.622 l 2.647 351.622 l 2.647 354.798 l 2.2031 354.798 l 0 351.755 l 0 351.12 l 2.146 351.12 l h 2.146 351.622 m 0.5293 351.622 l 2.146 353.802 l f 5.5747 354.798 m 5.124 354.798 4.7119 354.612 4.457 354.296 c 4.1445 353.867 3.9868 353.213 3.9868 352.308 c 3.9868 350.659 4.5327 349.781 5.5747 349.781 c 6.6016 349.781 7.1626 350.658 7.1626 352.266 c 7.1626 353.22 7.0137 353.853 6.6919 354.296 c 6.438 354.618 6.0352 354.798 5.5747 354.798 c h 5.5747 354.296 m 6.3027 354.296 6.6621 353.632 6.6621 352.321 c 6.6621 350.933 6.3091 350.283 5.5596 350.283 c 4.8472 350.283 4.4878 350.961 4.4878 352.3 c 4.4878 353.641 4.8472 354.296 5.5747 354.296 c f Q 27.511 345.496 m 26.931 345.496 l 26.931 346.419 l 26.429 346.419 l 26.429 345.496 l 25.856 345.496 l 25.856 344.993 l 26.429 344.993 l 26.429 342.228 l 26.429 341.859 26.66 341.649 27.075 341.649 c 27.202 341.649 27.33 341.663 27.511 341.696 c 27.511 342.187 l 27.434 342.158 27.349 342.149 27.24 342.149 c 26.999 342.149 26.931 342.219 26.931 342.479 c 26.931 344.992 l 27.511 344.992 l f 31.28 344.325 m 31.28 344.325 -3.3364 -0.50153 re 31.28 343.153 m 27.944 343.153 l 27.944 342.652 l 31.28 342.652 l f 33.453 345.27 m 33.453 341.817 l 33.953 341.817 l 33.953 346.666 l 33.566 346.666 l 33.358 345.919 33.225 345.817 32.315 345.7 c 32.315 345.272 l f 38.718 346.666 m 36.214 346.666 l 35.852 344.042 l 36.429 344.042 l 36.723 344.376 36.968 344.491 37.361 344.491 c 38.038 344.491 38.469 344.035 38.469 343.301 c 38.469 342.587 38.048 342.152 37.364 342.152 c 36.814 342.152 36.479 342.436 36.328 343.016 c 35.701 343.016 l 35.783 342.614 35.85 342.419 35.994 342.239 c 36.268 341.863 36.76 341.651 37.308 341.651 c 38.286 341.651 38.97 342.36 38.97 343.384 c 38.97 344.339 38.334 344.995 37.404 344.995 c 37.062 344.995 36.788 344.918 36.507 344.741 c 36.698 346.165 l 38.717 346.165 l f 68.729 345.496 m 68.15 345.496 l 68.15 346.419 l 67.647 346.419 l 67.647 345.496 l 67.076 345.496 l 67.076 344.993 l 67.647 344.993 l 67.647 342.228 l 67.647 341.859 67.879 341.649 68.294 341.649 c 68.421 341.649 68.55 341.663 68.729 341.696 c 68.729 342.187 l 68.655 342.158 68.568 342.149 68.461 342.149 c 68.219 342.149 68.15 342.219 68.15 342.479 c 68.15 344.992 l 68.729 344.992 l f 72.665 344.325 m 72.665 344.325 -3.335 -0.50153 re 72.665 343.153 m 69.33 343.153 l 69.33 342.652 l 72.665 342.652 l f 75.339 342.986 m 75.339 341.817 l 75.841 341.817 l 75.841 342.986 l 76.583 342.986 l 76.583 343.488 l 75.841 343.488 l 75.841 346.666 l 75.397 346.666 l 73.192 343.622 l 73.192 342.986 l 75.339 342.986 l h 75.339 343.488 m 73.724 343.488 l 75.339 345.669 l f 78.768 346.666 m 78.316 346.666 77.906 346.478 77.651 346.164 c 77.337 345.733 77.179 345.081 77.179 344.176 c 77.179 342.527 77.726 341.649 78.768 341.649 c 79.795 341.649 80.357 342.525 80.357 344.133 c 80.357 345.088 80.207 345.72 79.886 346.164 c 79.631 346.485 79.228 346.666 78.768 346.666 c h 78.768 346.164 m 79.496 346.164 79.855 345.499 79.855 344.189 c 79.855 342.798 79.503 342.15 78.754 342.15 c 78.041 342.15 77.682 342.828 77.682 344.168 c 77.682 345.506 78.041 346.164 78.768 346.164 c f 110.092 345.496 m 109.512 345.496 l 109.512 346.419 l 109.009 346.419 l 109.009 345.496 l 108.438 345.496 l 108.438 344.993 l 109.009 344.993 l 109.009 342.228 l 109.009 341.859 109.241 341.649 109.655 341.649 c 109.784 341.649 109.912 341.663 110.092 341.696 c 110.092 342.187 l 110.016 342.158 109.929 342.149 109.823 342.149 c 109.579 342.149 109.512 342.219 109.512 342.479 c 109.512 344.992 l 110.092 344.992 l f 114.028 344.325 m 114.028 344.325 -3.337 -0.50153 re 114.028 343.153 m 110.691 343.153 l 110.691 342.652 l 114.028 342.652 l f 117.793 345.496 m 117.677 346.229 117.159 346.666 116.425 346.666 c 115.893 346.666 115.417 346.403 115.133 345.972 c 114.832 345.499 114.695 344.904 114.695 344.02 c 114.695 343.206 114.817 342.683 115.102 342.253 c 115.36 341.861 115.777 341.649 116.306 341.649 c 117.219 341.649 117.874 342.332 117.874 343.286 c 117.874 344.19 117.241 344.825 116.346 344.825 c 115.852 344.825 115.465 344.654 115.199 344.325 c 115.206 345.506 115.603 346.164 116.323 346.164 c 116.765 346.164 117.068 345.919 117.168 345.496 c 117.793 345.496 l h 116.374 344.325 m 116.988 344.325 117.371 343.909 117.371 343.238 c 117.371 342.608 116.938 342.15 116.353 342.15 c 115.761 342.15 115.313 342.63 115.313 343.273 c 115.313 343.893 115.745 344.325 116.374 344.325 c f 121.467 346.666 m 118.963 346.666 l 118.6 344.042 l 119.179 344.042 l 119.471 344.376 119.716 344.491 120.109 344.491 c 120.789 344.491 121.217 344.035 121.217 343.301 c 121.217 342.587 120.795 342.152 120.112 342.152 c 119.562 342.152 119.228 342.436 119.077 343.016 c 118.449 343.016 l 118.531 342.614 118.598 342.419 118.742 342.239 c 119.016 341.863 119.508 341.651 120.056 341.651 c 121.035 341.651 121.719 342.36 121.719 343.384 c 121.719 344.339 121.084 344.995 120.152 344.995 c 119.811 344.995 119.536 344.918 119.255 344.741 c 119.447 346.165 l 121.464 346.165 l f 151.48 345.496 m 150.9 345.496 l 150.9 346.419 l 150.399 346.419 l 150.399 345.496 l 149.827 345.496 l 149.827 344.993 l 150.399 344.993 l 150.399 342.228 l 150.399 341.859 150.629 341.649 151.043 341.649 c 151.172 341.649 151.3 341.663 151.48 341.696 c 151.48 342.187 l 151.405 342.158 151.317 342.149 151.21 342.149 c 150.967 342.149 150.9 342.219 150.9 342.479 c 150.9 344.992 l 151.48 344.992 l f 155.249 344.325 m 155.249 344.325 -3.337 -0.50153 re 155.249 343.153 m 151.912 343.153 l 151.912 342.652 l 155.249 342.652 l f 156.114 342.933 m 156.23 342.128 156.755 341.649 157.5 341.649 c 158.039 341.649 158.528 341.91 158.811 342.341 c 159.122 342.813 159.259 343.409 159.259 344.294 c 159.259 345.111 159.138 345.631 158.854 346.063 c 158.591 346.453 158.174 346.666 157.646 346.666 c 156.736 346.666 156.082 345.979 156.082 345.029 c 156.082 344.126 156.716 343.488 157.618 343.488 c 158.09 343.488 158.436 343.641 158.758 343.991 c 158.751 342.807 158.345 342.15 157.612 342.15 c 157.162 342.15 156.852 342.435 156.749 342.933 c 156.114 342.933 l h 157.58 346.164 m 158.16 346.164 158.596 345.686 158.596 345.039 c 158.596 344.426 158.166 343.991 157.558 343.991 c 156.958 343.991 156.585 344.404 156.585 345.074 c 156.585 345.707 157.009 346.164 157.58 346.164 c f 161.352 346.666 m 160.899 346.666 160.489 346.478 160.234 346.164 c 159.919 345.733 159.763 345.081 159.763 344.176 c 159.763 342.527 160.31 341.649 161.352 341.649 c 162.378 341.649 162.94 342.525 162.94 344.133 c 162.94 345.088 162.789 345.72 162.468 346.164 c 162.215 346.485 161.811 346.666 161.352 346.666 c h 161.352 346.164 m 162.08 346.164 162.438 345.499 162.438 344.189 c 162.438 342.798 162.085 342.15 161.336 342.15 c 160.624 342.15 160.264 342.828 160.264 344.168 c 160.264 345.506 160.624 346.164 161.352 346.164 c f 192.113 345.496 m 191.531 345.496 l 191.531 346.419 l 191.03 346.419 l 191.03 345.496 l 190.458 345.496 l 190.458 344.993 l 191.03 344.993 l 191.03 342.228 l 191.03 341.859 191.26 341.649 191.675 341.649 c 191.804 341.649 191.931 341.663 192.113 341.696 c 192.113 342.187 l 192.038 342.158 191.949 342.149 191.843 342.149 c 191.6 342.149 191.531 342.219 191.531 342.479 c 191.531 344.992 l 192.113 344.992 l f 196.049 344.325 m 196.049 344.325 -3.336 -0.50153 re 196.049 343.153 m 192.713 343.153 l 192.713 342.652 l 196.049 342.652 l f 198.221 345.27 m 198.221 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l 199.92 157.828 l 46.945 157.828 l S 0 0 0 RG 46.945 267.711 m 199.92 267.711 l 46.945 157.828 m 199.92 157.828 l 199.92 267.71 l 46.945 157.828 m 46.945 267.71 l 46.945 157.828 m 199.92 157.828 l 46.945 157.828 m 46.945 267.71 l 46.945 157.828 m 46.945 159.378 l 46.945 267.711 m 46.945 266.219 l S 0 0 0 rg 47.02 154.43 m 46.573 154.43 46.168 154.213 45.917 153.85 c 45.606 153.429 45.451 152.789 45.451 151.904 c 45.451 150.292 45.992 149.434 47.02 149.434 c 48.034 149.434 48.588 150.292 48.588 151.863 c 48.588 152.795 48.438 153.416 48.121 153.85 c 47.871 154.221 47.471 154.43 47.02 154.43 c h 47.02 153.85 m 47.679 153.85 48.007 153.215 48.007 151.962 c 48.007 150.635 47.687 150.015 47.005 150.015 c 46.358 150.015 46.032 150.662 46.032 151.942 c 46.032 153.222 46.358 153.85 47.02 153.85 c f 97.899 157.828 m 97.899 159.377 l 97.899 267.71 m 97.899 266.218 l S 99.225 154.43 m 96.743 154.43 l 96.384 151.775 l 96.939 151.775 l 97.22 152.107 97.454 152.222 97.832 152.222 c 98.483 152.222 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151.876 151.962 c 151.876 150.635 151.556 150.015 150.875 150.015 c 150.229 150.015 149.901 150.662 149.901 151.942 c 149.901 153.222 150.229 153.85 150.888 153.85 c f 199.921 157.828 m 199.921 159.377 l 199.921 267.71 m 199.921 266.218 l S 197.885 153.026 m 197.885 149.551 l 198.467 149.551 l 198.467 154.43 l 198.084 154.43 l 197.876 153.68 197.746 153.576 196.846 153.459 c 196.846 153.026 l f 203.21 154.43 m 200.729 154.43 l 200.369 151.775 l 200.925 151.775 l 201.207 152.107 201.44 152.222 201.818 152.222 c 202.469 152.222 202.882 151.793 202.882 151.1 c 202.882 150.425 202.476 150.015 201.818 150.015 c 201.288 150.015 200.966 150.255 200.822 150.749 c 200.217 150.749 l 200.299 150.361 200.367 150.175 200.51 150.002 c 200.78 149.641 201.269 149.434 201.812 149.434 c 202.782 149.434 203.461 150.151 203.461 151.181 c 203.461 152.144 202.831 152.804 201.908 152.804 c 201.569 152.804 201.299 152.703 201.019 152.47 c 201.209 153.85 l 203.209 153.85 l f 46.945 157.828 m 48.438 157.828 l 199.921 157.828 m 198.372 157.828 l S 42.084 160.239 m 41.638 160.239 41.233 160.023 40.983 159.659 c 40.672 159.239 40.516 158.598 40.516 157.714 c 40.516 156.102 41.058 155.243 42.084 155.243 c 43.099 155.243 43.654 156.102 43.654 157.673 c 43.654 158.605 43.504 159.226 43.186 159.659 c 42.937 160.03 42.537 160.239 42.084 160.239 c h 42.084 159.659 m 42.744 159.659 43.073 159.024 43.073 157.771 c 43.073 156.444 42.751 155.824 42.07 155.824 c 41.423 155.824 41.097 156.472 41.097 157.751 c 41.097 159.031 41.423 159.659 42.084 159.659 c f 46.945 173.55 m 48.438 173.55 l 199.921 173.55 m 198.372 173.55 l S 43.401 175.925 m 40.919 175.925 l 40.561 173.269 l 41.116 173.269 l 41.396 173.601 41.63 173.716 42.008 173.716 c 42.66 173.716 43.073 173.288 43.073 172.593 c 43.073 171.92 42.667 171.509 42.008 171.509 c 41.479 171.509 41.157 171.75 41.012 172.243 c 40.409 172.243 l 40.489 171.857 40.559 171.669 40.7 171.496 c 40.972 171.135 41.46 170.929 42.002 170.929 c 42.973 170.929 43.652 171.644 43.652 172.674 c 43.652 173.638 43.021 174.298 42.099 174.298 c 41.759 174.298 41.489 174.197 41.209 173.964 c 41.4 175.344 l 43.4 175.344 l f 46.945 189.272 m 48.438 189.272 l 199.921 189.272 m 198.372 189.272 l S 38.076 190.205 m 38.076 186.73 l 38.657 186.73 l 38.657 191.61 l 38.274 191.61 l 38.068 190.859 37.938 190.755 37.037 190.638 c 37.037 190.205 l f 42.084 191.61 m 41.638 191.61 41.233 191.394 40.983 191.029 c 40.672 190.609 40.516 189.968 40.516 189.084 c 40.516 187.471 41.058 186.613 42.084 186.613 c 43.099 186.613 43.654 187.471 43.654 189.043 c 43.654 189.975 43.504 190.596 43.186 191.029 c 42.937 191.4 42.537 191.61 42.084 191.61 c h 42.084 191.029 m 42.744 191.029 43.073 190.394 43.073 189.14 c 43.073 187.815 42.751 187.194 42.07 187.194 c 41.423 187.194 41.097 187.842 41.097 189.121 c 41.097 190.402 41.423 191.029 42.084 191.029 c f 46.945 204.936 m 48.438 204.936 l 199.921 204.936 m 198.372 204.936 l S 38.076 205.89 m 38.076 202.414 l 38.657 202.414 l 38.657 207.295 l 38.274 207.295 l 38.068 206.544 37.938 206.44 37.037 206.324 c 37.037 205.89 l f 43.401 207.295 m 40.919 207.295 l 40.561 204.639 l 41.116 204.639 l 41.396 204.971 41.63 205.087 42.008 205.087 c 42.66 205.087 43.073 204.656 43.073 203.964 c 43.073 203.289 42.667 202.88 42.008 202.88 c 41.479 202.88 41.157 203.12 41.012 203.613 c 40.409 203.613 l 40.489 203.226 40.559 203.038 40.7 202.865 c 40.972 202.506 41.46 202.298 42.002 202.298 c 42.973 202.298 43.652 203.014 43.652 204.044 c 43.652 205.007 43.021 205.668 42.099 205.668 c 41.759 205.668 41.489 205.567 41.209 205.335 c 41.4 206.714 l 43.4 206.714 l f 46.945 220.659 m 48.438 220.659 l 199.921 220.659 m 198.372 220.659 l S 39.785 218.681 m 37.243 218.681 l 37.304 219.082 37.522 219.337 38.114 219.689 c 38.796 220.062 l 39.472 220.435 39.819 220.939 39.819 221.541 c 39.819 221.948 39.655 222.329 39.37 222.591 c 39.084 222.854 38.729 222.979 38.273 222.979 c 37.66 222.979 37.204 222.757 36.938 222.344 c 36.768 222.084 36.692 221.781 36.678 221.286 c 37.286 221.286 l 37.307 221.601 37.348 221.794 37.431 221.945 c 37.589 222.226 37.906 222.398 38.273 222.398 c 38.825 222.398 39.24 222.011 39.24 221.493 c 39.24 221.112 39.012 220.785 38.576 220.541 c 37.942 220.188 l 36.921 219.615 36.624 219.16 36.569 218.1 c 39.785 218.1 l f 42.084 222.98 m 41.638 222.98 41.233 222.764 40.983 222.398 c 40.672 221.98 40.516 221.338 40.516 220.453 c 40.516 218.841 41.058 217.984 42.084 217.984 c 43.099 217.984 43.654 218.841 43.654 220.413 c 43.654 221.345 43.504 221.965 43.186 222.398 c 42.937 222.771 42.537 222.98 42.084 222.98 c h 42.084 222.398 m 42.744 222.398 43.073 221.764 43.073 220.51 c 43.073 219.185 42.751 218.564 42.07 218.564 c 41.423 218.564 41.097 219.211 41.097 220.49 c 41.097 221.772 41.423 222.398 42.084 222.398 c f 46.945 236.323 m 48.438 236.323 l 199.921 236.323 m 198.372 236.323 l S 39.785 234.365 m 37.243 234.365 l 37.304 234.767 37.522 235.022 38.114 235.374 c 38.796 235.747 l 39.472 236.12 39.819 236.624 39.819 237.225 c 39.819 237.634 39.655 238.014 39.37 238.276 c 39.084 238.538 38.729 238.664 38.273 238.664 c 37.66 238.664 37.204 238.443 36.938 238.03 c 36.768 237.769 36.692 237.467 36.678 236.972 c 37.286 236.972 l 37.307 237.286 37.348 237.478 37.431 237.629 c 37.589 237.911 37.906 238.084 38.273 238.084 c 38.825 238.084 39.24 237.696 39.24 237.178 c 39.24 236.798 39.012 236.471 38.576 236.226 c 37.942 235.872 l 36.921 235.301 36.624 234.845 36.569 233.784 c 39.785 233.784 l f 43.401 238.665 m 40.919 238.665 l 40.561 236.009 l 41.116 236.009 l 41.396 236.341 41.63 236.457 42.008 236.457 c 42.66 236.457 43.073 236.027 43.073 235.333 c 43.073 234.659 42.667 234.249 42.008 234.249 c 41.479 234.249 41.157 234.49 41.012 234.983 c 40.409 234.983 l 40.489 234.596 40.559 234.408 40.7 234.235 c 40.972 233.875 41.46 233.668 42.002 233.668 c 42.973 233.668 43.652 234.384 43.652 235.415 c 43.652 236.378 43.021 237.037 42.099 237.037 c 41.759 237.037 41.489 236.936 41.209 236.705 c 41.4 238.084 l 43.4 238.084 l f 46.945 252.045 m 48.438 252.045 l 199.921 252.045 m 198.372 252.045 l S 37.856 251.677 m 38.196 251.677 l 38.883 251.677 39.238 251.393 39.238 250.848 c 39.238 250.276 38.854 249.934 38.211 249.934 c 37.54 249.934 37.21 250.238 37.17 250.889 c 36.554 250.889 l 36.583 250.506 36.65 250.258 36.768 250.044 c 37.016 249.588 37.497 249.353 38.167 249.353 c 39.172 249.353 39.819 249.947 39.819 250.861 c 39.819 251.476 39.578 251.817 38.992 252.014 c 39.466 252.191 39.704 252.531 39.704 253.018 c 39.704 253.849 39.145 254.349 38.214 254.349 c 37.228 254.349 36.704 253.813 36.683 252.775 c 37.265 252.775 l 37.271 253.056 37.3 253.213 37.378 253.357 c 37.521 253.613 37.835 253.769 38.229 253.769 c 38.786 253.769 39.124 253.469 39.124 252.981 c 39.124 252.656 38.992 252.461 38.709 252.357 c 38.534 252.291 38.307 252.265 37.857 252.259 c f 42.084 254.349 m 41.638 254.349 41.233 254.134 40.983 253.768 c 40.672 253.349 40.516 252.707 40.516 251.823 c 40.516 250.211 41.058 249.353 42.084 249.353 c 43.099 249.353 43.654 250.211 43.654 251.782 c 43.654 252.714 43.504 253.335 43.186 253.768 c 42.937 254.141 42.537 254.349 42.084 254.349 c h 42.084 253.768 m 42.744 253.768 43.073 253.134 43.073 251.881 c 43.073 250.554 42.751 249.934 42.07 249.934 c 41.423 249.934 41.097 250.581 41.097 251.86 c 41.097 253.141 41.423 253.768 42.084 253.768 c f 46.945 267.711 m 48.438 267.711 l 199.921 267.711 m 198.372 267.711 l S 37.856 267.362 m 38.196 267.362 l 38.883 267.362 39.238 267.08 39.238 266.532 c 39.238 265.961 38.854 265.619 38.211 265.619 c 37.54 265.619 37.21 265.923 37.17 266.574 c 36.554 266.574 l 36.583 266.192 36.65 265.944 36.768 265.729 c 37.016 265.273 37.497 265.039 38.167 265.039 c 39.172 265.039 39.819 265.633 39.819 266.547 c 39.819 267.161 39.578 267.501 38.992 267.7 c 39.466 267.878 39.704 268.217 39.704 268.704 c 39.704 269.535 39.145 270.035 38.214 270.035 c 37.228 270.035 36.704 269.498 36.683 268.46 c 37.265 268.46 l 37.271 268.741 37.3 268.898 37.378 269.042 c 37.521 269.298 37.835 269.456 38.229 269.456 c 38.786 269.456 39.124 269.155 39.124 268.668 c 39.124 268.342 38.992 268.147 38.709 268.042 c 38.534 267.977 38.307 267.95 37.857 267.944 c f 43.401 270.035 m 40.919 270.035 l 40.561 267.379 l 41.116 267.379 l 41.396 267.711 41.63 267.827 42.008 267.827 c 42.66 267.827 43.073 267.397 43.073 266.704 c 43.073 266.03 42.667 265.619 42.008 265.619 c 41.479 265.619 41.157 265.859 41.012 266.353 c 40.409 266.353 l 40.489 265.966 40.559 265.779 40.7 265.606 c 40.972 265.245 41.46 265.039 42.002 265.039 c 42.973 265.039 43.652 265.755 43.652 266.784 c 43.652 267.748 43.021 268.408 42.099 268.408 c 41.759 268.408 41.489 268.307 41.209 268.075 c 41.4 269.454 l 43.4 269.454 l f 46.945 267.711 m 199.92 267.711 l 46.945 157.828 m 199.92 157.828 l 199.92 267.71 l 46.945 157.828 m 46.945 267.71 l S q 46.945 157.771 m 199.977 157.771 l 199.977 267.711 l 46.945 267.711 l 46.945 157.771 l W n 1 0 0 RG 154.993 158.63 m 155.51 158.63 l 155.988 158.63 156.466 158.63 156.943 158.63 c 157.288 158.63 l 157.459 158.63 157.631 158.63 157.803 158.63 c 157.918 158.63 l 158.033 158.574 l 158.243 158.574 158.454 158.574 158.664 158.574 c 159.238 158.574 l 159.832 158.574 160.424 158.574 161.017 158.574 c 161.36 158.574 l 161.476 158.515 l 162.222 158.515 l 162.471 158.515 162.719 158.515 162.968 158.515 c 163.829 158.515 l 164.539 158.558 164.921 158.426 165.607 158.458 c 165.893 158.458 l 166.563 158.458 167.232 158.458 167.902 158.458 c 168.073 158.458 l 168.188 158.402 l 168.361 158.402 l 170.019 158.438 171.647 158.348 173.295 158.343 c 173.926 158.343 l 182.479 158.194 191.057 158.043 199.632 158.058 c 199.976 158.058 l S Q 1 0 0 RG 119.246 171.54 m 119.417 171.426 l 119.532 171.311 l 119.704 171.254 l 119.818 171.14 l 119.99 171.082 l 120.617 170.632 121.383 170.252 121.999 169.819 c 122.114 169.763 l 122.286 169.648 l 122.987 169.256 123.65 168.818 124.351 168.444 c 124.465 168.387 l 124.638 168.272 l 124.752 168.214 l 126.21 167.389 127.697 166.545 129.17 165.805 c 129.4 165.69 l 129.516 165.575 l 129.63 165.518 l 129.801 165.461 l 130.406 165.185 130.881 164.882 131.466 164.601 c 131.637 164.542 l 131.752 164.485 l 132.348 164.166 132.937 163.924 133.53 163.624 c 133.875 163.452 l 135.17 162.896 136.46 162.28 137.778 161.788 c 138.122 161.616 l 138.235 161.616 l 138.58 161.444 l 138.694 161.444 l 139.053 161.235 139.011 161.324 139.268 161.214 c 139.498 161.099 l 139.612 161.099 l 139.843 160.985 l 139.956 160.985 l 140.015 160.927 l 140.242 160.813 l 140.358 160.813 l 140.885 160.593 141.535 160.404 142.08 160.239 c 142.137 160.183 l 142.251 160.183 l 142.366 160.124 l 142.481 160.124 l 142.596 160.068 l 142.775 159.967 142.99 159.996 143.169 159.896 c 143.284 159.839 l 143.399 159.839 l 143.573 159.772 143.902 159.686 144.087 159.667 c 144.202 159.609 l 144.259 159.609 l 144.375 159.551 l 144.49 159.551 l 144.668 159.451 144.885 159.48 145.063 159.38 c 145.178 159.38 l 145.292 159.322 l 145.54 159.363 145.743 159.209 145.98 159.209 c 146.096 159.209 l 146.211 159.152 l 146.326 159.152 l 146.44 159.093 l 146.67 159.093 l 146.785 159.036 l 146.9 159.036 l 147.177 159.04 146.987 158.945 147.474 158.98 c 147.589 158.921 l 147.703 158.921 l 148.149 158.945 147.819 158.831 148.392 158.864 c 148.508 158.807 l 148.851 158.807 l 149.338 158.841 149.148 158.746 149.426 158.749 c 149.655 158.749 l 149.884 158.749 150.114 158.749 150.344 158.749 c 150.573 158.749 l 150.688 158.692 l 150.974 158.692 l 151.586 158.692 152.199 158.692 152.81 158.692 c 153.096 158.692 l 153.287 158.692 153.479 158.692 153.67 158.692 c 154.302 158.692 l 154.415 158.634 l 154.99 158.634 l S q 46.945 157.771 m 199.977 157.771 l 199.977 267.711 l 46.945 267.711 l 46.945 157.771 l W n 47.003 217.904 m 46.945 217.904 l 47.003 217.904 l 47.06 217.79 l 47.118 217.79 l 47.232 217.733 l 47.29 217.733 l 47.634 217.904 l 47.978 218.42 l 48.322 219.166 l 49.027 220.73 49.605 222.294 50.272 223.872 c 50.73 224.904 l 51.19 225.822 l 51.648 226.568 l 52.108 227.257 l 52.625 227.831 l 53.085 228.234 l 53.601 228.462 l 54.118 228.577 l 54.692 228.577 l 55.209 228.462 l 57.908 227.387 60.845 223.025 62.841 220.832 c 63.299 220.316 l 63.701 219.798 l 64.161 219.281 l 67.448 215.349 70.887 211.632 74.546 208.034 c 75.349 207.232 l 80.829 201.861 86.52 196.682 92.334 191.682 c 92.792 191.338 l 92.964 191.108 l 93.194 190.936 l 97.688 187.176 102.293 183.38 107.024 179.977 c 107.195 179.805 l 107.539 179.575 l 109.346 178.168 111.257 176.915 113.104 175.558 c 113.448 175.329 l 115.199 174.168 116.904 173.006 118.669 171.887 c 118.785 171.829 l 118.957 171.715 l 119.072 171.6 l 119.244 171.543 l S 0 1 0 RG 154.993 158.458 m 156.025 158.458 l 156.14 158.402 l 156.313 158.402 l 156.484 158.402 156.656 158.402 156.829 158.402 c 157.174 158.402 l 157.709 158.402 158.243 158.402 158.779 158.402 c 159.009 158.402 l 159.124 158.343 l 160.49 158.363 161.843 158.33 163.199 158.286 c 163.945 158.286 l 164.155 158.286 164.365 158.286 164.576 158.286 c 165.378 158.286 l 165.494 158.23 l 165.894 158.23 l 166.564 158.23 167.233 158.23 167.903 158.23 c 168.362 158.23 l 170.015 158.098 171.634 158.24 173.296 158.114 c 174.214 158.114 l 176 158.158 177.662 158.028 179.436 158.058 c 179.895 158.058 l 180.735 158.058 181.577 158.058 182.419 158.058 c 182.936 158.058 l 183.224 158.058 183.51 158.058 183.798 158.058 c 183.97 157.999 l 184.142 158.058 l 184.313 158.058 l 184.485 157.999 l 184.657 157.999 l 184.829 158.058 l 185.001 158.058 l 185.173 157.999 l 185.517 157.999 l 185.689 158.058 l 185.86 157.999 l 186.032 157.999 l 190.547 158.019 194.907 157.929 199.401 157.942 c 199.631 157.942 l 199.803 157.999 l 199.975 157.942 l S Q 0 1 0 RG 119.246 171.54 m 119.417 171.426 l 119.532 171.369 l 119.704 171.254 l 119.818 171.14 l 119.99 171.082 l 120.617 170.632 121.383 170.252 121.999 169.819 c 122.114 169.763 l 122.286 169.648 l 122.975 169.247 123.662 168.844 124.351 168.444 c 124.465 168.387 l 124.638 168.272 l 124.752 168.214 l 126.206 167.39 127.696 166.53 129.17 165.805 c 129.4 165.69 l 129.516 165.575 l 129.63 165.518 l 130.969 164.868 132.291 164.201 133.646 163.567 c 134.105 163.338 l 134.463 163.128 134.422 163.217 134.68 163.108 c 134.909 162.993 l 135.137 162.879 135.368 162.765 135.598 162.649 c 135.712 162.649 l 135.943 162.535 l 136.471 162.252 137.127 162.044 137.665 161.788 c 137.78 161.731 l 137.893 161.731 l 138.353 161.502 l 138.468 161.502 l 138.697 161.387 l 138.955 161.277 138.912 161.366 139.271 161.157 c 139.386 161.157 l 139.729 160.985 l 139.845 160.985 l 139.959 160.928 l 140.017 160.872 l 140.131 160.872 l 140.361 160.756 l 140.935 160.567 141.508 160.374 142.082 160.184 c 142.139 160.126 l 142.254 160.126 l 142.368 160.069 l 142.483 160.069 l 142.598 160.012 l 142.777 159.912 142.993 159.94 143.172 159.84 c 143.286 159.782 l 143.401 159.782 l 143.622 159.672 143.877 159.702 144.09 159.551 c 144.204 159.551 l 144.261 159.495 l 144.376 159.495 l 144.492 159.436 l 144.69 159.447 144.865 159.312 145.065 159.322 c 145.181 159.265 l 145.294 159.265 l 145.506 159.138 145.768 159.198 145.983 159.093 c 146.099 159.093 l 146.213 159.036 l 146.443 159.036 l 146.557 158.98 l 146.671 158.98 l 146.787 158.921 l 147.367 158.875 147.924 158.721 148.509 158.692 c 148.624 158.692 l 148.737 158.634 l 149.311 158.634 l 149.426 158.577 l 149.655 158.577 l 149.884 158.577 150.114 158.577 150.344 158.577 c 150.458 158.52 l 150.975 158.52 l 151.587 158.52 152.2 158.52 152.811 158.52 c 153.097 158.52 l 153.212 158.463 l 153.842 158.463 l 154.034 158.463 154.225 158.463 154.416 158.463 c 154.991 158.463 l 47.233 267.711 m 47.29 266.85 l 47.634 261.629 l 47.978 257.153 l 48.322 253.25 l 48.665 249.923 l 49.636 242.955 50.317 233.188 55.207 227.601 c 55.781 227.027 l 56.298 226.454 l 58.803 224.071 61.334 221.748 63.7 219.222 c 64.159 218.764 l 64.562 218.305 l 64.962 217.902 l 68.213 214.483 71.419 211.012 74.832 207.747 c 75.062 207.461 l 75.347 207.232 l 75.634 206.944 l 81.118 201.629 86.74 196.446 92.562 191.507 c 92.791 191.336 l 93.194 190.936 l 101.427 184.007 109.896 177.469 118.958 171.713 c 119.072 171.599 l 119.244 171.54 l S q 46.945 157.771 m 199.977 157.771 l 199.977 267.711 l 46.945 267.711 l 46.945 157.771 l W n 1 1 0 RG 154.993 157.885 m 155.623 157.885 l 155.795 157.885 155.967 157.885 156.14 157.885 c 156.313 157.885 l 156.601 157.869 156.351 157.971 156.829 157.941 c 157.174 157.941 l 157.709 157.941 158.243 157.941 158.779 157.941 c 159.238 157.941 l 159.545 158.065 160.61 157.966 161.017 157.999 c 161.245 157.999 l 161.956 157.963 162.366 158.098 163.083 158.056 c 163.944 158.056 l 164.154 158.056 164.364 158.056 164.575 158.056 c 164.86 158.056 l 165.172 158.095 165.052 158.134 165.492 158.113 c 165.893 158.113 l 166.563 158.113 167.232 158.113 167.902 158.113 c 168.073 158.171 l 168.361 158.171 l 170.052 158.127 171.62 158.254 173.295 158.228 c 174.386 158.228 l 174.5 158.285 l 174.767 158.285 175.037 158.285 175.304 158.285 c 175.59 158.285 l 175.857 158.285 176.126 158.285 176.393 158.285 c 176.852 158.285 l 177.741 158.242 178.407 158.365 179.261 158.343 c 179.779 158.343 l 181.727 158.307 183.561 158.443 185.516 158.401 c 186.032 158.401 l 190.493 158.48 194.939 158.466 199.401 158.458 c 199.975 158.458 l 119.246 171.483 m 119.417 171.427 l 119.532 171.311 l 119.704 171.197 l 122.82 169.267 126.012 167.355 129.286 165.689 c 129.4 165.575 l 129.63 165.46 l 129.801 165.403 l 130.375 165.112 130.869 164.818 131.466 164.542 c 131.637 164.485 l 131.752 164.427 l 132.348 164.107 132.937 163.867 133.53 163.566 c 133.99 163.338 l 134.609 162.986 135.117 162.835 135.711 162.534 c 136.056 162.362 l 136.17 162.362 l 136.859 162.019 l 136.974 162.019 l 137.547 161.731 l 137.663 161.731 l 138.235 161.444 l 138.35 161.444 l 138.58 161.33 l 139.015 161.156 139.757 160.917 140.129 160.699 c 140.244 160.699 l 140.473 160.584 l 140.588 160.584 l 140.932 160.412 l 141.047 160.412 l 141.277 160.298 l 141.392 160.298 l 141.621 160.183 l 141.736 160.183 l 141.965 160.068 l 142.08 160.068 l 142.137 160.011 l 142.251 159.954 l 142.366 159.954 l 142.596 159.839 l 142.709 159.839 l 142.939 159.724 l 143.054 159.724 l 143.283 159.61 l 143.398 159.61 l 143.625 159.526 143.86 159.464 144.086 159.38 c 144.201 159.38 l 144.258 159.322 l 144.374 159.266 l 144.489 159.266 l 144.667 159.166 144.883 159.194 145.062 159.094 c 145.177 159.036 l 145.292 159.036 l 145.465 158.97 145.795 158.884 145.98 158.864 c 146.095 158.807 l 146.21 158.807 l 146.325 158.75 l 146.439 158.75 l 146.554 158.692 l 146.668 158.692 l 146.783 158.634 l 146.897 158.634 l 147.077 158.533 147.293 158.563 147.472 158.463 c 147.701 158.463 l 147.875 158.395 148.205 158.311 148.39 158.291 c 148.505 158.291 l 148.62 158.235 l 148.849 158.235 l 148.964 158.176 l 149.078 158.176 l 149.193 158.119 l 149.422 158.119 l 149.536 158.063 l 149.651 158.063 l 150.097 158.087 149.768 157.971 150.34 158.004 c 150.454 157.947 l 150.798 157.947 l 151.946 157.823 153.381 157.921 154.585 157.89 c 154.987 157.89 l 46.945 250.38 m 46.945 250.552 l 47.001 250.552 l 47.117 250.897 l 47.232 251.068 l 47.289 251.183 l 47.633 251.584 l 47.977 251.642 l 48.321 251.469 l 48.664 251.01 l 49.066 250.321 l 49.467 249.402 l 49.87 248.369 l 50.27 247.223 l 50.729 245.903 l 51.476 243.458 52.347 241.055 53.082 238.615 c 53.598 237.18 l 54.115 235.86 l 54.689 234.426 l 56.61 229.543 59.104 225.26 62.377 221.172 c 62.837 220.597 l 63.295 220.081 l 63.696 219.563 l 67.072 215.683 70.574 211.903 74.254 208.318 c 75.058 207.515 l 80.564 202.085 86.271 196.919 92.1 191.85 c 92.789 191.333 l 92.961 191.104 l 97.511 187.305 102.038 183.597 106.792 180.088 c 107.02 179.915 l 107.364 179.685 l 109.188 178.253 111.184 176.9 113.101 175.554 c 113.618 175.21 l 114.345 174.62 115.134 174.236 115.856 173.66 c 116.027 173.547 l 116.199 173.488 l 116.926 172.896 117.761 172.498 118.496 171.938 c 118.667 171.881 l 118.781 171.766 l 118.953 171.653 l 119.068 171.594 l 119.241 171.481 l S 0 1 1 RG 154.993 157.885 m 155.623 157.885 l 155.795 157.885 155.967 157.885 156.14 157.885 c 156.313 157.885 l 156.79 157.854 156.54 157.958 156.829 157.941 c 157.174 157.941 l 157.709 157.941 158.243 157.941 158.779 157.941 c 159.123 157.941 l 160.481 157.941 161.839 157.941 163.197 157.941 c 163.944 157.941 l 164.154 157.941 164.364 157.941 164.575 157.941 c 164.86 157.941 l 165.172 157.98 165.052 158.02 165.492 157.999 c 165.893 157.999 l 166.563 157.999 167.232 157.999 167.902 157.999 c 168.361 157.999 l 170.006 157.999 171.651 157.999 173.295 157.999 c 174.042 157.999 l 177.924 157.999 181.806 157.999 185.689 157.999 c 186.205 157.999 l 188.251 157.999 190.299 157.999 192.346 157.999 c 193.092 157.999 l 193.585 158.032 193.516 157.908 194.011 157.941 c 194.355 157.941 l 195.02 157.888 194.934 158.11 195.56 158.056 c 195.903 158.056 l 196.132 157.999 l 196.304 157.999 l 197.017 158.244 196.489 158.011 197.222 158.056 c 197.451 158.056 l 197.623 157.999 l 198.351 158.127 198.137 158.141 198.829 158.056 c 199.632 158.056 l 199.804 158.113 l 199.976 158.113 l 119.246 171.483 m 119.417 171.369 l 119.532 171.311 l 119.704 171.197 l 119.818 171.084 l 119.99 171.025 l 120.104 170.911 l 120.276 170.853 l 120.449 170.738 l 120.563 170.681 l 120.735 170.568 l 120.85 170.452 l 121.022 170.395 l 121.136 170.28 l 121.416 170.201 121.603 169.956 121.883 169.878 c 121.997 169.763 l 122.113 169.706 l 122.284 169.591 l 122.974 169.189 123.661 168.787 124.35 168.387 c 124.464 168.33 l 124.636 168.214 l 124.751 168.158 l 126.216 167.321 127.663 166.475 129.169 165.748 c 129.284 165.632 l 129.627 165.461 l 129.799 165.404 l 130.33 165.07 130.898 164.83 131.463 164.543 c 131.635 164.485 l 131.75 164.428 l 132.387 164.059 132.807 163.792 133.528 163.567 c 133.988 163.339 l 134.555 163.04 135.125 162.77 135.709 162.535 c 135.938 162.42 l 136.476 162.165 137.132 161.956 137.661 161.674 c 137.775 161.674 l 138.233 161.444 l 138.349 161.444 l 138.579 161.33 l 139.07 161.121 139.655 160.946 140.128 160.699 c 140.242 160.699 l 140.358 160.641 l 140.885 160.42 141.553 160.23 142.08 160.01 c 142.137 160.01 l 142.366 159.895 l 142.481 159.895 l 142.95 159.69 143.732 159.525 144.202 159.32 c 144.259 159.32 l 144.375 159.263 l 144.49 159.263 l 144.603 159.206 l 144.719 159.206 l 144.949 159.092 l 145.063 159.092 l 145.178 159.033 l 145.292 159.033 l 145.466 158.967 145.797 158.881 145.98 158.862 c 146.096 158.805 l 146.211 158.805 l 146.326 158.748 l 146.44 158.748 l 146.555 158.69 l 146.668 158.69 l 146.784 158.632 l 146.898 158.632 l 147.078 158.531 147.294 158.56 147.473 158.46 c 147.589 158.46 l 147.702 158.404 l 147.816 158.404 l 147.932 158.345 l 148.16 158.345 l 148.276 158.288 l 148.39 158.288 l 148.505 158.232 l 148.733 158.232 l 148.849 158.174 l 149.332 158.198 148.941 158.091 149.423 158.117 c 149.538 158.061 l 149.767 158.061 l 149.882 158.002 l 150.111 158.002 l 150.226 157.945 l 150.685 157.945 l 150.798 157.888 l 152.061 157.888 153.323 157.888 154.585 157.888 c 154.987 157.888 l 46.945 247.857 m 46.945 247.742 l 47.001 247.742 l 47.117 247.398 l 47.232 247.226 l 47.289 247.054 l 47.633 246.193 l 49.451 240.843 50.605 235.165 53.6 230.299 c 54.117 229.495 l 54.691 228.749 l 57.009 225.623 59.721 223.049 62.38 220.257 c 62.839 219.855 l 63.7 218.994 l 67.239 215.459 70.675 211.816 74.258 208.322 c 75.062 207.518 l 80.565 202.1 86.264 196.906 92.104 191.854 c 92.563 191.509 l 92.791 191.279 l 101.098 184.202 109.79 177.517 118.957 171.656 c 119.072 171.599 l 119.244 171.483 l S 1 0 1 RG 154.993 158.458 m 155.51 158.458 l 155.988 158.458 156.466 158.458 156.943 158.458 c 157.346 158.458 l 157.459 158.402 l 158.033 158.402 l 158.243 158.402 158.454 158.402 158.664 158.402 c 159.123 158.402 l 160.481 158.402 161.839 158.402 163.197 158.402 c 163.542 158.402 l 166.851 158.402 170.159 158.402 173.468 158.402 c 174.214 158.402 l 175.985 158.441 177.669 158.311 179.436 158.343 c 179.78 158.343 l 181.692 158.343 183.605 158.343 185.517 158.343 c 186.033 158.343 l 190.49 158.343 194.947 158.343 199.403 158.343 c 199.976 158.343 l S Q 1 0 1 RG 119.246 171.483 m 119.417 171.427 l 119.532 171.311 l 119.704 171.197 l 122.877 169.256 125.983 167.376 129.286 165.689 c 129.516 165.575 l 129.63 165.46 l 129.801 165.403 l 130.421 165.119 130.881 164.845 131.466 164.542 c 131.637 164.485 l 131.752 164.427 l 132.348 164.107 132.937 163.867 133.53 163.566 c 134.104 163.279 l 134.462 163.069 134.421 163.159 134.679 163.05 c 134.908 162.935 l 135.137 162.821 135.366 162.706 135.596 162.592 c 135.711 162.592 l 135.942 162.477 l 136.47 162.194 137.126 161.986 137.664 161.73 c 137.779 161.673 l 137.892 161.673 l 138.352 161.443 l 138.466 161.443 l 138.581 161.386 l 139.011 161.138 139.757 161.003 140.131 160.755 c 140.245 160.755 l 140.589 160.583 l 140.704 160.583 l 140.934 160.468 l 141.048 160.468 l 141.278 160.353 l 141.393 160.353 l 141.622 160.238 l 141.737 160.238 l 141.966 160.124 l 142.081 160.124 l 142.138 160.067 l 142.253 160.01 l 142.367 160.01 l 142.482 159.953 l 142.597 159.953 l 142.826 159.838 l 142.94 159.838 l 143.055 159.781 l 143.169 159.781 l 143.399 159.666 l 143.584 159.646 143.913 159.561 144.087 159.494 c 144.202 159.436 l 144.259 159.436 l 144.375 159.379 l 144.92 159.287 145.549 159.07 146.096 158.979 c 146.211 158.979 l 146.326 158.921 l 146.44 158.921 l 146.555 158.863 l 146.784 158.863 l 146.898 158.806 l 147.013 158.806 l 147.128 158.749 l 147.357 158.749 l 147.472 158.691 l 147.701 158.691 l 147.815 158.633 l 148.16 158.633 l 148.275 158.577 l 148.733 158.577 l 148.849 158.518 l 149.04 158.518 149.231 158.518 149.423 158.518 c 149.538 158.461 l 149.652 158.461 l 149.882 158.461 150.112 158.461 150.341 158.461 c 150.801 158.461 l 152.064 158.461 153.325 158.461 154.587 158.461 c 154.99 158.461 l S q 46.945 157.771 m 199.977 157.771 l 199.977 267.711 l 46.945 267.711 l 46.945 157.771 l W n 46.945 189.215 m 46.945 188.182 l 47.388 182.471 47.482 176.705 48.322 171.025 c 48.665 170.451 l 49.067 172.058 l 49.469 174.985 l 49.87 178.427 l 50.271 181.985 l 50.73 185.887 l 51.189 189.502 l 51.647 192.657 l 52.107 195.412 l 52.624 198.167 l 53.083 200.692 l 53.6 202.93 l 54.117 204.995 l 54.878 207.638 55.62 210.276 56.872 212.741 c 57.503 213.774 l 58.077 214.576 l 58.651 215.265 l 60.738 217.473 62.997 216.934 65.307 215.553 c 65.651 215.324 l 66.051 215.094 l 66.338 214.864 l 69.684 212.565 72.878 209.236 75.921 206.487 c 76.436 205.97 l 76.723 205.74 l 82.005 200.713 87.46 195.862 92.961 191.109 c 93.42 190.765 l 93.649 190.536 l 101.744 183.72 110.065 177.348 118.954 171.658 c 119.069 171.602 l 119.242 171.486 l S Q 118.299 143.256 m 119.942 143.256 l 119.942 143.836 l 116.003 143.836 l 116.003 143.256 l 117.717 143.256 l 117.717 138.841 l 118.298 138.841 l f 121.088 142.442 m 121.088 142.442 -0.58199 -3.601 re 121.088 143.836 m 120.506 143.836 l 120.506 143.137 l 121.088 143.137 l f 122.017 142.442 m 122.017 138.841 l 122.598 138.841 l 122.598 141.055 l 122.598 141.567 122.976 141.979 123.443 141.979 c 123.868 141.979 124.109 141.722 124.109 141.271 c 124.109 138.841 l 124.689 138.841 l 124.689 141.055 l 124.689 141.567 125.066 141.979 125.535 141.979 c 125.953 141.979 126.2 141.716 126.2 141.271 c 126.2 138.841 l 126.78 138.841 l 126.78 141.551 l 126.78 142.2 126.408 142.559 125.734 142.559 c 125.251 142.559 124.962 142.413 124.625 142.001 c 124.412 142.392 124.124 142.559 123.655 142.559 c 123.173 142.559 122.857 142.377 122.547 141.94 c 122.547 142.442 l f 130.778 140.467 m 130.778 141.017 130.735 141.345 130.63 141.613 c 130.394 142.202 129.835 142.559 129.152 142.559 c 128.133 142.559 127.478 141.795 127.478 140.621 c 127.478 139.447 128.112 138.725 129.138 138.725 c 129.976 138.725 130.555 139.176 130.702 139.935 c 130.11 139.935 l 129.946 139.521 129.616 139.305 129.144 139.305 c 128.771 139.305 128.453 139.459 128.256 139.745 c 128.115 139.94 128.065 140.133 128.058 140.467 c 130.778 140.467 l h 128.133 140.932 m 128.181 141.567 128.587 141.979 129.166 141.979 c 129.73 141.979 130.165 141.534 130.165 140.972 c 130.165 140.959 130.165 140.944 130.157 140.932 c f 25.276 183.614 6.4551 0.464 re f 25.276 185.472 6.4551 0.46599 re f 28.409 188.528 m 26.67 189.74 l 26.67 189.092 l 27.973 188.226 l 26.67 187.358 l 26.67 186.704 l 28.437 187.909 l 30.272 186.635 l 30.272 187.29 l 28.888 188.205 l 30.272 189.108 l 30.272 189.776 l f 30.736 190.817 m 33.641 190.817 -2.9048 -0.464 re 30.736 190.817 m h 29.575 190.817 m 29.575 190.353 l 30.203 190.353 l 30.203 190.817 l f 28.413 191.441 0.4644 3.47 re f 25.276 195.696 m 30.272 195.696 l 30.272 196.277 l 28.254 196.277 l 27.508 196.277 27.019 196.669 27.019 197.267 c 27.019 197.456 27.083 197.644 27.187 197.783 c 27.306 197.951 27.479 198.021 27.739 198.021 c 30.273 198.021 l 30.273 198.601 l 27.541 198.601 l 26.934 198.601 26.555 198.161 26.555 197.45 c 26.555 196.933 26.716 196.619 27.161 196.277 c 25.277 196.277 l f 30.736 199.764 m 33.641 199.764 -2.9048 -0.466 re 30.736 199.764 m h 29.575 199.764 m 29.575 199.298 l 30.203 199.298 l 30.203 199.764 l f 28.413 200.387 0.4644 3.47 re f 25.276 204.643 m 30.272 204.643 l 30.272 205.224 l 28.254 205.224 l 27.508 205.224 27.019 205.614 27.019 206.214 c 27.019 206.402 27.083 206.59 27.187 206.73 c 27.306 206.898 27.479 206.966 27.739 206.966 c 30.273 206.966 l 30.273 207.547 l 27.541 207.547 l 26.934 207.547 26.555 207.107 26.555 206.397 c 26.555 205.88 26.716 205.565 27.161 205.224 c 25.277 205.224 l f 24.869 210.607 m 24.581 210.585 24.395 210.525 24.23 210.419 c 23.938 210.226 23.766 209.888 23.766 209.495 c 23.766 208.739 24.392 208.245 25.361 208.245 c 26.305 208.245 26.902 208.728 26.902 209.491 c 26.902 210.161 26.494 210.586 25.794 210.639 c 25.794 210.188 l 26.223 210.111 26.438 209.881 26.438 209.499 c 26.438 209.005 26.032 208.709 25.36 208.709 c 24.652 208.709 24.23 209 24.23 209.49 c 24.23 209.865 24.461 210.101 24.869 210.155 c f 25.276 211.381 6.4551 0.46501 re f 25.276 213.241 6.4551 0.46501 re f 33.177 217.047 m 33.177 215.013 l 32.851 215.063 32.644 215.236 32.359 215.712 c 32.056 216.256 l 31.751 216.796 31.344 217.074 30.856 217.074 c 30.525 217.074 30.217 216.944 30.004 216.714 c 29.792 216.486 29.689 216.202 29.689 215.837 c 29.689 215.347 29.872 214.983 30.213 214.769 c 30.429 214.632 30.681 214.572 31.089 214.562 c 31.089 215.047 l 30.823 215.064 30.664 215.097 30.537 215.164 c 30.299 215.29 30.154 215.545 30.154 215.837 c 30.154 216.278 30.469 216.611 30.888 216.611 c 31.198 216.611 31.461 216.428 31.66 216.081 c 31.946 215.572 l 32.409 214.756 32.779 214.518 33.639 214.474 c 33.639 217.048 l f 29.556 217.889 m 30.272 217.889 l 30.272 218.319 l 30.407 218.319 l 30.92 218.319 31.07 218.226 31.085 217.889 c 31.317 217.889 l 31.317 218.353 31.001 218.585 30.399 218.585 c 29.556 218.585 l f 26.67 220.328 m 30.272 220.328 -3.6015 -0.58101 re 26.67 220.328 m h 25.276 220.328 m 25.276 219.747 l 25.976 219.747 l 25.976 220.328 l 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41.41 31.856 c 42.382 31.856 43.061 32.571 43.061 33.602 c 43.061 34.565 42.429 35.225 41.505 35.225 c 41.166 35.225 40.894 35.117 40.615 34.87 c 40.806 36.27 l 42.809 36.27 l f 46.536 49.987 m 48.018 49.987 l 200.099 49.987 m 198.561 49.987 l S 37.482 50.9 m 37.482 47.423 l 38.063 47.423 l 38.063 52.304 l 37.678 52.304 l 37.473 51.554 37.34 51.449 36.437 51.333 c 36.437 50.9 l f 41.49 52.304 m 41.044 52.304 40.639 52.088 40.388 51.723 c 40.077 51.304 39.922 50.661 39.922 49.777 c 39.922 48.165 40.461 47.308 41.49 47.308 c 42.504 47.308 43.059 48.166 43.059 49.737 c 43.059 50.668 42.909 51.289 42.591 51.723 c 42.342 52.095 41.942 52.304 41.49 52.304 c h 41.49 51.723 m 42.151 51.723 42.478 51.088 42.478 49.834 c 42.478 48.51 42.157 47.889 41.476 47.889 c 40.829 47.889 40.502 48.534 40.502 49.815 c 40.502 51.095 40.829 51.723 41.49 51.723 c f 46.536 65.543 m 48.018 65.543 l 200.099 65.543 m 198.561 65.543 l S 37.482 66.469 m 37.482 62.992 l 38.063 62.992 l 38.063 67.873 l 37.678 67.873 l 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c 36.991 82.686 37.309 82.86 37.675 82.86 c 38.228 82.86 38.642 82.473 38.642 81.956 c 38.642 81.574 38.415 81.248 37.98 81.002 c 37.344 80.65 l 36.322 80.078 36.025 79.622 35.97 78.561 c 39.188 78.561 l f 41.49 83.442 m 41.044 83.442 40.639 83.226 40.388 82.86 c 40.077 82.442 39.922 81.8 39.922 80.914 c 39.922 79.302 40.461 78.445 41.49 78.445 c 42.504 78.445 43.059 79.303 43.059 80.875 c 43.059 81.807 42.909 82.427 42.591 82.86 c 42.342 83.233 41.942 83.442 41.49 83.442 c h 41.49 82.86 m 42.151 82.86 42.478 82.227 42.478 80.972 c 42.478 79.647 42.157 79.026 41.476 79.026 c 40.829 79.026 40.502 79.674 40.502 80.952 c 40.502 82.234 40.829 82.86 41.49 82.86 c f 46.536 96.597 m 48.018 96.597 l 200.099 96.597 m 198.561 96.597 l S 39.189 94.711 m 36.646 94.711 l 36.708 95.111 36.926 95.368 37.518 95.72 c 38.201 96.093 l 38.876 96.465 39.223 96.97 39.223 97.571 c 39.223 97.981 39.059 98.36 38.773 98.621 c 38.486 98.884 38.131 99.01 37.675 99.01 c 37.061 99.01 36.604 98.786 36.339 98.369 c 36.169 98.104 36.094 97.799 36.08 97.296 c 36.687 97.296 l 36.708 97.617 36.75 97.812 36.832 97.967 c 36.991 98.254 37.309 98.428 37.675 98.428 c 38.228 98.428 38.642 98.041 38.642 97.524 c 38.642 97.143 38.415 96.817 37.98 96.572 c 37.344 96.218 l 36.322 95.647 36.025 95.19 35.97 94.129 c 39.188 94.129 l f 42.808 99.01 m 40.322 99.01 l 39.963 96.339 l 40.519 96.339 l 40.801 96.683 41.034 96.803 41.412 96.803 c 42.064 96.803 42.478 96.374 42.478 95.679 c 42.478 95.005 42.072 94.596 41.413 94.596 c 40.884 94.596 40.562 94.831 40.417 95.32 c 39.813 95.32 l 39.894 94.936 39.964 94.749 40.105 94.577 c 40.377 94.22 40.867 94.015 41.41 94.015 c 42.382 94.015 43.061 94.73 43.061 95.761 c 43.061 96.724 42.429 97.383 41.505 97.383 c 41.166 97.383 40.894 97.276 40.615 97.028 c 40.806 98.428 l 42.809 98.428 l f 46.536 112.096 m 48.018 112.096 l 200.099 112.096 m 198.561 112.096 l S 37.251 111.79 m 37.593 111.79 l 38.285 111.79 38.644 111.507 38.644 110.961 c 38.644 110.389 38.257 110.047 37.615 110.047 c 36.944 110.047 36.615 110.348 36.574 110.991 c 35.958 110.991 l 35.985 110.612 36.054 110.367 36.171 110.153 c 36.418 109.7 36.902 109.468 37.57 109.468 c 38.577 109.468 39.224 110.061 39.224 110.976 c 39.224 111.591 38.978 111.932 38.379 112.13 c 38.787 112.309 38.992 112.649 38.992 113.134 c 38.992 113.965 38.456 114.465 37.56 114.465 c 36.612 114.465 36.107 113.92 36.087 112.867 c 36.669 112.867 l 36.675 113.154 36.702 113.316 36.775 113.463 c 36.91 113.725 37.206 113.884 37.573 113.884 c 38.096 113.884 38.411 113.584 38.411 113.096 c 38.411 112.77 38.29 112.574 38.032 112.472 c 37.871 112.406 37.665 112.379 37.251 112.373 c f 41.49 114.462 m 41.044 114.462 40.639 114.247 40.388 113.882 c 40.077 113.463 39.922 112.82 39.922 111.938 c 39.922 110.323 40.461 109.467 41.49 109.467 c 42.504 109.467 43.059 110.324 43.059 111.896 c 43.059 112.827 42.909 113.448 42.591 113.882 c 42.342 114.254 41.942 114.462 41.49 114.462 c h 41.49 113.882 m 42.151 113.882 42.478 113.247 42.478 111.993 c 42.478 110.668 42.157 110.047 41.476 110.047 c 40.829 110.047 40.502 110.694 40.502 111.975 c 40.502 113.254 40.829 113.882 41.49 113.882 c f 46.536 127.596 m 48.018 127.596 l 200.099 127.596 m 198.561 127.596 l S 37.251 127.243 m 37.593 127.243 l 38.285 127.243 38.644 126.959 38.644 126.413 c 38.644 125.842 38.257 125.501 37.615 125.501 c 36.944 125.501 36.615 125.799 36.574 126.445 c 35.958 126.445 l 35.985 126.065 36.054 125.818 36.171 125.606 c 36.418 125.152 36.902 124.919 37.57 124.919 c 38.577 124.919 39.224 125.515 39.224 126.428 c 39.224 127.043 38.978 127.383 38.379 127.582 c 38.787 127.76 38.992 128.1 38.992 128.586 c 38.992 129.418 38.456 129.917 37.56 129.917 c 36.612 129.917 36.107 129.372 36.087 128.319 c 36.669 128.319 l 36.675 128.607 36.702 128.769 36.775 128.915 c 36.91 129.176 37.206 129.336 37.573 129.336 c 38.096 129.336 38.411 129.037 38.411 128.547 c 38.411 128.222 38.29 128.026 38.032 127.923 c 37.871 127.86 37.665 127.831 37.251 127.825 c f 42.808 129.915 m 40.322 129.915 l 39.963 127.244 l 40.519 127.244 l 40.801 127.588 41.034 127.708 41.412 127.708 c 42.064 127.708 42.478 127.278 42.478 126.585 c 42.478 125.91 42.072 125.501 41.413 125.501 c 40.884 125.501 40.562 125.736 40.417 126.226 c 39.813 126.226 l 39.894 125.841 39.964 125.654 40.105 125.484 c 40.377 125.124 40.867 124.918 41.41 124.918 c 42.382 124.918 43.061 125.635 43.061 126.666 c 43.061 127.629 42.429 128.289 41.505 128.289 c 41.166 128.289 40.894 128.182 40.615 127.934 c 40.806 129.333 l 42.809 129.333 l f 46.536 127.596 m 200.099 127.596 l 46.536 18.932 m 200.099 18.932 l 200.099 127.596 l 46.536 18.932 m 46.536 127.596 l S q 46.536 18.876 m 200.158 18.876 l 200.158 127.596 l 46.536 127.596 l 46.536 18.876 l W n 0 0 1 RG 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 71.07 m 46.536 70.728 l 46.593 70.614 l 46.649 70.215 l 46.706 69.759 l 49.179 56.659 52.73 36.817 61.635 26.453 c 62.033 25.999 l 62.49 25.541 l 65.396 22.481 69.238 20.314 73.374 19.503 c 74.513 19.276 l 77.145 18.766 80.368 19.075 83.118 18.989 c 83.63 18.989 l 86.232 18.989 88.835 18.989 91.437 18.989 c 92.291 18.989 l 101.143 18.989 109.994 18.989 118.847 18.989 c 119.131 18.989 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 81.384 m 46.536 80.984 l 46.593 80.87 l 46.706 79.845 l 46.821 79.388 l 48.113 69.99 49.907 60.323 52.233 51.126 c 52.746 49.189 l 53.259 47.421 l 54.993 41.196 57.514 34.273 61.179 28.903 c 61.635 28.277 l 62.033 27.707 l 62.49 27.137 l 65.399 23.562 68.947 21.089 73.374 19.845 c 73.66 19.73 l 74.514 19.56 l 77.554 18.767 80.038 19.032 83.119 18.989 c 83.632 18.989 l 86.233 18.989 88.836 18.989 91.438 18.989 c 92.292 18.989 l 101.144 18.989 109.996 18.989 118.848 18.989 c 119.132 18.989 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 92.381 m 46.536 91.925 l 46.593 91.812 l 46.649 91.185 l 46.706 90.616 l 46.821 90.045 l 48.128 79.117 49.893 67.98 52.233 57.225 c 52.746 55.002 l 53.259 52.895 l 55.016 45.563 57.433 37.825 61.179 31.242 c 61.635 30.501 l 62.033 29.818 l 62.49 29.192 l 65.105 25.215 68.872 21.943 73.374 20.302 c 73.66 20.245 l 74.23 20.018 l 79.85 18.259 85.853 19.248 91.666 18.99 c 92.291 18.99 l 101.143 18.99 109.994 18.99 118.847 18.99 c 119.131 18.99 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 102.523 m 46.536 102.01 l 46.593 101.897 l 46.706 100.528 l 46.821 99.901 l 48.126 87.572 49.887 75.039 52.233 62.863 c 52.746 60.3 l 53.259 57.963 l 54.991 49.763 57.411 40.87 61.179 33.348 c 61.635 32.549 l 62.033 31.751 l 62.49 31.011 l 65.16 26.443 68.532 22.921 73.374 20.753 c 74.23 20.411 l 79.776 18.215 85.824 19.206 91.666 18.987 c 92.291 18.987 l 101.143 18.987 109.994 18.987 118.847 18.987 c 119.131 18.987 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 95.058 m 46.536 94.603 l 46.593 94.488 l 46.706 93.235 l 46.821 92.665 l 48.124 81.35 49.904 69.855 52.233 58.704 c 52.746 56.424 l 53.259 54.202 l 54.987 46.85 57.454 38.418 61.179 31.811 c 61.635 31.012 l 62.033 30.326 l 62.49 29.645 l 65.186 25.462 68.72 22.221 73.374 20.413 c 73.66 20.3 l 73.943 20.242 l 74.229 20.128 l 79.818 18.216 85.85 19.253 91.665 18.989 c 92.29 18.989 l 101.142 18.989 109.993 18.989 118.845 18.989 c 119.13 18.989 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 98.307 m 46.536 97.796 l 46.593 97.682 l 46.706 96.427 l 46.821 95.802 l 48.131 84.074 49.887 72.152 52.233 60.586 c 52.746 58.194 l 53.259 55.914 l 54.997 48.14 57.428 39.619 61.179 32.551 c 61.635 31.753 l 62.033 31.013 l 62.49 30.327 l 65.334 25.833 68.503 22.701 73.374 20.585 c 73.66 20.528 l 74.23 20.301 l 79.774 18.176 85.846 19.248 91.666 18.989 c 92.291 18.989 l 101.143 18.989 109.994 18.989 118.847 18.989 c 119.131 18.989 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 112.552 m 46.536 111.982 l 46.593 111.811 l 46.706 110.33 l 46.821 109.59 l 48.128 95.691 49.888 81.643 52.233 67.88 c 52.746 65.086 l 53.259 62.352 l 55.021 53.206 57.342 43.236 61.179 34.716 c 61.635 33.747 l 62.033 32.891 l 62.49 32.037 l 64.82 27.492 68.569 22.679 73.374 20.583 c 73.66 20.411 l 74.514 20.069 l 77.965 18.82 79.565 18.97 83.119 18.986 c 83.632 18.986 l 86.233 18.986 88.836 18.986 91.438 18.986 c 92.292 18.986 l 101.144 18.986 109.996 18.986 118.848 18.986 c 119.132 18.986 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 93.12 m 46.536 92.665 l 46.593 92.552 l 46.706 91.297 l 46.821 90.728 l 48.128 79.55 49.88 68.169 52.233 57.166 c 52.746 54.887 l 53.259 52.722 l 55.001 45.284 57.407 37.294 61.179 30.612 c 61.635 29.872 l 62.033 29.187 l 62.49 28.502 l 65.11 24.585 68.796 21.164 73.374 19.782 c 73.66 19.67 l 73.943 19.611 l 74.229 19.498 l 74.513 19.441 l 77.332 18.712 80.201 19.068 83.118 18.986 c 83.63 18.986 l 86.232 18.986 88.835 18.986 91.437 18.986 c 92.291 18.986 l 101.143 18.986 109.994 18.986 118.847 18.986 c 119.131 18.986 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 66.226 m 46.536 65.942 l 46.593 65.827 l 46.706 65.028 l 49.451 51.945 52.369 34.911 61.635 24.687 c 62.49 23.83 l 65.587 21.056 69.215 19.306 73.374 18.986 c 74.23 18.986 l 80.041 18.986 85.854 18.986 91.666 18.986 c 92.291 18.986 l 101.143 18.986 109.994 18.986 118.847 18.986 c 119.131 18.986 l 155.027 18.988 m 155.142 18.988 l 161.009 18.988 166.879 18.988 172.748 18.988 c 173.203 18.988 l 182.129 18.988 191.058 18.988 199.985 18.988 c 200.155 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 67.879 m 46.536 67.537 l 46.593 67.479 l 46.706 66.682 l 46.821 66.283 l 48.126 58.846 49.914 51.134 52.233 43.947 c 52.746 42.409 l 53.259 40.983 l 54.956 36.1 57.715 30.337 61.179 26.452 c 61.635 25.941 l 62.033 25.484 l 62.49 25.029 l 65.53 22.073 69.233 20.178 73.374 19.387 c 74.513 19.159 l 77.294 18.842 80.28 19.046 83.118 18.988 c 83.63 18.988 l 86.232 18.988 88.835 18.988 91.437 18.988 c 92.291 18.988 l 101.143 18.988 109.994 18.988 118.847 18.988 c 119.131 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 34.487 m 46.536 34.374 l 46.593 34.318 l 46.649 34.203 l 46.706 34.033 l 49.822 27.492 54.278 21.421 61.635 19.503 c 62.033 19.389 l 62.49 19.331 l 65.61 18.68 70.034 19.115 73.374 18.988 c 74.23 18.988 l 80.041 18.988 85.854 18.988 91.666 18.988 c 92.291 18.988 l 101.143 18.988 109.994 18.988 118.847 18.988 c 119.131 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 49.588 m 46.536 49.417 l 46.593 49.36 l 46.649 49.075 l 50.736 34.755 56.345 18.77 73.659 18.988 c 74.229 18.988 l 80.04 18.988 85.853 18.988 91.665 18.988 c 92.29 18.988 l 101.142 18.988 109.993 18.988 118.845 18.988 c 119.13 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 53.404 m 46.536 53.178 l 46.593 53.119 l 46.649 52.835 l 50.503 38.28 55.746 19.631 73.659 18.987 c 74.229 18.987 l 80.04 18.987 85.853 18.987 91.665 18.987 c 92.29 18.987 l 101.142 18.987 109.993 18.987 118.845 18.987 c 119.13 18.987 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 41.555 m 46.536 41.385 l 46.593 41.324 l 46.706 40.87 l 46.821 40.7 l 48.08 36.808 50.039 32.528 52.233 29.075 c 53.259 27.594 l 55.272 24.696 57.981 22.226 61.18 20.699 c 61.636 20.472 l 62.035 20.301 l 62.492 20.13 l 66.316 18.6 69.411 19.06 73.376 18.99 c 74.231 18.99 l 80.042 18.99 85.855 18.99 91.667 18.99 c 92.292 18.99 l 101.144 18.99 109.996 18.99 118.848 18.99 c 119.132 18.99 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 65.714 m 46.536 65.37 l 46.593 65.315 l 46.706 64.516 l 49.478 51.697 52.384 35.11 61.635 25.199 c 62.033 24.742 l 62.49 24.344 l 65.55 21.555 69.336 19.926 73.374 19.216 c 73.66 19.216 l 74.23 19.102 l 80.017 18.848 85.858 19.054 91.666 18.987 c 92.291 18.987 l 101.143 18.987 109.994 18.987 118.847 18.987 c 119.131 18.987 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 92.039 m 46.536 91.583 l 46.593 91.468 l 46.706 90.329 l 46.821 89.702 l 48.139 78.832 49.897 67.805 52.233 57.109 c 52.746 54.887 l 53.259 52.778 l 55.003 45.55 57.451 37.713 61.179 31.239 c 61.635 30.499 l 62.033 29.817 l 62.49 29.189 l 65.364 25.011 68.648 22.109 73.374 20.3 c 73.66 20.242 l 74.23 20.015 l 79.851 18.26 85.852 19.244 91.666 18.988 c 92.291 18.988 l 101.143 18.988 109.994 18.988 118.847 18.988 c 119.131 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 59.389 m 46.536 59.105 l 46.593 59.046 l 46.706 58.364 l 49.175 47.644 53.015 31.757 61.635 24.233 c 62.033 23.892 l 62.49 23.492 l 65.788 20.971 69.294 19.628 73.374 19.104 c 73.66 19.047 l 73.943 19.047 l 74.229 18.989 l 80.04 18.989 85.853 18.989 91.665 18.989 c 92.29 18.989 l 101.142 18.989 109.993 18.989 118.845 18.989 c 119.13 18.989 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 46.398 m 46.536 46.227 l 46.593 46.168 l 46.649 45.942 l 50.931 31.904 57.16 18.435 73.659 18.989 c 74.229 18.989 l 80.04 18.989 85.853 18.989 91.665 18.989 c 92.29 18.989 l 101.142 18.989 109.993 18.989 118.845 18.989 c 119.13 18.989 l 155.027 18.988 m 155.142 18.988 l 169.291 18.988 183.442 18.988 197.592 18.988 c 198.218 18.988 l 198.807 18.988 199.395 18.988 199.985 18.988 c 200.155 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 44.973 m 46.536 44.802 l 46.593 44.802 l 46.706 44.346 l 46.821 44.117 l 51.317 30.183 58.219 18.182 74.229 18.988 c 74.798 18.988 l 80.496 18.988 86.194 18.988 91.892 18.988 c 92.518 18.988 l 101.293 18.988 110.069 18.988 118.844 18.988 c 119.129 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 49.474 m 46.536 49.303 l 46.593 49.245 l 46.706 48.675 l 49.228 39.696 53.281 26.96 61.635 21.724 c 62.033 21.44 l 62.49 21.212 l 65.778 19.226 69.605 18.782 73.374 18.988 c 74.23 18.988 l 80.041 18.988 85.854 18.988 91.666 18.988 c 92.291 18.988 l 101.143 18.988 109.994 18.988 118.847 18.988 c 119.131 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 117.396 m 46.536 116.769 l 46.593 116.598 l 46.649 115.857 l 46.706 115.06 l 46.821 114.262 l 48.137 99.726 49.877 85.021 52.233 70.614 c 52.746 67.594 l 53.259 64.802 l 55.006 55.158 57.35 44.794 61.179 35.741 c 61.635 34.716 l 62.033 33.804 l 62.49 32.891 l 65.003 27.944 68.334 23.313 73.374 20.755 c 73.943 20.527 l 74.229 20.357 l 74.513 20.242 l 77.97 18.932 79.509 18.934 83.118 18.988 c 83.63 18.988 l 86.232 18.988 88.835 18.988 91.437 18.988 c 92.291 18.988 l 101.143 18.988 109.994 18.988 118.847 18.988 c 119.131 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 72.267 m 46.536 71.924 l 46.593 71.81 l 46.706 70.898 l 49.439 56.647 52.282 37.531 61.635 25.941 c 62.033 25.428 l 62.49 24.973 l 65.495 21.801 69.087 19.9 73.374 19.217 c 73.66 19.159 l 73.943 19.159 l 74.229 19.102 l 80.016 18.846 85.856 19.056 91.665 18.987 c 92.29 18.987 l 101.142 18.987 109.993 18.987 118.845 18.987 c 119.13 18.987 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 40.299 m 46.536 40.129 l 46.593 40.129 l 46.649 39.902 l 46.706 39.732 l 46.821 39.502 l 46.879 39.331 l 49.79 31.557 54.14 22.97 62.492 20.015 c 62.948 19.902 l 63.347 19.73 l 67.023 18.669 70.197 19.063 73.945 18.989 c 74.801 18.989 l 80.498 18.989 86.197 18.989 91.894 18.989 c 92.521 18.989 l 101.295 18.989 110.071 18.989 118.847 18.989 c 119.131 18.989 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 45.486 m 46.536 45.316 l 46.593 45.258 l 46.649 45.028 l 50.961 31.393 57.709 18.403 73.659 18.988 c 74.229 18.988 l 80.04 18.988 85.853 18.988 91.665 18.988 c 92.29 18.988 l 101.142 18.988 109.993 18.988 118.845 18.988 c 119.13 18.988 l 155.027 18.988 m 155.142 18.988 l 170.089 18.988 185.036 18.988 199.986 18.988 c 200.156 18.988 l 119.129 18.988 m 119.243 18.988 l 131.133 18.988 143.023 18.988 154.912 18.988 c 155.026 18.988 l 46.536 58.193 m 46.536 57.907 l 46.593 57.851 l 46.649 57.508 l 50.286 42.769 55.241 20.711 73.659 19.046 c 73.942 19.046 l 74.228 18.988 l 80.039 18.988 85.852 18.988 91.663 18.988 c 92.289 18.988 l 101.141 18.988 109.992 18.988 118.844 18.988 c 119.129 18.988 l S Q 118.183 4.531 m 119.798 4.531 l 119.798 5.112 l 115.887 5.112 l 115.887 4.531 l 117.604 4.531 l 117.604 0.116 l 118.184 0.116 l f 120.971 3.718 m 120.971 3.718 -0.581 -3.602 re 120.971 5.112 m 120.39 5.112 l 120.39 4.383 l 120.971 4.383 l f 121.901 3.718 m 121.901 0.116 l 122.481 0.116 l 122.481 2.331 l 122.481 2.841 122.859 3.253 123.327 3.253 c 123.751 3.253 123.993 2.997 123.993 2.545 c 123.993 0.116 l 124.573 0.116 l 124.573 2.331 l 124.573 2.841 124.951 3.253 125.418 3.253 c 125.837 3.253 126.083 2.989 126.083 2.545 c 126.083 0.116 l 126.664 0.116 l 126.664 2.826 l 126.664 3.475 126.293 3.833 125.618 3.833 c 125.137 3.833 124.847 3.682 124.509 3.254 c 124.295 3.659 124.007 3.833 123.538 3.833 c 123.056 3.833 122.739 3.648 122.429 3.193 c 122.429 3.718 l f 130.636 1.743 m 130.636 2.291 130.595 2.619 130.49 2.888 c 130.254 3.478 129.702 3.833 129.023 3.833 c 128.012 3.833 127.361 3.069 127.361 1.897 c 127.361 0.72398 127.992 0 129.01 0 c 129.842 0 130.417 0.44901 130.562 1.202 c 129.976 1.202 l 129.815 0.79501 129.487 0.58099 129.02 0.58099 c 128.648 0.58099 128.335 0.73601 128.14 1.02 c 128.001 1.214 127.952 1.408 127.945 1.743 c 130.636 1.743 l h 128.011 2.207 m 128.058 2.841 128.462 3.253 129.036 3.253 c 129.597 3.253 130.028 2.809 130.028 2.247 c 130.028 2.234 130.028 2.22 130.021 2.207 c f 20.99 37.104 6.4453 0.465 re f 20.99 38.963 6.4453 0.465 re f 24.124 42.006 m 22.384 43.208 l 22.384 42.566 l 23.702 41.703 l 22.384 40.843 l 22.384 40.194 l 24.152 41.391 l 25.986 40.125 l 25.986 40.775 l 24.612 41.684 l 25.986 42.579 l 25.986 43.243 l f 26.566 44.193 m 29.471 44.193 -2.9047 -0.46599 re 26.566 44.193 m h 25.522 44.193 m 25.522 43.727 l 26.058 43.727 l 26.058 44.193 l f 24.127 44.816 0.4648 3.445 re f 20.99 50.21 m 21.888 49.512 23.133 49.071 24.21 49.071 c 25.291 49.071 26.538 49.512 27.436 50.21 c 27.436 50.596 l 26.457 49.99 25.306 49.652 24.21 49.652 c 23.121 49.652 21.962 49.991 20.99 50.597 c f 23.778 52.092 m 23.778 54.444 l 23.198 54.444 l 23.198 52.092 l 21.571 52.092 l 21.571 54.773 l 20.99 54.773 l 20.99 51.512 l 25.986 51.512 l 25.986 52.092 l f 26.566 55.81 m 29.471 55.81 -2.9047 -0.46397 re 26.566 55.81 m h 25.522 55.81 m 25.522 55.346 l 26.058 55.346 l 26.058 55.81 l f 22.677 57.479 m 23.743 58.545 l 24.81 57.479 l 25.077 57.745 l 24.003 58.812 l 25.069 59.878 l 24.81 60.146 l 23.743 59.078 l 22.677 60.146 l 22.418 59.878 l 23.485 58.812 l 22.412 57.745 l 22.677 57.479 l h 23.721 56.507 m 25.039 56.507 26.103 57.545 26.103 58.83 c 26.103 60.117 25.039 61.154 23.721 61.154 c 22.402 61.154 21.339 60.117 21.339 58.83 c 21.339 57.545 22.403 56.507 23.721 56.507 c h 23.721 56.856 m 22.6 56.856 21.688 57.743 21.688 58.83 c 21.688 59.92 22.6 60.806 23.721 60.806 c 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87.477 l 121.247 86.859 l 121.416 86.298 l 121.191 85.624 l 121.08 85.343 l 120.709 84.897 120.505 84.536 119.9 84.614 c 119.675 84.557 l 119.506 84.557 l 119.506 84.669 l 119.562 84.725 l 119.562 84.669 l 119.506 84.725 l 119.562 84.725 l 119.562 84.781 l 119.562 84.725 l 119.619 84.781 l 119.562 84.725 l 119.506 84.725 l 119.562 84.781 l 119.562 84.725 l 119.562 84.781 l 119.619 84.781 l 119.562 84.725 l 119.619 84.725 l 119.562 84.781 l 119.562 84.725 l 119.619 84.781 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.781 l 119.562 84.725 l 119.562 84.669 l 119.562 84.781 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.725 l 119.619 84.725 l 119.562 84.669 l 119.619 84.725 l 119.562 84.725 l 119.619 84.669 l 119.562 84.725 l 119.619 84.669 l 119.619 84.725 l 119.562 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84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 119.562 84.725 l 119.506 84.725 l 69.257 116.672 m 69.481 116.615 l 69.763 116.559 l 69.986 116.446 l 70.212 116.391 l 71.446 116.11 l 72.626 115.773 l 73.806 115.493 l 74.984 115.155 l 80.431 113.527 l 87.664 111.078 94.977 108.218 101.597 104.377 c 104.797 102.523 l 107.547 100.727 l 108.558 100.053 l 111.535 97.939 114.74 95.354 117.205 92.642 c 118.328 91.407 l S 0 1 0 RG 81.945 30.266 m 81.777 30.434 l 81.608 30.66 l 75.901 37.98 63.198 56.688 66.618 66.479 c 66.787 66.873 l 66.899 67.321 l 68.014 70.473 72.23 75.133 75.769 72.543 c 75.938 72.431 l 76.106 72.431 l 76.106 72.318 l 75.994 72.206 l 75.938 72.206 l 75.994 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.106 72.319 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.206 l 76.106 72.263 l 76.051 72.263 l 76.106 72.206 l 76.051 72.206 l 76.106 72.263 l 76.106 72.206 l 76.106 72.263 l 76.051 72.206 l 76.106 72.263 l 76.106 72.206 l 76.106 72.263 l 76.051 72.263 l 76.106 72.206 l 76.051 72.206 l 76.106 72.263 l 76.051 72.206 l 76.106 72.263 l 76.106 72.206 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.206 l 76.106 72.263 l 76.106 72.206 l 76.106 72.263 l 76.051 72.263 l 76.106 72.206 l 76.106 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76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.263 l 76.106 72.263 l 76.051 72.206 l 76.051 72.263 l S 1 1 0 RG 121.191 42.898 m 121.08 42.786 l 120.967 42.617 l 120.855 42.505 l 117.327 37.912 112.691 33.625 107.661 30.77 c 104.741 29.198 l 101.933 27.963 l 98.799 26.653 93.657 25.423 90.086 25.549 c 89.469 25.604 l 88.347 25.716 l 87.784 25.829 l 85.358 26.124 82.408 27.002 80.205 28.074 c 79.307 28.579 l 78.521 29.029 l 77.674 29.551 76.222 30.7 75.713 31.612 c 75.713 31.725 l 75.882 31.894 l 75.994 31.948 l 76.106 31.837 l 76.106 31.781 l 76.106 31.894 l 76.051 31.894 l 76.106 31.837 l 75.994 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.894 l 76.106 31.781 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.781 l 76.106 31.837 l 76.051 31.781 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.781 l 76.106 31.837 l 76.106 31.781 l 76.163 31.781 l 76.106 31.837 l 76.106 31.781 l 76.106 31.837 l 76.106 31.781 l 76.163 31.781 l 76.106 31.781 l 76.163 31.781 l 76.106 31.837 l 76.106 31.781 l 76.163 31.781 l 76.106 31.781 l 76.163 31.781 l 76.106 31.837 l 76.106 31.781 l 76.163 31.837 l 76.106 31.837 l 76.163 31.781 l 76.106 31.837 l 76.163 31.837 l 76.106 31.781 l 76.163 31.837 l 76.106 31.781 l 76.106 31.837 l 76.106 31.781 l 76.163 31.837 l 76.106 31.837 l 76.051 31.781 l 76.106 31.837 l 76.106 31.781 l 76.106 31.837 l 76.051 31.837 l 76.106 31.781 l 76.163 31.781 l 76.106 31.837 l 76.106 31.781 l 76.106 31.837 l 76.163 31.837 l 76.106 31.781 l 76.106 31.837 l 76.106 31.781 l 76.163 31.781 l 76.106 31.837 l 76.051 31.837 l 76.106 31.781 l 76.106 31.837 l 76.051 31.781 l 76.106 31.837 l 76.163 31.837 l 76.106 31.781 l 76.163 31.837 l 76.106 31.781 l 76.163 31.837 l 76.163 31.894 l 76.106 31.837 l 76.106 31.894 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.894 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.894 l 76.106 31.837 l 76.106 31.894 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.894 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.837 l 76.106 31.837 l 76.051 31.781 l 76.051 31.837 l S 0 1 1 RG 119.506 19.317 m 119.562 19.375 l 119.562 19.317 l 119.562 19.375 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 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l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.562 19.317 l 119.506 19.317 l 119.619 19.375 m 119.563 19.375 l 119.619 19.375 l 119.563 19.317 l 119.563 19.375 l 119.619 19.375 l 119.563 19.375 l 119.619 19.375 l 119.563 19.317 l 119.563 19.375 l 119.563 19.317 l 119.619 19.375 l 119.563 19.317 l 119.506 19.317 l 119.563 19.375 l 119.563 19.317 l 119.619 19.317 l 119.563 19.317 l 119.619 19.375 l 119.563 19.317 l 119.563 19.375 l 119.563 19.317 l 119.619 19.317 l 119.563 19.317 l 119.619 19.375 l 119.563 19.317 l 119.563 19.375 l 119.563 19.317 l 119.619 19.317 l 119.563 19.317 l 119.619 19.317 l 119.563 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119.618 19.375 l 119.618 19.318 l 119.618 19.375 l 119.562 19.318 l 119.618 19.375 l 119.562 19.318 l 119.618 19.318 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.318 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.318 l 119.618 19.375 l 119.562 19.318 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.375 l 119.618 19.375 l 119.562 19.318 l 119.562 19.375 l 119.505 19.375 l 119.562 19.318 l 119.562 19.375 l 119.505 19.375 l 119.562 19.318 l 119.562 19.375 l 119.505 19.375 l 119.562 19.318 l 119.562 19.375 l 119.505 19.375 l 119.562 19.375 l 119.505 19.375 l 119.562 19.318 l 119.505 19.375 l 119.562 19.375 l 119.505 19.375 l 119.562 19.375 l 119.505 19.375 l 119.562 19.375 l 119.505 19.375 l 119.562 19.375 l 119.505 19.375 l 119.562 19.375 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19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 119.562 19.375 l 119.505 19.318 l 119.562 19.318 l 119.505 19.318 l 106.594 88.543 m 106.649 88.263 l 106.649 87.926 l 106.706 87.646 l 106.761 87.365 l 107.042 86.019 l 107.323 84.615 l 107.548 83.269 l 107.773 81.977 l 108.728 75.801 l 109.458 70.299 l 109.963 65.302 l 110.356 60.867 l 110.637 56.318 l 110.75 52.332 l 110.637 48.851 l 110.468 45.708 l 110.413 44.641 l 110.258 41.354 109.883 38.325 110.3 35.04 c 110.356 34.142 l 110.582 32.57 l 111.823 25.843 114.563 24.469 118.834 20.106 c 118.947 20.049 l 119.059 19.937 l 119.003 19.88 l 119.059 19.768 l 119.228 19.599 l 119.285 19.599 l 119.51 19.375 l 119.623 19.375 l 119.567 19.375 l 119.623 19.375 l S 1 0 1 RG 146.119 52.105 m 146.175 52.05 l 146.288 52.05 l 146.343 52.105 l 146.399 52.05 l 146.456 52.05 l 146.399 52.05 l 146.456 52.05 l 146.399 52.05 l 146.456 51.993 l 146.456 52.05 l 146.399 52.05 l 146.456 52.05 l 146.399 52.05 l 146.456 51.993 l 146.456 52.05 l 146.51 52.05 l 146.456 51.993 l 146.456 52.05 l 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146.398 51.993 l 146.454 51.993 l 146.398 51.993 l 146.454 51.993 l 146.398 51.993 l 146.454 51.993 l 146.398 52.05 l 146.398 51.993 l 146.454 52.05 l 146.398 51.993 l 146.398 52.05 l 108.952 37.229 m 108.952 37.397 l 108.896 37.51 l 104.857 49.76 114.722 58.835 126.131 59.069 c 128.152 58.844 l 129.107 58.675 l 133.521 57.896 137.86 56.513 141.795 54.353 c 142.469 53.959 l 143.031 53.621 l 143.536 53.342 l 143.984 53.116 l 144.265 52.947 l 144.49 52.778 l 144.77 52.666 l 144.995 52.555 l 145.164 52.498 l 145.276 52.44 l 145.444 52.385 l 145.613 52.216 l 145.725 52.216 l 145.894 52.16 l 146.006 52.104 l 146.119 52.104 l S 0 0 1 RG 104.797 77.707 m 104.853 77.707 l 105.322 77.707 105.789 77.707 106.256 77.707 c 106.313 77.764 l 106.368 77.707 l 107.941 77.707 109.513 77.707 111.085 77.707 c 111.141 77.764 l 111.198 77.707 l 111.254 77.707 l 111.311 77.764 l 111.367 77.707 l 111.423 77.707 l 111.478 77.764 l 111.535 77.707 l 111.59 77.764 l 111.646 77.764 l 111.702 77.707 l 111.758 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77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 114.06 77.707 l 114.117 77.707 l 85.877 37.341 m 85.82 37.396 l 85.82 37.509 l 85.765 37.621 l 85.765 37.677 l 84.467 41.554 83.615 45.576 83.125 49.636 c 82.956 51.545 l 83.013 53.285 l 83.099 55.22 83.467 57.777 83.911 59.686 c 83.967 60.08 l 84.079 60.472 l 84.191 60.81 l 85.329 65.669 87.37 70.001 89.974 74.229 c 90.255 74.62 l 90.424 74.9 l 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108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.745 l 108.725 70.745 l 108.669 70.689 l 108.669 70.745 l 62.352 86.522 m 62.07 85.567 l 61.847 84.894 l 61.791 84.612 l 61.679 84.275 l 61.504 83.311 61.274 82.563 61.174 81.58 c 61.285 80.906 l 61.509 79.199 61.952 78.533 62.858 77.146 c 63.14 76.921 l 63.363 76.64 l 63.588 76.416 l 65.457 74.658 67.542 74.009 69.933 73.439 c 70.102 73.439 l 70.271 73.385 l 70.439 73.385 l 70.551 73.327 l 71.687 73.148 72.886 72.958 74.031 72.879 c 74.199 72.822 l 74.312 72.822 l 75.35 72.74 76.313 72.556 77.343 72.43 c 77.512 72.374 l 77.736 72.374 l 77.849 72.317 l 77.961 72.317 l 80.099 71.993 82.224 71.591 84.361 71.307 c 84.473 71.307 l 84.585 71.251 l 84.81 71.251 l 85.052 71.249 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63.727 99.854 63.727 c 100.022 63.727 l 101.071 63.727 102.119 63.727 103.166 63.727 c 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.672 l 103.221 63.727 l 103.278 63.727 l 103.221 63.727 l 103.278 63.727 l 103.221 63.672 l 103.221 63.727 l 32.653 76.809 m 33.494 76.978 l 33.832 77.034 l 34.169 77.034 l 34.506 77.091 l 39.396 77.031 46.085 73.625 50.563 71.701 c 51.292 71.42 l 51.798 71.195 l 54.823 69.887 57.876 68.628 61.005 67.659 c 61.229 67.603 l 61.565 67.49 l 61.791 67.434 l 61.96 67.378 l 62.786 67.105 63.446 66.93 64.262 66.704 c 64.431 66.647 l 64.6 66.647 l 65.271 66.406 66.088 66.279 66.789 66.086 c 66.901 66.086 l 67.237 65.974 l 67.35 65.974 l 67.519 65.917 l 67.688 65.917 l 68.023 65.805 l 68.192 65.805 l 68.305 65.748 l 68.474 65.748 l 68.586 65.692 l 68.755 65.692 l 68.867 65.637 l 68.979 65.637 l 69.091 65.581 l 69.26 65.581 l 69.372 65.524 l 69.484 65.524 l 69.653 65.468 l 70.234 65.385 71.167 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108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.36 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.417 l 108.728 33.417 l 108.671 33.36 l 108.671 33.417 l 84.417 122.847 m 84.361 122.735 l 84.361 122.623 l 84.304 122.511 l 84.304 122.398 l 81.87 113.77 79.338 104.438 78.24 95.506 c 78.185 95.057 l 78.129 94.214 l 78.018 93.43 l 77.82 90.774 78.408 86.514 79.084 83.996 c 79.533 82.312 l 80.221 79.715 81.359 77.264 82.621 74.9 c 82.901 74.396 l 83.183 73.946 l 83.464 73.44 l 83.745 72.992 l 83.97 72.654 l 85.294 70.658 86.837 68.803 88.349 66.985 c 88.518 66.816 l 88.629 66.647 l 89.604 65.537 90.601 64.41 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114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 114.059 26.342 l 114.114 26.342 l 14.854 54.913 m 14.967 55.024 l 15.305 55.193 l 23.801 60.774 35.195 65.142 45.51 65.636 c 46.127 65.691 l 46.744 65.691 l 56.51 65.268 65.94 62.123 74.873 58.336 c 77.567 57.102 l 78.466 56.708 l 84.484 53.733 90.535 50.5 96.151 46.827 c 96.375 46.715 l 96.881 46.378 l 99.239 44.9 101.566 43.243 103.787 41.605 c 103.9 41.493 l 104.069 41.382 l 104.181 41.27 l 104.293 41.214 l 104.565 40.935 104.995 40.733 105.303 40.372 c 105.528 40.26 l 105.584 40.147 l 105.809 40.036 l 105.865 39.924 l 105.977 39.868 l 106.257 39.587 l 106.37 39.531 l 106.539 39.363 l 106.651 39.306 l 106.706 39.251 l 106.947 39.042 107.181 38.82 107.437 38.634 c 107.494 38.521 l 107.548 38.465 l 107.661 38.409 l 107.83 38.24 l 107.942 38.185 l 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46.37 111.141 46.103 c 111.198 45.99 l 111.253 45.935 l 111.499 45.844 111.628 45.493 111.927 45.26 c 112.095 45.091 l 112.095 45.035 l 112.209 44.979 l 112.263 44.866 l 112.32 44.811 l 112.452 44.68 112.583 44.548 112.713 44.418 c 112.882 44.249 l 112.882 44.192 l 113.164 43.912 l 113.164 43.855 l 113.275 43.744 l 113.526 43.65 113.392 43.577 113.668 43.351 c 113.781 43.238 l 114.112 42.938 113.787 43.146 114.117 42.845 c 114.342 42.621 l 114.286 42.621 l 114.342 42.621 l 114.455 42.509 l 114.455 42.453 l 114.511 42.397 l 114.567 42.397 l 114.622 42.341 l 114.622 42.285 l 114.959 41.947 l 114.903 41.947 l 114.959 41.947 l 115.016 41.893 l 115.016 41.836 l 115.408 41.444 l 115.353 41.444 l 115.408 41.444 l 115.464 41.388 l 115.464 41.331 l 115.858 40.938 l 115.802 40.938 l 115.858 40.938 l 115.97 40.825 l 115.97 40.769 l 116.363 40.377 l 116.363 40.32 l 116.7 39.982 l 116.7 39.927 l 117.037 39.589 l 117.037 39.534 l 117.318 39.253 l 117.318 39.197 l 117.711 38.804 l 117.711 38.748 l 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49.638 l 137.193 49.638 l 137.25 49.638 l 137.193 49.581 l 137.193 49.638 l 123.38 43.179 m 123.38 43.236 l 123.326 43.236 l 123.157 43.46 l 123.044 43.629 l 122.876 43.798 l 119.441 47.511 115.785 52.484 114.117 57.385 c 113.948 57.833 l 113.835 58.283 l 112.651 61.104 114.442 65.099 117.205 66.312 c 117.317 66.368 l 117.486 66.368 l 117.711 66.479 l 117.992 66.479 l 118.104 66.423 l 118.273 66.423 l 118.385 66.368 l 118.498 66.368 l 118.554 66.312 l 118.667 66.312 l 118.723 66.256 l 118.892 66.256 l 119.003 66.2 l 119.061 66.2 l 119.172 66.144 l 119.229 66.144 l 119.286 66.087 l 119.398 66.087 l 119.454 66.03 l 119.566 66.03 l 119.621 65.975 l 119.677 65.975 l 119.733 65.918 l 119.845 65.862 l 119.902 65.862 l 119.959 65.808 l 120.014 65.808 l 120.071 65.75 l 120.126 65.75 l 120.252 65.659 120.654 65.543 120.8 65.414 c 120.856 65.357 l 120.913 65.357 l 120.968 65.302 l 121.025 65.302 l 121.082 65.245 l 121.138 65.245 l 121.25 65.133 l 121.306 65.133 l 121.361 65.076 l 121.417 65.076 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Hinting Copyright (c) 1996 Y&Y, Inc.) readonly def /FullName (MTMS) readonly def /FamilyName (MathTime) readonly def /Weight (Normal) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -133 def /UnderlineThickness 20 def end readonly def /FontName /IXCNEZ+MTMS def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 71 /G put dup 73 /I put dup 76 /L put dup 78 /N put dup 85 /U put dup 86 /V put dup 87 /W put readonly def /FontBBox{27 -241 977 779}readonly def currentdict end currentfile eexec oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou][Lpgɬ`\zONPq8(= VۡVOJi 8bImj,k\g&C4/hOA+ʌXM37HS^<a}30bԻq{}w,?7F eQ=c/SF1pN_rxTD'". :W%<^Z5CsH1NԚYlciSImT >YeM ȁ!yÿIXy@fq; 3enF u%@EO|m@_z{ꗹOhDbỲ9/!mI#W#ƣ`[C̖߬Kr_dzݩ&A\/ſ'WbHO^otrd,lHΉ#ԛMuf_^vZ>GYQ@VFniұ9S5~#ˆ<'J= @E\JJ<F+/++h`S0 K}i0v9cus `}9?dE{PiTv L&l9:8gY{'U4Ӳk,F0XS3'xe*xv ,ܺ^_E\So\ڼle:ͣwMLC =^k=D̚-e̳JRP#Bl a->6tlF~?^V~\xG*MIfu=*+*9xrqYPh~뮟-n,pEӯ*Ϯu,D 4w@nxs"aͨ,oC`VSR`5>{3@3+-[E~_[cW*zxTIRמ\ENv S5Ƶs^wX;N~z4d+`1nQP3(Am &pX:;u0vAjOiyah:6ZcOaDJC/ЗM/WXlu)S1eŦEh7!!'7]/ㄫ8gUIʑxy#v2I = cF.D8pFn+%I|FP'bY$4ЉoH1=]fwxDwb?-cvsjpT+B&`*~|CX˼ՖCm#grZkz-,Ł>+9-T0go /i1LNR< ",0"E^{xPh`vwS2K14a|_:JyLm|ؾcwlȻȴ\đM׀EЕ[|wevΫ?On Y_ ˜1xjj> kW{5Im0ǏsuJTّ 2u+oKN쫭QW~5#3Ng;qe;ziE@Zԧjl ^rB$o@[ endstream endobj 70 0 obj << /CharSet (/E/G/I/L/N/U/V/W) /FontFile 69 0 R /ItalicAngle 0 /Descent -237 /CapHeight 666 /Flags 4 /Type /FontDescriptor /StemV 40 /FontName /IXCNEZ+MTMS /Ascent 710 /FontBBox [ 27 -241 977 779 ] /XHeight 441 >> endobj 71 0 obj [ 553 700 642 890 575 642 933 810 1013 805 745 745 800 880 571 560 902 728 914 ] endobj 72 0 obj << /Length1 1216 /Length2 4806 /Length 6022 /Length3 0 >> stream %!PS-AdobeFont-1.1: RMTMI 1.1 %%CreationDate: 1993 May 10 16:52:31 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. % MathTime is a trademark of The TeXplorators Corporation 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation. Hinting (c) 1992, 1993 Y&Y, Inc. (508) 371-3286. All Rights Reserved.) readonly def /FullName (RMTMI) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle -14.036 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /QNFQZX+RMTMI def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 11 /alpha put dup 12 /beta put dup 59 /comma put dup 13 /gamma put dup 62 /greater put dup 60 /less put dup 33 /omega put dup 46 /parenleft put dup 47 /parenright put dup 58 /period put dup 25 /pi put dup 18 /theta put dup 118 /v put dup 119 /w put dup 24 /xi put dup 16 /zeta put readonly def /FontBBox{0 -213 987 680}readonly def currentdict end currentfile eexec oc;j~EЪ+`U+1;[ihHlgtR@nk{#Y~gJ[. DI~ْ+%hapYz;3NO_O:Vп}KBhIϮԬ";eiwzVcW;I0a1]j"4[{ErGT1QeG0 Vw ߚOҎN'·4b>T(4^mѨnV8Bo8cpWTC 6j'-б^3;ZSd_ v9(+2Op?.BXsޝo!.Y([J$~8g@/Y.Y+S$C9S= iYRu |íPq.`1)KB/к!xYJK8,2(ŝ]#BEQw5,Ge2u fPQ6PnhH~l 棉l|6Ҿj;D鿂 "zGN8fYC8#SfMr =XZ2MIHv@}`6)ta}Y7Ϳ47_75Ww ^6u$; ӕcYfg_2ƨ4}ȱG}THl=YUX 3y-kHj7έD,3>w(=?vez#]2+P)pvt2kDrn}۠>r|QkcRõ[I+s k)r5$i!(=EN$^ɼ}Yatw^ ם %Lbz{;%G{j7H9;S(Y_*VuKڼ섥Yȗ(V١UD5'h̝-r0fsgZ@m-={>zNR y $N`x.+]o *<%ɢ 𽎴V=goCtWK] {Pa[h >2k<ݦΚs[^8x=(ɌRgo}vyΔ`hLwhTQ$s1XK|d@Pm ~E~+)gB.GD<,hݠ'WAvQU!J%O$.b\2M HPdZ_-"הoY4Ol:Y0;mUNuek됝͍*&6im&cth`<+ G3DթDSqNfJ*"STFږ Cbr66p6q*2]N*mU yZ9wy J{VVrjQO؄ni!TpLe u*VyTjDk%=JORUnz_Ju~ .묅] #NDIMEuu9Ï?0i3U65T,'Ra@{@Q# 'P*{5?XٛiNGVۓ =<[Jո];g?sz]w1J8*z], j*  q頋`я),4^+gd[JtiC|g*U%yK yH=HZ6x -Q/hw[q$`񧨙8g:\f;SxH }N]xZ-=ƴ:b- ۫†ػT[k޵pW쯱O՘wg)AД`AD~A r0ż7W󃟱98Q+l[{>0 Ⱦ&3|^L蹌zNde: ./Sg} l )0G(^J!VfF'HlC,YsKiJYhIq.9?+fV1̅Hd:=Q"܀awch*k9t8m]{DC[9,y)z9!ZFz1o6\N BQu">^7(Bў$nRN.5Gz5ĎkF|(q@qA(MH.T^|:bWh%؄!Ӵ~VqAN6Է٫| /S#0<= xkPl$dG}WKj}殩Ax/XRYGn^/1Q6__GF9zm҆TO5JLϺ8 |ų01LBF +w:z95P)zKS~Gu[R7Nb-T1>T';,ݣl ֣5g8UBhg ã'RP9l§lBzmcb8L%fOo; rfzZD |(StPߓ_ (I|ů>65snf8Y0y3 7K=\29XNZSyt lQ+@b?!>!`cF`"_+˚BVi m9g:/p eӔ;vj\/u6n![(1|@_23xmQۺ6Vlӧ (E6r9 L[ȹ9C`ҤARħ-ZZ]u+5rqZAF#0X n-~g֤{XG\8+ml4K"he@ bDSHWj"0 aFȵŜq7dvpm4sjVcHCէi5ȗs.'oh5-?ʗ)0JOuz>Dr*zX2Qv>"oUmYعIiJxT@LL%1M}YWwy=r6 endstream endobj 73 0 obj << /CharSet (/Delta/alpha/beta/comma/gamma/greater/less/omega/parenleft/parenright/period/pi/theta/v/w/xi/zeta) /FontFile 72 0 R /ItalicAngle -14 /Descent 0 /CapHeight 0 /Flags 4 /Type /FontDescriptor /StemV 73 /FontName /QNFQZX+RMTMI /Ascent 0 /FontBBox [ 0 -213 987 680 ] /XHeight 440 >> endobj 74 0 obj [ 792 788 796 764 820 798 651 764 686 827 571 564 502 430 437 430 520 440 300 492 547 686 472 426 600 545 534 433 554 577 588 704 655 452 590 834 547 524 562 1043 1043 1043 1043 319 319 373 373 642 804 802 796 762 832 762 740 794 767 275 331 780 470 780 472 458 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 419 412 445 948 948 468 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 487 735 ] endobj 75 0 obj << /Length1 828 /Length2 1236 /Length3 532 /Length 1822 /Filter /FlateDecode >> stream xRmFЧ~v?J"i&2{%&']Ax dO"q"X[A( 89 KQcdqx'v!RˤrPo$ 'r//$W#:R:R IsbA>{'첓rd( +>q!])_^MJ.S^خM_}?&&/fЕjņ4ƶĽ5d$x[ԧSf6`b/Ė/O9 uV(o/[˳,=AZ[|v:řPSlZT}>gnArbtvYE~LOT5@;Мn/hE>cb OU :NJ~n d.<[0̩pT_@X7Iɝ 7u kLUw 5Pzd1o'<5)$b9fbYc.F%s0+QLƟ}&ׅ?G0M.i WM= NZm;ay; R^`?9.Ecr⿛Ӟ^^xti(FeWJxĠ'nKphOU]E]o'lVipjiO=~HD/,BM3َ,+)J=bD:hn8@r|3~^rulk`oLn3h5®[_6f ʤڼ3h5]{k-19zŢZΜ6oNQ-5?t3CIҽڱE߂EJC[*[Wo6j䧏 T͓2c$z[sSLfrt3fe!Q94x? okި!w3#]رA+Ʃ}qƠs+OMiURyʽ5U3y·RcZ4c/V#OT,AS/ōѤ˔gnY%yOji "sZiE'7`l禎F_6}}9IF7m-?PT߸Mލ;ruծ~)Um5lystq /i6LBhPٯ鞳;o:wnxȜqqhlyPqn]zuUI3"fɷ1VwqH]7_Jʊm^)ԗq) }{F O' Q)"# endstream endobj 76 0 obj << /Type /Encoding /Differences [ 0 /.notdef 82 /R 83 /.notdef ] >> endobj 77 0 obj /BKFTGN+MSBM10 endobj 78 0 obj << /ItalicAngle 0 /Descent 0 /CapHeight 689 /Flags 4 /Type /FontDescriptor /StemV 40 /Ascent 464 /FontBBox [ -55 -420 2343 920 ] /XHeight 463 /FontName 77 0 R /FontFile 75 0 R >> endobj 79 0 obj [ 722.2 ] endobj 80 0 obj << /Length1 1542 /Length2 3786 /Length 5328 /Length3 0 >> stream %!PS-AdobeFont-1.1: MTEX 1.1 %%CreationDate: 1993 Jun 26 10:30:36 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. % MathTime is a trademark of The TeXplorators Corporation 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation. Hinting (c) 1992, 1993 Y&Y, Inc. (508) 371-3286. All Rights Reserved.) readonly def /FullName (MTEX) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /RRQQOB+MTEX def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 62 /braceex put dup 8 /braceleftbig put dup 26 /braceleftbigg put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 56 /bracelefttp put dup 9 /bracerightbig put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 16 /parenleftBig put dup 32 /parenleftBigg put dup 0 /parenleftbig put dup 18 /parenleftbigg put dup 64 /parenleftbt put dup 66 /parenleftex put dup 48 /parenlefttp put dup 17 /parenrightBig put dup 33 /parenrightBigg put dup 1 /parenrightbig put dup 19 /parenrightbigg put dup 65 /parenrightbt put dup 67 /parenrightex put dup 49 /parenrighttp put dup 88 /summationdisplay put dup 80 /summationtext put readonly def /FontBBox{-23 -2958 1456 766}readonly def currentdict end currentfile eexec oc;j~EЪ+`U+1;[ihHlgtR@nk{#Y~gJ[. DI~ْ+%hapYz;3NO_O:Vп}KBhIϮԬ";eiwzVcW;I0a1]j"4[{ErGT1QeG0 Vw ߚOҎN'·4b>T(4^mѨnV8Bo8cpWTC 6j'-б^3;ZSi 4LTVC}:)EuF+o1F}NNZ*1aD1U(H`b^;1Mac]&'kM.Lؐ1Sh3\9)Wyϋzoԡ!OWr%\ tA7e:蔧R1-~w1Dj EWNTl%4 {yBvV E=&AcW_}in|{^X&V%kB.]9ԥ]eb_X_ǒk3gԤRD-.H|%bA3.EKJ2\n""v\{0~¡IJU.N@֠OucSQzOiR `V=M7[U.2+gL~8#@ѽϦSR4.j.@3R/tJTD13׊]^CwRkF  ,g&sHo 8jY?;'s;| h3J7i@O;;̭Ĭvtk9L ϕkI4&S&% z1<#J14P.$bLrEjP0k1 a.T}zk;+S\e,=,.[ZJePK[/?BX-H4$p@ܬJ^NB `cՉ|}"ҘW\Ne-|iXDMn[{/embf6獝YhcSޜ `sXYڷW+uuӖjUמO b4@hDՏz!s M=`CzI>[CTMףFFƪ? q! vFѾ{pù`mFɐ_avDOыù6<ҳ$ /VF{`~N=N}шzP9IqYy}̪YGQ؆Gʚѓo+ǂ Oes}޳/1 -KS=")4>NG}0n-8k^y b\t/Dlw͗pDUݚጀ2:LMUQ\lXI[h@(K@S5*:Vg<4 2Je}5JfwEx _ 7piUJ( |Bg8M~o%%1seg~~bx  A~vou2,e|- 6rjY-}&!G7i]MgrSLX` izսԔ뚔ZmISю-a)M)@Bpߎ?%v]ӿUN?*%?&vRQK"oϜՀ>I:PqR*!ʢ\\@,+ (; eg9$t9h c/ù۫3~ZO+ɉR9T3`~ܐcP?cT$ N ]3? j'UHH4},b\D- q['۾-%dndI^P,)7+ Sc=e]t칡> @Ԡ%=OЍ K1[VRCt{{MFCLIʭo7qPv.b~7.=X,b,(Qٸfyv' &%ɉ|J')0êX4ɌKϷ͇HقG̠co=Ë *q.='?oaUt> f!GK$^$#.wV&(9[T%nШWI@K☖LLAy7Quz"j؂=eyQbIHNrgh(Ŝ6~ ,!(* 46&±Oڮ{a `lqVKt8JqX[s]12|_ r fuLݸ&?DJUI"| d ϙ䫗ܔy8F[Q[e&.<,>ǫ9r1 7b4yDi<Ӏk}o{AnūuIrbJ5+yn3ׁ&-9o8e^ endstream endobj 81 0 obj << /CharSet (/braceex/braceleftbig/braceleftbigg/braceleftbt/braceleftmid/bracelefttp/bracerightbig/bracketleftbigg/bracketrightbigg/parenleftBig/parenleftBigg/parenleftbig/parenleftbigg/parenleftbt/parenleftex/parenlefttp/parenrightBig/parenrightBigg/parenrightbig/parenrightbigg/parenrightbt/parenrightex/parenrighttp/summationdisplay/summationtext) /FontFile 80 0 R /ItalicAngle 0 /Descent -600 /CapHeight 0 /Flags 4 /Type /FontDescriptor /StemV 67 /FontName /RRQQOB+MTEX /Ascent 46 /FontBBox [ -23 -2958 1456 766 ] /XHeight 462 >> endobj 82 0 obj [ 403 403 394 394 504 504 504 504 474 474 262 262 325 533 626 626 545 545 675 675 545 545 612 612 612 612 618 618 429 429 1107 1107 693 693 621 621 674 674 674 674 690 690 554 554 1348 1348 866 866 799 799 729 729 729 729 729 729 792 792 792 792 792 792 792 575 799 799 799 799 346 346 984 1235 458 528 1110 1511 1110 1511 1110 1511 1045 940 458 940 940 940 940 940 1415 ] endobj 83 0 obj << /Widths 71 0 R /BaseFont /IXCNEZ+MTMS /FirstChar 69 /LastChar 87 /FontDescriptor 70 0 R /Subtype /Type1 /Type /Font >> endobj 84 0 obj << /Widths 74 0 R /BaseFont /QNFQZX+RMTMI /FirstChar 1 /LastChar 119 /FontDescriptor 73 0 R /Subtype /Type1 /Type /Font >> endobj 85 0 obj << /Widths 79 0 R /FirstChar 82 /LastChar 82 /FontDescriptor 78 0 R /Subtype /Type1 /Type /Font /BaseFont 77 0 R /Encoding 76 0 R >> endobj 86 0 obj << /Widths 82 0 R /BaseFont /RRQQOB+MTEX /FirstChar 0 /LastChar 88 /FontDescriptor 81 0 R /Subtype /Type1 /Type /Font >> endobj 87 0 obj << /Length1 1281 /Length2 1259 /Length 2540 /Length3 0 >> stream %!PS-AdobeFont-1.0: t1-gul-symbol 001.000 %%Title: t1-gul-symbol %Version: 001.000 %%CreationDate: Mon May 12 14:48:11 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Created by CV Radhakrishnan,,, with FontForge 2.0 %Copyright: (http://fontforge.sf.net) % 2008-5-12: Created. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-symbol known{/t1-gul-symbol findfont dup/UniqueID known{dup /UniqueID get 4083185 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /HWNAVD+t1-gul-symbol def /FontBBox {5 -213 895 789 }readonly def /UniqueID 4083185 def /XUID [1021 992 867865827 11599217] def /PaintType 0 def /FontInfo 9 dict dup begin /version (001.000) readonly def /Notice (Created by CV Radhakrishnan,,, with FontForge 2.0 \050http://fontforge.sf.net\051) readonly def /FullName (t1-gul-symbol) readonly def /FamilyName (t1) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 39 /copyright put readonly def currentdict end currentfile eexec oc;jAw-6n}H#vݟ~Lڎko:FVvixؕBv0_ dĮ&8`}-AʌOǦ\Q]&8~a0[V2v)}H6p4aDPf0?IGrq㋒nDJ,52 HEh M/Z1hR 3 |/AF>"T6`~yxd<^;CNJ idjITR⏢Ɂw'ƺVTqرޡc%C TQIC:/*nX̅M}1ba) /h6A!7\PG|~zh~8^8s!BMYI:ꓩua!7h*){7sw2zI۳V,DK-yp~ONi8&ǁHkZr!U-UlM2U6cN=h",Η`%-9 5DpHa>-YÜbh@@XfY|M#X ž endstream endobj 88 0 obj << /CharSet (/copyright) /FontFile 87 0 R /ItalicAngle 0 /Descent 0 /CapHeight 0 /Flags 4 /Type /FontDescriptor /StemV 54 /FontName /HWNAVD+t1-gul-symbol /Ascent 0 /FontBBox [ 5 -213 895 789 ] /XHeight 0 >> endobj 89 0 obj [ 790 ] endobj 90 0 obj << /Length1 2224 /Length2 6536 /Length 8760 /Length3 0 >> stream %!PS-AdobeFont-1.0: t1-gul-regular-smallcaps 001.001 %%Title: t1-gul-regular-smallcaps %Version: 001.001 %%CreationDate: Mon May 26 10:39:46 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Gulliver, Giant amongst Dwarfs. %Copyright: This typeface offers excellent readability at very small %Copyright: sizes. %Copyright: %Copyright: The digitally encoded machine readable outline data for %Copyright: producing the typefaces licensed to you is copyrighted (c), %Copyright: 1994, 2005 by and the property of Gerard Unger. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-regular-smallcaps known{/t1-gul-regular-smallcaps findfont dup/UniqueID known{dup /UniqueID get 4084430 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /QDTHNW+t1-gul-regular-smallcaps def /FontBBox {-115 -321 1407 1009 }readonly def /UniqueID 4084430 def /XUID [1021 992 867865856 15320446] def /PaintType 0 def /FontInfo 11 dict dup begin /version (001.001) readonly def /Notice (Gulliver, Giant amongst Dwarfs.\012This typeface offers excellent readability at very small sizes.\012\012The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted \050c\051, 1994, 2005 by and the property of Gerard Unger.) readonly def % Gulliver, Giant amongst Dwarfs. % This typeface offers excellent readability at very small sizes. % % The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted (c), 1994, 2005 by and the property of Gerard Unger. /FullName (Gulliver SCOsF) readonly def /FamilyName (Gulliver SCOsF) readonly def /Weight (Regular) readonly def /FSType 4 def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -75 def /UnderlineThickness 50 def /ascent 789 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 108 /l put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put readonly def currentdict end currentfile eexec oc;jAw-36Uu4 l.Nk48DPh>[ME7wk9B.H.CSoZqO O)9OHl~Q:ɾD0j J'JZ `B 5ԆG tbY7:Ϳ2hK@,'$Qr[GB_720 qs`a|Xu\ӅZ?.PcN7.?WֺYq^$^VA7Up c?{RlG9a% #SȣP^-qTo8g^Z#Z #v.Cows?**hfy&;D bÍ!*=8-T9wPa4ԩ^vqB }p ;?IX`D-5 %[!Ӟ1o gn/yhgD`Ce}zB-8Zvʼ-ki8˹HCW*e*~V7gHmWrM)OlPlSN hUGXǧ=v%vӈ ^o66'%&AT( uw7 :L{|&( ,cY44rf*go&z* {NhJl0r1xР%syX\8 ]n`85˲#sBIr:lr܎eǪ7o~!sPAz18xA նNthTw6I[T]`T: v5Z*nZ o)f{H0jer9;Q"}l|a/osARS#݅mrnWe$h1Љ^XY{c+qi|l#mH PJ uSCB`ְ{FflVηiޢɊڿ;%rh0x 1y=XZ |~{rwy)&W$.6K6'ؘǿ6BA%dד\vu;7w}`-!/@ )$9vg޽ȭ2,8tv"# 3 $Buw`f aMG8aOһYbI#mM E.i [qI]4>stU'5upLQvE\ oG~$T2i=$v>ÅN.ȿ&6 ?XxKBal߉X+ıybhrm:dïi9 s܋J`I>:X|xE6l">\#M^>)Ʋ}}s14_;ũ yW-D}#/WML윰k7q7t>O@tlӱ%@WǼD^P ;1 ہZU0jm b{e(zaX ,9s~ƣK ͔?;8C=" C; jc: vhu"w@<]Lجt^}2 ԍnK^j*-FK8:s FBJ27+EP A@F''` H+O 9kI^SL<}Ir>4P :)H1䁜ž5[_RUCAxl=_0 p#ks-K~'G OS@~zk9j?qeVp9rAOAM;n] @`}Bx*QVO9_y|=I_ 8ȅQ({KqKbAanm *.Jh-a~Q&wiܪtP*AH)Hk&E}ZOmzMo\ ּ]8JvxJdo_P lz*o{ۡjWհ#GMN].ɨ2e'%_P2̬W'MPAYQps]_HNs&zt~몙~?K _̤H4GyV(Akj.Q䐧HJ:ux\jLFzoSﴔd!в.- cmnWċַ|Flb`.Tv#HYB\)UґV:ҳ?v?&$AOF GlxbF(qfƂgR]8vWJ7krx7M dyF#qgݸts5r ֤cLm3+NW0: )AI!%A7vac;2FERVނGdE90N!tʆH7l#V]^%2ShԿ CΟ^c.2 ),vo,{(ݞK:LlwM 2Y_?l6EPA>YlQP?7Q%1bt [-F˕<1BoqH D'sRrz,Ռbct"׳1&&3e"G Ƙ# 6|a.T_gCAkm 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TR'g>NPl`6CmQ{,%>rtFz=1sQ^TfMpδ7W$WBB#~%jĸ endstream endobj 91 0 obj << /CharSet (/a/b/c/e/f/i/l/n/o/r/s/t) /FontFile 90 0 R /ItalicAngle 0 /Descent 0 /CapHeight 742 /Flags 4 /Type /FontDescriptor /StemV 96 /FontName /QDTHNW+t1-gul-regular-smallcaps /Ascent 564 /FontBBox [ -115 -321 1407 1009 ] /XHeight 566 >> endobj 92 0 obj [ 550 541 528 628 510 476 593 669 316 307 574 455 822 652 611 520 618 562 464 479 ] endobj 93 0 obj << /Length1 1592 /Length2 1005 /Length3 532 /Length 1825 /Filter /FlateDecode >> stream xTkT bEGTA y@Jkt ˁЕ`9c tC%zNBB"Hr@)`j*$8XT4# AEBĵ`5'6Crē,1 Fq H Wk W  Cx!2r,ΐ#:XfIZ2 C3`FR,` YӡڈLÐZY100c5dYD{LQ iCs $BJD%!)@JEh$Nh5c cفpB:0:@@UNs*W/ԗ`K1k˳XV˱xdoŸRxR{1ilJ8%h30"* [$Iv1 @ p r0( tŒx1V6A;r ` ig-~?b s^b%NU ,u1dDĆ~14oS8Mwxa0O($(Fg  \͡-@Ţ)rM$gZA@}m&@J)gp'/D~]#6ߢ), ;X|ޘm5'K|~е<\2JXퟖ4˩`JǜJOͮхrzW%_[vthEםK!ч_TΘ?vJ yG/2,&v9?~Xx\YmqL'IM^nb!`?|#AFٶsF>'۫a%k]‚`PKz9ͯ\L|J+7/jvw[79MyrO/2غPSC#q^>u?Im}7[>}tm)I^~g|ܓ|sQ/N^رC@H=u|x' c8:cxnr, endstream endobj 94 0 obj << /Type /Encoding /Differences [ 0 /.notdef 73 /a36 74 /.notdef ] >> endobj 95 0 obj /HNBIRM+Dingbats endobj 96 0 obj << /ItalicAngle 0 /Descent 0 /CapHeight 708 /Flags 4 /Type /FontDescriptor /StemV 0 /Ascent 708 /FontBBox [ -1 -143 981 819 ] /XHeight 400 /FontName 95 0 R /FontFile 93 0 R >> endobj 97 0 obj [ 823 ] endobj 98 0 obj << /Length1 1771 /Length2 15290 /Length 17061 /Length3 0 >> stream %!PS-AdobeFont-1.0: t1-uni-regular 002.000 %%Title: t1-uni-regular %Version: 002.000 %%CreationDate: Sat Apr 12 22:19:08 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Copyright (c) 1987, 1991, 1993, 1994, 1998 Adobe Systems %Copyright: Incorporated. All Rights Reserved.Univers is a trademark %Copyright: of Linotype-Hell AG and/or its subsidiaries. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-uni-regular known{/t1-uni-regular findfont dup/UniqueID known{dup /UniqueID get 4172112 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /USCGMP+t1-uni-regular def /FontBBox {-168 -250 992 997 }readonly def /UniqueID 4172112 def /PaintType 0 def /FontInfo 9 dict dup begin /version (002.000) readonly def /Notice (Copyright \050c\051 1987, 1991, 1993, 1994, 1998 Adobe Systems Incorporated. All Rights Reserved.Univers is a trademark of Linotype-Hell AG and/or its subsidiaries.) readonly def /FullName (Univers 55 Roman) readonly def /FamilyName (Univers) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 68 /D put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 58 /colon put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 46 /period put dup 114 /r put dup 115 /s put dup 47 /slash put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put readonly def currentdict end currentfile eexec oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5CV]_I50$zEL>6µ3-O"Ղ,vw ;q8Q^Epd4_PsxO^2|jp5Ժ *Vg/ T"rɵ8t~k W%3M?$ۛWuGt5o6.2|#ԧ@ rد|C1k}')˃Umt8;:?2>GSQs2 KJۋaq%3(jv'T#o映ӲXƴpi-=@ؚi YCuC 纞 Wj/: IqyMG?rKiߣg d@rQKѴ:,] n0a]b g6ˈ}R2,^3>J TŘXbM]&Q2U}o=!X3Sq m0_׬P!C IKV.]!Nu}&QR0NtX.2_%R/d^4^˞Oqq+Q c,ީ)|.'ȣ_Ȁ`( H;1A CF=V˅O׼ s' k܎W;>) aݳaXY7Z bݱϚقf/?8U7>p'p 2ÅHA"&xt՝cs-|2N}i鍜`U+2&cW\LG.51n{uD Q'qGSe9ޡ(!@m:)IΏ;ipU@>\DKCV${Kt \׫̒O̗Ӌ9 ӦL-??sp!/$OMQ':Εz)|Y<^J8\qa_\ތQ*g{@N HnHƌoE kF%'nH깻L}j~RL^lV@vOkc}-e r % ME-eKi7ӈO^+l%"s1ZZ[%)%b??ihogC!4ZuuNT!ؼUpD΅"#pQ]gCǨ}dڌ%=c^C : Tix5j[U?SSӓ]!?dN@pBn.X֚^[AOsDMqAA[ 7?Dv +rʈ7^BS R9M?^ݬ@Q8@b6X.)ՆbgݷDY i$3/̯\! Yll)RQ8xgsaU ApZB:ud*R\ ܶh ?\NIv3!=uEPڇ]Ѐſ֨켃LS/̈-J8jU^4gu7EvE鵈qU :j`-zg?ؿ<*dß-Ͽ;r`_zu{K˗F3\,3*^  }\t׳?_|L'ijGwpXku?K# $}DQ hzO\*8dqS(0c__2F+*"Q鳐JE3NDUA4 ]ֱ21 A0_"j>2qڐcIsA{h/c )Z'ďxrxtr3hͽ Pnd[cwL]#K>O96a6Rzv`+c]# -V(r/.gsIߢh O"!jmk31EvUA8q/(*cf v7GWc&2$ q C"O sy…d{ BpΡ">;Z[!*_=9Gl5GPl,xFcɗ'ZCǸs<~{.#WB#shC ӑA2x>uRi'i?1p;J&k?cV? 4cH!P, @1Št$:gLBWcئzG> (y,F6ծMnQ}IMhcpQ?Bt#ɚyZ8=ٙ/NzKȪ&!FEZTd$Vta3 pW}d{N.\Oj@km=:TnPo-s;5^- VK ˽b#7.2JJw^%\6$@)RQC䕝p*+XK^?FH582N~9VAky΢od=Jc y5[܊$PKI`Lد"Iz=( aodwF=tts(*qYrpyڡ,0z$nA6_ה˞T4KH N{rT(4AIT¯nH93"l(*"TՊz_&Hȱy]k4ԋi R7+L2v:BZ\çkiSd[*#\E鞭!C:#ɌnI$fYu\5M\_ oFMlc0Xi{wŠ%xgNJ!cEtYmě/qey9K!& eڶ]A6(2> wTlPYs.9{D˔aΝJ76ӵbVe2[,%ܘWiPB1I CL5g2c»6V]iU6*F|ID'"?W}6O;l0?j;q"k,u_ĆwD: I 2Sk3}|x$xQMS?ϋ?昝{N4_}euc<,70Gޅ8ۼL&uayΊHa#m93פi̔@NjS6!9#U*%",k/ٿ]M }x piC2ٗ6,Uc+)m w(!hAg*gU-65SHr0G ﷴ$~0`⪯MiF.!Xe0CeEcޣ%]tIt:< Q)Z`*Vs`fntmht\:0җF_:%O$uIqqb'i%>C@x{bFSOd*cZ_ 06krCV^H4 #~bs i8O|GO7:d3Au{CS?)mɴQ;%Ilø_Z/$T~߬[.9zfA3v|'a|a5 J?#YF$+˜Zn%Ԋ<\p 'Wo]VuzȐ1wD딁_i\qzLX&S9$Wx( LIGa=r8vK|,_D$oZNHؑ c |y*Tt]3oB[6>$9q,dylCz /)(S|["$> zQ R/G,YԶ٥X#rP_xOddH$1eE4 l5؛ pQLZU[7"3te{Vװ428&>L;QqI~$,@[b_=\Ve?eeɉ#`CRvNk9\}k! :/BR͑G axe3·d1~T}Ggs=؎1&h*т6N_wo,lX49RU9Suli(=THx" Z^P'!nW߁k~0kGa=1,3ڪG\SXvtQD4j^˺9y(9py@$j)nt),y1g[ʮqt׃:)ŒdLҟ<54 6T\M08(b b{:Hȏ׶\LR\G:fY;2?R%L=qz.ivj֏[C'jSl!Stɶ_ĬMuYTEڰiG:aV<7=(7U/F;&iiسE8.U6SV ƭG'19HrH+Ԍ ۢa3!Xzvk;b(LJܚDD%B2[qg@}<ڭ:He Y9+~?`G0Y&Y-c} =YyX&j %\3^]cMM9b+A YHk2xZTu-lX!x!xy<,򀙄U5d_%B+$1ჷr)\qu-ެnrH/8qbpw=()OzYF1H/$Lt1tLWT\ h*x2 EzJ\hxe:*WT7?}Y ~":ujDQ:oJg9O0M6!6o U9pQ](耝ul!q>yjf:CȢLJG2Y!$ٔ{Ũk{g=+͞IV@H梗1籇5)(l5f1Y4PW!gYA2*(ׄUw}J;AN2ubrTmoOoxv>J 1 -)p>r)$Dϭ@*"{Ht ]pt`TcQ + =ȤQzmpJ0fG@q*͐p~ ??׎VeG1۸Lá9%c.6#؈R}Dui';^-[~dOrGfH"$zGZznRUjQ˼#9qEŽbg[A ief3MWPq  . Z Awpnmp ';p7yC2nnڪdwS6`<ڄ_੝gmˈhɸ Nhυgy=ߞ.9I gH=øY2l"99T;E^ UK rb$&Ƀ ~> 6>ixY`a`y&5Tyfa{TX5 k]FTrISa4 Zmwu??-TO<¶̲#. /=2{( cj=JP8B;W!FN49jSAC:]mU]_Hw,t&}lvSDޕٳRjouH=n{ )ْFX"1{{@ OzdDivrr+GXןAI:5H:)fr}:^fZ5.^՚r>}{~]F@E *k*~?E6Ȓ(䀐)yn9H\"bSg7o,2io` [`mbs]h,񖪹(H=;+׭2-2=.7HITsshfIPb[q}Kf;57;_k)|^Ru{g&vfֺ+ ׎!]!k߉SQum$XEMp@Sf@O/$C`l=>amvFw~p!@i`ـ ԏ g_)j8ߛuNjm#B3~֊ȑM H%jT2 YAPo[@kq9V1m켭pnTw?2QZ*7ܔxg 2]酶 Yt@RpG֥5Mn2Ϙel%| F›B^,D~bXc'tlW=r4d7&Q ˾zR! |~`z$ 3=,T>^/6Z1 %}HKGr G2971ĽBMO~X{=dWe$ ye6p6M@ |qKM\2(P Q#'ĥ_-S{<萦.ZE&Ӝۣ#spď`dW#CM{#,gcH{%MM[RLX_ {ИN!o(12֮2ʕGIW<,zhO[3a7:Gݍ[G{RzJx{ r o\%[T!\^-%/R.ytӘD2}/H%{`WmZ[^L+̩3Y#'$V0m@ђR;]0sʓ`ikЇh _ޒIũՁ}"i2ۚ y\YcnKuaI%|>'_I;OIĂN<x+b{bFf g%,nQnAd:F>ZnRy׏ٜW ;)5"&Di;6Tqzisυjmg2|EG; KycHxpaՅLoZШ`l !?S@~n^t͍vP++jsX[3irļauOf@ (a ԋyKdi* x2|k:N]k8R3 ͏h~G.:ȟ* (w$_!Uwp15t53hcuHv6\ߛj2B~;zcRեIG {'l{& .|HL:Ϳ%FGmJ*5ln0dosRӫbs;iӎ)A0JC[.KX盽-4dEC+lM4aT@l БK5ir{fI|QA[lYS\4Rvxmƥru=ͅ3vPG#뼂^nӉMN[$Ifu;L)1==`q@Fq/!̜QU|E@ѿ'%YR]''"E)rT*\L0yeϊXގG`T0MKkh8esG(|+ebƛt>u+]9ٻ92G5}v J3U_%.YyLF˼fn;qgc儩xt־|۲C lD/R&ٞ!~&|(|M;E8A`J9@em^+i*{0ׯjcǸ8@kx6zcRեIG {$'pLa$+Kб4$˪-xr/V]򩩐-8{2LQ`7G0H5|iJ oͮ ;tT&TE;? 2ҁ_ie.)poϐԥɄo+S{ Yd}[w> =0,?&,H? +Bf% x+2Z <4礐ƒψcH3/U,9S@ondML-Ydr P+KOagU!`&Pc0L5%)պc0X:ў%m0`x{1]HzSZDJ*|9isJנ69W;#8@ ^E~yU3M7`XUbԆSbρzPxQgk]amN1E%4]O<1[޶z\pT:UKb@@-қTU"]}x XqQZ'~ (bmݫ/2T -%\O/D:($2&IC)4[+zF*SSctטtj56Q ai\/#ѯm֯X0϶t07Rv,#HLq 2 TnM#] ONI7j}0n#5n>@-Ki{ݚ@S:(^[t ꕹFMia}lrj5:0O/L>6i9*2hb7g2vx#WjR=3l#̈Tz9-[N|tamb*ZKZUkL}%Gl䩀y'TԚ.&* VeÔ 71]<3)etIOQz|ޗ˭JU=ooxj Հjiy eNa62a2h9 9 Pt`2<#^mF̶a%$s1*ތ= (sD 윗I(dگ´ln!NJy~JYM&n%秇j"cbkM'-3;tpJ}={_EXbgR )*e7`hPVg 43CѲf*ZpR!'2`J瓬v\wFI neL ,A}iC>@qK.%Us=ARQ^7 m'9'jJ F>lm]e֭[rvRfJIDXMs2y ٌ'M{v2oN^)Ri@kg4ɕ5<(느|ŜfU„/\n;d@YRDR-'pZÆ+wmyc>ںObx${`)Ж ]I:RbxcCJ=ZgB'֔qFOD]0\n[\K(Mu _yO"kt̝])HX4I^(1=6QaH:1[F˼3("ȿ6z>x<K|8$>7s.i?uC, \[ۧFX5mȦ_1?RM4MHK7,c.DNԝ1rbM0|q%cI ^G G"ۜ4N (ϝy;iQ[h!9sۃ*neazXm H+d;Y!)\"^*!rUpzO1ܳ8bO`/ zQ\ޥ3xVc PʾC~LČ&j2MEt3bdxs89QӃen(<۪۠a5.wn TbXA;Q?ȋ>g|8'g0~?Jg@!ganRϝUΧ"tcQ D*d/!"W%>Ux&L82j 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10:28:22 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Gulliver, Giant amongst Dwarfs. %Copyright: This typeface offers excellent readability at very small %Copyright: sizes. %Copyright: %Copyright: The digitally encoded machine readable outline data for %Copyright: producing the typefaces licensed to you is copyrighted (c), %Copyright: 1994, 2005 by and the property of Gerard Unger. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-regular known{/t1-gul-regular findfont dup/UniqueID known{dup /UniqueID get 4179227 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /LUUSOD+t1-gul-regular def /FontBBox {-115 -321 1042 1054 }readonly def /UniqueID 4179227 def /XUID [1021 938 1479029120 7154960] def /PaintType 0 def /FontInfo 11 dict dup begin /version (001.001) readonly def /Notice (Gulliver, Giant amongst 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OhCڇuNA3_~Q1\iod_-32TvSa /up|y irEϒ g4dI<>Utj?XmiU Y݂d_VEg6q`BG k9Ny_¯JZ3~,ZMdL:Q%˺rL{LK^: =htc l@˧M \p|A6T5Ò{j6@B(c.,B.^Q@A7DϐtG wŶخ'uyZ񆻛OVo^ Q::"|?hj}$=݇ yU SkN}-&\rL+V:3W{ r!be@&8Q#(&T8\<!r $]k*d[\G^lTKu}1Rz<`B:Dk^+1E9}02.jhcX)j52̈́bh?(^A QWg3N4r|PCZp0\s䟳inD^kmzK8Y, tKcLV@|)b$mmelbh/~[˯n\P2" EQ&]=iǓf8l ̆`jjnnxSov0\ڱ-˘:@aWO/r*I:z|ɤU"A&02ı?oV`V LQ4OϠ{ޥ-3aYW#B81cj…Q@ pei$d,RqovoGmo` DEMJH U`_xU"2lI~XWP| *N>TMhTzT ( u'K :xIo\1J+=acN ~&-Ҷ ԛOa>{ SJ"L|&s pWax)nFP%+rZ\-ٖ6@ ``i@}Ľx-ѹey+|| (ԋX71E]ߨ.@I]r. ߢЀ[ts7#gGY4ً +Zh- 2`jj7(A.buHn!/{x:쪮N*T1Nv!XYoAp;Z RZt]kJL#4$uw_rma;a+)|_wE[KlиHv??JS{DqE""YXR#`l*C%2}qN;J⩻npQSFuM;;x~WN[U| L+m;@o+K}!.=/;'>Y /ؗ|o"fٴXHׅgXQ ;d깄euf,`rVD-Dͷ4m^:uj( CyB^c砜DʭOqQĸ'9&%,%n+GhJ.Ä^hFPL5䖿mI~ P?Z% Z_|^I $JhMj EF9d,(}qKwpDRO\,j2Clj$\@!jj3ۣY6\uΊ(?&< %DZn쿠O8t26vp2df=wH¤r:hMe_0\Sl; >yFLzwǘzm4V:աEz'yv,Y, a[$΀ Ŀqf^\XE5͈?HQeӪI ^Y+s˅)P^a{'R4HleLke/ 2,Nل%)ܴ}t/"/s8XcfNģɥ,zTҟʛ.6w-|B@m|Rhƻ Ӣ6YUu8Ҧoe$DDl2LMUo{"vΩ]!ޞƌdp⮃:HcD" 9JCxGBPE*oT*_XˇkHTd_cSE!quFhHw5ʠǍ؇/iHK|+K:q"]-YJ>v5ğw-+8 ),@Men񂨙]۬ٸj&bVH;:n͚@yMJ184"=x>y>qir]r,RF'uO_ &:ZE j/ڽh&-$)TtEY՟h(k2Q88?jۦ|"tVy6{o2J}wr2XmڦVUQ"b %0 aG3t Tjy5;#'j(12 oǿ~|bkhj b*>C@G!@P^6mO?#\H f(/h-^Pa+K3eRhfc}{tZM_' endstream endobj 105 0 obj << /CharSet (/arrowdblboth/arrowdblleft/arrowdblright/arrowright/asteriskmath/backslash/bar/bardbl/braceleft/braceright/bracketleft/bracketright/circlemultiply/colon/dotaccent/element/emptyset/equal/equivalence/greaterequal/infinity/intersection/lessequal/minus/multiply/negationslash/periodcentered/perpendicular/plus/prime/propersubset/semicolon/triangle) /FontFile 104 0 R /ItalicAngle 0 /Descent -90 /CapHeight 362 /Flags 4 /Type /FontDescriptor /StemV 50 /FontName /ZJIDCI+MTSYN /Ascent 667 /FontBBox [ 0 -954 1043 900 ] /XHeight 460 >> endobj 106 0 obj [ 780 278 784 521 780 556 780 780 800 800 800 800 800 1000 500 500 780 780 780 780 754 754 754 754 780 780 780 780 984 984 754 754 1099 1099 616 616 1043 985 985 780 1043 1043 704 704 1043 985 985 762 270 1021 629 629 784 784 1 1 556 519 722 556 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eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /VCFXMS+t1-gul-regular-italic def /FontBBox {-141 -321 1053 1055 }readonly def /UniqueID 4109950 def /XUID [1021 938 1479029120 1353546] def /PaintType 0 def /FontInfo 11 dict dup begin /version (001.001) readonly def /Notice (Gulliver, Giant amongst Dwarfs.\012This typeface offers excellent readability at very small sizes.\012\012The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted \050c\051, 1994, 2005 by and the property of Gerard Unger.) readonly def % Gulliver, Giant amongst Dwarfs. % This typeface offers excellent readability at very small sizes. % % The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted (c), 1994, 2005 by and the property of Gerard Unger. /FullName (Gulliver Italic) readonly def /FamilyName (Gulliver) readonly def /Weight (Regular) readonly def /FSType 4 def /ItalicAngle -8.5 def /isFixedPitch false def /UnderlinePosition -75 def /UnderlineThickness 50 def /ascent 789 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 71 /G put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 97 /a put dup 38 /ampersand put dup 98 /b put dup 99 /c put dup 58 /colon put dup 44 /comma put dup 100 /d put dup 101 /e put dup 56 /eight put dup 21 /endash put dup 102 /f put dup 53 /five put dup 52 /four put dup 103 /g put dup 104 /h put dup 45 /hyphen put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 57 /nine put dup 111 /o put dup 49 /one put dup 112 /p put dup 40 /parenleft put dup 41 /parenright put dup 46 /period put dup 113 /q put dup 39 /quoteright put dup 114 /r put dup 115 /s put dup 59 /semicolon put dup 55 /seven put dup 54 /six put dup 47 /slash put dup 116 /t put dup 51 /three put dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 48 /zero put readonly def currentdict end currentfile eexec oc;jAw-24 WEvQC<3A2kX0k^|:ٴfb,|=sLu2KZ`3ndgRw@),q՜G<&h'. ΍883 ABAԾI$s@F25ڪ,i pK>6K` %E((bsX5QE8:'1#x[ob0S)õa *eTZD<oWNņHXx͓Tt i?Xn~/G?]3IX6-$r|ƌyS AQXM(u0x۫3+1?&cC1@UV*Z .A"]Y yER\kb7P4 K$Qh+63ήo:U.,tk~uP+J ?"&O H0fS2 .?GPO "/]xkJ"JӚ#B 1u!> ׵ Zvb,:S}2U7I=NEq]`њۿeۺ'B[xe%-g9*fP &y Иrc/8>~i8>LFf|B*G_˙VX0 &: ~'ިP |q)̶m&©+ X^݌i6Cz k"ǬL r]ݚSa="p"?+G| !Y " :A%:δ%{:c?n &f(%)oŕ0NnVL@oi'I_ c `3;z8qefJ U#)rE-oɁ4W(7BT `%G÷>dߋq ;:O<#̄ʃʭ҆vEfhK!%ĻtQ VO4jx.'v84s!QtҴ\ƶJ{)[P 3̞*4,s+%V׎MZe%Cx<{ߕ`Fqo~g_oxhO'o=a`JYBdPWOn^qmYkO}8B=K_3K5`:AVHe6k۲nTcrjt,S@P@'nOh:FPN掏y!8mA{,\DC2\N~4 8Ǎ1DB$eVUB+#MQ{M+8زudAխHq : `͜͜ҵx tJH.VS/ΝL e<^tޑ'RU;Y]f'dG1VW֐-}%0[aD07,kꌪe@ޣWA 6oBsb ^\j!ApxKP!p`( R)a4iWʴ(uRX E9R():+~R֗5I)m8kB +깋[/UtWh SS]ep3zv?νbR<l dk2u'[ʨ `aco Wp&Vmy! !b//6i`x'벑7x  <7NqKZpҰoaZ4M%M.%H"Pΐ=FQ."T9TH֦ —" rb]l"jUI[)`^{GeN.w>˕4%i0&1,aN/ᴦFhCەWфopJ?}'#=KV Ph*H?`+hvfD,>W1;Q݈4ưϫO_97]G? p˳aNHQڼˠ ̣%Q\{e?-m`|vTB9hj511޸=eh# Cd"|?""Me]r ȧ?|˓ap WRu/-F ǑIUœ~1K"?׳Gp\zKT<;EDͨru9Zr\HwM=g?O+p[ƥMW1D+.A{AV:e]RxƝ[%YF4|95ɜ+\#:rz(-[n GSAwROtrN dG|~X8&D8`&w P4nH`NPAr2\ +02Ř3,{>^;1;)N9-?j nK; Nm晼@]\І-@MWWi#s޻&m{:uKlDK{/6*bqvbT hsg`؈+n1쮸tz-8z, u^zH-ZDĊ[2%ޚ 5ağ!5S)"_Jz󭄌"{5 9pC^q]r+@fϽ;6j\'j/_ ;q#( ȅ"Rݴ B{m͙/hmOQ qV*Ci_&'x1MPb;sVUz1;7qP~56:f 'Fص¸iDJ+TǬH_5y8y#'z^uβ^G5B;DܿL*ۍ$:1UGS4]O(Ge7Phi5,Gd# Q㴭K(P^|(ێ<=Vp&c{i70ݔ*Ss툃n)q쿂@tg_aW;󦦓Q_ ͱT:ȕЁ$?DBч׊7 sd Wbk 7"bzy6 P<QC//|NvSdw U!_Ph&ֵ1V1cw"u] S cvr87N[klux\WM{7ŹǠ HI~azaws~?$˛Rȧtb3v?#XVx lcdD Eֈ ~A8/+>x9*%p gx0>Ar =~̀Mj' cҒ3l'U2rZ"Z8U<򖊮WK#!Uj qˌ,">/T ֔?#@[Ѷ ]JW "y4kOtbC?2=ѝI@|; ʌ@ZT,4}J#;=:7U&YT=ކ1qHPHiٔ ww6{臠n,/|- |sڒA(Ni .;6k l;}l8Ml|%zvȡWms\?[H40HrۘזzROx$ň2Õ ݸTwVMP9T~K%6"G)seUٟ:ya 9/rY\&k<3N ZeFJ (T#d5S5D!#.* 鍨(-5+JǶ=3W&3FcnT(ÉvY~7៸iC J+z!!{2TJx6 #h|ͬb.C< ~[yH{BXUHZe ]vKmVփkHAfƚjG2JoC7y=Ϊ m 14^J&RhkِGkJYC$xB\}T1j [$yڬ;-TieKԦVO3șOSKcYc\Ay -*/(F [@vl 2*"JS%\+,V$ Xpo cCP4W8Kh֥34Fad/?$hsjnnǻ"3{m`>Am^i(NOvD|;U-a fI4fAlp]V`d w,ފɍB>?:-,y: %+.NըdEkj6׳ ֵ0IkJ} $=g'y"B&Ϯw,f<%VćХk<8R(F2K.RˆQcu_*ĘP|v7w13jO퍂wcF|3~rwS fFW\ d2oa3C%32ɺ[҂.}~(t/| (v_>%&N}? #*!~H9/kiDiS5XMz׭_7 {vM/>%[ ?KW=Uu*+Y#V˕bC]"l"5YJaGulD|xkO|# ]fR<7" ߌtq#kXCTG9:{eGS~,Ђ/ڼ=lfP 5zVadWp1!*5k}遲@H+VP)js~WhzcאF.7T]ڻØƆGiTU9<)ݟKB<;::rt+FyVު}g#X˅ZL6y$@oVv=ĝ;8dLmxdc>A?όBOtů:1QSuBTkh ܆Q[SM,3_El'ݮp A\$}]Jې+ ȿcshL\<_NMպZF-z0o . ,z؇>ݰv;lڶz%u _~1}W΀ ьFt_ʏ5rƷClD\p!1be38 ٧qX=иnzFݠO' XCm~;+EI).S =Ft3u^j 1xӷ)HuWkv>1>_Tm4+Z,]@^r\L:)zp i ݰ@< _+-4d o Q:c3cCvtA5æ:mrS/;F6fDv 8=ή =\=Iti2pWT-a Q >-]4T>fBi߬,uOLa8 baZ<.'2w]Η'tw4EPqo&^v`J1miqKa!MswxyŅ=]iE+{reGE.)nĔ r7hV+N@Pr㢤;|EW C6L+ |7 .F6LZQB8uՠNy`y70rAo4-لyWK!r6ye(ҎP{UEdYR=Kmƅ!Y;R%)|v['PwFL*יJsh|M |Qxî6Mv&U%.NТ.hjc+VĹ_ԅUVއW@/nc-y16Iko-C׀wp'0DzpOlxzgUMyj)my-T,xd ]D!0X@WC- H Ú3 gʜs6Gib6gț^*?C*1IΣJ5> |r 2腀Q6x;yV3wuwWsTf)1X<` Y^4 BDWY0NbBo7(:ĸ^e*8#Mi8#ΨNf=_GQwL) aİn"W1Aਪ;vkf;t?xjDoLzQf}מrϯC.Ǒsĩӗ8Oȣܧ.&ɇ]D4oQ:Q"8\)fUʐHEwk."=*H%4Ŏ [N~_ jk H+,m:>اu{}ĨqXGպ*nX~п1;쯔~gۧ:WA[2ii_nۊ524s=($QK;[rK+'\ܜ{P| ! %wq/%[TX ~QN9o&X)=S" APv"@H8+n~:C_Lk L};&r>x͜SN["`<OӂePy*a:,^3RMgwT aͷ,E}Dy_AlC"R_R0r4eqַf ۊB @T Zqf !xl84ӒA @-w)$^Y/!Tn*yUNn:JIuDQ8|1 G"bЛǹq%loc|դDtrȴfb}m>ۓv̅νV)u_@5Oeu.;E< ;WF\w{d\KaA֨$@l^5vM NWdBK)+5W#{!h;nm, }- ď{I'x H\3Ҷ6X&nEkϪ'mbyc4r'1(^Y$~%v2@խc5CewR[i4_*JO-9}1 5?>/ax)eC jAAJák&fla68]7#+CSP_bCOriϔ&." gEK_O1N{#C-삧cVb!6.<4?38A~ƽUQ;d@f8F&7l93Zj^4r VA麏b8iA9 ፝ɉ 3=Sr4mgC4Ԣ^|M(:5@= <rR@Hx7@PL_1 =IePnO+&K+Փ boUZfz+TX0#<׬VFQ`UqKZyd|&pÝ8lŪnkq\ԙʡ|Hd&u7XľQܷ^zy߿fG>{+Ե{T ϹU9zEQ*r#{P\ͭQ+HhWD1H^R_SRUJ8͔h[Od)x3ۃA= թ/?('#'W2[@rѬqei/{6~F Fv5I/mg>B9jøYd%).+ʝhf/G6+k)qTڀ وFqoݏt[3 \$ “YN{1dL+X>&dYlv%1]*f{ >=E C\F=5gs8k9ϋQ2fpOPla8r3E Zz1fdpJZHmɳ ~x{S43xKb:o2Lb8V/,!.SlGqh-_0<|.\9Aᴯwv#d~h>QMVNӯ3 >"Hk'f%S)#¦ -[!K縉11)# l5>$ dU[Gv5NP/l@W [pb]p#UYrTifQ$`/nC,bvrxopr|~Zk5rwLM{5@ˢȰ 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6.6311 Tf 54.475 561.397 Td [(systems.)]TJ/F41 6.6311 Tf 27.83 0 Td [(SIAM)-250(Journal)-250(on)-250(Control)-250(and)-250(Optimization)]TJ/F22 6.6311 Tf 122.755 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(38)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0503\051,)-250(751\025766.)]TJ ET 1 0 0 1 42.52 561.397 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -553.427 cm BT /F22 6.6311 Tf 42.52 553.427 Td [(Cort\351s,)-610(J.)-609(\0502006\051.)-609(Finite-time)-609(convergent)-610(gradient)-609(flows)-609(with)-610(applications)-609(to)]TJ ET 1 0 0 1 42.52 553.427 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -553.427 cm BT /F22 6.6311 Tf 54.475 545.457 Td [(network)-250(consensus.)]TJ/F41 6.6311 Tf 62.033 0 Td [(Automatica)]TJ/F22 6.6311 Tf 33.766 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(42)]TJ/F22 6.6311 Tf 7.334 0 Td [(\05011\051,)-250(1993\0252000.)]TJ ET 1 0 0 1 42.52 545.457 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -537.487 cm BT /F22 6.6311 Tf 42.52 537.487 Td [(Couzin,)-290(I.)-290(D.,)-290(Krause,)-291(J.,)-290(Franks,)-290(N.)-290(R.,)-290(&)-290(Levin,)-290(S.)-290(A.)-291(\0502005\051.)-290(Effective)-290(leadership)-290(and)]TJ ET 1 0 0 1 42.52 537.487 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -537.487 cm BT /F22 6.6311 Tf 54.475 529.517 Td [(decision-making)-250(in)-250(animal)-250(groups)-250(on)-250(themove.)]TJ/F41 6.6311 Tf 145.167 0 Td [(Nature)]TJ/F22 6.6311 Tf 20.172 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(433)]TJ/F22 6.6311 Tf 11.001 0 Td [(\0503\051,)-250(513\025516.)]TJ ET 1 0 0 1 42.52 529.517 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -521.547 cm BT /F22 6.6311 Tf 42.52 521.547 Td [(Egerstedt,)-427(M.,)-427(&)-426(Hu,)-427(X.)-427(\0502001\051.)-426(Formation)-427(constrained)-427(multi-agent)-426(control.)]TJ/F41 6.6311 Tf 238.34 0 Td [(IEEE)]TJ ET 1 0 0 1 42.52 521.547 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -521.547 cm BT /F41 6.6311 Tf 54.475 513.576 Td [(Transactions)-250(on)-250(Robotics)-250(and)-250(Automation)]TJ/F22 6.6311 Tf 121.136 0 Td [(,)]TJ/F41 6.6311 Tf 3.21 0 Td [(17)]TJ/F22 6.6311 Tf 7.333 0 Td [(\0506\051,)-250(947\025951.)]TJ ET 1 0 0 1 42.52 513.576 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -505.606 cm BT /F22 6.6311 Tf 42.52 505.606 Td [(Egerstedt,)-186(M.,)-185(Hu,)-186(X.,)-186(&)-185(Stotsky,)-186(A.)-186(\0502001\051.)-185(Control)-186(of)-185(mobile)-186(platforms)-186(using)-185(a)-186(virtual)]TJ ET 1 0 0 1 42.52 505.606 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -505.606 cm BT /F22 6.6311 Tf 54.475 497.636 Td [(vehicle)-250(approach.)]TJ/F41 6.6311 Tf 55.084 0 Td [(IEEE)-250(Transactions)-250(on)-250(Automatic)-250(Control)]TJ/F22 6.6311 Tf 115.447 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(46)]TJ/F22 6.6311 Tf 7.334 0 Td [(\05011\051,)-250(1777\0251782.)]TJ ET 1 0 0 1 42.52 497.636 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -489.666 cm BT /F22 6.6311 Tf 42.52 489.666 Td [(Fax,)-181(J.)-180(A.,)-181(&)-180(Murray,)-181(R.)-180(M.)-181(\0502004\051.)-181(Information)-180(flow)-181(and)-180(cooperative)-181(control)-180(of)-181(vehicle)]TJ ET 1 0 0 1 42.52 489.666 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -489.666 cm BT /F22 6.6311 Tf 54.475 481.696 Td [(formations.)]TJ/F41 6.6311 Tf 36.683 0 Td [(IEEE)-250(Transactions)-250(on)-250(Automatic)-250(Control)]TJ/F22 6.6311 Tf 115.447 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(49)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0509\051,)-250(1465\0251476.)]TJ ET 1 0 0 1 42.52 481.696 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -473.726 cm BT /F22 6.6311 Tf 42.52 473.726 Td [(Haimo,)-295(V.)-295(T.)-295(\0501986\051.)-295(Finite)-295(time)-295(controllers.)]TJ/F41 6.6311 Tf 134.584 0 Td [(SIAM)-295(Journal)-295(Control)-295(and)-295(Optimization)]TJ/F22 6.6311 Tf 114.923 0 Td [(,)]TJ ET 1 0 0 1 42.52 473.726 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -473.726 cm BT /F41 6.6311 Tf 54.475 465.756 Td [(24)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0504\051,)-250(760\025770.)]TJ ET 1 0 0 1 42.52 465.756 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -457.786 cm BT /F22 6.6311 Tf 42.52 457.786 Td [(Hartman,)-250(P.)-250(\0501982\051.)]TJ/F41 6.6311 Tf 60.813 0 Td [(Ordinary)-250(differential)-250(equations)]TJ/F22 6.6311 Tf 91.602 0 Td [(\0502nd)-250(ed.\051.)-250(Birkh\344user.)]TJ ET 1 0 0 1 42.52 457.786 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -449.816 cm BT /F22 6.6311 Tf 42.52 449.816 Td [(Johansson,)-661(B.,)-661(Speranzon,)-661(A.,)-662(Johansson,)-661(M.,)-661(&)-661(Johansson,)-661(K.)-660(H.)-661(\0502008\051.)-661(On)]TJ ET 1 0 0 1 42.52 449.816 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -449.816 cm BT /F22 6.6311 Tf 54.475 441.845 Td [(decentralized)-237(negotiation)-237(of)-237(optimal)-236(consensus.)]TJ/F41 6.6311 Tf 146.907 0 Td [(Automatica)]TJ/F22 6.6311 Tf 33.765 0 Td [(,)]TJ/F41 6.6311 Tf 3.123 0 Td [(44)]TJ/F22 6.6311 Tf 7.333 0 Td [(\0504\051,)-237(1175\0251179.)]TJ ET 1 0 0 1 42.52 441.845 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -433.875 cm BT /F22 6.6311 Tf 42.52 433.875 Td [(Keviczky,)-391(T.,)-391(&)-390(Johansson,)-391(K.)-391(H.)-390(\0502008\051.)-391(A)-390(study)-391(on)-391(distributed)-390(model)-391(predictive)]TJ ET 1 0 0 1 42.52 433.875 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -433.875 cm BT /F22 6.6311 Tf 54.475 425.905 Td [(consensus.)-249(In)]TJ/F41 6.6311 Tf 42.251 0 Td [(Proceedings)-249(of)-249(the)-248(17th)-249(world)-249(congress,)-249(the)-249(international)-248(federation)]TJ ET 1 0 0 1 42.52 425.905 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -425.905 cm BT /F41 6.6311 Tf 54.475 417.935 Td [(of)-250(automatic)-250(control)]TJ/F22 6.6311 Tf 60.92 0 Td [(\050pp.)-250(1516\0251521\051.)]TJ ET 1 0 0 1 42.52 417.935 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -409.965 cm BT /F22 6.6311 Tf 42.52 409.965 Td [(Lafferriere,)-298(G.,)-297(Williams,)-298(A.,)-297(Caughman,)-298(J.,)-298(&)-297(Veerman,)-298(J.)-297(J.)-298(P.)-297(\0502005\051.)-298(Decentralized)]TJ ET 1 0 0 1 42.52 409.965 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -409.965 cm BT /F22 6.6311 Tf 54.475 401.995 Td [(control)-250(of)-250(vehicle)-250(formations.)]TJ/F41 6.6311 Tf 91.25 0 Td [(Systems)-250(&)-250(Control)-250(Letters)]TJ/F22 6.6311 Tf 74.526 0 Td [(,)]TJ/F41 6.6311 Tf 3.21 0 Td [(54)]TJ/F22 6.6311 Tf 7.334 0 Td [(,)-250(899\025910.)]TJ ET 1 0 0 1 42.52 401.995 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -394.025 cm BT /F22 6.6311 Tf 42.52 394.025 Td [(Leonard,)-618(N.)-618(E.,)-619(&)-618(Fiorelli,)-618(E.)-618(\0502001\051.)-618(Virtual)-618(leaders,)-618(artificial)-618(potentials)-618(and)]TJ ET 1 0 0 1 42.52 394.025 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -394.025 cm BT /F22 6.6311 Tf 54.475 386.055 Td [(coordinated)-434(control)-434(of)-434(groups.)-434(In)]TJ/F41 6.6311 Tf 107.573 0 Td [(Proceedings)-434(of)-434(the)-434(40th)-434(IEEE)-434(conference)-434(on)]TJ ET 1 0 0 1 42.52 386.055 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -386.055 cm BT /F41 6.6311 Tf 54.475 378.085 Td [(decision)-250(and)-250(control)]TJ/F22 6.6311 Tf 60.429 0 Td [(\050pp.)-250(2968\0252973\051.)]TJ ET 1 0 0 1 42.52 378.085 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.971 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -370.114 cm BT /F22 6.6311 Tf 42.52 370.114 Td [(Lewis,)-243(M.)-242(A.,)-243(&)-243(Tan,)-242(K.-H.)-243(\0501997\051.)-243(High)-242(precision)-243(formation)-243(control)-243(of)-242(mobile)-243(robots)]TJ ET 1 0 0 1 42.52 370.114 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -370.114 cm BT /F22 6.6311 Tf 54.475 362.144 Td [(using)-250(virtual)-250(structures.)]TJ/F41 6.6311 Tf 74.188 0 Td [(Autonomous)-250(Robots)]TJ/F22 6.6311 Tf 58.181 0 Td [(,)]TJ/F41 6.6311 Tf 3.21 0 Td [(4)]TJ/F22 6.6311 Tf 3.667 0 Td [(,)-250(387\025403.)]TJ ET 1 0 0 1 42.52 362.144 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -354.174 cm BT /F22 6.6311 Tf 42.52 354.174 Td [(Lumelsky,)-436(V.)-436(J.,)-435(&)-436(Harinarayan,)-436(K.)-436(R.)-435(\0501997\051.)-436(Decentralized)-436(motion)-435(planning)-436(for)]TJ ET 1 0 0 1 42.52 354.174 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -354.174 cm BT /F22 6.6311 Tf 54.475 346.204 Td [(multiple)-436(mobile)-436(robots:)-436(The)-436(cocktail)-436(party)-435(model.)]TJ/F41 6.6311 Tf 161.289 0 Td [(Autonomous)-436(Robots)]TJ/F22 6.6311 Tf 59.413 0 Td [(,)]TJ/F41 6.6311 Tf 4.443 0 Td [(4)]TJ/F22 6.6311 Tf 3.667 0 Td [(\0501\051,)]TJ ET 1 0 0 1 42.52 346.204 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -346.204 cm BT /F22 6.6311 Tf 54.475 338.234 Td [(121\025135.)]TJ ET 1 0 0 1 42.52 338.234 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -330.264 cm BT /F22 6.6311 Tf 42.52 330.264 Td [(Mart\355nez,)-430(S.,)-429(Cort\351s,)-430(J.,)-429(&)-430(Bullo,)-429(F.)-429(\0502007\051.)-430(Motion)-429(coordination)-430(with)-429(distributed)]TJ ET 1 0 0 1 42.52 330.264 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -330.264 cm BT /F22 6.6311 Tf 54.475 322.294 Td [(information.)]TJ/F41 6.6311 Tf 39.733 0 Td [(IEEE)-250(Control)-250(Systems)-250(Magazine)]TJ/F22 6.6311 Tf 90.872 0 Td [(,)]TJ/F41 6.6311 Tf 3.21 0 Td [(27)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0504\051.)]TJ ET 1 0 0 1 42.52 322.294 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -314.324 cm BT /F22 6.6311 Tf 42.52 314.324 Td [(Olfati-Saber,)-377(R.,)-376(Fax,)-377(J.)-376(A.,)-377(&)-376(Murray,)-377(R.)-376(M.)-377(\0502007\051.)-376(Consensus)-377(and)-376(cooperation)-377(in)]TJ ET 1 0 0 1 42.52 314.324 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -314.324 cm BT /F22 6.6311 Tf 54.475 306.354 Td [(networked)-250(multi-agent)-250(systems.)]TJ/F41 6.6311 Tf 100.732 0 Td [(Proceedings)-250(of)-250(the)-250(IEEE)]TJ/F22 6.6311 Tf 67.568 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(95)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0501\051,)-250(215\025233.)]TJ ET 1 0 0 1 42.52 306.354 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.971 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -298.383 cm BT /F22 6.6311 Tf 42.52 298.383 Td [(Olfati-Saber,)-548(R.,)-547(&)-548(Murray,)-547(R.)-548(M.)-547(\0502004\051.)-547(Consensus)-548(problems)-547(in)-548(netw)1(orks)-548(of)]TJ ET 1 0 0 1 42.52 298.383 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -298.383 cm BT /F22 6.6311 Tf 54.475 290.413 Td [(agents)-194(with)-195(switching)-194(topology)-195(and)-194(time-delays.)]TJ/F41 6.6311 Tf 147.944 0 Td [(IEEE)-194(Transactions)-195(on)-194(Automatic)]TJ ET 1 0 0 1 42.52 290.413 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -290.413 cm BT /F41 6.6311 Tf 54.475 282.443 Td [(Control)]TJ/F22 6.6311 Tf 21.525 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(49)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0509\051,)-250(1520\0251533.)]TJ ET 1 0 0 1 42.52 282.443 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -274.473 cm BT /F22 6.6311 Tf 42.52 274.473 Td [(Ren,)-438(W.)-437(\0502006\051.)-438(Consensus)-438(based)-437(formation)-438(control)-438(strategies)-437(for)-438(multi-vehicle)]TJ ET 1 0 0 1 42.52 274.473 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -274.473 cm BT /F22 6.6311 Tf 54.475 266.503 Td [(systems.)-195(In)]TJ/F41 6.6311 Tf 34.832 0 Td [(Proceedings)-195(of)-195(the)-195(2006)-195(american)-195(cont)1(rol)-195(conference)]TJ/F22 6.6311 Tf 152.477 0 Td [(\050pp.)-195(4237\0254242\051.)]TJ ET 1 0 0 1 42.52 266.503 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -258.533 cm BT /F22 6.6311 Tf 42.52 258.533 Td [(Ren,)-547(W.)-546(\0502007\051.)-547(Multi-vehicle)-546(consensus)-547(with)-546(a)-547(time-varying)-546(reference)-547(state.)]TJ ET 1 0 0 1 42.52 258.533 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -258.533 cm BT /F41 6.6311 Tf 54.475 250.563 Td [(Systems)-250(&)-250(Control)-250(Letters)]TJ/F22 6.6311 Tf 74.527 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(56)]TJ/F22 6.6311 Tf 7.334 0 Td [(,)-250(474\025483.)]TJ ET 1 0 0 1 42.52 250.563 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -242.593 cm BT /F22 6.6311 Tf 42.52 242.593 Td [(Ren,)-383(W.,)-383(&)-383(Beard,)-383(R.)-383(W.)-383(\0502005\051.)-383(Consensus)-382(seeking)-383(in)-383(multiagent)-383(systems)-383(under)]TJ ET 1 0 0 1 42.52 242.593 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -242.593 cm BT /F22 6.6311 Tf 54.475 234.623 Td [(dynamically)-426(changing)-425(interaction)-426(topologies.)]TJ/F41 6.6311 Tf 143.344 0 Td [(IEEE)-426(Transactions)-425(on)-426(Automatic)]TJ ET 1 0 0 1 42.52 234.623 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -234.623 cm BT /F41 6.6311 Tf 54.475 226.652 Td [(Control)]TJ/F22 6.6311 Tf 21.525 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(50)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0505\051,)-250(655\025661.)]TJ ET 1 0 0 1 42.52 226.652 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -218.682 cm BT /F22 6.6311 Tf 42.52 218.682 Td [(Ren,)-204(W.,)-204(Beard,)-204(R.)-204(W.,)-204(&)-204(Atkins,)-204(E.)-204(M.)-204(\0502007\051.)-204(Information)-204(consensus)-204(in)-204(multi-vehicle)]TJ ET 1 0 0 1 42.52 218.682 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -218.682 cm BT /F22 6.6311 Tf 54.475 210.712 Td [(cooperative)-250(control.)]TJ/F41 6.6311 Tf 62.611 0 Td [(IEEE)-250(Control)-250(Systems)-250(Magazine)]TJ/F22 6.6311 Tf 90.872 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(27)]TJ/F22 6.6311 Tf 7.334 0 Td [(\0502\051,)-250(71\02582.)]TJ ET 1 0 0 1 42.52 210.712 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -202.742 cm BT /F22 6.6311 Tf 42.52 202.742 Td [(Shao,)-290(J.,)-291(Xie,)-290(G.,)-291(&)-290(Wang,)-291(L.)-290(\0502007\051.)-290(Leader-following)-291(formation)-290(control)-290(of)-291(multiple)]TJ ET 1 0 0 1 42.52 202.742 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -202.742 cm BT /F22 6.6311 Tf 54.475 194.772 Td [(mobile)-250(vehicles.)]TJ/F41 6.6311 Tf 50.774 0 Td [(IET)-250(Control)-250(Theory)-250(and)-250(Applications)]TJ/F22 6.6311 Tf 104.161 0 Td [(,)]TJ/F41 6.6311 Tf 3.209 0 Td [(1)]TJ/F22 6.6311 Tf 3.667 0 Td [(\0502\051,)-250(545\025552.)]TJ ET 1 0 0 1 42.52 194.772 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -38.535 -186.802 cm BT /F22 6.6311 Tf 42.52 186.802 Td [(Sundaram,)-495(S.,)-495(&)-495(Hadjicostis,)-495(C.)-495(N.)-495(\0502007\051.)-494(Finite-time)-495(distributed)-495(consensus)-495(in)]TJ ET 1 0 0 1 42.52 186.802 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -186.802 cm BT /F22 6.6311 Tf 54.475 178.832 Td [(graphs)-385(with)-384(time-invariant)-385(topologies.)-385(In)]TJ/F41 6.6311 Tf 131.477 0 Td [(Proceedings)-385(of)-384(the)-385(american)-385(control)]TJ ET 1 0 0 1 42.52 178.832 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -178.832 cm BT /F41 6.6311 Tf 54.475 170.862 Td [(conference)]TJ/F22 6.6311 Tf 32.996 0 Td [(\050pp.)-250(711\025716\051.)]TJ ET 1 0 0 1 42.52 170.862 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -7.97 cm 0 g 0 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[(ics)-322(from)-322(Inner)-322(Mongolia)-321(University,)-322(Huhhot,)-322(in)-322(2001)-322(and)]TJ ET 1 0 0 1 311.511 629.086 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -629.086 cm BT /F22 6.6311 Tf 386.826 621.116 Td [(2004,)-260(respectively,)-259(and)-260(the)-259(Ph.D.)-260(degree)-259(from)-260(Peking)-259(Uni-)]TJ ET 1 0 0 1 311.511 621.116 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -621.116 cm BT /F22 6.6311 Tf 386.826 613.146 Td [(versity,)-199(Beijing,)-200(in)-199(2008.)-200(He)-199(currently)-200(is)-199(a)-199(Lecturer)-200(with)-199(the)]TJ ET 1 0 0 1 311.511 613.146 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -613.146 cm BT /F22 6.6311 Tf 386.826 605.176 Td [(School)-250(of)-250(Automation,)-250(Beijing)-250(Institute)-250(of)-250(Technology.)]TJ ET 1 0 0 1 311.511 605.176 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -605.176 cm BT /F22 6.6311 Tf 398.782 597.206 Td [(His)-266(research)-266(interests)-266(are)-266(in)-267(the)-266(fields)-266(of)-266(coordination)]TJ ET 1 0 0 1 311.511 597.206 cm 0 g 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[(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.585 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F185 9.5641 Tf 4.791 0 Td [(;)]TJ/F22 8.2889 Tf 47.573 43.852 Td [(\0503\051)]TJ ET 1 0 0 1 42.52 613.755 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -613.755 cm BT /F22 8.2889 Tf 42.52 554.722 Td [(where)-361(weighting)-360(factors)]TJ/F41 8.2889 Tf 97.719 0 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 8.845 1.435 Td [(>)]TJ/F22 8.2889 Tf 12.47 0 Td [(0)-361(and)-360(parameters)-361(0)]TJ/F185 9.5641 Tf 81.36 0 Td [(<)-524(\013)-564(<)]TJ/F22 8.2889 Tf 35.794 0 Td [(1,)]TJ ET 1 0 0 1 42.52 554.722 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -554.722 cm BT /F185 9.5641 Tf 42.52 544.41 Td [(\014)-348(>)]TJ/F22 8.2889 Tf 18.837 0 Td [(0,)]TJ/F185 9.5641 Tf 8.811 0 Td [(\015)]TJ/F179 9.5641 Tf 8.988 0 Td [(\025)]TJ/F22 8.2889 Tf 9.868 0 Td [(0.)]TJ ET 1 0 0 1 42.52 544.41 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -19.71 cm 0 g 0 G 1 0 0 1 -38.535 -524.7 cm BT /F153 8.2889 Tf 42.52 524.7 Td [(Corollary)-250(5.)]TJ ET 1 0 0 1 88.506 524.7 cm 0 g 0 G 1 0 0 1 -88.506 -524.7 cm BT /F41 8.2889 Tf 92.491 524.7 Td [(Under)-453(protocol)]TJ ET 1 0 0 1 152.457 524.7 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -152.457 -524.7 cm BT /F22 8.2889 Tf 152.457 524.7 Td [(\0503\051)]TJ ET 1 0 0 1 163.382 524.7 cm 0 g 0 G 1 0 0 1 -163.382 -524.7 cm BT /F41 8.2889 Tf 167.139 524.7 Td [(and)-453(Assumption)-453(\050A1\051\025\050A4\051,)-454(the)-453(n)]TJ ET 1 0 0 1 42.52 524.7 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -524.7 cm BT /F41 8.2889 Tf 42.52 514.388 Td [(agents)-237(will)-237(be)-237(in)-237(time-invariant)-237(formatio)1(n)]TJ/F185 9.5641 Tf 154.566 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.674 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F41 8.2889 Tf 5.531 0 Td [(in)-237(finite)-237(time,)-237(where)]TJ ET 1 0 0 1 42.52 514.388 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -514.388 cm BT /F41 8.2889 Tf 42.52 504.076 Td [(the)-250(first)-335(m)-250(agents)-250(are)-250(leaders)-250(and)-250(the)-250(rest)-250(are)-250(followers.)]TJ ET 1 0 0 1 42.52 504.076 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -15.398 cm 0 g 0 G 1 0 0 1 -38.535 -488.678 cm BT /F153 8.2889 Tf 42.52 488.678 Td [(Proof.)]TJ ET 1 0 0 1 66.748 488.678 cm 0 g 0 G 1 0 0 1 -66.748 -488.678 cm BT /F22 8.2889 Tf 70.733 488.678 Td [(By)-379(observing)-379(Eq.)]TJ ET 1 0 0 1 138.644 488.678 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -138.644 -488.678 cm BT /F22 8.2889 Tf 138.644 488.678 Td [(\0503\051)]TJ ET 1 0 0 1 149.569 488.678 cm 0 g 0 G 1 0 0 1 -149.569 -488.678 cm BT /F22 8.2889 Tf 152.711 488.678 Td [(and)-379(by)]TJ ET 1 0 0 1 182.585 488.678 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -182.585 -488.678 cm BT /F22 8.2889 Tf 182.585 488.678 Td [(Theorem)-379(3)]TJ ET 1 0 0 1 224.677 488.678 cm 0 g 0 G 1 0 0 1 -224.677 -488.678 cm BT /F22 8.2889 Tf 224.677 488.678 Td [(,)]TJ/F41 8.2889 Tf 5.083 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(i)]TJ/F179 9.5641 Tf 5.381 1.435 Td [(\000)]TJ/F41 8.2889 Tf 10.683 0 Td [(h)]TJ/F41 5.8022 Tf 4.674 -1.435 Td [(i)]TJ/F22 8.2889 Tf 2.158 1.435 Td [(,)]TJ/F41 8.2889 Tf 5.083 0 Td [(i)]TJ/F179 9.5641 Tf 7.771 0 Td [(2)]TJ/F181 8.9265 Tf 11.416 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.435 Td [(m)]TJ/F22 8.2889 Tf 5.511 1.435 Td [(,)]TJ ET 1 0 0 1 42.52 488.678 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -488.678 cm BT /F22 8.2889 Tf 42.52 478.366 Td [(will)-334(reach)-334(consensus)-335(in)-334(finite)-334(time)]TJ/F41 8.2889 Tf 136.72 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.52 Td [(\003)]TJ/F22 5.8022 Tf -0.708 -6.213 Td [(1)]TJ/F22 8.2889 Tf 4.694 2.693 Td [(.)-335(Let)-334(the)-334(consensus)-335(state)-334(be)]TJ ET 1 0 0 1 42.52 478.366 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -478.366 cm BT /F41 8.2889 Tf 42.52 468.054 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F22 8.2889 Tf 3.518 -3.472 Td [(.)-250(Then)-250(after)-250(time)]TJ/F41 8.2889 Tf 64.794 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.519 Td [(\003)]TJ/F22 5.8022 Tf -0.709 -6.212 Td [(1)]TJ/F22 8.2889 Tf 4.695 2.693 Td [(,)]TJ/F41 8.2889 Tf 4.012 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(C)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F22 8.2889 Tf 3.518 -3.472 Td [(,)]TJ/F41 8.2889 Tf 4.012 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(2)]TJ/F181 8.9265 Tf 8.673 0 Td [(I)]TJ/F41 5.8022 Tf 5.132 -1.435 Td [(m)]TJ/F22 8.2889 Tf 5.512 1.435 Td [(.)]TJ ET 1 0 0 1 42.52 468.054 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -468.054 cm BT /F22 8.2889 Tf 54.475 458.039 Td [(Consider)-475(the)-476(dynamics)-475(of)-476(followers)-475(after)-476(time)]TJ/F41 8.2889 Tf 188.957 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.52 Td [(\003)]TJ/F22 5.8022 Tf -0.708 -6.213 Td [(1)]TJ/F22 8.2889 Tf 4.695 2.693 Td [(.)-477(Since)-475(the)]TJ ET 1 0 0 1 42.52 458.039 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -458.039 cm BT /F22 8.2889 Tf 42.52 447.727 Td [(positions)-182(of)-183(leaders)-182(are)-183(constant,)-182(by)]TJ ET 1 0 0 1 177.633 447.727 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -177.633 -447.727 cm BT /F22 8.2889 Tf 177.633 447.727 Td [(Corollary)-182(4)]TJ ET 1 0 0 1 218.923 447.727 cm 0 g 0 G 1 0 0 1 -218.923 -447.727 cm BT /F22 8.2889 Tf 218.923 447.727 Td [(,)-182(there)-183(exists)-182(a)-183(finite)]TJ ET 1 0 0 1 42.52 447.727 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -447.727 cm BT /F22 8.2889 Tf 42.52 437.415 Td [(time)]TJ/F41 8.2889 Tf 19.694 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.52 Td [(\003)]TJ/F22 5.8022 Tf -0.709 -6.213 Td [(2)]TJ/F22 8.2889 Tf 4.695 2.693 Td [(,)-250(after)-250(which)-250(the)-250(position)-250(of)-250(follower)]TJ/F41 8.2889 Tf 141.043 0 Td [(i)]TJ/F22 8.2889 Tf 4.443 0 Td [(is)]TJ/F41 8.2889 Tf 8.255 0 Td [(F)]TJ/F41 5.8022 Tf 4.029 -1.435 Td [(i)]TJ/F41 8.2889 Tf 2.157 1.435 Td [(x)]TJ/F22 8.2889 Tf 4.07 0 Td [(.)]TJ ET 1 0 0 1 42.52 437.415 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -437.415 cm BT /F22 8.2889 Tf 54.475 427.4 Td [(To)-356(conclude,)-357(the)]TJ/F41 8.2889 Tf 67.019 0 Td [(n)]TJ/F22 8.2889 Tf 7.745 0 Td [(agents)-356(will)-357(be)-356(in)-357(formation)]TJ/F185 9.5641 Tf 109.099 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.675 0 Td [(;)]TJ/F41 8.2889 Tf 4.759 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F22 8.2889 Tf 6.522 0 Td [(in)-356(finite)]TJ ET 1 0 0 1 42.52 427.4 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -427.4 cm BT /F22 8.2889 Tf 42.52 417.088 Td [(time.)]TJ/F166 7.9701 Tf 29.931 0 Td [(\004)]TJ ET 1 0 0 1 42.52 417.088 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -417.088 cm BT /F41 8.2889 Tf 42.52 396.836 Td [(4.3.)-500(Time-varying)-250(formation)]TJ ET 1 0 0 1 42.52 396.836 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -396.836 cm BT /F22 8.2889 Tf 54.475 376.434 Td [(In)-451(many)-452(practical)-451(situations,)-452(such)-451(as)-452(to)-451(avoid)-452(obstacles,)-451(the)]TJ ET 1 0 0 1 42.52 376.434 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -376.434 cm BT /F22 8.2889 Tf 42.52 366.122 Td [(formation)-365(is)-365(required)-365(to)-365(be)-365(changing)-365(with)-365(time.)-365(In)-365(this)-365(case,)-366(we)]TJ ET 1 0 0 1 42.52 366.122 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -366.122 cm BT /F22 8.2889 Tf 42.52 355.81 Td [(assume)-213(that)-214(the)-213(studied)-213(multi-agent)-214(system)-213(satisfies)-213(the)-214(following)]TJ ET 1 0 0 1 42.52 355.81 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -355.81 cm BT /F22 8.2889 Tf 42.52 345.498 Td [(assumptions)-250(together)-250(with)-250(Assumptions)-250(\050A1,)-250(A2\051:)]TJ ET 1 0 0 1 42.52 345.498 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -14.401 cm 0 g 0 G 1 0 0 1 -42.52 -331.097 cm BT /F22 8.2889 Tf 42.52 331.097 Td [(\050A3'\051)]TJ ET 1 0 0 1 60.855 331.097 cm 0 g 0 G 1 0 0 1 -60.855 -331.097 cm BT /F22 8.2889 Tf 64.84 331.097 Td [(leader)]TJ/F41 8.2889 Tf 26.885 0 Td [(i)]TJ/F22 8.2889 Tf 2.371 0 Td [(,)]TJ/F41 8.2889 Tf 5.004 0 Td [(i)]TJ/F179 9.5641 Tf 7.568 0 Td [(2)]TJ/F181 8.9265 Tf 11.214 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.435 Td [(m)]TJ/F22 8.2889 Tf 5.511 1.435 Td [(,)-370(can)-369(get)-370(the)-369(global)-370(formation)-370(inform)1(ation)]TJ ET 1 0 0 1 42.52 331.097 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -331.097 cm BT /F41 8.2889 Tf 64.84 320.785 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F22 8.2889 Tf 2.157 1.435 Td [(,)]TJ/F179 9.5641 Tf 5.085 1.96 Td [(P)]TJ/F41 8.2889 Tf -0.745 -1.96 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F22 8.2889 Tf 4.558 1.435 Td [(and)-290(the)-289(local)-290(information)]TJ/F41 8.2889 Tf 99.891 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.637 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.922 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(j)]TJ/F22 8.2889 Tf 2.174 1.435 Td [(,)]TJ/F41 8.2889 Tf 4.341 0 Td [(j)]TJ/F179 9.5641 Tf 5.892 0 Td [(2)]TJ/F181 8.9265 Tf 9.514 0 Td [(N)]TJ/F41 5.8022 Tf 7.186 -1.435 Td [(i)]TJ/F22 8.2889 Tf 2.157 1.435 Td [(,)-290(and)-289(send)-290(the)]TJ ET 1 0 0 1 42.52 320.785 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -320.785 cm BT /F22 8.2889 Tf 64.84 310.473 Td [(information)]TJ/F41 8.2889 Tf 47.719 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(h)]TJ/F41 5.8022 Tf 4.674 -1.435 Td [(i)]TJ/F22 8.2889 Tf 4.23 1.435 Td [(and)]TJ/F41 8.2889 Tf 16.321 0 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.435 Td [(i)]TJ/F22 8.2889 Tf 4.23 1.435 Td [(to)-250(other)-250(agents;)]TJ ET 1 0 0 1 42.52 310.473 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.015 cm 0 g 0 G 1 0 0 1 -42.52 -300.458 cm BT /F22 8.2889 Tf 42.52 300.458 Td [(\050A4'\051)]TJ ET 1 0 0 1 60.855 300.458 cm 0 g 0 G 1 0 0 1 -60.855 -300.458 cm BT /F22 8.2889 Tf 64.84 300.458 Td [(follower)]TJ/F41 8.2889 Tf 35.549 0 Td [(i)]TJ/F22 8.2889 Tf 2.37 0 Td [(,)]TJ/F41 8.2889 Tf 5.495 0 Td [(i)]TJ/F179 9.5641 Tf 8.827 0 Td [(2)-675(f)]TJ/F41 8.2889 Tf 16.011 0 Td [(m)]TJ/F179 9.5641 Tf 10.806 0 Td [(C)]TJ/F22 8.2889 Tf 11.105 0 Td [(1)]TJ/F185 9.5641 Tf 4.8 0 Td [(;)]TJ/F41 8.2889 Tf 4.759 0 Td [(m)]TJ/F179 9.5641 Tf 10.807 0 Td [(C)]TJ/F22 8.2889 Tf 11.105 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F179 9.5641 Tf 4.791 0 Td [(g)]TJ/F22 8.2889 Tf 3.539 0 Td [(,)-429(can)-429(get)-428(the)-429(local)]TJ ET 1 0 0 1 42.52 300.458 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -300.458 cm BT /F22 8.2889 Tf 64.84 290.146 Td [(formation)-533(information)]TJ/F41 8.2889 Tf 92.617 0 Td [(F)]TJ/F41 5.8022 Tf 4.028 -1.435 Td [(i)]TJ/F22 8.2889 Tf 2.158 1.435 Td [(,)]TJ/F179 9.5641 Tf 7.288 1.96 Td [(P)]TJ/F41 8.2889 Tf -0.93 -1.96 Td [(F)]TJ/F41 5.8022 Tf 4.029 -1.435 Td [(i)]TJ/F22 8.2889 Tf 2.157 1.435 Td [(,)-533(and)-533(can)-533(obtain)-533(the)-533(relativ)1(e)]TJ ET 1 0 0 1 42.52 290.146 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -290.146 cm BT /F22 8.2889 Tf 64.84 279.834 Td [(positions)-250(and)-250(control)-250(inputs)-250(of)-250(its)-250(neighbors.)]TJ ET 1 0 0 1 42.52 279.834 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -279.834 cm BT /F22 8.2889 Tf 54.475 264.912 Td [(The)-250(allowable)-250(time-varying)-250(formation)-250(control)-250(protocol)-250(is)]TJ ET 1 0 0 1 42.52 264.912 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -264.912 cm BT /F41 8.2889 Tf 42.52 194.889 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.434 Td [(i)]TJ/F179 9.5641 Tf 4.814 1.434 Td [(D)]TJ/F189 9.5641 Tf 10.117 56.907 Td [(8)]TJ 0 -8.608 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(<)]TJ 0 -17.215 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(:)]TJ/F179 9.5641 Tf 8.319 91.268 Td [(P)]TJ/F41 8.2889 Tf -0.745 -1.96 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F189 9.5641 Tf 10.676 13.428 Td [(\022)]TJ 6.456 -4.342 Td [(X)]TJ/F41 5.8022 Tf 0.347 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.353 Td [(i)]TJ/F41 8.2889 Tf 3.862 11.809 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F189 9.5641 Tf 3.835 9.124 Td [(\000)]TJ/F185 9.5641 Tf 3.854 -7.689 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 5.692 0 Td [(\000)]TJ/F185 9.5641 Tf 9.586 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.567 7.689 Td [(\001)]TJ 3.854 5.739 Td [(\023)]TJ/F185 6.6948 Tf 6.456 -1.567 Td [(\013)]TJ/F179 9.5641 Tf -150.263 -33.863 Td [(C)]TJ/F185 9.5641 Tf 9.054 0 Td [(\015)]TJ/F189 9.5641 Tf 7.925 9.086 Td [(X)]TJ/F41 5.8022 Tf 0.348 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F41 8.2889 Tf 3.862 11.808 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F189 9.5641 Tf 3.834 9.125 Td [(\000)]TJ/F185 9.5641 Tf 3.855 -7.69 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(h)]TJ/F41 5.8022 Tf 4.674 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 5.693 0 Td [(\000)]TJ/F185 9.5641 Tf 9.585 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.568 7.69 Td [(\001)]TJ/F185 9.5641 Tf 3.854 -7.69 Td [(;)]TJ/F41 8.2889 Tf -19.582 -20.238 Td [(i)]TJ/F179 9.5641 Tf 5.028 0 Td [(D)]TJ/F22 8.2889 Tf 10.116 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F22 8.2889 Tf 4.76 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(m)]TJ/F185 9.5641 Tf 7.162 0 Td [(;)]TJ/F41 5.8022 Tf -169.81 -7.402 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.02 Td [(X)]TJ/F41 5.8022 Tf 1.638 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.221 0 Td [(1)]TJ/F185 9.5641 Tf 4.997 10.457 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.679 -6.523 Td [(j)]TJ/F41 8.2889 Tf 3.836 2.573 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.301 1.435 Td [(C)]TJ 10.075 1.96 Td [(P)]TJ/F41 8.2889 Tf -0.49 -1.96 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.678 -6.523 Td [(j)]TJ/F41 8.2889 Tf 3.836 2.573 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.174 1.435 Td [(/)]TJ/F179 9.5641 Tf 5.693 0 Td [(C)]TJ/F185 9.5641 Tf 9.586 0 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F189 9.5641 Tf 10.676 13.428 Td [(\022)]TJ/F41 5.8022 Tf 11.546 -2.323 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.637 -19.543 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 6.591 10.457 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.678 -6.523 Td [(j)]TJ/F185 9.5641 Tf 3.836 2.573 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.567 13.428 Td [(\023)]TJ/F185 6.6948 Tf 6.456 -1.567 Td [(\013)]TJ/F179 9.5641 Tf -144.075 -39.976 Td [(C)]TJ/F185 9.5641 Tf 9.054 0 Td [(\015)]TJ/F41 5.8022 Tf 13.015 11.105 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.638 -19.543 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 6.591 10.457 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.679 -6.523 Td [(j)]TJ/F185 9.5641 Tf 3.836 2.573 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/;)]TJ/F41 8.2889 Tf 16.616 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(D)]TJ/F41 8.2889 Tf 10.116 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.586 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.585 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F185 9.5641 Tf 4.791 0 Td [(;)]TJ/F22 8.2889 Tf 27.523 43.07 Td [(\0504\051)]TJ ET 1 0 0 1 42.52 194.889 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -194.889 cm BT /F22 8.2889 Tf 42.52 127.028 Td [(where)-279(weighting)-279(factors)]TJ/F41 8.2889 Tf 95.685 0 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.434 Td [(ij)]TJ/F185 9.5641 Tf 7.106 1.434 Td [(>)]TJ/F22 8.2889 Tf 10.732 0 Td [(0,)-279(parameters)-279(0)]TJ/F185 9.5641 Tf 62.968 0 Td [(<)-342(\013)-382(<)]TJ/F22 8.2889 Tf 30.579 0 Td [(1,)]TJ/F185 9.5641 Tf 9.051 0 Td [(\014)-412(>)]TJ/F22 8.2889 Tf 20.067 0 Td [(0,)]TJ ET 1 0 0 1 42.52 127.028 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -127.028 cm BT /F185 9.5641 Tf 42.52 116.716 Td [(\015)]TJ/F179 9.5641 Tf 8.988 0 Td [(\025)]TJ/F22 8.2889 Tf 9.868 0 Td [(0.)]TJ ET 1 0 0 1 42.52 116.716 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -19.709 cm 0 g 0 G 1 0 0 1 -38.535 -97.007 cm BT /F153 8.2889 Tf 42.52 97.007 Td [(Corollary)-250(6.)]TJ ET 1 0 0 1 88.506 97.007 cm 0 g 0 G 1 0 0 1 -88.506 -97.007 cm BT /F41 8.2889 Tf 92.491 97.007 Td [(Suppose)-417(that)-502(h)-417(and)-417(F)-540(are)-417(continuous)-417(and)-417(piece-wise)]TJ ET 1 0 0 1 42.52 97.007 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -97.007 cm BT /F41 8.2889 Tf 42.52 86.695 Td [(differentiable.)-331(Under)-331(protocol)]TJ ET 1 0 0 1 153.558 86.695 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -153.558 -86.695 cm BT /F22 8.2889 Tf 153.558 86.695 Td [(\0504\051)]TJ ET 1 0 0 1 164.483 86.695 cm 0 g 0 G 1 0 0 1 -164.483 -86.695 cm BT /F41 8.2889 Tf 167.223 86.695 Td [(and)-331(Assumption)-330(\050A1,)-331(A2,)-330(A3',)-331(A4'\051,)]TJ ET 1 0 0 1 42.52 86.695 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -86.695 cm BT /F41 8.2889 Tf 42.52 76.382 Td [(the)-250(n)-250(agents)-250(will)-250(be)-250(in)-250(formation)]TJ/F185 9.5641 Tf 120.171 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.675 0 Td [(;)]TJ/F41 8.2889 Tf 4.759 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F41 8.2889 Tf 5.64 0 Td [(in)-250(finite)-250(time.)]TJ ET 1 0 0 1 42.52 76.382 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -15.397 cm 0 g 0 G 1 0 0 1 -38.535 -60.985 cm BT /F153 8.2889 Tf 42.52 60.985 Td [(Proof.)]TJ ET 1 0 0 1 66.748 60.985 cm 0 g 0 G 1 0 0 1 -66.748 -60.985 cm BT /F22 8.2889 Tf 70.733 60.985 Td [(Also)-268(by)]TJ ET 1 0 0 1 100.856 60.985 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -100.856 -60.985 cm BT /F22 8.2889 Tf 100.856 60.985 Td [(Theorem)-268(3)]TJ ET 1 0 0 1 142.023 60.985 cm 0 g 0 G 1 0 0 1 -142.023 -60.985 cm BT /F22 8.2889 Tf 142.023 60.985 Td [(,)]TJ/F41 8.2889 Tf 4.158 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.432 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.735 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F22 8.2889 Tf 2.158 1.435 Td [(,)]TJ/F41 8.2889 Tf 4.157 0 Td [(i)]TJ/F179 9.5641 Tf 5.401 0 Td [(2)]TJ/F181 8.9265 Tf 9.047 0 Td [(I)]TJ/F41 5.8022 Tf 5.132 -1.435 Td [(m)]TJ/F22 8.2889 Tf 5.512 1.435 Td [(,)-268(will)-267(reach)-268(consensus)-267(in)]TJ ET 1 0 0 1 42.52 60.985 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -60.985 cm BT /F22 8.2889 Tf 42.52 50.673 Td [(finite)-213(time)]TJ/F41 8.2889 Tf 41.365 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.519 Td [(\003)]TJ/F22 5.8022 Tf -0.709 -6.212 Td [(1)]TJ/F22 8.2889 Tf 4.695 2.693 Td [(.)-213(Denote)-214(the)-213(consensus)-213(state)-213(by)]TJ/F41 8.2889 Tf 119.53 0 Td [(h)]TJ/F41 5.8022 Tf 4.674 3.472 Td [(c)]TJ/F22 8.2889 Tf 5.286 -3.472 Td [(and)-213(then)-213(after)-214(time)]TJ ET 1 0 0 1 42.52 50.673 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -50.673 cm BT /F41 8.2889 Tf 42.52 40.361 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.519 Td [(\003)]TJ/F22 5.8022 Tf -0.709 -6.212 Td [(1)]TJ/F22 8.2889 Tf 4.695 2.693 Td [(,)]TJ/F41 8.2889 Tf 4.012 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 5.693 0 Td [(C)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.471 Td [(c)]TJ/F22 8.2889 Tf 3.518 -3.471 Td [(.)]TJ ET 1 0 0 1 42.52 40.361 cm 0 g 0 G 0 g 0 G 1 0 0 1 260.025 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -302.545 -40.361 cm BT /F22 8.2889 Tf 323.466 720.809 Td [(Rewrite)-250(the)-250(second)-250(equation)-250(of)-250(protocol)]TJ ET 1 0 0 1 478.244 720.809 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -478.244 -720.809 cm BT /F22 8.2889 Tf 478.244 720.809 Td [(\0504\051)]TJ ET 1 0 0 1 489.168 720.809 cm 0 g 0 G 1 0 0 1 -489.168 -720.809 cm BT /F22 8.2889 Tf 491.241 720.809 Td [(as)]TJ ET 1 0 0 1 311.511 720.809 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -720.809 cm BT /F22 8.2889 Tf 312.706 697.704 Td [(d)]TJ/F185 9.5641 Tf 4.932 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F179 9.5641 Tf 4.282 1.434 Td [(\000)]TJ/F41 5.8022 Tf 13.038 9.193 Td [(n)]TJ/F189 9.5641 Tf -3.32 -2.02 Td [(P)]TJ/F41 5.8022 Tf -0.132 -15.717 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 4.953 8.544 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.572 Td [(i)]TJ -1.678 -6.264 Td [(j)]TJ/F41 8.2889 Tf 3.836 2.692 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(j)]TJ/F185 9.5641 Tf 2.174 1.434 Td [(/)]TJ ET q 1 0 0 1 312.706 685.332 cm []0 d 0 J 0.44 w 0 0 m 54.424 0 l S Q BT /F22 8.2889 Tf 335.631 676.15 Td [(d)]TJ/F41 8.2889 Tf 4.932 0 Td [(t)]TJ/F179 9.5641 Tf 30.42 6.79 Td [(D)]TJ/F185 9.5641 Tf 10.117 0 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F189 9.5641 Tf 10.676 13.428 Td [(\022)]TJ/F41 5.8022 Tf 11.546 -2.323 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.638 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.676 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 6.591 10.456 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.678 -6.522 Td [(j)]TJ/F185 9.5641 Tf 3.836 2.572 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.434 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(/)]TJ/F189 9.5641 Tf 3.568 13.428 Td [(\023)]TJ/F185 6.6948 Tf 6.455 -1.566 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -11.862 Td [(C)]TJ/F185 9.5641 Tf 9.586 0 Td [(\015)]TJ/F41 5.8022 Tf 13.015 11.105 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.638 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.676 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 6.591 10.456 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.678 -6.522 Td [(j)]TJ/F185 9.5641 Tf 3.836 2.572 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.434 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(/;)]TJ ET 1 0 0 1 311.511 682.94 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -682.94 cm BT /F41 8.2889 Tf 319.8 659.848 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.585 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.585 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F185 9.5641 Tf 4.791 0 Td [(:)]TJ ET 1 0 0 1 311.511 659.848 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -659.848 cm BT /F22 8.2889 Tf 311.511 642.252 Td [(By)]TJ ET 1 0 0 1 323.226 642.252 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -323.226 -642.252 cm BT /F22 8.2889 Tf 323.226 642.252 Td [(Theorem)-261(3)]TJ ET 1 0 0 1 364.341 642.252 cm 0 g 0 G 1 0 0 1 -364.341 -642.252 cm BT /F22 8.2889 Tf 364.341 642.252 Td [(,)]TJ/F41 8.2889 Tf 4.105 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F179 9.5641 Tf 4.379 1.434 Td [(\000)]TJ/F189 9.5641 Tf 9.682 7.173 Td [(P)]TJ/F41 5.8022 Tf 9.994 -2.584 Td [(n)]TJ 0 -7.314 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 5.452 2.725 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.572 Td [(i)]TJ -1.679 -6.264 Td [(j)]TJ/F41 8.2889 Tf 3.836 2.692 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(j)]TJ/F22 8.2889 Tf 2.175 1.434 Td [(,)]TJ/F41 8.2889 Tf 4.106 0 Td [(i)]TJ/F179 9.5641 Tf 5.267 0 Td [(D)]TJ/F41 8.2889 Tf 10.357 0 Td [(m)]TJ/F179 9.5641 Tf 9.383 0 Td [(C)]TJ/F22 8.2889 Tf 9.682 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(m)]TJ/F179 9.5641 Tf 9.383 0 Td [(C)]TJ/F22 8.2889 Tf 9.681 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F22 8.2889 Tf 4.791 0 Td [(,)-261(will)-262(reach)]TJ ET 1 0 0 1 311.511 642.252 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -642.252 cm BT /F22 8.2889 Tf 311.511 630.658 Td [(zero)-302(in)-302(finite)-302(time)]TJ/F41 8.2889 Tf 71.951 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.519 Td [(\003)]TJ/F22 5.8022 Tf -0.708 -6.212 Td [(2)]TJ/F22 8.2889 Tf 4.695 2.693 Td [(.)-302(Denote)]TJ/F41 8.2889 Tf 34.436 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.472 Td [(\003)]TJ/F179 9.5641 Tf 7.751 -3.472 Td [(D)]TJ/F22 8.2889 Tf 11.224 0 Td [(max)]TJ/F179 9.5641 Tf 16.578 0 Td [(f)]TJ/F41 8.2889 Tf 3.539 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.519 Td [(\003)]TJ/F22 5.8022 Tf -0.709 -6.212 Td [(1)]TJ/F185 9.5641 Tf 4.695 2.693 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.519 Td [(\003)]TJ/F22 5.8022 Tf -0.709 -6.212 Td [(2)]TJ/F179 9.5641 Tf 4.695 2.693 Td [(g)]TJ/F22 8.2889 Tf 3.538 0 Td [(,)-302(after)-302(which)-302(the)]TJ/F41 8.2889 Tf 65.96 0 Td [(n)]TJ ET 1 0 0 1 311.511 630.658 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -630.658 cm BT /F22 8.2889 Tf 311.511 619.966 Td [(agents)-250(are)-250(in)-250(formation)]TJ/F185 9.5641 Tf 90.945 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.674 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(.)]TJ/F166 7.9701 Tf 12.309 0 Td [(\004)]TJ ET 1 0 0 1 311.511 619.966 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -619.966 cm BT /F41 8.2889 Tf 311.511 593.556 Td [(4.4.)-500(Trajectory)-250(tracking)]TJ ET 1 0 0 1 311.511 593.556 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -593.556 cm BT /F22 8.2889 Tf 323.466 570.55 Td [(We)-251(assume)-250(that)]TJ/F41 8.2889 Tf 63.44 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F22 8.2889 Tf 3.518 -3.472 Td [(,)-251(representing)-250(the)-251(expected)-250(trajectory)-251(of)-250(the)]TJ ET 1 0 0 1 311.511 570.55 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -570.55 cm BT /F22 8.2889 Tf 311.511 559.858 Td [(formation,)-250(satisfies)-250(the)-250(following)-250(differential)-250(equation)]TJ ET 1 0 0 1 311.511 559.858 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -559.858 cm BT /F179 9.5641 Tf 312.256 541.773 Td [(P)]TJ/F41 8.2889 Tf -0.745 -1.96 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.95 Td [(c)]TJ/F179 9.5641 Tf 6.175 -3.95 Td [(D)]TJ/F41 8.2889 Tf 10.116 0 Td [(f)]TJ/F185 9.5641 Tf 4.166 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(h)]TJ/F41 5.8022 Tf 4.674 3.95 Td [(c)]TJ/F185 9.5641 Tf 3.519 -3.95 Td [(/;)]TJ/F22 8.2889 Tf 194.839 0 Td [(\0505\051)]TJ ET 1 0 0 1 311.511 539.813 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -539.813 cm BT /F22 8.2889 Tf 311.511 522.152 Td [(and)-185(the)-185(leaders)-185(of)-185(the)-185(studied)-185(system)-185(satisfy)-185(the)-185(following)-185(assump-)]TJ ET 1 0 0 1 311.511 522.152 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -522.152 cm BT /F22 8.2889 Tf 311.511 511.46 Td [(tion)]TJ ET 1 0 0 1 311.511 511.46 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -17.526 cm 0 g 0 G 1 0 0 1 -311.511 -493.934 cm BT /F22 8.2889 Tf 311.511 493.934 Td [(\050A5\051)]TJ ET 1 0 0 1 327.906 493.934 cm 0 g 0 G 1 0 0 1 -327.906 -493.934 cm BT /F22 8.2889 Tf 331.891 493.934 Td [(some)-231(root)-231(agents)-231(in)-231(the)-231(local)-231(interaction)-231(topology)-231(among)-231(the)]TJ ET 1 0 0 1 311.511 493.934 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -493.934 cm BT /F22 8.2889 Tf 331.891 483.241 Td [(leaders)-250(can)-250(access)-250(the)-250(reference)-250(trajectory.)]TJ ET 1 0 0 1 311.511 483.241 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -483.241 cm BT /F22 8.2889 Tf 311.511 466.178 Td [(The)-281(same)-281(problem)-281(was)-281(studied)-281(in)]TJ ET 1 0 0 1 443.004 466.178 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -443.004 -466.178 cm BT /F22 8.2889 Tf 443.004 466.178 Td [(Ren)]TJ ET 1 0 0 1 457.509 466.178 cm 0 g 0 G 1 0 0 1 2.329 0 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -459.838 -466.178 cm BT /F22 8.2889 Tf 459.838 466.178 Td [(\050)]TJ ET 1 0 0 1 462.905 466.178 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -462.905 -466.178 cm BT /F22 8.2889 Tf 462.905 466.178 Td [(2007)]TJ ET 1 0 0 1 482.102 466.178 cm 0 g 0 G 1 0 0 1 -482.102 -466.178 cm BT /F22 8.2889 Tf 482.102 466.178 Td [(\051)-281(in)-281(the)-281(development)]TJ ET 1 0 0 1 311.511 466.178 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -466.178 cm BT /F22 8.2889 Tf 311.511 455.486 Td [(of)-250(consensus)-250(theory.)-250(The)-250(available)-250(protocol)-250(in)-250(our)-250(framework)-250(is)]TJ ET 1 0 0 1 311.511 455.486 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -455.486 cm BT /F41 8.2889 Tf 311.511 356.462 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.814 1.435 Td [(D)]TJ/F189 9.5641 Tf 10.117 82.729 Td [(8)]TJ 0 -8.608 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(<)]TJ 0 -17.215 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.87 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(>)]TJ 0 -2.869 Td [(:)]TJ/F179 9.5641 Tf 8.32 150.279 Td [(P)]TJ/F41 8.2889 Tf -0.745 -1.96 Td [(h)]TJ/F41 5.8022 Tf 4.674 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(C)]TJ/F41 8.2889 Tf 9.586 0 Td [(f)]TJ/F185 9.5641 Tf 4.165 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.95 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.95 Td [(/)]TJ/F179 9.5641 Tf -34.583 -17.584 Td [(C)]TJ/F185 9.5641 Tf 9.054 0 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F189 9.5641 Tf 10.676 13.428 Td [(\022)]TJ 6.456 -4.342 Td [(X)]TJ/F41 5.8022 Tf 0.347 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F41 8.2889 Tf 3.862 11.808 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F189 9.5641 Tf 3.835 9.124 Td [(\000)]TJ/F185 9.5641 Tf 3.854 -7.689 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.301 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 5.692 0 Td [(\000)]TJ/F185 9.5641 Tf 9.586 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.567 7.689 Td [(\001)]TJ/F179 9.5641 Tf -138.753 -35.412 Td [(C)]TJ/F41 8.2889 Tf 9.054 0 Td [(W)]TJ/F41 5.8022 Tf 9.247 3.95 Td [(c)]TJ -1.115 -6.523 Td [(i)]TJ/F189 9.5641 Tf 4.633 10.262 Td [(\000)]TJ/F41 8.2889 Tf 3.854 -7.689 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.95 Td [(c)]TJ/F179 9.5641 Tf 5.643 -3.95 Td [(\000)]TJ/F185 9.5641 Tf 9.586 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.567 13.428 Td [(\023\023)]TJ/F185 6.6948 Tf 12.912 -1.567 Td [(\013)]TJ/F179 9.5641 Tf -90.394 -35.393 Td [(C)]TJ/F185 9.5641 Tf 9.054 0 Td [(\015)]TJ/F189 9.5641 Tf 6.332 13.428 Td [(\022)]TJ 6.456 -4.342 Td [(X)]TJ/F41 5.8022 Tf 0.347 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F41 8.2889 Tf 3.862 11.808 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F189 9.5641 Tf 3.834 9.125 Td [(\000)]TJ/F185 9.5641 Tf 3.855 -7.69 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 5.692 0 Td [(\000)]TJ/F185 9.5641 Tf 9.586 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.568 7.69 Td [(\001)]TJ/F179 9.5641 Tf -128.345 -35.051 Td [(C)]TJ/F41 8.2889 Tf 9.054 0 Td [(W)]TJ/F41 5.8022 Tf 9.247 3.95 Td [(c)]TJ -1.115 -6.523 Td [(i)]TJ/F189 9.5641 Tf 4.633 10.262 Td [(\000)]TJ/F41 8.2889 Tf 3.854 -7.689 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.95 Td [(c)]TJ/F179 9.5641 Tf 5.643 -3.95 Td [(\000)]TJ/F185 9.5641 Tf 9.586 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.283 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.567 7.689 Td [(\001)]TJ 3.854 5.739 Td [(\023)]TJ/F185 9.5641 Tf 6.456 -13.428 Td [(;)]TJ/F41 8.2889 Tf 13.049 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(D)]TJ/F22 8.2889 Tf 10.117 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F22 8.2889 Tf 4.76 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(m)]TJ/F185 9.5641 Tf 7.161 0 Td [(;)]TJ/F41 5.8022 Tf -162.895 -13.35 Td [(n)]TJ/F189 9.5641 Tf -5.089 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.637 -19.543 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F185 9.5641 Tf 4.997 10.457 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.678 -6.523 Td [(j)]TJ/F41 8.2889 Tf 3.836 2.573 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(C)]TJ 10.076 1.96 Td [(P)]TJ/F41 8.2889 Tf -0.491 -1.96 Td [(f)]TJ/F41 5.8022 Tf 4.166 3.95 Td [(i)]TJ -1.679 -6.523 Td [(j)]TJ/F41 8.2889 Tf 3.836 2.573 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 5.693 0 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F189 9.5641 Tf 10.676 13.428 Td [(\022)]TJ/F41 5.8022 Tf 11.545 -2.323 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.638 -19.543 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 6.591 10.457 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.679 -6.523 Td [(j)]TJ/F185 9.5641 Tf 3.836 2.573 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.301 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.568 13.428 Td [(\023)]TJ/F185 6.6948 Tf 6.456 -1.567 Td [(\013)]TJ/F179 9.5641 Tf -144.076 -39.976 Td [(C)]TJ/F185 9.5641 Tf 9.054 0 Td [(\015)]TJ/F41 5.8022 Tf 13.016 11.105 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.637 -19.543 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 6.591 10.457 Td [(f)]TJ/F41 5.8022 Tf 4.165 3.95 Td [(i)]TJ -1.678 -6.523 Td [(j)]TJ/F185 9.5641 Tf 3.836 2.573 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/;)]TJ/F41 8.2889 Tf 16.616 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.585 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.585 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F185 9.5641 Tf 4.791 0 Td [(;)]TJ/F22 8.2889 Tf 27.524 69.791 Td [(\0506\051)]TJ ET 1 0 0 1 311.511 356.462 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -356.462 cm BT /F22 8.2889 Tf 311.511 259.599 Td [(where)-306(parameters)-305(0)]TJ/F185 9.5641 Tf 81.502 0 Td [(<)-402(\013)-441(<)]TJ/F22 8.2889 Tf 32.286 0 Td [(1,)]TJ/F185 9.5641 Tf 9.273 0 Td [(\014)-472(>)]TJ/F22 8.2889 Tf 21.206 0 Td [(0,)]TJ/F185 9.5641 Tf 9.273 0 Td [(\015)]TJ/F179 9.5641 Tf 10.172 0 Td [(\025)]TJ/F22 8.2889 Tf 11.052 0 Td [(0,)-306(weighting)-305(factors)]TJ ET 1 0 0 1 311.511 259.599 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -259.599 cm BT /F41 8.2889 Tf 311.511 248.907 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 6.554 1.435 Td [(>)]TJ/F22 8.2889 Tf 10.18 0 Td [(0,)]TJ/F41 8.2889 Tf 8.836 0 Td [(W)]TJ/F41 5.8022 Tf 9.246 3.572 Td [(c)]TJ -1.115 -6.264 Td [(i)]TJ/F179 9.5641 Tf 7.353 2.692 Td [(\025)]TJ/F22 8.2889 Tf 9.931 0 Td [(0,)-253(and)]TJ/F41 8.2889 Tf 25.181 0 Td [(W)]TJ/F41 5.8022 Tf 9.246 3.572 Td [(c)]TJ -1.115 -6.264 Td [(i)]TJ/F185 9.5641 Tf 7.353 2.692 Td [(>)]TJ/F22 8.2889 Tf 10.179 0 Td [(0)-253(if)-253(and)-253(only)-253(if)-253(leader)]TJ/F41 8.2889 Tf 82.688 0 Td [(i)]TJ/F22 8.2889 Tf 4.467 0 Td [(can)-253(access)-253(the)]TJ ET 1 0 0 1 311.511 248.907 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -248.907 cm BT /F22 8.2889 Tf 311.511 238.214 Td [(reference)-250(trajectory.)]TJ ET 1 0 0 1 311.511 238.214 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.992 cm 0 g 0 G 1 0 0 1 -307.526 -215.222 cm BT /F153 8.2889 Tf 311.511 215.222 Td [(Corollary)-250(7.)]TJ ET 1 0 0 1 357.497 215.222 cm 0 g 0 G 1 0 0 1 -357.497 -215.222 cm BT /F41 8.2889 Tf 361.483 215.222 Td [(Suppose)-236(that)-321(h,)-235(F)-358(and)-236(h)]TJ/F41 5.8022 Tf 85.375 3.471 Td [(c)]TJ/F41 8.2889 Tf 5.471 -3.471 Td [(are)-236(continuous)-235(and)-236(piece-wise)]TJ ET 1 0 0 1 311.511 215.222 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -215.222 cm BT /F41 8.2889 Tf 311.511 204.529 Td [(differentiable.)-373(Under)-372(protocol)]TJ ET 1 0 0 1 423.592 204.529 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -423.592 -204.529 cm BT /F22 8.2889 Tf 423.592 204.529 Td [(\0506\051)]TJ ET 1 0 0 1 434.517 204.529 cm 0 g 0 G 1 0 0 1 -434.517 -204.529 cm BT /F41 8.2889 Tf 437.604 204.529 Td [(and)-372(Assumption)-373(\050A1,)-372(A2,)-373(A3',)-372(A4',)]TJ ET 1 0 0 1 311.511 204.529 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -204.529 cm BT /F41 8.2889 Tf 311.511 193.837 Td [(A5\051,)-214(the)-214(n)-214(agents)-213(will)-214(be)-214(in)-214(formation)]TJ/F185 9.5641 Tf 134.469 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.674 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F41 8.2889 Tf 5.34 0 Td [(in)-214(finite)-214(time,)-214(tracking)-213(the)]TJ ET 1 0 0 1 311.511 193.837 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -193.837 cm BT /F41 8.2889 Tf 311.511 183.145 Td [(trajectory)-250(described)-250(by)-250(Eq.)]TJ ET 1 0 0 1 409.643 183.145 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -409.643 -183.145 cm BT /F22 8.2889 Tf 409.643 183.145 Td [(\0505\051)]TJ ET 1 0 0 1 420.567 183.145 cm 0 g 0 G 1 0 0 1 -420.567 -183.145 cm BT /F41 8.2889 Tf 420.567 183.145 Td [(.)]TJ ET 1 0 0 1 311.511 183.145 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -18.523 cm 0 g 0 G 1 0 0 1 -307.526 -164.622 cm BT /F153 8.2889 Tf 311.511 164.622 Td [(Proof.)]TJ ET 1 0 0 1 335.739 164.622 cm 0 g 0 G 1 0 0 1 -335.739 -164.622 cm BT /F22 8.2889 Tf 339.724 164.622 Td [(We)-407(only)-407(consider)-407(the)-407(dynamics)-407(of)-407(the)-407(leaders.)-408(By)]TJ ET 1 0 0 1 540.455 164.622 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -540.455 -164.622 cm BT /F22 8.2889 Tf 540.455 164.622 Td [(Theo-)]TJ ET 1 0 0 1 311.511 164.622 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -164.622 cm BT /F22 8.2889 Tf 311.511 153.93 Td [(rem)-329(3)]TJ ET 1 0 0 1 334.482 153.93 cm 0 g 0 G 1 0 0 1 -334.482 -153.93 cm BT /F22 8.2889 Tf 334.482 153.93 Td [(,)-329(there)-330(exists)-329(a)-329(finite)-330(time,)-329(after)-329(which)]TJ/F41 8.2889 Tf 151.534 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.957 1.435 Td [(\000)]TJ/F41 8.2889 Tf 10.26 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.957 1.435 Td [(\000)]TJ/F41 8.2889 Tf 10.259 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F22 8.2889 Tf 6.248 -3.472 Td [(will)-329(be)]TJ ET 1 0 0 1 311.511 153.93 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -153.93 cm BT /F22 8.2889 Tf 311.511 143.238 Td [(equal)-226(to)-226(zero,)-226(namely,)-227(the)-226(leaders)-226(will)-226(form)-226(the)-226(formation)-226(frame)]TJ/F41 8.2889 Tf 244.444 0 Td [(h)]TJ/F22 8.2889 Tf 4.675 0 Td [(,)]TJ ET 1 0 0 1 311.511 143.238 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -143.238 cm BT /F22 8.2889 Tf 311.511 132.545 Td [(tracking)-250(the)-250(trajectory)]TJ/F41 8.2889 Tf 87.439 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F22 8.2889 Tf 3.518 -3.472 Td [(.)]TJ/F166 7.9701 Tf 12.309 0 Td [(\004)]TJ ET 1 0 0 1 311.511 132.545 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -132.545 cm BT /F153 8.2889 Tf 311.511 106.136 Td [(5.)-500(Simulations)]TJ ET 1 0 0 1 311.511 106.136 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -106.136 cm BT /F22 8.2889 Tf 323.466 83.13 Td [(In)-348(the)-348(following)-347(examples,)-348(protocol)-348(parameters)]TJ/F185 9.5641 Tf 187.499 0 Td [(\013)]TJ/F179 9.5641 Tf 10.578 0 Td [(D)]TJ/F22 5.8022 Tf 13.39 3.864 Td [(1)]TJ ET q 1 0 0 1 534.933 85.521 cm []0 d 0 J 0.44 w 0 0 m 3.359 0 l S Q BT /F22 5.8022 Tf 534.933 79.735 Td [(3)]TJ/F22 8.2889 Tf 4.555 3.395 Td [(,)]TJ/F185 9.5641 Tf 4.823 0 Td [(\014)]TJ/F179 9.5641 Tf 10.798 0 Td [(D)]TJ ET 1 0 0 1 311.511 83.13 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -83.13 cm BT /F185 9.5641 Tf 311.511 72.438 Td [(\015)]TJ/F179 9.5641 Tf 10.022 0 Td [(D)]TJ/F22 8.2889 Tf 11.151 0 Td [(1,)-299(weighting)-298(factors)-299(are)-299(all)-298(equal)-299(to)-299(2,)-298(and)-299(the)-299(total)-298(number)]TJ ET 1 0 0 1 311.511 72.438 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -72.438 cm BT /F22 8.2889 Tf 311.511 61.745 Td [(of)-332(members)-332(is)-332(30.)-332(Assume)-332(that)-332(the)-331(first)-332(5)-332(agents)-332(are)-332(leaders)-332(and)]TJ ET 1 0 0 1 311.511 61.745 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -61.745 cm BT /F22 8.2889 Tf 311.511 51.053 Td [(all)-345(the)-346(agents)-345(move)-345(on)-346(a)-345(plane,)-345(namely,)]TJ/F41 8.2889 Tf 158.209 0 Td [(N)]TJ/F179 9.5641 Tf 11.235 0 Td [(D)]TJ/F22 8.2889 Tf 12.144 0 Td [(2.)-346(The)-345(anticipated)]TJ ET 1 0 0 1 311.511 51.053 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -51.053 cm BT /F22 8.2889 Tf 311.511 40.361 Td [(formation)-250(is)-250(a)-250(pentagon,)-250(specifically,)]TJ ET 1 0 0 1 311.511 40.361 cm 0 g 0 G 0 g 0 G 1 0 0 1 -268.991 -11.955 cm 0 g 0 G 1 0 0 1 520.05 0 cm 0 g 0 G endstream endobj 153 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (./main.pdf) /PTEX.PageNumber 4 /PTEX.InfoDict 131 0 R /Matrix [ 1 0 0 1 0 0 ] /BBox [ 0 0 595.275 793.701 ] /Resources << /Font << /F189 86 0 R /F169 85 0 R /F185 84 0 R /F22 125 0 R /F166 68 0 R /F153 128 0 R /F179 126 0 R /F181 83 0 R /F41 127 0 R >> /ProcSet [ /PDF /Text ] >> /Length 52942 >> stream 1 0 0 1 32.706 740.734 cm 0 g 0 G 1 0 0 1 -32.706 -740.734 cm BT /F22 6.6311 Tf 32.706 740.734 Td [(2608)]TJ/F41 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[(n)]TJ/F189 9.5641 Tf -3.321 -2.019 Td [(P)]TJ/F41 5.8022 Tf -0.123 -15.717 Td [(i)]TJ/F179 6.6948 Tf 1.66 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F189 9.5641 Tf 4.953 16.234 Td [(\000)]TJ/F185 6.6948 Tf 5.05 -3.242 Td [(!)]TJ/F41 4.9734 Tf 4.385 -1.352 Td [(i)]TJ/F185 6.6948 Tf 1.92 1.352 Td [(\015)]TJ ET q 1 0 0 1 171.896 692.032 cm []0 d 0 J 0.44 w 0 0 m 10.738 0 l S Q BT /F22 5.8022 Tf 175.585 686.246 Td [(2)]TJ/F189 9.5641 Tf 8.244 11.085 Td [(\001)]TJ/F22 4.9734 Tf 7.288 0.56 Td [(2)]TJ/F185 5.7385 Tf 2.879 0 Td [(\013)]TJ ET q 1 0 0 1 188.879 696.86 cm []0 d 0 J 0.308 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 188.879 692.581 Td [(1)]TJ/F179 5.7385 Tf 2.879 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ/F179 9.5641 Tf 6.794 -2.94 Td [(j)]TJ/F41 8.2889 Tf 2.736 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(i)]TJ/F179 9.5641 Tf 2.157 1.435 Td [(j)]TJ/F22 4.9734 Tf 6.169 6.886 Td [(4)]TJ/F185 5.7385 Tf 2.88 0 Td [(\013)]TJ ET q 1 0 0 1 216.195 695.496 cm []0 d 0 J 0.308 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 216.195 691.217 Td [(1)]TJ/F179 5.7385 Tf 2.88 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ ET 1 0 0 1 32.706 703.726 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -703.726 cm BT /F166 7.9701 Tf 58.819 668.691 Td [(,)]TJ/F185 9.2055 Tf 10.699 0 Td [(\001)]TJ/F22 5.8022 Tf 7.29 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F185 9.5641 Tf 4.344 0 Td [(/:)]TJ ET 1 0 0 1 32.706 668.691 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -668.691 cm BT /F22 8.2889 Tf 32.706 651.73 Td [(The)-321(third)-321(inequality)-320(follows)-321(from)-321(the)-321(fact)-321(that)]TJ/F41 8.2889 Tf 181.38 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.434 Td [(i)]TJ/F22 8.2889 Tf 4.817 1.434 Td [(and)-321(sig)]TJ/F185 9.5641 Tf 27.583 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.472 Td [(\013)]TJ/F22 8.2889 Tf 7.248 -3.472 Td [(are)]TJ ET 1 0 0 1 32.706 651.73 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -651.73 cm BT /F22 8.2889 Tf 32.706 641.165 Td [(with)-250(the)-250(same)-250(sign.)]TJ ET 1 0 0 1 32.706 641.165 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -641.165 cm BT /F22 8.2889 Tf 44.661 630.391 Td [(Let)]TJ/F181 8.9265 Tf 14.183 0 Td [(W)]TJ/F179 9.5641 Tf 13.092 0 Td [(D)-418(f)]TJ/F185 9.5641 Tf 14.996 0 Td [(\030)]TJ/F179 9.5641 Tf 9.123 0 Td [(2)]TJ/F169 8.6077 Tf 10.012 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.471 Td [(n)]TJ/F179 9.5641 Tf 7.848 -3.471 Td [(V)]TJ/F22 8.2889 Tf 6.627 0 Td [(1)]TJ/F179 9.5641 Tf 8.795 0 Td [(\024)-418(k)]TJ/F185 9.5641 Tf 15.971 0 Td [(\030)]TJ/F179 9.5641 Tf 5.127 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.435 Td [(1)]TJ/F179 9.5641 Tf 11.33 1.435 Td [(\024)-418(k)]TJ/F41 8.2889 Tf 15.97 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F41 5.8022 Tf 4.763 -1.435 Td [(i)]TJ/F179 6.6948 Tf 1.66 0 Td [(1)]TJ/F179 9.5641 Tf 7.333 1.435 Td [(k)]TJ/F41 8.2889 Tf 4.763 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F22 8.2889 Tf 3.567 0 Td [(0)]TJ/F185 9.5641 Tf 4.8 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.435 Td [(1)]TJ/F179 9.5641 Tf 7.334 1.435 Td [(g)]TJ/F22 8.2889 Tf 3.538 0 Td [(,)-313(where)]TJ ET 1 0 0 1 32.706 630.391 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -630.391 cm BT /F179 9.5641 Tf 32.706 619.825 Td [(k)-244(\001)-243(k)]TJ/F41 5.8022 Tf 16.844 -1.434 Td [(i)]TJ/F179 6.6948 Tf 1.66 0 Td [(1)]TJ/F22 8.2889 Tf 9.605 1.434 Td [(is)-274(the)-274(induced)-274(matrix)-274(norm)-274(of)-274(maximum)-274(norm)]TJ/F179 9.5641 Tf 181.554 0 Td [(k)-244(\001)-243(k)]TJ/F179 6.6948 Tf 16.845 -1.434 Td [(1)]TJ/F22 8.2889 Tf 7.333 1.434 Td [(.)-274(We)]TJ ET 1 0 0 1 32.706 619.825 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -619.825 cm BT /F22 8.2889 Tf 32.706 609.26 Td [(first)-384(suppose)]TJ/F181 8.9265 Tf 53.154 0 Td [(W)]TJ/F179 9.5641 Tf 14.608 0 Td [(6)1(D)-576(;)]TJ/F22 8.2889 Tf 18.289 0 Td [(.)-385(Then)-384(it)-385(is)-384(compact,)-385(and)-384(for)-384(any)]TJ/F185 9.5641 Tf 131.806 0 Td [(\030)]TJ/F179 9.5641 Tf 10.638 0 Td [(2)]TJ/F181 8.9265 Tf 11.528 0 Td [(W)]TJ/F22 8.2889 Tf 9.096 0 Td [(,)]TJ ET 1 0 0 1 32.706 609.26 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -609.26 cm BT /F185 9.2055 Tf 32.706 598.695 Td [(\001)]TJ/F22 5.8022 Tf 7.291 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(.\030)-110(/)]TJ/F179 9.5641 Tf 14.918 0 Td [(6)1(D)]TJ/F22 8.2889 Tf 10.117 0 Td [(0.)-207(Thus)-207(min)]TJ/F185 6.6948 Tf 43.697 -1.435 Td [(\030)]TJ/F179 6.6948 Tf 3.588 0 Td [(2)]TJ/F181 6.2485 Tf 4.212 0 Td [(W)]TJ/F185 9.2055 Tf 8.459 1.435 Td [(\001)]TJ/F22 5.8022 Tf 7.291 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(.\030)-110(/)]TJ/F22 8.2889 Tf 12.261 0 Td [(,)-207(denoted)-207(by)]TJ/F41 8.2889 Tf 47.822 0 Td [(k)]TJ/F22 5.8022 Tf 4.31 -1.435 Td [(2)]TJ/F22 8.2889 Tf 3.857 1.435 Td [(,)-207(exists,)-207(and)-206(is)-207(larger)]TJ ET 1 0 0 1 32.706 598.695 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -598.695 cm BT /F22 8.2889 Tf 32.706 588.129 Td [(than)-193(zero.)-194(Therefore,)-193(if)]TJ/F41 8.2889 Tf 86.552 0 Td [(y)]TJ/F179 9.5641 Tf 7 0 Td [(2)]TJ/F181 8.9265 Tf 8.673 0 Td [(W)]TJ/F22 8.2889 Tf 9.096 0 Td [(,)-193(then)]TJ/F179 9.5641 Tf 22.64 0 Td [(4)]TJ/F22 5.8022 Tf 7.498 -2.151 Td [(2)]TJ/F185 9.5641 Tf 3.858 2.151 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(\025)]TJ/F41 8.2889 Tf 9.868 0 Td [(k)]TJ/F22 5.8022 Tf 4.311 -1.434 Td [(2)]TJ/F22 8.2889 Tf 3.857 1.434 Td [(.)-194(On)-193(the)-193(other)-193(hand,)]TJ ET 1 0 0 1 32.706 588.129 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -588.129 cm BT /F22 8.2889 Tf 32.706 577.564 Td [(if)]TJ/F41 8.2889 Tf 7.023 0 Td [(y)]TJ/F179 9.5641 Tf 7 0 Td [(6)1(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(W)]TJ/F22 8.2889 Tf 10.872 0 Td [(or)-214(if)]TJ/F181 8.9265 Tf 16.897 0 Td [(W)]TJ/F179 9.5641 Tf 11.753 0 Td [(D)-278(;)]TJ/F22 8.2889 Tf 15.434 0 Td [(,)-214(it)-215(fo)1(llows)-215(from)]TJ/F179 9.5641 Tf 61.097 0 Td [(k)]TJ/F41 8.2889 Tf 4.763 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.434 Td [(1)]TJ/F179 9.5641 Tf 9.99 1.434 Td [(D)-278(k)-127(\000)]TJ/F41 8.2889 Tf 24.767 0 Td [(L)]TJ/F185 9.5641 Tf 3.928 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F185 9.5641 Tf 4.069 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.434 Td [(1)]TJ/F179 9.5641 Tf 9.99 1.434 Td [(\024)]TJ ET 1 0 0 1 32.706 577.564 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -577.564 cm BT /F179 9.5641 Tf 32.706 566.999 Td [(k)]TJ/F41 8.2889 Tf 4.763 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F41 5.8022 Tf 4.763 -1.435 Td [(i)]TJ/F179 6.6948 Tf 1.659 0 Td [(1)]TJ/F179 9.5641 Tf 7.334 1.435 Td [(k)]TJ/F41 8.2889 Tf 4.763 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.435 Td [(1)]TJ/F179 9.5641 Tf 10.091 1.435 Td [(\024)-288(k)]TJ/F41 8.2889 Tf 14.732 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F179 9.5641 Tf 3.568 0 Td [(k)]TJ/F41 5.8022 Tf 4.763 -1.435 Td [(i)]TJ/F179 6.6948 Tf 1.659 0 Td [(1)]TJ/F179 9.5641 Tf 7.334 1.435 Td [(k)]TJ/F41 8.2889 Tf 4.762 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F22 8.2889 Tf 3.568 0 Td [(0)]TJ/F185 9.5641 Tf 4.799 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.435 Td [(1)]TJ/F22 8.2889 Tf 9.445 1.435 Td [(that)-255(0)]TJ/F185 9.5641 Tf 25.168 0 Td [(<)]TJ/F179 9.5641 Tf 10.217 0 Td [(k)]TJ/F41 8.2889 Tf 4.763 0 Td [(y)]TJ/F179 9.5641 Tf 4.344 0 Td [(k)]TJ/F179 6.6948 Tf 4.763 -1.435 Td [(1)]TJ/F185 9.5641 Tf 10.09 1.435 Td [(<)]TJ/F22 8.2889 Tf 10.218 0 Td [(1.)-255(In)-254(this)]TJ ET 1 0 0 1 32.706 566.999 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -566.999 cm BT /F22 8.2889 Tf 32.706 556.434 Td [(case,)]TJ ET 1 0 0 1 32.706 556.434 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -556.434 cm BT /F185 9.2055 Tf 32.706 520.852 Td [(\001)]TJ/F22 5.8022 Tf 7.291 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)-278(>)]TJ/F41 8.2889 Tf 17.536 13.59 Td [(k)]TJ/F22 5.8022 Tf 4.311 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(\014)]TJ/F22 5.8022 Tf 6.064 3.471 Td [(2)]TJ/F41 5.8022 Tf 8.895 5.721 Td [(n)]TJ/F189 9.5641 Tf -3.32 -2.019 Td [(P)]TJ/F41 5.8022 Tf -0.124 -15.717 Td [(i)]TJ/F179 6.6948 Tf 1.66 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F179 9.5641 Tf 4.953 8.544 Td [(j)]TJ/F41 8.2889 Tf 2.736 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(i)]TJ/F179 9.5641 Tf 2.157 1.435 Td [(j)]TJ/F22 5.8022 Tf 2.736 3.471 Td [(2)]TJ/F185 6.6948 Tf 3.359 0 Td [(\013)]TJ ET q 1 0 0 1 69.301 523.243 cm []0 d 0 J 0.44 w 0 0 m 51.437 0 l S Q BT /F22 8.2889 Tf 70.885 508.247 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(!)]TJ/F22 5.8022 Tf 6.265 -1.435 Td [(0)]TJ/F41 5.8022 Tf 8.895 10.627 Td [(n)]TJ/F189 9.5641 Tf -3.32 -2.019 Td [(P)]TJ/F41 5.8022 Tf -0.123 -15.717 Td [(i)]TJ/F179 6.6948 Tf 1.659 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F179 9.5641 Tf 4.953 8.544 Td [(j)]TJ/F41 8.2889 Tf 2.736 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(i)]TJ/F179 9.5641 Tf 2.158 1.435 Td [(j)]TJ/F22 5.8022 Tf 2.735 2.764 Td [(2)]TJ/F185 6.6948 Tf 3.359 0 Td [(\013)]TJ/F179 9.5641 Tf 10.025 9.841 Td [(D)]TJ/F41 8.2889 Tf 11.312 6.704 Td [(k)]TJ/F22 5.8022 Tf 4.31 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(\014)]TJ/F22 5.8022 Tf 6.064 3.472 Td [(2)]TJ ET q 1 0 0 1 135.903 523.243 cm []0 d 0 J 0.44 w 0 0 m 18.089 0 l S Q BT /F22 8.2889 Tf 137.487 514.061 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(!)]TJ/F22 5.8022 Tf 6.265 -1.434 Td [(0)]TJ/F185 9.5641 Tf 6.637 8.225 Td [(;)]TJ ET 1 0 0 1 32.706 520.852 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -520.852 cm BT /F22 8.2889 Tf 32.706 476.26 Td [(where)]TJ/F185 9.5641 Tf 26.334 0 Td [(!)]TJ/F22 5.8022 Tf 6.264 -1.434 Td [(0)]TJ/F179 9.5641 Tf 6.515 1.434 Td [(D)]TJ/F22 8.2889 Tf 10.116 0 Td [(max)]TJ/F189 9.5641 Tf 16.578 7.69 Td [(\010)]TJ 4.533 2.869 Td [(\020)]TJ/F185 6.6948 Tf 7.469 -6.111 Td [(!)]TJ/F41 4.9734 Tf 4.385 -1.352 Td [(i)]TJ/F185 6.6948 Tf 1.921 1.352 Td [(\014)]TJ ET q 1 0 0 1 109.454 478.651 cm []0 d 0 J 0.44 w 0 0 m 12.672 0 l S Q BT /F22 5.8022 Tf 109.454 472.865 Td [(1)]TJ/F179 6.6948 Tf 3.36 0 Td [(C)]TJ/F185 6.6948 Tf 5.222 0 Td [(\013)]TJ/F189 9.5641 Tf 5.286 13.954 Td [(\021)]TJ/F22 4.9734 Tf 8.646 0.56 Td [(2)]TJ/F185 5.7385 Tf 2.879 0 Td [(\013)]TJ ET q 1 0 0 1 129.73 486.348 cm []0 d 0 J 0.308 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 129.73 482.07 Td [(1)]TJ/F179 5.7385 Tf 2.879 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ/F185 9.5641 Tf 6.794 -5.81 Td [(;)]TJ/F189 9.5641 Tf 4.76 7.69 Td [(\000)]TJ/F185 6.6948 Tf 5.05 -3.242 Td [(!)]TJ/F41 4.9734 Tf 4.385 -1.352 Td [(i)]TJ/F185 6.6948 Tf 1.92 1.352 Td [(\015)]TJ ET q 1 0 0 1 153.689 478.651 cm []0 d 0 J 0.44 w 0 0 m 10.738 0 l S Q BT /F22 5.8022 Tf 157.378 472.865 Td [(2)]TJ/F189 9.5641 Tf 8.244 11.085 Td [(\001)]TJ/F22 4.9734 Tf 7.288 0.56 Td [(2)]TJ/F185 5.7385 Tf 2.879 0 Td [(\013)]TJ ET q 1 0 0 1 170.672 483.479 cm []0 d 0 J 0.308 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 170.672 479.2 Td [(1)]TJ/F179 5.7385 Tf 2.879 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ/F185 9.5641 Tf 6.794 -2.94 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.434 Td [(n)]TJ/F189 9.5641 Tf 3.852 9.124 Td [(\011)]TJ/F22 8.2889 Tf 4.533 -7.69 Td [(.)]TJ ET 1 0 0 1 32.706 476.26 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -476.26 cm BT /F22 8.2889 Tf 44.661 458.187 Td [(Let)]TJ/F41 8.2889 Tf 13.66 0 Td [(K)]TJ/F22 5.8022 Tf 5.106 -1.434 Td [(1)]TJ/F179 9.5641 Tf 6.514 1.434 Td [(D)]TJ/F22 8.2889 Tf 10.117 0 Td [(min)]TJ/F189 9.5641 Tf 15.194 7.69 Td [(\010)]TJ/F41 8.2889 Tf 4.533 -7.69 Td [(k)]TJ/F22 5.8022 Tf 4.31 -1.434 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(;)]TJ/F41 5.8022 Tf 5.955 4.404 Td [(k)]TJ/F22 4.9734 Tf 3.017 -1.353 Td [(1)]TJ/F185 6.6948 Tf 3.378 1.353 Td [(\014)]TJ/F22 4.9734 Tf 4.244 2.43 Td [(2)]TJ ET q 1 0 0 1 113.908 460.578 cm []0 d 0 J 0.44 w 0 0 m 14.017 0 l S Q BT /F22 5.8022 Tf 115.355 454.792 Td [(2)]TJ/F185 6.6948 Tf 3.36 0 Td [(!)]TJ/F22 4.9734 Tf 4.385 -1.353 Td [(0)]TJ/F189 9.5641 Tf 6.02 12.438 Td [(\011)]TJ/F22 8.2889 Tf 4.534 -7.69 Td [(.)-250(Then)-250(the)-250(claim)-250(holds.)]TJ ET 1 0 0 1 32.706 458.187 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -458.187 cm BT /F41 8.2889 Tf 32.706 442.421 Td [(Step)]TJ/F22 8.2889 Tf 18.059 0 Td [(2:)-299(Next,)-299(we)-298(suppose)-299(that)]TJ/F181 8.9265 Tf 98.527 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 6.043 0 Td [(has)-299(a)-298(spanning)-299(tree,)-299(the)-299(asso-)]TJ ET 1 0 0 1 32.706 442.421 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -442.421 cm BT /F22 8.2889 Tf 32.706 431.855 Td [(ciated)-248(root)-249(vertex)-248(has)-248(no)-248(parent)-249(vertex,)-248(and)-248(the)-248(subgraph)-249(induced)]TJ ET 1 0 0 1 32.706 431.855 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -431.855 cm BT /F22 8.2889 Tf 32.706 421.29 Td [(by)-250(the)-250(other)-250(vertices)-250(is)-250(strongly)-250(connected.)]TJ ET 1 0 0 1 32.706 421.29 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -421.29 cm BT /F22 8.2889 Tf 44.661 410.516 Td [(Without)-375(loss)-375(of)-375(generality,)-375(assume)-374(that)-375(the)-375(root)-375(vertex)-375(is)]TJ/F185 9.5641 Tf 228.646 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(n)]TJ/F22 8.2889 Tf 3.852 1.435 Td [(.)]TJ ET 1 0 0 1 32.706 410.516 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -410.516 cm BT /F22 8.2889 Tf 32.706 399.951 Td [(Then)-323(we)-323(get)-323(that)]TJ/F41 8.2889 Tf 68.66 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(n)]TJ/F22 5.8022 Tf 3.354 0 Td [(1)]TJ/F179 9.5641 Tf 8.062 1.435 Td [(D)]TJ/F41 8.2889 Tf 11.665 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(n)]TJ/F22 5.8022 Tf 3.354 0 Td [(2)]TJ/F179 9.5641 Tf 8.062 1.435 Td [(D)-440(\001)-166(\001)-167(\001)-440(D)]TJ/F41 8.2889 Tf 38.7 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(nn)]TJ/F179 9.5641 Tf 11.41 1.435 Td [(D)]TJ/F22 8.2889 Tf 11.665 0 Td [(0)-323(and)]TJ/F41 8.2889 Tf 24.4 0 Td [(a)]TJ/F22 5.8022 Tf 4.418 -1.435 Td [(1)]TJ/F41 5.8022 Tf 3.36 0 Td [(n)]TJ/F22 8.2889 Tf 3.851 1.435 Td [(,)]TJ/F41 8.2889 Tf 4.617 0 Td [(a)]TJ/F22 5.8022 Tf 4.418 -1.435 Td [(2)]TJ/F41 5.8022 Tf 3.359 0 Td [(n)]TJ/F185 9.5641 Tf 3.852 1.435 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ ET 1 0 0 1 32.706 399.951 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -399.951 cm BT /F41 8.2889 Tf 32.706 389.385 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.434 Td [(n)]TJ/F179 6.6948 Tf 3.354 0 Td [(\000)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F185 6.6948 Tf 3.359 0 Td [(;)]TJ/F41 5.8022 Tf 2.216 0 Td [(n)]TJ/F22 8.2889 Tf 7.794 1.434 Td [(are)-476(not)-475(all)-476(zeros.)-477(For)-475(simplicity,)-476(let)]TJ/F41 8.2889 Tf 146.031 0 Td [(b)]TJ/F179 9.5641 Tf 11.952 0 Td [(D)-779(T)]TJ/F41 8.2889 Tf 18.097 0 Td [(a)]TJ/F22 5.8022 Tf 4.418 -1.434 Td [(1)]TJ/F41 5.8022 Tf 3.359 0 Td [(n)]TJ/F185 9.5641 Tf 3.852 1.434 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(a)]TJ/F22 5.8022 Tf 4.418 -1.434 Td [(2)]TJ/F41 5.8022 Tf 3.359 0 Td [(n)]TJ/F185 9.5641 Tf 3.852 1.434 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ ET 1 0 0 1 32.706 389.385 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -389.385 cm BT /F41 8.2889 Tf 32.706 378.82 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(n)]TJ/F179 6.6948 Tf 3.354 0 Td [(\000)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F185 6.6948 Tf 3.359 0 Td [(;)]TJ/F41 5.8022 Tf 2.216 0 Td [(n)]TJ/F179 9.5641 Tf 3.852 1.435 Td [(U)]TJ/F22 5.8022 Tf 3.185 3.472 Td [(T)]TJ/F22 8.2889 Tf 3.735 -3.472 Td [(,)-327(let)]TJ/F41 8.2889 Tf 17.296 0 Td [(A)]TJ/F22 5.8022 Tf 5.031 3.472 Td [(0)]TJ/F179 9.5641 Tf 8.156 -3.472 Td [(D)-449(T)]TJ/F41 8.2889 Tf 14.943 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(ij)]TJ/F179 9.5641 Tf 3.835 1.435 Td [(U)]TJ/F22 5.8022 Tf 3.184 -1.435 Td [(1)]TJ/F179 6.6948 Tf 3.36 0 Td [(\024)]TJ/F41 5.8022 Tf 5.048 0 Td [(i)]TJ/F185 6.6948 Tf 1.659 0 Td [(;)]TJ/F41 5.8022 Tf 2.216 0 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(\024)]TJ/F41 5.8022 Tf 5.048 0 Td [(n)]TJ/F179 6.6948 Tf 3.354 0 Td [(\000)]TJ/F22 5.8022 Tf 5.221 0 Td [(1)]TJ/F22 8.2889 Tf 3.858 1.435 Td [(,)-327(let)]TJ/F41 8.2889 Tf 17.295 0 Td [(y)]TJ/F41 5.8022 Tf 4.344 -1.435 Td [(i)]TJ/F179 9.5641 Tf 6.456 1.435 Td [(D)]TJ/F189 9.5641 Tf 11.758 7.173 Td [(P)]TJ/F41 5.8022 Tf 9.995 -2.584 Td [(n)]TJ 0 -7.315 Td [(j)]TJ/F179 6.6948 Tf 1.676 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 5.452 2.726 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(z)]TJ/F41 5.8022 Tf 3.713 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.957 1.435 Td [(\000)]TJ/F41 8.2889 Tf 10.242 0 Td [(z)]TJ/F41 5.8022 Tf 3.713 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)]TJ/F41 8.2889 Tf 4.653 0 Td [(i)]TJ/F179 9.5641 Tf 6.669 0 Td [(D)]TJ/F22 8.2889 Tf 11.759 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ ET 1 0 0 1 32.706 378.82 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -378.82 cm BT /F22 8.2889 Tf 32.706 365.947 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F179 9.5641 Tf 6.916 0 Td [(\000)]TJ/F22 8.2889 Tf 9.586 0 Td [(1,)-250(and)-250(let)]TJ/F41 8.2889 Tf 37.134 0 Td [(y)]TJ/F22 5.8022 Tf 4.343 3.472 Td [(0)]TJ/F179 9.5641 Tf 6.514 -3.472 Td [(D)-278(T)]TJ/F41 8.2889 Tf 13.302 0 Td [(y)]TJ/F22 5.8022 Tf 4.343 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(;)]TJ/F41 8.2889 Tf 4.759 0 Td [(y)]TJ/F22 5.8022 Tf 4.344 -1.434 Td [(2)]TJ/F185 9.5641 Tf 3.857 1.434 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.434 Td [(n)]TJ/F179 6.6948 Tf 3.354 0 Td [(\000)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F179 9.5641 Tf 3.858 1.434 Td [(U)]TJ/F22 5.8022 Tf 3.184 3.472 Td [(T)]TJ/F22 8.2889 Tf 3.736 -3.472 Td [(.)]TJ ET 1 0 0 1 32.706 365.947 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -365.947 cm BT /F22 8.2889 Tf 44.661 355.173 Td [(Because)-172(the)-173(subgraph)-172(induced)-173(by)]TJ/F185 9.5641 Tf 125.959 0 Td [(v)]TJ/F22 5.8022 Tf 4.657 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(;)-167(v)]TJ/F22 5.8022 Tf 9.417 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(v)]TJ/F41 5.8022 Tf 26.849 -1.435 Td [(m)]TJ/F22 8.2889 Tf 6.941 1.435 Td [(is)-172(strongly)-173(con-)]TJ ET 1 0 0 1 32.706 355.173 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -355.173 cm BT /F22 8.2889 Tf 32.706 344.608 Td [(nected,)-284(i.e.,)]TJ/F181 8.9265 Tf 45.072 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F22 5.8022 Tf 5.031 3.471 Td [(0)]TJ/F185 9.5641 Tf 3.858 -3.471 Td [(/)]TJ/F22 8.2889 Tf 5.924 0 Td [(is)-284(strongly)-285(connected,)-284(by)]TJ ET 1 0 0 1 199.633 344.608 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -199.633 -344.608 cm BT /F22 8.2889 Tf 199.633 344.608 Td [(Lemma)-284(1)]TJ ET 1 0 0 1 234.946 344.608 cm 0 g 0 G 1 0 0 1 -234.946 -344.608 cm BT /F22 8.2889 Tf 234.946 344.608 Td [(,)-284(there)-285(exists)]TJ ET 1 0 0 1 32.706 344.608 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -344.608 cm BT /F22 8.2889 Tf 32.706 334.042 Td [(a)-254(positive)-254(column)-254(vector)]TJ/F185 9.5641 Tf 95.832 0 Td [(!)]TJ/F22 5.8022 Tf 6.456 3.472 Td [(0)]TJ/F179 9.5641 Tf 6.596 -3.472 Td [(D)-286(T)]TJ/F185 9.5641 Tf 13.384 0 Td [(w)]TJ/F22 5.8022 Tf 7.03 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(;)-167(w)]TJ/F22 5.8022 Tf 11.789 -1.434 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(w)]TJ/F41 5.8022 Tf 29.221 -1.434 Td [(m)]TJ/F179 9.5641 Tf 5.511 1.434 Td [(U)]TJ/F22 5.8022 Tf 3.185 3.472 Td [(T)]TJ/F179 9.5641 Tf 6.475 -3.472 Td [(2)]TJ/F169 8.6077 Tf 8.755 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(m)]TJ/F22 8.2889 Tf 7.615 -3.472 Td [(such)-254(that)]TJ ET 1 0 0 1 32.706 334.042 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -334.042 cm BT /F185 9.5641 Tf 32.706 323.477 Td [(!)]TJ/F22 5.8022 Tf 6.456 3.472 Td [(0)]TJ/F41 8.2889 Tf 3.857 -3.472 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F22 5.8022 Tf 5.031 3.472 Td [(0)]TJ/F185 9.5641 Tf 3.858 -3.472 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F22 8.2889 Tf 10.116 0 Td [(0.)-250(Differentiate)-250(Lyapunov)-250(candidate)]TJ ET 1 0 0 1 32.706 323.477 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -323.477 cm BT /F41 8.2889 Tf 32.706 298.968 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F41 5.8022 Tf 14.377 11.105 Td [(m)]TJ/F189 9.5641 Tf -4.26 -2.019 Td [(X)]TJ/F41 5.8022 Tf 1.646 -19.543 Td [(i)]TJ/F179 6.6948 Tf 1.659 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F185 9.5641 Tf 6.6 10.457 Td [(!)]TJ/F41 5.8022 Tf 6.264 -1.435 Td [(i)]TJ/F189 9.5641 Tf 3.752 14.863 Td [(\022)]TJ/F185 9.5641 Tf 15.796 -6.724 Td [(\014)]TJ ET q 1 0 0 1 97.957 301.359 cm []0 d 0 J 0.44 w 0 0 m 22.354 0 l S Q BT /F22 8.2889 Tf 97.957 292.177 Td [(1)]TJ/F179 9.5641 Tf 6.925 0 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\013)]TJ/F179 9.5641 Tf 7.039 6.791 Td [(j)]TJ/F41 8.2889 Tf 2.736 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(i)]TJ/F179 9.5641 Tf 2.157 1.435 Td [(j)]TJ/F22 5.8022 Tf 2.736 3.95 Td [(1)]TJ/F179 6.6948 Tf 3.359 0 Td [(C)]TJ/F185 6.6948 Tf 5.222 0 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(C)]TJ/F185 9.5641 Tf 10.781 6.704 Td [(\015)]TJ ET q 1 0 0 1 159.554 301.359 cm []0 d 0 J 0.44 w 0 0 m 6.331 0 l S Q BT /F22 8.2889 Tf 160.32 292.177 Td [(2)]TJ/F41 8.2889 Tf 6.761 6.791 Td [(y)]TJ/F22 5.8022 Tf 4.343 3.95 Td [(2)]TJ/F41 5.8022 Tf 0 -6.523 Td [(i)]TJ/F189 9.5641 Tf 3.858 16.001 Td [(\023)]TJ/F185 9.5641 Tf 8.05 -13.428 Td [(;)]TJ ET 1 0 0 1 32.706 298.968 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -298.968 cm BT /F22 8.2889 Tf 32.706 273.643 Td [(with)-250(respect)-250(to)-250(time)-250(and)-250(we)-250(have)]TJ ET 1 0 0 1 32.706 273.643 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -273.643 cm BT /F22 8.2889 Tf 33.902 257.932 Td [(d)]TJ/F41 8.2889 Tf 4.931 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.434 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ ET q 1 0 0 1 33.902 253.619 cm []0 d 0 J 0.44 w 0 0 m 24.615 0 l S Q BT /F22 8.2889 Tf 41.922 244.437 Td [(d)]TJ/F41 8.2889 Tf 4.932 0 Td [(t)]TJ/F179 9.5641 Tf 16.345 6.791 Td [(D)]TJ/F189 9.5641 Tf 10.947 7.69 Td [(\000)]TJ/F185 9.5641 Tf 3.854 -7.69 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F22 5.8022 Tf 4.344 3.95 Td [(0)]TJ/F185 9.5641 Tf 3.857 -3.95 Td [(/)]TJ/F185 6.6948 Tf 3.568 3.95 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\015)]TJ/F41 8.2889 Tf 6.331 0 Td [(y)]TJ/F22 5.8022 Tf 4.344 3.95 Td [(0)]TJ/F189 9.5641 Tf 3.857 3.74 Td [(\001)]TJ/F22 5.8022 Tf 3.855 -1.806 Td [(T)]TJ ET 1 0 0 1 32.706 251.228 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -251.228 cm BT /F179 9.5641 Tf 74.146 228.921 Td [(\002)]TJ/F189 9.5641 Tf 7.498 10.559 Td [(\020)]TJ/F179 9.5641 Tf 5.213 -10.559 Td [(\000)]TJ/F22 8.2889 Tf 7.46 0 Td [(diag)]TJ/F185 9.5641 Tf 16.204 0 Td [(.w)]TJ/F22 5.8022 Tf 10.884 3.95 Td [(0)]TJ/F185 9.5641 Tf 3.858 -3.95 Td [(/)]TJ/F41 8.2889 Tf 3.567 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F22 5.8022 Tf 5.031 3.95 Td [(0)]TJ/F185 9.5641 Tf 3.858 -3.95 Td [(/)]TJ/F179 9.5641 Tf 5.692 0 Td [(\000)]TJ/F22 8.2889 Tf 9.586 0 Td [(diag)]TJ/F185 9.5641 Tf 16.204 0 Td [(.!)]TJ/F22 5.8022 Tf 10.023 3.95 Td [(0)]TJ/F185 9.5641 Tf 3.858 -3.95 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(diag)]TJ/F185 9.5641 Tf 16.205 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(b)]TJ/F185 9.5641 Tf 4.501 0 Td [(/)]TJ/F189 9.5641 Tf 3.568 10.559 Td [(\021)]TJ ET 1 0 0 1 32.706 228.921 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -228.921 cm BT /F179 9.5641 Tf 74.146 210.251 Td [(\002)]TJ/F189 9.5641 Tf 7.498 7.689 Td [(\000)]TJ/F185 9.5641 Tf 3.855 -7.689 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F22 5.8022 Tf 4.343 3.95 Td [(0)]TJ/F185 9.5641 Tf 3.858 -3.95 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.95 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\015)]TJ/F41 8.2889 Tf 6.332 0 Td [(y)]TJ/F22 5.8022 Tf 4.343 3.95 Td [(0)]TJ/F189 9.5641 Tf 3.858 3.739 Td [(\001)]TJ/F185 9.5641 Tf 3.854 -7.689 Td [(:)]TJ ET 1 0 0 1 32.706 210.251 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -210.251 cm BT /F22 8.2889 Tf 44.661 193.081 Td [(Given)-257(initial)-257(state)]TJ/F41 8.2889 Tf 69.466 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F22 8.2889 Tf 3.567 0 Td [(0)]TJ/F185 9.5641 Tf 4.799 0 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(,)-257(with)-257(the)-257(same)-256(arguments)-257(as)-257(in)-257(the)-257(first)]TJ ET 1 0 0 1 32.706 193.081 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -193.081 cm BT /F22 8.2889 Tf 32.706 182.516 Td [(step,)-250(we)-250(can)-250(prove)-250(that)-250(there)-250(exists)]TJ/F41 8.2889 Tf 136.89 0 Td [(K)]TJ/F22 5.8022 Tf 5.106 -1.435 Td [(2)]TJ/F185 9.5641 Tf 6.514 1.435 Td [(>)]TJ/F22 8.2889 Tf 10.117 0 Td [(0)-250(such)]TJ ET 1 0 0 1 32.706 182.516 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -182.516 cm BT /F22 8.2889 Tf 33.902 166.805 Td [(d)]TJ/F41 8.2889 Tf 4.931 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ ET q 1 0 0 1 33.902 162.492 cm []0 d 0 J 0.44 w 0 0 m 24.615 0 l S Q BT /F22 8.2889 Tf 41.922 153.31 Td [(d)]TJ/F41 8.2889 Tf 4.932 0 Td [(t)]TJ/F179 9.5641 Tf 15.515 6.791 Td [(\024)-278(\000)]TJ/F41 8.2889 Tf 17.328 0 Td [(K)]TJ/F22 5.8022 Tf 5.106 -1.435 Td [(2)]TJ/F41 8.2889 Tf 3.857 1.435 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 4.9734 Tf 7.001 6.885 Td [(2)]TJ/F185 5.7385 Tf 2.88 0 Td [(\013)]TJ ET q 1 0 0 1 109.539 165.955 cm []0 d 0 J 0.308 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 109.539 161.677 Td [(1)]TJ/F179 5.7385 Tf 2.88 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ/F185 9.5641 Tf 5.2 -1.576 Td [(;)]TJ ET 1 0 0 1 32.706 160.101 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -160.101 cm BT /F22 8.2889 Tf 32.706 139.273 Td [(and)-220(thus)]TJ/F41 8.2889 Tf 34.683 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 5.388 0 Td [(will)-220(reach)-219(zero)-220(in)-220(finite)-219(time.)-220(Therefore,)-220(in)-219(this)-220(case,)]TJ ET 1 0 0 1 32.706 139.273 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -139.273 cm BT /F22 8.2889 Tf 32.706 128.708 Td [(the)-366(system)-365(solves)-366(a)-365(finite-time)-366(consensus)-365(problem)-366(and)-365(the)-366(final)]TJ ET 1 0 0 1 32.706 128.708 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -128.708 cm BT /F22 8.2889 Tf 32.706 118.142 Td [(state)-250(is)]TJ/F41 8.2889 Tf 28.862 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(n)]TJ/F22 8.2889 Tf 3.851 1.434 Td [(.)]TJ ET 1 0 0 1 32.706 118.142 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -118.142 cm BT /F41 8.2889 Tf 32.706 104.17 Td [(Step)]TJ/F22 8.2889 Tf 17.073 0 Td [(3:)-180(Finally,)-180(by)-180(induction)-179(we)-180(prove)-180(the)-180(correctness)-179(of)-180(the)-180(general)]TJ ET 1 0 0 1 32.706 104.17 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -104.17 cm BT /F22 8.2889 Tf 32.706 93.605 Td [(case,)-250(namely,)-250(the)-250(case)-250(when)]TJ/F181 8.9265 Tf 109.264 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 5.64 0 Td [(has)-250(a)-250(spanning)-250(tree.)]TJ ET 1 0 0 1 32.706 93.605 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -93.605 cm BT /F22 8.2889 Tf 44.661 82.831 Td [(Consider)-255(the)-254(directed)-255(graph)]TJ/F181 8.9265 Tf 108.198 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F22 8.2889 Tf 5.677 0 Td [(with)-255(the)-254(strongly)-255(connected)]TJ ET 1 0 0 1 32.706 82.831 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -82.831 cm BT /F22 8.2889 Tf 32.706 72.266 Td [(components)-185(of)]TJ/F181 8.9265 Tf 57.735 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 5.103 0 Td [(as)-185(its)-185(vertices.)]TJ/F181 8.9265 Tf 53.678 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.471 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.471 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 5.103 0 Td [(is)-185(defined)-185(in)-186(Section)]TJ ET 1 0 0 1 263.182 72.266 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -263.182 -72.266 cm BT /F22 8.2889 Tf 263.182 72.266 Td [(2)]TJ ET 1 0 0 1 267.981 72.266 cm 0 g 0 G 1 0 0 1 -267.981 -72.266 cm BT /F22 8.2889 Tf 269.516 72.266 Td [(and)]TJ ET 1 0 0 1 32.706 72.266 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -72.266 cm BT /F22 8.2889 Tf 32.706 61.7 Td [(by)-250(its)-250(definition,)]TJ/F181 8.9265 Tf 64.123 0 Td [(G)]TJ/F41 5.8022 Tf 5.73 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 5.64 0 Td [(contains)-250(only)-250(one)-250(root)-250(vertex.)]TJ ET 1 0 0 1 32.706 61.7 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -61.7 cm BT /F22 8.2889 Tf 44.661 50.926 Td [(\0501\051)-323(The)-324(dynamics)-323(of)-324(agents)-323(corresponding)-324(to)-323(the)-323(vertex)-324(set)-323(of)]TJ ET 1 0 0 1 32.706 50.926 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -50.926 cm BT /F22 8.2889 Tf 32.706 40.361 Td [(the)-242(root)-243(of)]TJ/F181 8.9265 Tf 41.854 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.471 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.471 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F22 8.2889 Tf 5.577 0 Td [(is)-242(not)-243(affected)-242(by)-243(others)-242(and)-243(by)-242(the)-243(conclusion)-242(of)]TJ ET 1 0 0 1 32.706 40.361 cm 0 g 0 G 0 g 0 G 1 0 0 1 260.025 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -292.731 -40.361 cm BT /F22 8.2889 Tf 301.697 720.809 Td [(the)-209(first)-208(step,)-208(the)-209(states)-208(of)-209(them)-208(will)-209(reach)-208(consensus)-209(in)-208(finite)-209(time.)]TJ ET 1 0 0 1 301.697 720.809 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -720.809 cm BT /F22 8.2889 Tf 301.697 710.57 Td [(Denote)-250(their)-250(final)-250(state)-250(by)]TJ/F41 8.2889 Tf 101.116 0 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.435 Td [(0)]TJ/F22 8.2889 Tf 3.857 1.435 Td [(.)]TJ ET 1 0 0 1 301.697 710.57 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -710.57 cm BT /F22 8.2889 Tf 313.653 700.773 Td [(\0502\051)-179(Consider)-179(the)-179(agents)-179(that)-179(constitute)-179(some)-179(strongly)-179(connected)]TJ ET 1 0 0 1 301.697 700.773 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -700.773 cm BT /F22 8.2889 Tf 301.697 690.534 Td [(component)-314(of)-313(the)-314(interaction)-314(topology)]TJ/F181 8.9265 Tf 152.031 0 Td [(G)]TJ/F22 8.2889 Tf 5.731 0 Td [(,)-314(but)-314(not)-313(the)-314(root)-314(vertex)]TJ ET 1 0 0 1 301.697 690.534 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -690.534 cm BT /F22 8.2889 Tf 301.697 680.294 Td [(of)]TJ/F181 8.9265 Tf 10.395 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(.)-355(Obviously,)-354(their)-354(dynamics)-354(is)-354(only)-354(affected)-354(by)-354(the)-354(other)]TJ ET 1 0 0 1 301.697 680.294 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -680.294 cm BT /F22 8.2889 Tf 301.697 670.055 Td [(agents)-312(that)-312(can)-312(be)-311(connected)-312(to)-312(them)-312(by)-312(paths.)-312(Suppose)-312(that)-312(the)]TJ ET 1 0 0 1 301.697 670.055 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -670.055 cm BT /F22 8.2889 Tf 301.697 659.815 Td [(states)-211(of)-211(the)-211(``affecting'')-211(agents)-211(have)-211(already)-211(reached)-211(an)-211(agreement)]TJ ET 1 0 0 1 301.697 659.815 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -659.815 cm BT /F22 8.2889 Tf 301.697 649.576 Td [(and)-186(maintain)-186(their)-186(current)-186(values)-186(as)-186(time)-186(evolves.)-186(Suppose)-186(that)-186(the)]TJ ET 1 0 0 1 301.697 649.576 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -649.576 cm BT /F22 8.2889 Tf 301.697 639.337 Td [(common)-229(state)-229(is)-230(also)]TJ/F41 8.2889 Tf 81.246 0 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.435 Td [(0)]TJ/F22 8.2889 Tf 5.757 1.435 Td [(and)-229(denote)-229(the)-230(index)-229(set)-229(of)-229(the)-229(``affecting'')]TJ ET 1 0 0 1 301.697 639.337 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -639.337 cm BT /F22 8.2889 Tf 301.697 629.097 Td [(agents)-246(by)]TJ/F181 8.9265 Tf 38.369 0 Td [(L)]TJ/F22 8.2889 Tf 7.231 0 Td [(.)-245(Consider)-246(the)-245(dynamics)-246(of)-245(``affected'')-246(agent)]TJ/F41 8.2889 Tf 165.905 0 Td [(i)]TJ/F22 8.2889 Tf 2.37 0 Td [(.)-246(We)-245(have)]TJ ET 1 0 0 1 301.697 629.097 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -629.097 cm BT /F41 8.2889 Tf 301.697 606.01 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.434 Td [(i)]TJ/F179 9.5641 Tf 5.645 1.434 Td [(D)]TJ/F185 9.5641 Tf 10.947 0 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F189 9.5641 Tf 10.676 13.428 Td [(\022)]TJ 10.263 -4.342 Td [(X)]TJ/F41 5.8022 Tf -3.807 -19.555 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F179 6.6948 Tf 1.921 1.352 Td [(n)]TJ/F181 6.2485 Tf 3.246 0 Td [(L)]TJ/F41 8.2889 Tf 6.656 10.469 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.434 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.434 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(/)]TJ/F179 9.5641 Tf 5.692 0 Td [(C)]TJ/F189 9.5641 Tf 9.586 13.428 Td [(\022)]TJ 10.875 -4.342 Td [(X)]TJ/F41 5.8022 Tf -4.419 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.676 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F179 6.6948 Tf 1.921 1.352 Td [(\134)]TJ/F181 6.2485 Tf 4.472 0 Td [(L)]TJ/F41 8.2889 Tf 6.655 10.456 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.434 Td [(ij)]TJ/F189 9.5641 Tf 3.834 14.862 Td [(\023)]TJ/F185 9.5641 Tf 6.456 -13.428 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.434 Td [(0)]TJ/F179 9.5641 Tf 5.983 1.434 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(/)]TJ/F189 9.5641 Tf 3.567 13.428 Td [(\023)]TJ/F185 6.6948 Tf 6.456 -1.566 Td [(\013)]TJ ET 1 0 0 1 301.697 606.01 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -606.01 cm BT /F179 9.5641 Tf 323.08 574.65 Td [(C)]TJ/F185 9.5641 Tf 9.054 0 Td [(\015)]TJ/F189 9.5641 Tf 6.331 13.428 Td [(\022)]TJ 10.263 -4.342 Td [(X)]TJ/F41 5.8022 Tf -3.807 -19.555 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.353 Td [(i)]TJ/F179 6.6948 Tf 1.92 1.353 Td [(n)]TJ/F181 6.2485 Tf 3.247 0 Td [(L)]TJ/F41 8.2889 Tf 6.656 10.469 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.434 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.434 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(/)]TJ/F179 9.5641 Tf 5.692 0 Td [(C)]TJ/F189 9.5641 Tf 9.586 13.428 Td [(\022)]TJ 10.875 -4.342 Td [(X)]TJ/F41 5.8022 Tf -4.42 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F179 6.6948 Tf 1.921 1.352 Td [(\134)]TJ/F181 6.2485 Tf 4.472 0 Td [(L)]TJ/F41 8.2889 Tf 6.655 10.456 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.434 Td [(ij)]TJ/F189 9.5641 Tf 3.834 14.862 Td [(\023)]TJ/F185 9.5641 Tf 6.456 -13.428 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.434 Td [(0)]TJ/F179 9.5641 Tf 5.983 1.434 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(/)]TJ/F189 9.5641 Tf 3.567 13.428 Td [(\023)]TJ/F185 9.5641 Tf 6.456 -13.428 Td [(:)]TJ ET 1 0 0 1 301.697 574.65 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -574.65 cm BT /F22 8.2889 Tf 301.697 548.829 Td [(By)-284(the)-283(above)-284(expression,)-283(for)-284(the)-283(``affected'')-284(agents,)-283(the)-284(``affecting'')]TJ ET 1 0 0 1 301.697 548.829 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -548.829 cm BT /F22 8.2889 Tf 301.697 538.589 Td [(agents,)-341(as)-341(a)-341(whole,)-341(can)-341(be)-341(seen)-341(as)-341(one)-340(virtual)-341(agent.)-342(By)-341(the)-341(con-)]TJ ET 1 0 0 1 301.697 538.589 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -538.589 cm BT /F22 8.2889 Tf 301.697 528.35 Td [(clusion)-289(obtained)-290(in)-289(the)-289(second)-290(step,)-289(the)-290(states)-289(of)-289(those)-290(``affected'')]TJ ET 1 0 0 1 301.697 528.35 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -528.35 cm BT /F22 8.2889 Tf 301.697 518.111 Td [(agents)-398(will)-397(reach)-398(consensus)-397(in)-398(finite)-397(time)-398(and)-397(the)-398(final)-397(state)-398(of)]TJ ET 1 0 0 1 301.697 518.111 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -518.111 cm BT /F22 8.2889 Tf 301.697 507.871 Td [(them)-250(is)]TJ/F41 8.2889 Tf 30.487 0 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.434 Td [(0)]TJ/F22 8.2889 Tf 3.857 1.434 Td [(.)]TJ ET 1 0 0 1 301.697 507.871 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -507.871 cm BT /F22 8.2889 Tf 313.653 498.075 Td [(\0503\051)-507(With)-506(the)-507(above)-507(conclusions)-506(and)-507(by)-507(the)-506(fact)-507(that)]TJ/F181 8.9265 Tf 217.688 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.471 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.471 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ ET 1 0 0 1 301.697 498.075 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -498.075 cm BT /F22 8.2889 Tf 301.697 487.835 Td [(has)-406(no)-406(loop,)-406(we)-406(can)-406(employ)-406(the)-406(mathematical)-406(induction)-406(to)-406(de-)]TJ ET 1 0 0 1 301.697 487.835 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -487.835 cm BT /F22 8.2889 Tf 301.697 477.596 Td [(rive)-264(the)-263(conclusion)-264(that)-264(the)-263(system)-264(solves)-263(a)-264(finite-time)-264(consensus)]TJ ET 1 0 0 1 301.697 477.596 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -477.596 cm BT /F22 8.2889 Tf 301.697 467.356 Td [(problem.)]TJ/F166 7.9701 Tf 44.686 0 Td [(\004)]TJ ET 1 0 0 1 301.697 467.356 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -19.349 cm 0 g 0 G 1 0 0 1 -297.712 -448.007 cm BT /F153 8.2889 Tf 301.697 448.007 Td [(Remark.)]TJ ET 1 0 0 1 335.392 448.007 cm 0 g 0 G 1 0 0 1 -335.392 -448.007 cm BT /F22 8.2889 Tf 339.377 448.007 Td [(The)-631(convergence)-631(rate)-631(of)-631(the)-631(proposed)-631(algorithm)-631(is)]TJ ET 1 0 0 1 301.697 448.007 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -448.007 cm BT /F22 8.2889 Tf 301.697 437.768 Td [(closely)-353(related)-354(to)-353(the)-353(interaction)-354(topology)-353(and)-353(protocol)-354(parame-)]TJ ET 1 0 0 1 301.697 437.768 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -437.768 cm BT /F22 8.2889 Tf 301.697 427.529 Td [(ter)]TJ/F185 9.5641 Tf 14.144 0 Td [(\013)]TJ/F22 8.2889 Tf 5.844 0 Td [(.)-398(Especially,)-398(in)-397(the)-398(bidirectional)-397(interaction)-397(case,)-398(i.e.,)-397(when)]TJ ET 1 0 0 1 301.697 427.529 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -427.529 cm BT /F41 8.2889 Tf 301.697 417.289 Td [(A)]TJ/F22 5.8022 Tf 5.032 3.472 Td [(T)]TJ/F179 9.5641 Tf 8.49 -3.472 Td [(D)]TJ/F41 8.2889 Tf 12.215 0 Td [(A)]TJ/F22 8.2889 Tf 5.031 0 Td [(,)-349(we)-349(can)-348(show)-349(that)-349(larger)-348(algebraic)-349(connectivity)-349(of)]TJ/F181 8.9265 Tf 200.454 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)]TJ ET 1 0 0 1 301.697 417.289 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -417.289 cm BT /F22 8.2889 Tf 301.697 407.05 Td [(namely,)-204(the)-204(second)-203(smallest)-204(eigenvalue)-204(of)]TJ/F41 8.2889 Tf 160.18 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)-204(will)-204(lead)-203(to)-204(shorter)]TJ ET 1 0 0 1 301.697 407.05 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -407.05 cm BT /F22 8.2889 Tf 301.697 396.81 Td [(convergence)-290(time)-290(and)-290(we)-291(also)-290(can)-290(shown)-290(that)-290(smaller)]TJ/F185 9.5641 Tf 211.054 0 Td [(\013)]TJ/F22 8.2889 Tf 8.249 0 Td [(can)-290(lead)]TJ ET 1 0 0 1 301.697 396.81 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -396.81 cm BT /F22 8.2889 Tf 301.697 386.571 Td [(to)-205(a)-206(higher)-205(convergence)-205(rate)-206(when)-205(agents')-205(states)-206(differ)-205(a)-205(little)-206(from)]TJ ET 1 0 0 1 301.697 386.571 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -386.571 cm BT /F22 8.2889 Tf 301.697 376.332 Td [(each)-426(other,)-427(and)-426(larger)]TJ/F185 9.5641 Tf 90.966 0 Td [(\013)]TJ/F22 8.2889 Tf 9.377 0 Td [(can)-426(lead)-427(to)-426(a)-426(higher)-427(convergence)-426(rate)]TJ ET 1 0 0 1 301.697 376.332 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -376.332 cm BT /F22 8.2889 Tf 301.697 366.092 Td [(when)-214(agents)-214(states)-214(differ)-213(a)-214(lot)-214(from)-214(each)-214(other.)-214(Moreover,)-214(by)-214(some)]TJ ET 1 0 0 1 301.697 366.092 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -366.092 cm BT /F22 8.2889 Tf 301.697 355.853 Td [(straightforward)-222(arguments,)-223(it)-222(can)-223(be)-222(shown)-222(that)-223(the)-222(system)-223(under)]TJ ET 1 0 0 1 301.697 355.853 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -355.853 cm BT /F22 8.2889 Tf 301.697 345.613 Td [(protocol)]TJ ET 1 0 0 1 336.411 345.613 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -336.411 -345.613 cm BT /F22 8.2889 Tf 336.411 345.613 Td [(\0502\051)]TJ ET 1 0 0 1 347.336 345.613 cm 0 g 0 G 1 0 0 1 -347.336 -345.613 cm BT /F22 8.2889 Tf 350.054 345.613 Td [(converges)-328(faster)-328(to)-328(some)-328(extent)-328(than)-328(that)-328(under)-328(the)]TJ ET 1 0 0 1 301.697 345.613 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -345.613 cm BT /F22 8.2889 Tf 301.697 335.374 Td [(linear)-250(counterpart)-250(of)-250(protocol)]TJ ET 1 0 0 1 416.746 335.374 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -416.746 -335.374 cm BT /F22 8.2889 Tf 416.746 335.374 Td [(\0502\051)]TJ ET 1 0 0 1 427.671 335.374 cm 0 g 0 G 1 0 0 1 -427.671 -335.374 cm BT /F22 8.2889 Tf 427.671 335.374 Td [(.)]TJ ET 1 0 0 1 301.697 335.374 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -335.374 cm BT /F22 8.2889 Tf 313.653 320.153 Td [(We)-322(present)-322(the)-321(following)-322(corollary)-322(and)-322(omit)-322(the)-321(proof)-322(details)]TJ ET 1 0 0 1 301.697 320.153 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -320.153 cm BT /F22 8.2889 Tf 301.697 309.914 Td [(due)-250(to)-250(the)-250(limit)-250(of)-250(paper)-250(length.)]TJ ET 1 0 0 1 301.697 309.914 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -18.907 cm 0 g 0 G 1 0 0 1 -297.712 -291.007 cm BT /F153 8.2889 Tf 301.697 291.007 Td [(Corollary)-250(4.)]TJ ET 1 0 0 1 347.684 291.007 cm 0 g 0 G 1 0 0 1 -347.684 -291.007 cm BT /F41 8.2889 Tf 351.669 291.007 Td [(Consider)-196(system)]TJ ET 1 0 0 1 411.729 291.007 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -411.729 -291.007 cm BT /F22 8.2889 Tf 411.729 291.007 Td [(\0501\051)]TJ ET 1 0 0 1 422.654 291.007 cm 0 g 0 G 1 0 0 1 -422.654 -291.007 cm BT /F41 8.2889 Tf 424.282 291.007 Td [(under)-196(protocol)]TJ ET 1 0 0 1 479.087 291.007 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -479.087 -291.007 cm BT /F22 8.2889 Tf 479.087 291.007 Td [(\0502\051)]TJ ET 1 0 0 1 490.012 291.007 cm 0 g 0 G 1 0 0 1 -490.012 -291.007 cm BT /F41 8.2889 Tf 490.012 291.007 Td [(.)-197(Given)-196(any)-197(initial)]TJ ET 1 0 0 1 301.697 291.007 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -291.007 cm BT /F41 8.2889 Tf 301.697 280.768 Td [(states,)-362(there)-362(exists)-362(a)-362(finite)-362(time,)-362(after)-362(which)-363(the)-362(states)-362(of)-362(all)-362(agents)]TJ ET 1 0 0 1 301.697 280.768 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -280.768 cm BT /F41 8.2889 Tf 301.697 270.529 Td [(will)-278(remain)-278(constant,)-278(and)-278(the)-278(state)-278(of)-278(each)-278(agent)-279(wil)1(l)-279(reach)-278(a)-278(convex)]TJ ET 1 0 0 1 301.697 270.529 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -270.529 cm BT /F41 8.2889 Tf 301.697 260.289 Td [(combination)-250(of)-250(its)-250(neighbors')-250(states.)-250(More)-250(explicitly,)]TJ ET 1 0 0 1 301.697 260.289 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -260.289 cm BT /F41 8.2889 Tf 301.697 229.899 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F179 9.5641 Tf 4.814 1.434 Td [(D)]TJ/F189 9.5641 Tf 12.735 22.107 Td [(P)]TJ/F41 5.8022 Tf -1.422 -15.716 Td [(j)]TJ/F179 6.6948 Tf 1.676 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F41 8.2889 Tf 3.515 9.895 Td [(W)]TJ/F41 5.8022 Tf 8.131 -1.435 Td [(ij)]TJ/F41 8.2889 Tf 3.835 1.435 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ ET q 1 0 0 1 321.894 232.291 cm []0 d 0 J 0.44 w 0 0 m 32.643 0 l S Q BT /F189 9.5641 Tf 326.438 230.282 Td [(P)]TJ/F41 5.8022 Tf -1.422 -15.716 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.352 Td [(i)]TJ/F41 8.2889 Tf 3.514 9.895 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 8.152 8.225 Td [(;)]TJ/F41 8.2889 Tf 13.049 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.434 Td [(n)]TJ/F185 9.5641 Tf 3.852 1.434 Td [(:)]TJ ET 1 0 0 1 301.697 229.899 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -229.899 cm BT /F41 8.2889 Tf 301.697 186.148 Td [(4.2.)-500(Time-invariant)-250(formation)]TJ ET 1 0 0 1 301.697 186.148 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -186.148 cm BT /F22 8.2889 Tf 313.653 166.001 Td [(In)-243(this)-242(subsection,)-243(we)-242(first)-243(assume)-242(that)-243(the)-243(expected)-242(formation)]TJ ET 1 0 0 1 301.697 166.001 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -166.001 cm BT /F185 9.5641 Tf 301.697 155.762 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.675 0 Td [(;)]TJ/F41 8.2889 Tf 4.759 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F22 8.2889 Tf 5.263 0 Td [(is)-205(tim)1(e-invariant)-205(and)-205(make)-204(the)-205(following)-204(assumptions)-205(about)]TJ ET 1 0 0 1 301.697 155.762 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -155.762 cm BT /F22 8.2889 Tf 301.697 145.522 Td [(the)-250(multi-agent)-250(system:)]TJ ET 1 0 0 1 301.697 145.522 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -13.892 cm 0 g 0 G 1 0 0 1 -301.697 -131.63 cm BT /F22 8.2889 Tf 301.697 131.63 Td [(\050A1\051)]TJ ET 1 0 0 1 318.093 131.63 cm 0 g 0 G 1 0 0 1 -318.093 -131.63 cm BT /F22 8.2889 Tf 322.078 131.63 Td [(the)-621(local)-622(interaction)-621(topology)-621(among)-622(the)-621(leaders)-621(has)-622(a)]TJ ET 1 0 0 1 301.697 131.63 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -131.63 cm BT /F22 8.2889 Tf 322.078 121.39 Td [(spanning)-197(tree)-197(and)-197(the)-197(leaders')-196(dynamics)-197(is)-197(not)-197(affected)-197(by)-197(the)]TJ ET 1 0 0 1 301.697 121.39 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -121.39 cm BT /F22 8.2889 Tf 322.078 111.151 Td [(followers;)]TJ ET 1 0 0 1 301.697 111.151 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.797 cm 0 g 0 G 1 0 0 1 -301.697 -101.354 cm BT /F22 8.2889 Tf 301.697 101.354 Td [(\050A2\051)]TJ ET 1 0 0 1 318.093 101.354 cm 0 g 0 G 1 0 0 1 -318.093 -101.354 cm BT /F22 8.2889 Tf 322.078 101.354 Td [(the)-456(neighbors)-456(of)-456(follower)]TJ/F41 8.2889 Tf 105.026 0 Td [(i)]TJ/F22 8.2889 Tf 2.371 0 Td [(,)]TJ/F41 8.2889 Tf 5.721 0 Td [(i)]TJ/F179 9.5641 Tf 9.404 0 Td [(2)-735(f)]TJ/F41 8.2889 Tf 16.589 0 Td [(m)]TJ/F179 9.5641 Tf 11.037 0 Td [(C)]TJ/F22 8.2889 Tf 11.337 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(m)]TJ/F179 9.5641 Tf 11.037 0 Td [(C)]TJ/F22 8.2889 Tf 11.337 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F179 9.5641 Tf 4.791 0 Td [(g)]TJ/F22 8.2889 Tf 3.538 0 Td [(,)]TJ ET 1 0 0 1 301.697 101.354 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -101.354 cm BT /F22 8.2889 Tf 322.078 91.115 Td [(should)-297(inclu)1(de)-297(all)-297(such)-296(agent)]TJ/F41 8.2889 Tf 114.517 0 Td [(j)]TJ/F22 8.2889 Tf 4.853 0 Td [(that)-297(the)]TJ/F41 8.2889 Tf 32.891 0 Td [(j)]TJ/F22 8.2889 Tf 2.396 0 Td [(th)-297(entry)-296(of)-297(vector)]TJ/F41 8.2889 Tf 69.835 0 Td [(F)]TJ/F41 5.8022 Tf 4.028 -1.435 Td [(i)]TJ ET 1 0 0 1 301.697 91.115 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 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[(h)]TJ/F185 9.5641 Tf 4.675 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F22 8.2889 Tf 7.321 0 Td [(if)]TJ ET 1 0 0 1 42.52 691.154 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -691.154 cm BT /F22 8.2889 Tf 57.429 681.038 Td [(there)-461(exists)-462(a)]TJ/F169 8.6077 Tf 57.934 0 Td [(R)]TJ/F41 5.8022 Tf 6.216 3.472 Td [(N)]TJ/F22 8.2889 Tf 5.085 -3.472 Td [(-valued)-461(function)]TJ/F41 8.2889 Tf 68.631 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 7.392 0 Td [(such)-461(that)]TJ/F41 8.2889 Tf 40.822 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.642 0 Td [(/)]TJ/F179 9.5641 Tf 10.718 0 Td [(!)]TJ ET 1 0 0 1 42.52 681.038 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -681.038 cm BT /F41 8.2889 Tf 57.429 670.923 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 7.271 0 Td [(C)]TJ/F41 8.2889 Tf 11.164 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/;)]TJ/F41 8.2889 Tf 8.327 0 Td [(i)]TJ/F179 9.5641 Tf 8.973 0 Td [(2)]TJ/F181 8.9265 Tf 12.619 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.435 Td [(m)]TJ/F22 8.2889 Tf 5.511 1.435 Td [(,)-436(and)]TJ/F41 8.2889 Tf 23.412 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 10.17 0 Td [(!)]TJ/F185 9.5641 Tf 17.114 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(F)]TJ/F41 5.8022 Tf 4.029 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.642 0 Td [(/)]TJ/F179 9.5641 Tf 7.272 0 Td [(\012)]TJ/F41 8.2889 Tf 11.355 0 Td [(I)]TJ/F41 5.8022 Tf 2.495 -1.435 Td [(N)]TJ/F185 9.5641 Tf 5.084 1.435 Td [(/)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)]TJ/F41 8.2889 Tf 5.553 0 Td [(i)]TJ/F179 9.5641 Tf 8.973 0 Td [(D)]TJ ET 1 0 0 1 42.52 670.923 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -670.923 cm BT /F41 8.2889 Tf 57.429 660.808 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.586 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F22 8.2889 Tf 4.791 0 Td [(,)-250(as)]TJ/F41 8.2889 Tf 14.074 0 Td [(t)]TJ/F179 9.5641 Tf 6.3 0 Td [(!)-278(1)]TJ/F22 8.2889 Tf 22.932 0 Td [(;)]TJ ET 1 0 0 1 42.52 660.808 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.425 cm 0 g 0 G 1 0 0 1 -42.52 -651.383 cm BT /F22 8.2889 Tf 42.52 651.383 Td [(\0503\051)]TJ ET 1 0 0 1 53.444 651.383 cm 0 g 0 G 1 0 0 1 -53.444 -651.383 cm BT /F22 8.2889 Tf 57.429 651.383 Td [(the)]TJ/F41 8.2889 Tf 15.152 0 Td [(n)]TJ/F22 8.2889 Tf 7.468 0 Td [(agents)-323(will)-323(be)-323(in)-323(formation)]TJ/F185 9.5641 Tf 107.712 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(h)]TJ/F185 9.5641 Tf 4.675 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.043 0 Td [(/)]TJ/F22 8.2889 Tf 6.245 0 Td [(in)-323(finite)-323(time)-323(if)-323(there)]TJ ET 1 0 0 1 42.52 651.383 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -651.383 cm BT /F22 8.2889 Tf 57.429 641.268 Td [(exist)-365(time)]TJ/F41 8.2889 Tf 41.91 0 Td [(t)]TJ/F179 6.6948 Tf 3.642 3.472 Td [(\003)]TJ/F185 9.5641 Tf 9.088 -3.472 Td [(>)]TJ/F22 8.2889 Tf 12.562 0 Td [(0)-365(and)-365(a)]TJ/F169 8.6077 Tf 32.419 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(N)]TJ/F22 8.2889 Tf 5.084 -3.472 Td [(-valued)-365(function)]TJ/F41 8.2889 Tf 67.033 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 6.593 0 Td [(such)-365(that)]TJ ET 1 0 0 1 42.52 641.268 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -641.268 cm BT /F41 8.2889 Tf 57.429 631.152 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 8.431 0 Td [(D)]TJ/F41 8.2889 Tf 12.324 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.576 0 Td [(C)]TJ/F41 8.2889 Tf 10.468 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/;)]TJ/F41 8.2889 Tf 8.327 0 Td [(i)]TJ/F179 9.5641 Tf 7.235 0 Td [(2)]TJ/F181 8.9265 Tf 10.879 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.434 Td [(m)]TJ/F22 8.2889 Tf 5.511 1.434 Td [(,)-354(and)]TJ/F41 8.2889 Tf 22.055 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 8.431 0 Td [(D)]TJ/F185 9.5641 Tf 12.324 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(F)]TJ/F41 5.8022 Tf 4.028 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.575 0 Td [(\012)]TJ/F41 8.2889 Tf 10.66 0 Td [(I)]TJ/F41 5.8022 Tf 2.495 -1.434 Td [(N)]TJ/F185 9.5641 Tf 5.085 1.434 Td [(/)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(,)]TJ ET 1 0 0 1 42.52 631.152 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -631.152 cm BT /F41 8.2889 Tf 57.429 621.037 Td [(i)]TJ/F179 9.5641 Tf 5.028 0 Td [(D)]TJ/F41 8.2889 Tf 10.116 0 Td [(m)]TJ/F179 9.5641 Tf 9.287 0 Td [(C)]TJ/F22 8.2889 Tf 9.586 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(n)]TJ/F22 8.2889 Tf 4.791 0 Td [(,)-250(for)-250(all)]TJ/F41 8.2889 Tf 28.264 0 Td [(t)]TJ/F179 9.5641 Tf 6.3 0 Td [(\025)]TJ/F41 8.2889 Tf 9.868 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.472 Td [(\003)]TJ/F22 8.2889 Tf 3.986 -3.472 Td [(.)]TJ ET 1 0 0 1 42.52 621.037 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -621.037 cm BT /F22 8.2889 Tf 42.52 608.013 Td [(In)-316(the)-315(above)-316(three)-315(cases,)-316(the)-315(first)]TJ/F41 8.2889 Tf 131.121 0 Td [(m)]TJ/F22 8.2889 Tf 9.777 0 Td [(agents)-316(ar)1(e)-316(called)]TJ/F41 8.2889 Tf 67.369 0 Td [(leaders)]TJ/F22 8.2889 Tf 28.543 0 Td [(and)]TJ ET 1 0 0 1 42.52 608.013 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -608.013 cm BT /F22 8.2889 Tf 42.52 597.898 Td [(the)-250(rest)-250(are)-250(called)]TJ/F41 8.2889 Tf 69.875 0 Td [(followers)]TJ/F22 8.2889 Tf 33.196 0 Td [(.)]TJ ET 1 0 0 1 42.52 597.898 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -597.898 cm BT /F22 8.2889 Tf 54.475 583.359 Td [(In)-475(formation)]TJ/F185 9.5641 Tf 53.602 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(h)]TJ/F185 9.5641 Tf 4.675 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.043 0 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(,)-475(vector)]TJ/F41 8.2889 Tf 33.826 0 Td [(h)]TJ/F22 8.2889 Tf 8.611 0 Td [(defines)-475(the)-475(basic)-475(frame)-474(of)-475(the)]TJ ET 1 0 0 1 42.52 583.359 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -583.359 cm BT /F22 8.2889 Tf 42.52 573.244 Td [(expected)-456(formation)-456(formed)-455(by)-456(leaders)-456(and)-456(nonnegative)-456(matrix)]TJ ET 1 0 0 1 42.52 573.244 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -573.244 cm BT /F41 8.2889 Tf 42.52 563.128 Td [(F)]TJ/F22 8.2889 Tf 8.423 0 Td [(specifies)-408(the)-408(local)-407(position-restrictions)-408(of)-408(followers)-408(related)-407(to)]TJ ET 1 0 0 1 42.52 563.128 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -563.128 cm BT /F22 8.2889 Tf 42.52 553.013 Td [(their)-418(neighbors,)-418(in)-417(other)-418(words,)-418(matrix)]TJ/F41 8.2889 Tf 158.482 0 Td [(F)]TJ/F22 8.2889 Tf 8.506 0 Td [(determines)-418(the)-418(space)]TJ ET 1 0 0 1 42.52 553.013 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -553.013 cm BT /F22 8.2889 Tf 42.52 542.898 Td [(distribution)-407(of)-408(followers.)-408(Since)-407(each)-407(row)-408(entry)-407(sum)-407(of)]TJ/F41 8.2889 Tf 217.971 0 Td [(F)]TJ/F22 8.2889 Tf 8.42 0 Td [(equals)]TJ ET 1 0 0 1 42.52 542.898 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -542.898 cm BT /F22 8.2889 Tf 42.52 532.782 Td [(1,)-528(followers)-528(in)-529(the)-528(formation)-528(should)-528(lie)-528(in)-528(the)-528(convex)-529(region)]TJ ET 1 0 0 1 42.52 532.782 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -532.782 cm BT /F22 8.2889 Tf 42.52 522.667 Td [(covered)-394(by)-394(leaders.)-394(Column)-394(vector)]TJ/F41 8.2889 Tf 139.218 0 Td [(h)]TJ/F41 5.8022 Tf 4.675 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.518 -3.472 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 6.832 0 Td [(decides)-394(the)-394(position)-393(of)]TJ ET 1 0 0 1 42.52 522.667 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -522.667 cm BT /F22 8.2889 Tf 42.52 512.551 Td [(the)-344(formation)-345(and)-344(may)-345(be)-344(dependent)-344(on)-345(initial)-344(states)-345(or)-344(may)-345(be)]TJ ET 1 0 0 1 42.52 512.551 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -512.551 cm BT /F22 8.2889 Tf 42.52 502.436 Td [(an)-369(external)-370(input,)-369(used)-370(to)-369(guide)-370(the)-369(group)-370(of)-369(agents)-370(to)-369(track)-370(an)]TJ ET 1 0 0 1 42.52 502.436 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -502.436 cm BT /F22 8.2889 Tf 42.52 492.321 Td [(anticipated)-250(trajectory.)]TJ ET 1 0 0 1 42.52 492.321 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -492.321 cm BT /F153 8.2889 Tf 42.52 471.398 Td [(4.)-500(Main)-250(results)]TJ ET 1 0 0 1 42.52 471.398 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -471.398 cm BT /F41 8.2889 Tf 42.52 452.031 Td [(4.1.)-500(Finite-time)-250(consensus)]TJ ET 1 0 0 1 42.52 452.031 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -452.031 cm BT /F22 8.2889 Tf 54.475 432.318 Td [(Before)-319(presenting)-318(the)-319(control)-318(strategies)-319(for)-319(finite-time)-318(forma-)]TJ ET 1 0 0 1 42.52 432.318 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -432.318 cm BT /F22 8.2889 Tf 42.52 422.203 Td [(tion,)-337(we)-336(study)-337(the)-336(simplest)-337(case)-337(of)-336(the)-337(formation)]TJ/F185 9.5641 Tf 194.394 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(h)]TJ/F185 9.5641 Tf 4.674 0 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(F)]TJ/F185 9.5641 Tf 5.044 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)-337(namely,)]TJ ET 1 0 0 1 42.52 422.203 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -422.203 cm BT /F22 8.2889 Tf 42.52 412.087 Td [(agreement)-312(over)-313(the)-312(location)-313(of)-312(agents)-313(or)-312(rendezvous)-313(problem.)-313(In)]TJ ET 1 0 0 1 42.52 412.087 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -412.087 cm BT /F22 8.2889 Tf 42.52 401.972 Td [(this)-250(case,)]TJ/F41 8.2889 Tf 36.703 0 Td [(h)]TJ/F22 5.8022 Tf 4.675 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F41 8.2889 Tf 10.116 0 Td [(h)]TJ/F22 5.8022 Tf 4.675 -1.434 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)-278(\001)-166(\001)-167(\001)-278(D)]TJ/F41 8.2889 Tf 34.055 0 Td [(h)]TJ/F41 5.8022 Tf 4.674 -1.434 Td [(m)]TJ/F185 9.5641 Tf 5.512 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 5.64 0 Td [(and)]TJ/F41 8.2889 Tf 16.32 0 Td [(m)]TJ/F179 9.5641 Tf 9.819 0 Td [(D)]TJ/F41 8.2889 Tf 10.116 0 Td [(n)]TJ/F22 8.2889 Tf 4.791 0 Td [(.)]TJ ET 1 0 0 1 42.52 401.972 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -401.972 cm BT /F22 8.2889 Tf 54.475 392.029 Td [(Given)-328(protocol)]TJ/F41 8.2889 Tf 59.628 0 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(;)]TJ/F41 8.2889 Tf 4.759 0 Td [(i)]TJ/F179 9.5641 Tf 6.684 0 Td [(2)]TJ/F181 8.9265 Tf 10.328 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.435 Td [(n)]TJ/F22 8.2889 Tf 3.851 1.435 Td [(,)]TJ/F41 8.2889 Tf 4.659 0 Td [(u)]TJ/F41 5.8022 Tf 4.79 -1.435 Td [(i)]TJ/F22 8.2889 Tf 4.876 1.435 Td [(or)-328(this)-328(multi-agent)-328(system)]TJ/F41 8.2889 Tf 105.729 0 Td [(solves)]TJ ET 1 0 0 1 42.52 392.029 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -392.029 cm BT /F41 8.2889 Tf 42.52 381.914 Td [(a)-395(consensus)-394(problem)-395(asymptotically)]TJ/F22 8.2889 Tf 137.983 0 Td [(if)-395(for)-395(any)-394(initial)-395(states,)-395(there)]TJ ET 1 0 0 1 42.52 381.914 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -381.914 cm BT /F22 8.2889 Tf 42.52 371.799 Td [(exists)-423(an)-424(as)1(ymptotically)-424(stable)-423(equilibrium)]TJ/F41 8.2889 Tf 172.817 0 Td [(x)]TJ/F179 6.6948 Tf 4.07 3.472 Td [(\003)]TJ/F179 9.5641 Tf 10.326 -3.472 Td [(2)]TJ/F169 8.6077 Tf 12.355 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(N)]TJ/F22 8.2889 Tf 8.593 -3.472 Td [(such)-423(that)]TJ ET 1 0 0 1 42.52 371.799 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -371.799 cm BT /F41 8.2889 Tf 42.52 361.683 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 8.876 0 Td [(!)]TJ/F41 8.2889 Tf 15.82 0 Td [(x)]TJ/F179 6.6948 Tf 4.07 3.472 Td [(\003)]TJ/F22 8.2889 Tf 7.092 -3.472 Td [(as)]TJ/F41 8.2889 Tf 11.097 0 Td [(t)]TJ/F179 9.5641 Tf 8.951 0 Td [(!)-555(1)]TJ/F22 8.2889 Tf 28.691 0 Td [(for)-375(any)]TJ/F41 8.2889 Tf 30.93 0 Td [(i)]TJ/F179 9.5641 Tf 7.68 0 Td [(2)]TJ/F181 8.9265 Tf 11.324 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.434 Td [(n)]TJ/F22 8.2889 Tf 6.958 1.434 Td [(\050)]TJ ET 1 0 0 1 205.646 361.683 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -205.646 -361.683 cm BT /F22 8.2889 Tf 205.646 361.683 Td [(Olfati-Saber)]TJ ET 1 0 0 1 251.309 361.683 cm 0 g 0 G 1 0 0 1 3.106 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -254.415 -361.683 cm BT /F22 8.2889 Tf 254.415 361.683 Td [(&)]TJ ET 1 0 0 1 260.176 361.683 cm 0 g 0 G 1 0 0 1 3.106 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -263.282 -361.683 cm BT /F22 8.2889 Tf 263.282 361.683 Td [(Murray,)]TJ ET 1 0 0 1 293.578 361.683 cm 0 g 0 G 1 0 0 1 -251.058 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.115 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -42.52 -351.568 cm BT /F22 8.2889 Tf 42.52 351.568 Td [(2004)]TJ ET 1 0 0 1 61.717 351.568 cm 0 g 0 G 1 0 0 1 -61.717 -351.568 cm BT /F22 8.2889 Tf 61.717 351.568 Td [(\051;)]TJ/F41 8.2889 Tf 8.481 0 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.435 Td [(i)]TJ/F22 8.2889 Tf 4.662 1.435 Td [(or)-302(this)-302(multi-agent)-302(system)]TJ/F41 8.2889 Tf 104.876 0 Td [(solves)-302(a)-302(finite-time)-302(consensus)]TJ ET 1 0 0 1 42.52 351.568 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -351.568 cm BT /F41 8.2889 Tf 42.52 341.453 Td [(problem)]TJ/F22 8.2889 Tf 32.734 0 Td [(if)-302(for)-302(any)-302(initial)-303(states,)-302(there)-302(exist)-302(a)-302(finite)-303(time)]TJ/F41 8.2889 Tf 182.121 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.471 Td [(\003)]TJ/F22 8.2889 Tf 6.49 -3.471 Td [(and)-302(an)]TJ ET 1 0 0 1 42.52 341.453 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -341.453 cm BT /F22 8.2889 Tf 42.52 331.337 Td [(asymptotically)-250(stab)1(le)-250(equilibrium)]TJ/F41 8.2889 Tf 130.232 0 Td [(x)]TJ/F179 6.6948 Tf 4.07 3.472 Td [(\003)]TJ/F179 9.5641 Tf 6.643 -3.472 Td [(2)]TJ/F169 8.6077 Tf 8.672 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(N)]TJ/F22 8.2889 Tf 7.153 -3.472 Td [(such)-250(that)]TJ/F41 8.2889 Tf 37.31 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(x)]TJ/F179 6.6948 Tf 4.07 3.472 Td [(\003)]TJ/F22 8.2889 Tf 6.055 -3.472 Td [(for)]TJ ET 1 0 0 1 42.52 331.337 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -331.337 cm BT /F22 8.2889 Tf 42.52 321.222 Td [(all)]TJ/F41 8.2889 Tf 11.322 0 Td [(t)]TJ/F179 9.5641 Tf 6.3 0 Td [(\025)]TJ/F41 8.2889 Tf 9.868 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.472 Td [(\003)]TJ/F22 8.2889 Tf 6.058 -3.472 Td [(and)-250(all)]TJ/F41 8.2889 Tf 27.643 0 Td [(i)]TJ/F179 9.5641 Tf 5.028 0 Td [(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.435 Td [(n)]TJ/F22 8.2889 Tf 3.852 1.435 Td [(.)]TJ ET 1 0 0 1 42.52 321.222 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -321.222 cm BT /F22 8.2889 Tf 54.475 311.279 Td [(Next,)-196(we)-196(provide)-196(a)-197(class)-196(of)-196(new)-196(nonlinear)-196(finite-time)-196(consensus)]TJ ET 1 0 0 1 42.52 311.279 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -311.279 cm BT /F22 8.2889 Tf 42.52 301.164 Td [(protocols:)]TJ ET 1 0 0 1 42.52 301.164 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -301.164 cm BT /F41 8.2889 Tf 42.52 275.822 Td [(u)]TJ/F41 5.8022 Tf 4.791 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.814 1.435 Td [(D)]TJ/F185 9.5641 Tf 10.117 0 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F189 9.5641 Tf 12.27 16.297 Td [(\040)]TJ 6.628 -7.211 Td [(X)]TJ/F41 5.8022 Tf 0.347 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.03 -1.353 Td [(i)]TJ/F41 8.2889 Tf 3.862 11.809 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.3 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.586 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(/)]TJ/F189 9.5641 Tf 3.568 16.297 Td [(!)]TJ/F185 6.6948 Tf 6.627 -2.144 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -14.153 Td [(C)]TJ/F185 9.5641 Tf 9.586 0 Td [(\015)]TJ/F189 9.5641 Tf 7.925 9.086 Td [(X)]TJ/F41 5.8022 Tf 0.348 -19.542 Td [(j)]TJ/F179 6.6948 Tf 1.676 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(N)]TJ/F41 4.9734 Tf 5.031 -1.352 Td [(i)]TJ/F41 8.2889 Tf 3.861 11.808 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ/F41 5.8022 Tf 4.069 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.301 1.435 Td [(\000)]TJ/F41 8.2889 Tf 9.585 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(/;)]TJ/F22 8.2889 Tf 51.344 0 Td [(\0502\051)]TJ ET 1 0 0 1 42.52 275.822 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -275.822 cm BT /F22 8.2889 Tf 42.52 252.042 Td [(where)-255(0)]TJ/F185 9.5641 Tf 33.943 0 Td [(<)-289(\013)-330(<)]TJ/F22 8.2889 Tf 29.064 0 Td [(1,)]TJ/F185 9.5641 Tf 8.854 0 Td [(\014)-359(>)]TJ/F22 8.2889 Tf 19.058 0 Td [(0,)]TJ/F185 9.5641 Tf 8.854 0 Td [(\015)]TJ/F179 9.5641 Tf 9.098 0 Td [(\025)]TJ/F22 8.2889 Tf 9.979 0 Td [(0,)-255(and)]TJ/F41 8.2889 Tf 25.217 0 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 6.601 1.435 Td [(>)]TJ/F22 8.2889 Tf 10.227 0 Td [(0)-255(are)-255(called)]TJ/F41 8.2889 Tf 45.71 0 Td [(weighting)]TJ ET 1 0 0 1 42.52 252.042 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -252.042 cm BT /F41 8.2889 Tf 42.52 241.927 Td [(factors)]TJ/F22 8.2889 Tf 26.731 0 Td [(\050)]TJ ET 1 0 0 1 72.318 241.927 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -72.318 -241.927 cm BT /F22 8.2889 Tf 72.318 241.927 Td [(Ren)]TJ ET 1 0 0 1 86.824 241.927 cm 0 g 0 G 1 0 0 1 2.072 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -88.896 -241.927 cm BT /F22 8.2889 Tf 88.896 241.927 Td [(&)]TJ ET 1 0 0 1 94.657 241.927 cm 0 g 0 G 1 0 0 1 2.072 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -96.729 -241.927 cm BT /F22 8.2889 Tf 96.729 241.927 Td [(Beard,)]TJ ET 1 0 0 1 120.659 241.927 cm 0 g 0 G 1 0 0 1 2.072 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -122.731 -241.927 cm BT /F22 8.2889 Tf 122.731 241.927 Td [(2005)]TJ ET 1 0 0 1 141.928 241.927 cm 0 g 0 G 1 0 0 1 -141.928 -241.927 cm BT /F22 8.2889 Tf 141.928 241.927 Td [(\051.)]TJ ET 1 0 0 1 42.52 241.927 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -241.927 cm BT /F22 8.2889 Tf 54.475 231.984 Td [(Protocol)]TJ ET 1 0 0 1 87.789 231.984 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -87.789 -231.984 cm BT /F22 8.2889 Tf 87.789 231.984 Td [(\0502\051)]TJ ET 1 0 0 1 98.714 231.984 cm 0 g 0 G 1 0 0 1 -98.714 -231.984 cm BT /F22 8.2889 Tf 100.315 231.984 Td [(represents)-193(a)-193(class)-193(of)-194(protocols)-193(with)-193(free)-193(parameters)]TJ ET 1 0 0 1 42.52 231.984 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -231.984 cm BT /F185 9.5641 Tf 42.52 221.869 Td [(\013)-40(;)-167(\014)]TJ/F22 8.2889 Tf 21.431 0 Td [(and)]TJ/F185 9.5641 Tf 19.012 0 Td [(\015)]TJ/F22 8.2889 Tf 6.331 0 Td [(.)-577(If)]TJ/F185 9.5641 Tf 16.822 0 Td [(\014)]TJ/F179 9.5641 Tf 15.622 0 Td [(D)]TJ/F22 8.2889 Tf 17.018 0 Td [(0,)]TJ/F185 9.5641 Tf 11.505 0 Td [(\015)]TJ/F179 9.5641 Tf 15.89 0 Td [(D)]TJ/F22 8.2889 Tf 17.018 0 Td [(1,)-575(then)-575(the)-574(above)-575(protocol)]TJ ET 1 0 0 1 42.52 221.869 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -221.869 cm BT /F22 8.2889 Tf 42.52 211.753 Td [(becomes)-404(the)-405(linear)-404(protocol,)-405(which)-404(was)-405(studied)-404(by)]TJ ET 1 0 0 1 247.915 211.753 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -247.915 -211.753 cm BT /F22 8.2889 Tf 247.915 211.753 Td [(Olfati-Saber)]TJ ET 1 0 0 1 293.578 211.753 cm 0 g 0 G 1 0 0 1 -251.058 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.115 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -42.52 -201.638 cm BT /F22 8.2889 Tf 42.52 201.638 Td [(and)]TJ ET 1 0 0 1 56.768 201.638 cm 0 g 0 G 1 0 0 1 2.351 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -59.119 -201.638 cm BT /F22 8.2889 Tf 59.119 201.638 Td [(Murray)]TJ ET 1 0 0 1 87.475 201.638 cm 0 g 0 G 1 0 0 1 2.35 0 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -89.825 -201.638 cm BT /F22 8.2889 Tf 89.825 201.638 Td [(\050)]TJ ET 1 0 0 1 92.892 201.638 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -92.892 -201.638 cm BT /F22 8.2889 Tf 92.892 201.638 Td [(2004)]TJ ET 1 0 0 1 112.089 201.638 cm 0 g 0 G 1 0 0 1 -112.089 -201.638 cm BT /F22 8.2889 Tf 112.089 201.638 Td [(\051)-284(and)-283(was)-284(proven)-283(to)-284(solve)-283(a)-284(consensus)-284(proble)1(m)]TJ ET 1 0 0 1 42.52 201.638 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -201.638 cm BT /F22 8.2889 Tf 42.52 191.523 Td [(asymptotically)-372(under)-371(appropriate)-372(conditions.)-373(If)]TJ/F185 9.5641 Tf 186.693 0 Td [(\013)]TJ/F179 9.5641 Tf 11.088 0 Td [(D)]TJ/F22 8.2889 Tf 12.705 0 Td [(0,)]TJ/F185 9.5641 Tf 9.821 0 Td [(\014)]TJ/F179 9.5641 Tf 11.308 0 Td [(6)1(D)]TJ/F22 8.2889 Tf 12.704 0 Td [(0,)]TJ ET 1 0 0 1 42.52 191.523 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -191.523 cm BT /F22 8.2889 Tf 42.52 181.407 Td [(the)-422(above)-421(protocol)-422(becomes)-421(discontinuous.)-423(This)-421(case)-422(is)-422(beyond)]TJ ET 1 0 0 1 42.52 181.407 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -181.407 cm BT /F22 8.2889 Tf 42.52 171.292 Td [(the)-367(scope)-366(of)-367(our)-366(research.)-368(However,)-366(it)-367(is)-366(worth)-367(mentioning)-367(that)]TJ ET 1 0 0 1 42.52 171.292 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -171.292 cm BT /F22 8.2889 Tf 42.52 161.177 Td [(discontinuous)-190(protocols)-190(were)-190(studied)-190(by)-190(Cort\351s.)-191(Interested)-190(readers)]TJ ET 1 0 0 1 42.52 161.177 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -161.177 cm BT /F22 8.2889 Tf 42.52 151.061 Td [(can)-250(be)-250(referred)-250(to)]TJ ET 1 0 0 1 112.013 151.061 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -112.013 -151.061 cm BT /F22 8.2889 Tf 112.013 151.061 Td [(Cort\351s)]TJ ET 1 0 0 1 136.25 151.061 cm 0 g 0 G 1 0 0 1 2.072 0 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -138.322 -151.061 cm BT /F22 8.2889 Tf 138.322 151.061 Td [(\050)]TJ ET 1 0 0 1 141.389 151.061 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -141.389 -151.061 cm BT /F22 8.2889 Tf 141.389 151.061 Td [(2006)]TJ ET 1 0 0 1 160.586 151.061 cm 0 g 0 G 1 0 0 1 -160.586 -151.061 cm BT /F22 8.2889 Tf 160.586 151.061 Td [(\051.)]TJ ET 1 0 0 1 42.52 151.061 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -17.914 cm 0 g 0 G 1 0 0 1 -38.535 -133.147 cm BT /F153 8.2889 Tf 42.52 133.147 Td [(Remark.)]TJ ET 1 0 0 1 76.214 133.147 cm 0 g 0 G 1 0 0 1 -76.214 -133.147 cm BT /F22 8.2889 Tf 80.199 133.147 Td [(Note)-183(that)-183(under)-183(the)-183(above)-183(protocol,)-184(the)-183(dynamics)-183(of)-183(each)]TJ ET 1 0 0 1 42.52 133.147 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -133.147 cm BT /F22 8.2889 Tf 42.52 123.032 Td [(dimension)-191(of)-191(position)-190(vectors)-191(is)-191(independent)-191(of)-191(others.)-191(We)-191(assume)]TJ ET 1 0 0 1 42.52 123.032 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -123.032 cm BT /F22 8.2889 Tf 42.52 112.916 Td [(that)]TJ/F41 8.2889 Tf 17.821 0 Td [(N)]TJ/F179 9.5641 Tf 9.847 0 Td [(D)]TJ/F22 8.2889 Tf 10.754 0 Td [(1)-280(without)-280(loss)-280(of)-280(generality.)-280(In)-280(this)-280(case,)-280(each)-280(agent)-280(be-)]TJ ET 1 0 0 1 42.52 112.916 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -112.916 cm BT /F22 8.2889 Tf 42.52 102.801 Td [(comes)-336(a)-336(s)1(ingle)-336(integrator.)-337(Networks)-335(of)-336(multiple)-336(integrators)-336(have)]TJ ET 1 0 0 1 42.52 102.801 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -102.801 cm BT /F22 8.2889 Tf 42.52 92.686 Td [(been)-196(studied)-195(by)-196(many)-195(researchers)-196(and)-196(there)-195(still)-196(exist)-195(a)-196(large)-196(num-)]TJ ET 1 0 0 1 42.52 92.686 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -92.686 cm BT /F22 8.2889 Tf 42.52 82.57 Td [(ber)-313(of)-313(interesting)-312(but)-313(unsolved)-313(problems.)-313(Some)-313(researchers)-313(have)]TJ ET 1 0 0 1 42.52 82.57 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -82.57 cm BT /F22 8.2889 Tf 42.52 72.455 Td [(also)-170(investigated)-170(more)-170(realistic)-171(and)-170(complex)-170(agent)-170(dynamics)-170(in)-171(dif-)]TJ ET 1 0 0 1 42.52 72.455 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -72.455 cm BT /F22 8.2889 Tf 42.52 62.34 Td [(ferent)-181(frameworks)-180(\050)]TJ ET 1 0 0 1 117.593 62.34 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -117.593 -62.34 cm BT /F22 8.2889 Tf 117.593 62.34 Td [(Johansson,)]TJ ET 1 0 0 1 158.275 62.34 cm 0 g 0 G 1 0 0 1 1.497 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -159.772 -62.34 cm BT /F22 8.2889 Tf 159.772 62.34 Td [(Speranzon,)]TJ ET 1 0 0 1 201.962 62.34 cm 0 g 0 G 1 0 0 1 1.498 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -203.46 -62.34 cm BT /F22 8.2889 Tf 203.46 62.34 Td [(Johansson,)]TJ ET 1 0 0 1 244.142 62.34 cm 0 g 0 G 1 0 0 1 1.497 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -245.639 -62.34 cm BT /F22 8.2889 Tf 245.639 62.34 Td [(&)]TJ ET 1 0 0 1 251.4 62.34 cm 0 g 0 G 1 0 0 1 1.497 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -252.897 -62.34 cm BT /F22 8.2889 Tf 252.897 62.34 Td [(Johansson,)]TJ ET 1 0 0 1 293.578 62.34 cm 0 g 0 G 1 0 0 1 -251.058 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.116 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -42.52 -52.224 cm BT /F22 8.2889 Tf 42.52 52.224 Td [(2008)]TJ ET 1 0 0 1 61.717 52.224 cm 0 g 0 G 1 0 0 1 -61.717 -52.224 cm BT /F22 8.2889 Tf 61.717 52.224 Td [(;)]TJ ET 1 0 0 1 66.923 52.224 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -66.923 -52.224 cm BT /F22 8.2889 Tf 66.923 52.224 Td [(Keviczky)]TJ ET 1 0 0 1 100.891 52.224 cm 0 g 0 G 1 0 0 1 2.288 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -103.179 -52.224 cm BT /F22 8.2889 Tf 103.179 52.224 Td [(&)]TJ ET 1 0 0 1 108.94 52.224 cm 0 g 0 G 1 0 0 1 2.288 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -111.228 -52.224 cm BT /F22 8.2889 Tf 111.228 52.224 Td [(Johansson,)]TJ ET 1 0 0 1 151.909 52.224 cm 0 g 0 G 1 0 0 1 2.289 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -154.198 -52.224 cm BT /F22 8.2889 Tf 154.198 52.224 Td [(2008)]TJ ET 1 0 0 1 173.395 52.224 cm 0 g 0 G 1 0 0 1 -173.395 -52.224 cm BT /F22 8.2889 Tf 173.395 52.224 Td [(\051,)-276(which)-276(is)-276(one)-276(of)-276(our)-276(future)-276(re-)]TJ ET 1 0 0 1 42.52 52.224 cm 0 g 0 G 0 g 0 G 1 0 0 1 -42.52 -52.224 cm BT /F22 8.2889 Tf 42.52 42.109 Td [(search)-250(topics.)]TJ ET 1 0 0 1 42.52 42.109 cm 0 g 0 G 0 g 0 G 1 0 0 1 260.025 -1.748 cm 0 g 0 G 0 g 0 G 1 0 0 1 -302.545 -40.361 cm BT /F22 8.2889 Tf 323.466 720.809 Td [(Since)-290(function)-289(sig)]TJ/F185 9.5641 Tf 67.716 0 Td [(.)]TJ/F179 9.5641 Tf 3.567 0 Td [(\001)]TJ/F185 9.5641 Tf 2.659 0 Td [(/)]TJ/F22 8.2889 Tf 5.969 0 Td [(is)-290(continuous,)-289(by)-290(Peano's)-290(Existence)-290(Theo-)]TJ ET 1 0 0 1 311.511 720.809 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -720.809 cm BT /F22 8.2889 Tf 311.511 710.179 Td [(rem)-331(and)-331(Extension)-330(Theorem)-331(\050)]TJ ET 1 0 0 1 427.044 710.179 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -427.044 -710.179 cm BT /F22 8.2889 Tf 427.044 710.179 Td [(Hartman,)]TJ ET 1 0 0 1 462.951 710.179 cm 0 g 0 G 1 0 0 1 2.743 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -465.694 -710.179 cm BT /F22 8.2889 Tf 465.694 710.179 Td [(1982)]TJ ET 1 0 0 1 484.891 710.179 cm 0 g 0 G 1 0 0 1 -484.891 -710.179 cm BT /F22 8.2889 Tf 484.891 710.179 Td [(\051,)-331(it)-331(can)-331(be)-330(obtained)]TJ ET 1 0 0 1 311.511 710.179 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -710.179 cm BT /F22 8.2889 Tf 311.511 699.549 Td [(that)-239(for)-238(any)-239(initial)-239(state,)-239(there)-238(exists)-239(at)-239(least)-238(one)-239(solution)-239(of)-239(differ-)]TJ ET 1 0 0 1 311.511 699.549 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -699.549 cm BT /F22 8.2889 Tf 311.511 688.919 Td [(ential)-250(equations)]TJ ET 1 0 0 1 374.879 688.919 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -374.879 -688.919 cm BT /F22 8.2889 Tf 374.879 688.919 Td [(\0501\051)]TJ ET 1 0 0 1 385.804 688.919 cm 0 g 0 G 1 0 0 1 -385.804 -688.919 cm BT /F22 8.2889 Tf 387.876 688.919 Td [(under)-250(protocol)]TJ ET 1 0 0 1 446.71 688.919 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -446.71 -688.919 cm BT /F22 8.2889 Tf 446.71 688.919 Td [(\0502\051)]TJ ET 1 0 0 1 457.635 688.919 cm 0 g 0 G 1 0 0 1 -457.635 -688.919 cm BT /F22 8.2889 Tf 459.707 688.919 Td [(on)-250(time)-250(interval)]TJ/F179 9.5641 Tf 63.186 0 Td [(T)]TJ/F22 8.2889 Tf 3.185 0 Td [(0)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F179 9.5641 Tf 4.76 0 Td [(1)]TJ/F185 9.5641 Tf 9.765 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(.)]TJ ET 1 0 0 1 311.511 688.919 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -688.919 cm BT /F22 8.2889 Tf 323.466 677.951 Td [(The)-456(following)-457(theorem)-456(characterizes)-457(the)-456(finite-time)-456(conver-)]TJ ET 1 0 0 1 311.511 677.951 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -677.951 cm BT /F22 8.2889 Tf 311.511 667.321 Td [(gence)-250(property)-250(of)-250(protocol)]TJ ET 1 0 0 1 414.865 667.321 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -414.865 -667.321 cm BT /F22 8.2889 Tf 414.865 667.321 Td [(\0502\051)]TJ ET 1 0 0 1 425.789 667.321 cm 0 g 0 G 1 0 0 1 -425.789 -667.321 cm BT /F22 8.2889 Tf 425.789 667.321 Td [(:)]TJ ET 1 0 0 1 311.511 667.321 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.369 cm 0 g 0 G 1 0 0 1 -307.526 -644.952 cm BT /F153 8.2889 Tf 311.511 644.952 Td [(Theorem)-250(3.)]TJ ET 1 0 0 1 356.511 644.952 cm 0 g 0 G 1 0 0 1 -356.511 -644.952 cm BT /F41 8.2889 Tf 360.496 644.952 Td [(If)-340(the)-339(interaction)-339(topology)]TJ/F181 8.9265 Tf 99.524 0 Td [(G)]TJ/F41 8.2889 Tf 8.545 0 Td [(has)-339(a)-340(spanning)-339(tree,)-340(then)]TJ ET 1 0 0 1 311.511 644.952 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -644.952 cm BT /F41 8.2889 Tf 311.511 634.322 Td [(protocol)]TJ ET 1 0 0 1 343.672 634.322 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -343.672 -634.322 cm BT /F22 8.2889 Tf 343.672 634.322 Td [(\0502\051)]TJ ET 1 0 0 1 354.596 634.322 cm 0 g 0 G 1 0 0 1 -354.596 -634.322 cm BT /F41 8.2889 Tf 356.669 634.322 Td [(solves)-250(a)-250(finite-time)-250(consensus)-250(problem.)]TJ ET 1 0 0 1 311.511 634.322 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -17.961 cm 0 g 0 G 1 0 0 1 -307.526 -616.361 cm BT /F153 8.2889 Tf 311.511 616.361 Td [(Proof.)]TJ ET 1 0 0 1 335.739 616.361 cm 0 g 0 G 1 0 0 1 -335.739 -616.361 cm BT /F22 8.2889 Tf 339.724 616.361 Td [(We)-250(first)-250(define)-250(a)-250(new)-250(matrix)]TJ/F41 8.2889 Tf 111.137 0 Td [(A)]TJ/F179 9.5641 Tf 7.688 0 Td [(D)-278(T)]TJ/F41 8.2889 Tf 13.302 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.434 Td [(ij)]TJ/F179 9.5641 Tf 3.834 1.434 Td [(U)]TJ/F22 8.2889 Tf 5.257 0 Td [(by)]TJ ET 1 0 0 1 311.511 616.361 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -616.361 cm BT /F41 8.2889 Tf 311.511 592.182 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(ij)]TJ/F179 9.5641 Tf 6.491 1.435 Td [(D)]TJ/F189 9.5641 Tf 10.117 13.428 Td [(\032)]TJ/F41 8.2889 Tf 5.91 -7.899 Td [(W)]TJ/F41 5.8022 Tf 8.132 -1.434 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.434 Td [(;)]TJ/F22 8.2889 Tf 18.368 0 Td [(if)]TJ/F41 8.2889 Tf 7.319 0 Td [(j)]TJ/F179 9.5641 Tf 5.052 0 Td [(2)]TJ/F181 8.9265 Tf 8.673 0 Td [(N)]TJ/F41 5.8022 Tf 7.186 -1.434 Td [(i)]TJ/F22 8.2889 Tf -54.98 -9.026 Td [(0)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F22 8.2889 Tf 16.711 0 Td [(otherwise)]TJ/F185 9.5641 Tf 38.237 0 Td [(:)]TJ ET 1 0 0 1 311.511 592.182 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -592.182 cm BT /F22 8.2889 Tf 311.511 569.084 Td [(This)-250(theorem)-250(is)-250(proven)-250(through)-250(the)-250(following)-250(three)-250(steps.)]TJ ET 1 0 0 1 311.511 569.084 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -569.084 cm BT /F41 8.2889 Tf 311.511 554.789 Td [(Step)]TJ/F22 8.2889 Tf 17.655 0 Td [(1:)-250(Suppose)-250(that)]TJ/F181 8.9265 Tf 61.445 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 5.64 0 Td [(is)-250(strongly)-250(connected.)]TJ ET 1 0 0 1 311.511 554.789 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -554.789 cm BT /F22 8.2889 Tf 323.466 543.821 Td [(By)]TJ ET 1 0 0 1 335.797 543.821 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -335.797 -543.821 cm BT /F22 8.2889 Tf 335.797 543.821 Td [(Lemma)-336(1)]TJ ET 1 0 0 1 371.536 543.821 cm 0 g 0 G 1 0 0 1 -371.536 -543.821 cm BT /F22 8.2889 Tf 371.536 543.821 Td [(,)-336(there)-335(exists)-336(a)-336(positive)-335(vector)]TJ/F185 9.5641 Tf 119.377 0 Td [(!)]TJ/F179 9.5641 Tf 10.933 0 Td [(D)-468(T)]TJ/F185 9.5641 Tf 15.122 0 Td [(!)]TJ/F22 5.8022 Tf 6.264 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(;)-167(!)]TJ/F22 5.8022 Tf 11.024 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ ET 1 0 0 1 311.511 543.821 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -543.821 cm BT /F185 9.5641 Tf 311.511 533.191 Td [(!)]TJ/F41 5.8022 Tf 6.264 -1.435 Td [(n)]TJ/F179 9.5641 Tf 3.852 1.435 Td [(U)]TJ/F22 5.8022 Tf 3.185 3.472 Td [(T)]TJ/F179 9.5641 Tf 7.642 -3.472 Td [(2)]TJ/F169 8.6077 Tf 9.921 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(n)]TJ/F22 8.2889 Tf 6.411 -3.472 Td [(such)-309(that)]TJ/F185 9.5641 Tf 38.291 0 Td [(!)]TJ/F22 5.8022 Tf 6.455 3.472 Td [(T)]TJ/F41 8.2889 Tf 3.736 -3.472 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F179 9.5641 Tf 7.473 0 Td [(D)]TJ/F22 8.2889 Tf 11.366 0 Td [(0,)-309(where)]TJ/F41 8.2889 Tf 36.119 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F179 9.5641 Tf 7.473 0 Td [(D)-408(T)]TJ/F41 8.2889 Tf 14.551 0 Td [(l)]TJ/F41 5.8022 Tf 2.271 -1.435 Td [(ij)]TJ/F179 9.5641 Tf 3.834 1.435 Td [(U)]TJ/F22 8.2889 Tf 5.744 0 Td [(denotes)-309(the)]TJ ET 1 0 0 1 311.511 533.191 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -533.191 cm BT /F22 8.2889 Tf 311.511 522.561 Td [(graph)-201(Laplacian)-200(of)]TJ/F181 8.9265 Tf 70.545 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)-201(defined)-200(in)-201(Section)]TJ ET 1 0 0 1 472.898 522.561 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -472.898 -522.561 cm BT /F22 8.2889 Tf 472.898 522.561 Td [(2)]TJ ET 1 0 0 1 477.697 522.561 cm 0 g 0 G 1 0 0 1 -477.697 -522.561 cm BT /F22 8.2889 Tf 477.697 522.561 Td [(.)-201(Let)]TJ/F41 8.2889 Tf 16.864 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.814 1.435 Td [(D)]TJ/F189 9.5641 Tf 10.117 7.173 Td [(P)]TJ/F41 5.8022 Tf 9.994 -2.584 Td [(n)]TJ 0 -7.315 Td [(j)]TJ/F179 6.6948 Tf 1.677 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F41 8.2889 Tf 5.452 2.726 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(j)]TJ/F179 9.5641 Tf 3.04 1.435 Td [(\000)]TJ ET 1 0 0 1 311.511 522.561 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -522.561 cm BT /F41 8.2889 Tf 311.511 509.688 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(/)]TJ/F22 8.2889 Tf 5.64 0 Td [(and)]TJ/F41 8.2889 Tf 16.321 0 Td [(y)]TJ/F179 9.5641 Tf 7 0 Td [(D)-278(T)]TJ/F41 8.2889 Tf 13.301 0 Td [(y)]TJ/F22 5.8022 Tf 4.344 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F41 8.2889 Tf 4.76 0 Td [(y)]TJ/F22 5.8022 Tf 4.343 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(n)]TJ/F179 9.5641 Tf 3.852 1.435 Td [(U)]TJ/F22 5.8022 Tf 3.185 3.472 Td [(T)]TJ/F22 8.2889 Tf 3.735 -3.472 Td [(.)-250(Then)]TJ/F185 9.5641 Tf 25.124 0 Td [(!)]TJ/F179 9.5641 Tf 9.112 0 Td [(?)]TJ/F41 8.2889 Tf 10.117 0 Td [(y)]TJ/F22 8.2889 Tf 6.415 0 Td [(and)]TJ ET 1 0 0 1 311.511 509.688 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -509.688 cm BT /F179 9.5641 Tf 312.09 492.578 Td [(P)]TJ/F41 8.2889 Tf -0.579 -0.174 Td [(y)]TJ/F179 9.5641 Tf 7 0 Td [(D)-278(\000)]TJ/F185 9.5641 Tf 17.577 0 Td [(\014)]TJ/F41 8.2889 Tf 6.063 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.95 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(\000)]TJ/F185 9.5641 Tf 9.586 0 Td [(\015)]TJ/F41 8.2889 Tf 6.331 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F185 9.5641 Tf 4.344 0 Td [(:)]TJ ET 1 0 0 1 311.511 492.404 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -492.404 cm BT /F22 8.2889 Tf 323.466 474.781 Td [(Choose)-250(Lyapunov)-250(candidate)]TJ ET 1 0 0 1 311.511 474.781 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -474.781 cm BT /F41 8.2889 Tf 311.511 450.014 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F41 5.8022 Tf 15.206 11.105 Td [(n)]TJ/F189 9.5641 Tf -5.089 -2.02 Td [(X)]TJ/F41 5.8022 Tf 1.646 -19.542 Td [(i)]TJ/F179 6.6948 Tf 1.659 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F185 9.5641 Tf 6.6 10.457 Td [(!)]TJ/F41 5.8022 Tf 6.264 -1.435 Td [(i)]TJ/F189 9.5641 Tf 3.752 14.863 Td [(\022)]TJ/F185 9.5641 Tf 15.796 -6.724 Td [(\014)]TJ ET q 1 0 0 1 376.762 452.405 cm []0 d 0 J 0.44 w 0 0 m 22.354 0 l S Q BT /F22 8.2889 Tf 376.762 443.223 Td [(1)]TJ/F179 9.5641 Tf 6.925 0 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\013)]TJ/F179 9.5641 Tf 7.039 6.791 Td [(j)]TJ/F41 8.2889 Tf 2.735 0 Td [(y)]TJ/F41 5.8022 Tf 4.344 -1.435 Td [(i)]TJ/F179 9.5641 Tf 2.157 1.435 Td [(j)]TJ/F22 5.8022 Tf 2.736 3.95 Td [(1)]TJ/F179 6.6948 Tf 3.359 0 Td [(C)]TJ/F185 6.6948 Tf 5.222 0 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(C)]TJ/F185 9.5641 Tf 10.781 6.704 Td [(\015)]TJ ET q 1 0 0 1 438.359 452.405 cm []0 d 0 J 0.44 w 0 0 m 6.331 0 l S Q BT /F22 8.2889 Tf 439.125 443.223 Td [(2)]TJ/F41 8.2889 Tf 6.761 6.791 Td [(y)]TJ/F41 5.8022 Tf 4.343 -1.435 Td [(i)]TJ/F22 5.8022 Tf 2.158 5.385 Td [(2)]TJ/F189 9.5641 Tf 3.857 9.478 Td [(\023)]TJ/F185 9.5641 Tf 8.05 -13.428 Td [(:)]TJ ET 1 0 0 1 311.511 450.014 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -450.014 cm BT /F22 8.2889 Tf 311.511 424.221 Td [(Obviously)]TJ/F41 8.2889 Tf 40.184 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(\025)]TJ/F22 8.2889 Tf 9.868 0 Td [(0)-250(and)]TJ ET 1 0 0 1 311.511 424.221 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -424.221 cm BT /F22 8.2889 Tf 312.706 408.251 Td [(d)]TJ/F41 8.2889 Tf 4.932 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ ET q 1 0 0 1 312.706 403.938 cm []0 d 0 J 0.44 w 0 0 m 24.615 0 l S Q BT /F22 8.2889 Tf 320.727 394.756 Td [(d)]TJ/F41 8.2889 Tf 4.931 0 Td [(t)]TJ/F179 9.5641 Tf 15.516 6.791 Td [(D)-278(\000)]TJ/F189 9.5641 Tf 17.576 7.69 Td [(\000)]TJ/F185 9.5641 Tf 3.855 -7.69 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F185 6.6948 Tf 3.568 3.95 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\015)]TJ/F41 8.2889 Tf 6.331 0 Td [(y)]TJ/F189 9.5641 Tf 4.344 7.69 Td [(\001)]TJ/F22 5.8022 Tf 3.854 -1.806 Td [(T)]TJ/F22 8.2889 Tf 3.736 -5.884 Td [(diag)]TJ/F185 9.5641 Tf 16.204 0 Td [(.!)-20(/)]TJ/F41 8.2889 Tf 13.591 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F189 9.5641 Tf 3.567 7.69 Td [(\000)]TJ/F185 9.5641 Tf 3.854 -7.69 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F185 9.5641 Tf 4.344 0 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.95 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.95 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\015)]TJ/F41 8.2889 Tf 6.332 0 Td [(y)]TJ/F189 9.5641 Tf 4.343 7.69 Td [(\001)]TJ/F185 9.5641 Tf 3.855 -7.69 Td [(:)]TJ ET 1 0 0 1 311.511 401.547 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -401.547 cm BT /F41 8.2889 Tf 311.511 376.795 Td [(Claim:)]TJ/F22 8.2889 Tf 25.695 0 Td [(Given)-250(initial)-250(state)]TJ/F41 8.2889 Tf 69.295 0 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F22 8.2889 Tf 3.567 0 Td [(0)]TJ/F185 9.5641 Tf 4.8 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)-250(there)-250(exists)]TJ/F41 8.2889 Tf 50.322 0 Td [(K)]TJ/F22 5.8022 Tf 5.105 -1.434 Td [(1)]TJ/F185 9.5641 Tf 6.515 1.434 Td [(>)]TJ/F22 8.2889 Tf 10.116 0 Td [(0)-250(such)-250(that)]TJ ET 1 0 0 1 311.511 376.795 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -376.795 cm BT /F22 8.2889 Tf 312.706 360.91 Td [(d)]TJ/F41 8.2889 Tf 4.932 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ ET q 1 0 0 1 312.706 356.597 cm []0 d 0 J 0.44 w 0 0 m 24.615 0 l S Q BT /F22 8.2889 Tf 320.727 347.415 Td [(d)]TJ/F41 8.2889 Tf 4.931 0 Td [(t)]TJ/F179 9.5641 Tf 15.516 6.791 Td [(\024)-278(\000)]TJ/F41 8.2889 Tf 17.328 0 Td [(K)]TJ/F22 5.8022 Tf 5.106 -1.435 Td [(1)]TJ/F41 8.2889 Tf 3.857 1.435 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 4.9734 Tf 7.001 6.886 Td [(2)]TJ/F185 5.7385 Tf 2.88 0 Td [(\013)]TJ ET q 1 0 0 1 388.344 360.061 cm []0 d 0 J 0.308 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 388.344 355.782 Td [(1)]TJ/F179 5.7385 Tf 2.88 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ/F185 9.5641 Tf 5.199 -1.576 Td [(:)]TJ ET 1 0 0 1 311.511 354.206 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -354.206 cm BT /F22 8.2889 Tf 323.466 332.754 Td [(By)-373(the)-373(above)-373(claim,)]TJ/F41 8.2889 Tf 79.885 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F22 8.2889 Tf 6.658 0 Td [(will)-373(reach)-373(zero)-373(in)-372(finite)-373(time)]TJ/F41 8.2889 Tf 116.087 0 Td [(t)]TJ/F179 6.6948 Tf 3.643 3.471 Td [(\003)]TJ/F179 9.5641 Tf 9.255 -3.471 Td [(D)]TJ ET 1 0 0 1 311.511 332.754 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -332.754 cm BT /F185 6.6948 Tf 312.706 319.85 Td [(.)]TJ/F22 5.8022 Tf 2.498 0 Td [(1)]TJ/F179 6.6948 Tf 3.359 0 Td [(C)]TJ/F185 6.6948 Tf 5.222 0 Td [(\013)-40(/)]TJ/F41 5.8022 Tf 6.588 0 Td [(V)]TJ/F22 4.9734 Tf 3.533 -1.353 Td [(1)]TJ/F185 6.6948 Tf 3.378 1.353 Td [(.)]TJ/F22 5.8022 Tf 2.497 0 Td [(0)]TJ/F185 6.6948 Tf 3.36 0 Td [(/)]TJ/F22 4.9734 Tf 3.692 6.342 Td [(1)]TJ/F179 5.7385 Tf 2.88 0 Td [(\000)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ ET q 1 0 0 1 346.833 325.309 cm []0 d 0 J 0.264 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 346.833 321.096 Td [(1)]TJ/F179 5.7385 Tf 2.88 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ ET q 1 0 0 1 312.706 317.837 cm []0 d 0 J 0.44 w 0 0 m 46.682 0 l S Q BT /F41 5.8022 Tf 323.739 312.051 Td [(K)]TJ/F22 4.9734 Tf 3.574 -1.353 Td [(1)]TJ/F185 6.6948 Tf 3.377 1.353 Td [(.)]TJ/F22 5.8022 Tf 2.498 0 Td [(1)]TJ/F179 6.6948 Tf 3.359 0 Td [(\000)]TJ/F185 6.6948 Tf 5.222 0 Td [(\013)-40(/)]TJ/F22 8.2889 Tf 18.815 3.395 Td [(,)-272(which)-272(implies)-272(that)]TJ/F41 8.2889 Tf 78.229 0 Td [(y)]TJ/F22 8.2889 Tf 6.598 0 Td [(will)-272(be)-272(zero.)-272(Since)]TJ/F41 8.2889 Tf 71.483 0 Td [(y)]TJ/F179 9.5641 Tf 7.467 0 Td [(D)-327(\000)]TJ/F41 8.2889 Tf 18.044 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F41 8.2889 Tf 3.568 0 Td [(x)]TJ ET 1 0 0 1 311.511 315.446 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -315.446 cm BT /F22 8.2889 Tf 311.511 303.131 Td [(and)-448(rank)]TJ/F185 9.5641 Tf 35.289 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(//)]TJ/F179 9.5641 Tf 14.007 0 Td [(D)]TJ/F41 8.2889 Tf 14.333 0 Td [(n)]TJ/F179 9.5641 Tf 8.603 0 Td [(\000)]TJ/F22 8.2889 Tf 11.272 0 Td [(1)-448(\050by)]TJ ET 1 0 0 1 435.75 303.131 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -435.75 -303.131 cm BT /F22 8.2889 Tf 435.75 303.131 Td [(Lemma)-448(1)]TJ ET 1 0 0 1 472.423 303.131 cm 0 g 0 G 1 0 0 1 -472.423 -303.131 cm BT /F22 8.2889 Tf 472.423 303.131 Td [(\051,)]TJ/F41 8.2889 Tf 8.716 0 Td [(y)]TJ/F179 9.5641 Tf 11.216 0 Td [(D)]TJ/F22 8.2889 Tf 14.333 0 Td [(0)-448(implies)-449(that)]TJ ET 1 0 0 1 311.511 303.131 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -303.131 cm BT /F41 8.2889 Tf 311.511 292.501 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.435 Td [(1)]TJ/F179 9.5641 Tf 7.961 1.435 Td [(D)]TJ/F41 8.2889 Tf 11.564 0 Td [(x)]TJ/F22 5.8022 Tf 4.07 -1.435 Td [(2)]TJ/F179 9.5641 Tf 7.962 1.435 Td [(D)-429(\001)-167(\001)-166(\001)-430(D)]TJ/F41 8.2889 Tf 38.396 0 Td [(x)]TJ/F41 5.8022 Tf 4.07 -1.435 Td [(n)]TJ/F22 8.2889 Tf 6.489 1.435 Td [(and)]TJ/F179 9.5641 Tf 17.327 0.174 Td [(P)]TJ/F41 8.2889 Tf -0.442 -0.174 Td [(x)]TJ/F185 9.5641 Tf 4.07 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 7.672 0 Td [(D)]TJ/F22 8.2889 Tf 11.564 0 Td [(0.)-318(Therefore)-319(this)-318(system)-318(solves)]TJ ET 1 0 0 1 311.511 292.501 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -292.501 cm BT /F22 8.2889 Tf 311.511 281.871 Td [(a)-250(finite-time)-250(consensus)-250(problem.)]TJ ET 1 0 0 1 311.511 281.871 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -281.871 cm BT /F22 8.2889 Tf 323.466 270.903 Td [(It)-250(is)-250(left)-250(to)-250(us)-250(to)-250(prove)-250(that)-250(the)-250(above)-250(claim)-250(holds.)]TJ ET 1 0 0 1 311.511 270.903 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -270.903 cm BT /F22 8.2889 Tf 323.466 254.336 Td [(Suppose)-409(that)]TJ/F41 8.2889 Tf 54.298 0 Td [(V)]TJ/F22 5.8022 Tf 5.048 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.858 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(t)]TJ/F185 9.5641 Tf 3.643 0 Td [(/)]TJ/F179 9.5641 Tf 9.611 0 Td [(6)1(D)]TJ/F22 8.2889 Tf 13.504 0 Td [(0.)-410(Let)]TJ/F185 9.2055 Tf 25.129 0 Td [(\001)]TJ/F22 5.8022 Tf 7.291 -1.434 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.434 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F179 9.5641 Tf 9.611 0 Td [(D)-632(\000)]TJ/F22 4.9734 Tf 28.347 9.541 Td [(d)]TJ/F41 4.9734 Tf 2.959 0 Td [(V)]TJ/F22 4.9734 Tf 3.029 -1.704 Td [(1)]TJ/F185 5.7385 Tf 3.377 1.704 Td [(.)]TJ/F41 4.9734 Tf 2.141 0 Td [(t)]TJ/F185 5.7385 Tf 2.186 0 Td [(/)]TJ ET q 1 0 0 1 499.141 261.711 cm []0 d 0 J 0.308 w 0 0 m 15.832 0 l S Q BT /F22 4.9734 Tf 504.485 257.432 Td [(d)]TJ/F41 4.9734 Tf 2.959 0 Td [(t)]TJ ET q 1 0 0 1 492.954 256.727 cm []0 d 0 J 0.44 w 0 0 m 28.207 0 l S Q BT /F41 5.8022 Tf 492.954 245.908 Td [(V)]TJ/F22 4.9734 Tf 3.533 -1.353 Td [(1)]TJ/F185 6.6948 Tf 3.378 1.353 Td [(.)]TJ/F41 5.8022 Tf 2.497 0 Td [(t)]TJ/F185 6.6948 Tf 2.55 0 Td [(/)]TJ/F22 4.9734 Tf 5.931 6.343 Td [(2)]TJ/F185 5.7385 Tf 2.879 0 Td [(\013)]TJ ET q 1 0 0 1 508.605 251.367 cm []0 d 0 J 0.264 w 0 0 m 10.862 0 l S Q BT /F22 4.9734 Tf 508.605 247.154 Td [(1)]TJ/F179 5.7385 Tf 2.879 0 Td [(C)]TJ/F185 5.7385 Tf 4.476 0 Td [(\013)]TJ/F22 8.2889 Tf 6.396 7.182 Td [(,)-409(let)]TJ/F41 8.2889 Tf 18.657 0 Td [(M)]TJ/F179 9.5641 Tf 14.096 0 Td [(D)]TJ ET 1 0 0 1 311.511 254.336 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -254.336 cm BT /F22 5.8022 Tf 312.706 238.955 Td [(1)]TJ ET q 1 0 0 1 312.706 237.482 cm []0 d 0 J 0.44 w 0 0 m 3.359 0 l S Q BT /F22 5.8022 Tf 312.706 231.695 Td [(2)]TJ/F189 9.5641 Tf 4.555 11.085 Td [(\000)]TJ/F22 8.2889 Tf 3.855 -7.689 Td [(diag)]TJ/F185 9.5641 Tf 16.204 0 Td [(.!)-20(/)]TJ/F41 8.2889 Tf 13.591 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F179 9.5641 Tf 6.452 0 Td [(C)]TJ/F41 8.2889 Tf 10.346 0 Td [(L)]TJ/F185 9.5641 Tf 3.928 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 5.8022 Tf 3.568 3.471 Td [(T)]TJ/F22 8.2889 Tf 3.735 -3.471 Td [(diag)]TJ/F185 9.5641 Tf 16.205 0 Td [(.!)-20(/)]TJ/F189 9.5641 Tf 13.591 7.689 Td [(\001)]TJ/F22 8.2889 Tf 6.667 -7.689 Td [(and)-339(let)]TJ/F181 8.9265 Tf 29.805 0 Td [(U)]TJ/F179 9.5641 Tf 12.608 0 Td [(D)-476(f)]TJ/F185 9.5641 Tf 15.555 0 Td [(\030)]TJ/F179 9.5641 Tf 9.683 0 Td [(2)]TJ/F169 8.6077 Tf 10.572 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.471 Td [(n)]TJ/F179 9.5641 Tf 8.408 -3.471 Td [(V)]TJ/F185 9.5641 Tf 7.187 0 Td [(\030)]TJ/F22 5.8022 Tf 5.126 3.471 Td [(T)]TJ/F185 9.5641 Tf 3.736 -3.471 Td [(\030)]TJ/F179 9.5641 Tf 9.683 0 Td [(D)]TJ ET 1 0 0 1 311.511 235.091 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -235.091 cm BT /F22 8.2889 Tf 311.511 224.461 Td [(1)-250(and)]TJ/F185 9.5641 Tf 23.192 0 Td [(\030)]TJ/F179 9.5641 Tf 8.304 0 Td [(D)]TJ/F185 9.5641 Tf 10.637 0 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.\020)-130(/)]TJ/F185 6.6948 Tf 12.491 3.471 Td [(\013)]TJ/F179 9.5641 Tf 6.922 -3.471 Td [(C)]TJ/F185 9.5641 Tf 9.794 0 Td [(\015)-160(\020)]TJ/F22 8.2889 Tf 13.759 0 Td [(for)-250(some)]TJ/F185 9.5641 Tf 35.443 0 Td [(\020)]TJ/F179 9.5641 Tf 8.533 0 Td [(?)]TJ/F185 9.5641 Tf 10.638 0 Td [(!)]TJ/F179 9.5641 Tf 6.455 0 Td [(g)]TJ/F22 8.2889 Tf 3.539 0 Td [(.)-275(Then)]TJ/F181 8.9265 Tf 25.531 0 Td [(U)]TJ/F22 8.2889 Tf 10.327 0 Td [(is)-274(a)-275(bounded)]TJ ET 1 0 0 1 311.511 224.461 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -224.461 cm BT /F22 8.2889 Tf 311.511 213.831 Td [(closed)-389(set.)-389(Since)-389(function)]TJ/F185 9.5641 Tf 102.368 0 Td [(\030)]TJ/F22 5.8022 Tf 5.127 3.472 Td [(T)]TJ/F41 8.2889 Tf 3.736 -3.472 Td [(M)]TJ/F185 9.5641 Tf 8.052 0 Td [(\030)]TJ/F22 8.2889 Tf 8.349 0 Td [(is)-389(continuous)-389(with)-389(resp)1(ect)-389(to)]TJ/F185 9.5641 Tf 118.3 0 Td [(\030)]TJ ET 1 0 0 1 311.511 213.831 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -213.831 cm BT /F22 8.2889 Tf 311.511 203.201 Td [(and)-427(for)-428(any)]TJ/F185 9.5641 Tf 49.595 0 Td [(\030)]TJ/F179 9.5641 Tf 11.555 0 Td [(2)]TJ/F181 8.9265 Tf 12.444 0 Td [(U)]TJ/F22 8.2889 Tf 8.051 0 Td [(,)]TJ/F185 9.5641 Tf 5.484 0 Td [(\030)]TJ/F22 5.8022 Tf 5.127 3.472 Td [(T)]TJ/F41 8.2889 Tf 3.736 -3.472 Td [(M)]TJ/F185 9.5641 Tf 8.052 0 Td [(\030)]TJ/F179 9.5641 Tf 11.555 0 Td [(6)1(D)]TJ/F22 8.2889 Tf 13.888 0 Td [(0)-427(\050by)]TJ ET 1 0 0 1 465.292 203.201 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -465.292 -203.201 cm BT /F22 8.2889 Tf 465.292 203.201 Td [(Lemma)-427(1)]TJ ET 1 0 0 1 501.791 203.201 cm 0 g 0 G 1 0 0 1 -501.791 -203.201 cm BT /F22 8.2889 Tf 501.791 203.201 Td [(\051,)-428(we)-427(have)-428(that)]TJ ET 1 0 0 1 311.511 203.201 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -203.201 cm BT /F22 8.2889 Tf 311.511 192.571 Td [(min)]TJ/F185 6.6948 Tf 15.193 -1.435 Td [(\030)]TJ/F179 6.6948 Tf 3.589 0 Td [(2)]TJ/F181 6.2485 Tf 4.211 0 Td [(U)]TJ/F185 9.5641 Tf 7.728 1.435 Td [(\030)]TJ/F22 5.8022 Tf 5.127 3.472 Td [(T)]TJ/F41 8.2889 Tf 3.735 -3.472 Td [(M)]TJ/F185 9.5641 Tf 8.053 0 Td [(\030)]TJ/F22 8.2889 Tf 5.126 0 Td [(,)-495(denoted)-495(by)]TJ/F41 8.2889 Tf 54.983 0 Td [(k)]TJ/F22 5.8022 Tf 4.31 -1.435 Td [(1)]TJ/F22 8.2889 Tf 3.858 1.435 Td [(,)-495(exists)-495(and)-494(is)-495(larger)-495(that)-494(zero.)-496(It)]TJ ET 1 0 0 1 311.511 192.571 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -192.571 cm BT /F22 8.2889 Tf 311.511 181.941 Td [(follows)-250(from)]TJ/F185 9.5641 Tf 50.62 0 Td [(!)]TJ/F179 9.5641 Tf 9.112 0 Td [(?)]TJ/F41 8.2889 Tf 10.117 0 Td [(y)]TJ/F22 8.2889 Tf 6.416 0 Td [(that)]TJ ET 1 0 0 1 311.511 181.941 cm 0 g 0 G 0 g 0 G 1 0 0 1 -311.511 -181.941 cm BT /F189 9.5641 Tf 312.706 169.891 Td [(\000)]TJ/F185 9.5641 Tf 3.855 -7.689 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F185 6.6948 Tf 3.568 3.471 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.471 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\015)]TJ/F41 8.2889 Tf 6.331 0 Td [(y)]TJ/F189 9.5641 Tf 4.344 7.689 Td [(\001)]TJ/F22 5.8022 Tf 3.854 -1.805 Td [(T)]TJ/F41 8.2889 Tf 3.736 -5.884 Td [(M)]TJ/F189 9.5641 Tf 8.052 7.689 Td [(\000)]TJ/F185 9.5641 Tf 3.855 -7.689 Td [(\014)]TJ/F22 8.2889 Tf 6.063 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.471 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -3.471 Td [(C)]TJ/F185 9.5641 Tf 9.586 0 Td [(\015)]TJ/F41 8.2889 Tf 6.331 0 Td [(y)]TJ/F189 9.5641 Tf 4.344 7.689 Td [(\001)]TJ ET q 1 0 0 1 312.706 157.315 cm []0 d 0 J 0.44 w 0 0 m 137.589 0 l S Q BT /F189 9.5641 Tf 316.733 153.127 Td [(\000)]TJ/F185 9.5641 Tf 3.854 -7.689 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F185 9.5641 Tf 4.343 0 Td [(/)]TJ/F185 6.6948 Tf 3.568 2.764 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -2.764 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td [(\015)]TJ/F41 8.2889 Tf 6.332 0 Td [(y)]TJ/F189 9.5641 Tf 4.343 7.689 Td [(\001)]TJ/F22 5.8022 Tf 3.854 -1.805 Td [(T)]TJ/F189 9.5641 Tf 3.736 1.805 Td [(\000)]TJ/F185 9.5641 Tf 3.854 -7.689 Td [(\014)]TJ/F22 8.2889 Tf 6.064 0 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(y)]TJ/F185 9.5641 Tf 4.344 0 Td [(/)]TJ/F185 6.6948 Tf 3.567 2.764 Td [(\013)]TJ/F179 9.5641 Tf 6.714 -2.764 Td [(C)]TJ/F185 9.5641 Tf 9.585 0 Td 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ET 1 0 0 1 240.962 564.901 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -240.962 -564.901 cm BT /F22 8.2889 Tf 240.962 564.901 Td [(Xiao)]TJ ET 1 0 0 1 257.979 564.901 cm 0 g 0 G 1 0 0 1 -257.979 -564.901 cm BT /F22 8.2889 Tf 257.979 564.901 Td [(,)]TJ ET 1 0 0 1 259.919 564.901 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 1.731 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -261.65 -564.901 cm BT /F22 8.2889 Tf 261.65 564.901 Td [(2008)]TJ ET 1 0 0 1 280.847 564.901 cm 0 g 0 G 1 0 0 1 -280.847 -564.901 cm BT /F22 8.2889 Tf 280.847 564.901 Td [(;)]TJ ET 1 0 0 1 32.706 564.901 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.398 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -32.706 -554.503 cm BT /F22 8.2889 Tf 32.706 554.503 Td [(Xiao)]TJ ET 1 0 0 1 49.723 554.503 cm 0 g 0 G 1 0 0 1 3.074 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -52.797 -554.503 cm BT /F22 8.2889 Tf 52.797 554.503 Td [(&)]TJ ET 1 0 0 1 58.558 554.503 cm 0 g 0 G 1 0 0 1 3.074 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -61.632 -554.503 cm BT /F22 8.2889 Tf 61.632 554.503 Td [(Wang,)]TJ ET 1 0 0 1 86.018 554.503 cm 0 g 0 G 1 0 0 1 3.075 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -89.093 -554.503 cm BT /F22 8.2889 Tf 89.093 554.503 Td [(2008a,b)]TJ ET 1 0 0 1 119.322 554.503 cm 0 g 0 G 1 0 0 1 -119.322 -554.503 cm BT /F22 8.2889 Tf 119.322 554.503 Td [(\051)-371(and)-371(has)-371(been)-370(successfully)-371(applied)-371(in)-371(the)]TJ ET 1 0 0 1 32.706 554.503 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -554.503 cm BT /F22 8.2889 Tf 32.706 544.105 Td [(formation)-192(control)-192(\050)]TJ ET 1 0 0 1 104.458 544.105 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -104.458 -544.105 cm BT /F22 8.2889 Tf 104.458 544.105 Td [(Lafferriere)]TJ ET 1 0 0 1 144.17 544.105 cm 0 g 0 G 1 0 0 1 1.593 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -145.763 -544.105 cm BT /F22 8.2889 Tf 145.763 544.105 Td [(et)-192(al.)]TJ ET 1 0 0 1 163.528 544.105 cm 0 g 0 G 1 0 0 1 -163.528 -544.105 cm BT /F22 8.2889 Tf 163.528 544.105 Td [(,)]TJ ET 1 0 0 1 165.467 544.105 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 1.594 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -167.061 -544.105 cm BT /F22 8.2889 Tf 167.061 544.105 Td [(2005)]TJ ET 1 0 0 1 186.258 544.105 cm 0 g 0 G 1 0 0 1 -186.258 -544.105 cm BT /F22 8.2889 Tf 186.258 544.105 Td [(;)]TJ ET 1 0 0 1 190.77 544.105 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -190.77 -544.105 cm BT /F22 8.2889 Tf 190.77 544.105 Td [(Ren)]TJ ET 1 0 0 1 205.275 544.105 cm 0 g 0 G 1 0 0 1 -205.275 -544.105 cm BT /F22 8.2889 Tf 205.275 544.105 Td [(,)]TJ ET 1 0 0 1 207.215 544.105 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 1.594 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -208.809 -544.105 cm BT /F22 8.2889 Tf 208.809 544.105 Td [(2006)]TJ ET 1 0 0 1 228.006 544.105 cm 0 g 0 G 1 0 0 1 -228.006 -544.105 cm BT /F22 8.2889 Tf 228.006 544.105 Td [(\051.)-193(One)-192(main)-192(re-)]TJ ET 1 0 0 1 32.706 544.105 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -544.105 cm BT /F22 8.2889 Tf 32.706 533.707 Td [(search)-227(issue)-227(in)-227(consensus)-227(problems)-227(is)-227(how)-227(to)-227(design)-227(effective)-227(con-)]TJ ET 1 0 0 1 32.706 533.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -533.707 cm BT /F22 8.2889 Tf 32.706 523.309 Td [(sensus)-397(pro)1(tocols,)-397(which)-397(are)-396(distributed)-397(interaction)-396(rules)-397(among)]TJ ET 1 0 0 1 32.706 523.309 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -523.309 cm BT /F22 8.2889 Tf 32.706 512.911 Td [(agents)-456(and)-456(are)-456(aimed)-456(at)-456(ensuring)-456(that)-456(the)-456(concerned)-456(states)-456(of)]TJ ET 1 0 0 1 32.706 512.911 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -512.911 cm BT /F22 8.2889 Tf 32.706 502.513 Td [(agents)-295(converge)-294(to)-295(a)-294(common)-295(value.)-294(This)-295(paper)-295(discusses)-294(the)-295(de-)]TJ ET 1 0 0 1 32.706 502.513 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -502.513 cm BT /F22 8.2889 Tf 32.706 492.115 Td [(sign)-305(problem)-305(of)-304(finite-time)-305(consensus)-305(protocols.)-305(It)-305(is)-305(well)-305(known)]TJ ET 1 0 0 1 32.706 492.115 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -492.115 cm BT /F22 8.2889 Tf 32.706 481.717 Td [(that)-408(finite-time)-409(convergence)-408(systems)-408(possess)-409(the)-408(advantages)-409(of)]TJ ET 1 0 0 1 32.706 481.717 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -481.717 cm BT /F22 8.2889 Tf 32.706 471.319 Td [(higher)-330(control)-331(accuracy,)-330(better)-331(disturbance)-330(rejection)-330(and)-331(robust-)]TJ ET 1 0 0 1 32.706 471.319 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -471.319 cm BT /F22 8.2889 Tf 32.706 460.921 Td [(ness)-278(against)-277(uncertainties)-278(\050)]TJ ET 1 0 0 1 137.094 460.921 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -137.094 -460.921 cm BT /F22 8.2889 Tf 137.094 460.921 Td [(Bhat)]TJ ET 1 0 0 1 154.508 460.921 cm 0 g 0 G 1 0 0 1 2.301 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -156.809 -460.921 cm BT /F22 8.2889 Tf 156.809 460.921 Td [(&)]TJ ET 1 0 0 1 162.57 460.921 cm 0 g 0 G 1 0 0 1 2.301 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -164.871 -460.921 cm BT /F22 8.2889 Tf 164.871 460.921 Td [(Bernstein,)]TJ ET 1 0 0 1 203.256 460.921 cm 0 g 0 G 1 0 0 1 2.302 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -205.558 -460.921 cm BT /F22 8.2889 Tf 205.558 460.921 Td [(2000)]TJ ET 1 0 0 1 224.754 460.921 cm 0 g 0 G 1 0 0 1 -224.754 -460.921 cm BT /F22 8.2889 Tf 224.754 460.921 Td [(;)]TJ ET 1 0 0 1 229.973 460.921 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -229.973 -460.921 cm BT /F22 8.2889 Tf 229.973 460.921 Td [(Haimo)]TJ ET 1 0 0 1 255.321 460.921 cm 0 g 0 G 1 0 0 1 -255.321 -460.921 cm BT /F22 8.2889 Tf 255.321 460.921 Td [(,)]TJ ET 1 0 0 1 257.26 460.921 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 2.301 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -259.561 -460.921 cm BT /F22 8.2889 Tf 259.561 460.921 Td [(1986)]TJ ET 1 0 0 1 278.758 460.921 cm 0 g 0 G 1 0 0 1 -278.758 -460.921 cm BT /F22 8.2889 Tf 278.758 460.921 Td [(\051.)]TJ ET 1 0 0 1 32.706 460.921 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -460.921 cm BT /F22 8.2889 Tf 32.706 450.523 Td [(So)-315(far)-314(several)-315(kinds)-315(of)-314(finite-time)-315(consensus)-314(protocols)-315(have)-315(been)]TJ ET 1 0 0 1 32.706 450.523 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -450.523 cm BT /F22 8.2889 Tf 32.706 440.125 Td [(presented,)-209(see)-209(\050)]TJ ET 1 0 0 1 91.774 440.125 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -91.774 -440.125 cm BT /F22 8.2889 Tf 91.774 440.125 Td [(Cort\351s)]TJ ET 1 0 0 1 116.01 440.125 cm 0 g 0 G 1 0 0 1 -116.01 -440.125 cm BT /F22 8.2889 Tf 116.01 440.125 Td [(,)]TJ ET 1 0 0 1 117.95 440.125 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 1.733 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -119.683 -440.125 cm BT /F22 8.2889 Tf 119.683 440.125 Td [(2006)]TJ ET 1 0 0 1 138.88 440.125 cm 0 g 0 G 1 0 0 1 -138.88 -440.125 cm BT /F22 8.2889 Tf 138.88 440.125 Td [(;)]TJ ET 1 0 0 1 143.531 440.125 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -143.531 -440.125 cm BT /F22 8.2889 Tf 143.531 440.125 Td [(Sundaram)]TJ ET 1 0 0 1 182.497 440.125 cm 0 g 0 G 1 0 0 1 1.733 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -184.23 -440.125 cm BT /F22 8.2889 Tf 184.23 440.125 Td [(&)]TJ ET 1 0 0 1 189.991 440.125 cm 0 g 0 G 1 0 0 1 1.732 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -191.723 -440.125 cm BT /F22 8.2889 Tf 191.723 440.125 Td [(Hadjicostis,)]TJ ET 1 0 0 1 235.737 440.125 cm 0 g 0 G 1 0 0 1 1.733 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -237.47 -440.125 cm BT /F22 8.2889 Tf 237.47 440.125 Td [(2007)]TJ ET 1 0 0 1 256.667 440.125 cm 0 g 0 G 1 0 0 1 -256.667 -440.125 cm BT /F22 8.2889 Tf 256.667 440.125 Td [(;)]TJ ET 1 0 0 1 261.318 440.125 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -261.318 -440.125 cm BT /F22 8.2889 Tf 261.318 440.125 Td [(Wang)]TJ ET 1 0 0 1 283.765 440.125 cm 0 g 0 G 1 0 0 1 -251.059 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.398 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -32.706 -429.727 cm BT /F22 8.2889 Tf 32.706 429.727 Td [(&)]TJ ET 1 0 0 1 38.467 429.727 cm 0 g 0 G 1 0 0 1 2.972 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -41.439 -429.727 cm BT /F22 8.2889 Tf 41.439 429.727 Td [(Hong,)]TJ ET 1 0 0 1 63.777 429.727 cm 0 g 0 G 1 0 0 1 2.973 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -66.75 -429.727 cm BT /F22 8.2889 Tf 66.75 429.727 Td [(2008)]TJ ET 1 0 0 1 85.947 429.727 cm 0 g 0 G 1 0 0 1 -85.947 -429.727 cm BT /F22 8.2889 Tf 85.947 429.727 Td [(;)]TJ ET 1 0 0 1 91.839 429.727 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -91.839 -429.727 cm BT /F22 8.2889 Tf 91.839 429.727 Td [(Xiao)]TJ ET 1 0 0 1 108.856 429.727 cm 0 g 0 G 1 0 0 1 2.972 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -111.828 -429.727 cm BT /F22 8.2889 Tf 111.828 429.727 Td [(&)]TJ ET 1 0 0 1 117.589 429.727 cm 0 g 0 G 1 0 0 1 2.972 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -120.561 -429.727 cm BT /F22 8.2889 Tf 120.561 429.727 Td [(Wang,)]TJ ET 1 0 0 1 144.947 429.727 cm 0 g 0 G 1 0 0 1 2.973 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -147.92 -429.727 cm BT /F22 8.2889 Tf 147.92 429.727 Td [(2007)]TJ ET 1 0 0 1 167.117 429.727 cm 0 g 0 G 1 0 0 1 -167.117 -429.727 cm BT /F22 8.2889 Tf 167.117 429.727 Td [(\051.)-359(Compared)-359(with)-358(the)-359(existing)]TJ ET 1 0 0 1 32.706 429.727 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -429.727 cm BT /F22 8.2889 Tf 32.706 419.329 Td [(ones,)-287(our)-287(proposed)-287(protocols)-287(are)-287(in)-287(different)-287(forms)-287(and)-287(can)-287(guar-)]TJ ET 1 0 0 1 32.706 419.329 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -419.329 cm BT /F22 8.2889 Tf 32.706 408.931 Td [(antee)-294(the)-294(states)-293(of)-294(agents)-294(to)-294(reach)-294(co)1(nsensus)-294(in)-294(finite)-294(time)-294(under)]TJ ET 1 0 0 1 32.706 408.931 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -408.931 cm BT /F22 8.2889 Tf 32.706 398.533 Td [(more)-250(relaxable)-250(conditions.)]TJ ET 1 0 0 1 32.706 398.533 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -398.533 cm BT /F22 8.2889 Tf 44.661 388.166 Td [(The)-416(contributions)-416(of)-416(this)-416(paper)-416(are)-416(twofold.)-417(First,)-416(this)-416(paper)]TJ ET 1 0 0 1 32.706 388.166 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -388.166 cm BT /F22 8.2889 Tf 32.706 377.768 Td [(presents)-168(a)-169(class)-168(of)-169(new)-168(nonlinear)-169(consensus)-168(protocols)-169(for)-168(state)-169(con-)]TJ ET 1 0 0 1 32.706 377.768 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -377.768 cm BT /F22 8.2889 Tf 32.706 367.37 Td [(sensus)-257(of)-258(multi-agent)-257(systems.)-258(These)-257(protocols)-258(have)-257(the)-258(form)-257(of)-258(a)]TJ ET 1 0 0 1 32.706 367.37 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -367.37 cm BT /F22 8.2889 Tf 32.706 356.972 Td [(continuous)-276(state)-275(feedback)-276(and)-275(bridge)-276(the)-275(gap)-276(between)-276(asymptot-)]TJ ET 1 0 0 1 32.706 356.972 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -356.972 cm BT /F22 8.2889 Tf 32.706 346.574 Td [(ical)-293(consensus)-294(protocols)-293(and)-293(discontinuous)-293(finite-time)-294(consensus)]TJ ET 1 0 0 1 32.706 346.574 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -346.574 cm BT /F22 8.2889 Tf 32.706 336.176 Td [(protocols)-290(\050)]TJ ET 1 0 0 1 73.871 336.176 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -73.871 -336.176 cm BT /F22 8.2889 Tf 73.871 336.176 Td [(Cort\351s,)]TJ ET 1 0 0 1 100.047 336.176 cm 0 g 0 G 1 0 0 1 2.407 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -102.454 -336.176 cm BT /F22 8.2889 Tf 102.454 336.176 Td [(2006)]TJ ET 1 0 0 1 121.651 336.176 cm 0 g 0 G 1 0 0 1 -121.651 -336.176 cm BT /F22 8.2889 Tf 121.651 336.176 Td [(\051.)-291(S)1(econd,)-291(by)-290(applying)-290(the)-291(finite-time)-290(con-)]TJ ET 1 0 0 1 32.706 336.176 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -336.176 cm BT /F22 8.2889 Tf 32.706 325.778 Td [(vergence)-308(protocols,)-309(this)-308(paper)-309(develops)-308(a)-309(new)-308(finite-time)-309(forma-)]TJ ET 1 0 0 1 32.706 325.778 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -325.778 cm BT /F22 8.2889 Tf 32.706 315.38 Td [(tion)-358(framework)-357(for)-358(multi-agent)-357(systems)-358(with)-357(a)-358(large)-358(population)]TJ ET 1 0 0 1 32.706 315.38 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -315.38 cm BT /F22 8.2889 Tf 32.706 304.982 Td [(of)-234(members)-235(and)-234(considers)-234(time-invariant)-234(formation,)-235(time-varying)]TJ ET 1 0 0 1 32.706 304.982 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -304.982 cm BT /F22 8.2889 Tf 32.706 294.584 Td [(formation)-250(and)-250(trajectory)-250(tracking)-250(problem)-250(respectively.)]TJ ET 1 0 0 1 32.706 294.584 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -294.584 cm BT /F22 8.2889 Tf 44.661 284.217 Td [(An)-549(outline)-549(of)-549(this)-549(paper)-549(is)-549(as)-548(follows:)-550(in)-549(Section)]TJ ET 1 0 0 1 252.033 284.217 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -252.033 -284.217 cm BT /F22 8.2889 Tf 252.033 284.217 Td [(2)]TJ ET 1 0 0 1 256.832 284.217 cm 0 g 0 G 1 0 0 1 -256.832 -284.217 cm BT /F22 8.2889 Tf 256.832 284.217 Td [(,)-549(some)]TJ ET 1 0 0 1 32.706 284.217 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -284.217 cm BT /F22 8.2889 Tf 32.706 273.819 Td [(preliminary)-271(notions)-272(in)-271(graph)-271(theory)-271(and)-272(a)-271(preliminary)-271(lemma)-272(are)]TJ ET 1 0 0 1 32.706 273.819 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -273.819 cm BT /F22 8.2889 Tf 32.706 263.421 Td [(assembled;)-323(in)-322(Section)]TJ ET 1 0 0 1 119.444 263.421 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -119.444 -263.421 cm BT /F22 8.2889 Tf 119.444 263.421 Td [(3)]TJ ET 1 0 0 1 124.244 263.421 cm 0 g 0 G 1 0 0 1 -124.244 -263.421 cm BT /F22 8.2889 Tf 124.244 263.421 Td [(,)-322(the)-323(problem)-322(is)-323(formulated;)-322(in)-323(Section)]TJ ET 1 0 0 1 277.026 263.421 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -277.026 -263.421 cm BT /F22 8.2889 Tf 277.026 263.421 Td [(4)]TJ ET 1 0 0 1 281.825 263.421 cm 0 g 0 G 1 0 0 1 -281.825 -263.421 cm BT /F22 8.2889 Tf 281.825 263.421 Td [(,)]TJ ET 1 0 0 1 32.706 263.421 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -263.421 cm BT /F22 8.2889 Tf 32.706 253.023 Td [(the)-197(main)-197(results)-198(a)1(re)-198(presented;)-197(in)-197(Section)]TJ ET 1 0 0 1 190.462 253.023 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -190.462 -253.023 cm BT /F22 8.2889 Tf 190.462 253.023 Td [(5)]TJ ET 1 0 0 1 195.261 253.023 cm 0 g 0 G 1 0 0 1 -195.261 -253.023 cm BT /F22 8.2889 Tf 195.261 253.023 Td [(,)-197(numerical)-197(simulations)]TJ ET 1 0 0 1 32.706 253.023 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -253.023 cm BT /F22 8.2889 Tf 32.706 242.625 Td [(are)-326(given)-325(to)-326(illustrate)-326(the)-326(effectiveness)-325(of)-326(the)-326(theoretical)-326(results;)]TJ ET 1 0 0 1 32.706 242.625 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -242.625 cm BT /F22 8.2889 Tf 32.706 232.227 Td [(finally,)-250(concluding)-250(remarks)-250(are)-250(made)-250(in)-250(Section)]TJ ET 1 0 0 1 215.533 232.227 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -215.533 -232.227 cm BT /F22 8.2889 Tf 215.533 232.227 Td [(6)]TJ ET 1 0 0 1 220.332 232.227 cm 0 g 0 G 1 0 0 1 -220.332 -232.227 cm BT /F22 8.2889 Tf 220.332 232.227 Td [(.)]TJ ET 1 0 0 1 32.706 232.227 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -232.227 cm BT /F153 8.2889 Tf 32.706 218.997 Td [(Notation:)]TJ/F22 8.2889 Tf 41.492 0 Td [(In)-426(this)-426(paper,)]TJ/F181 8.9265 Tf 56.395 0 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.434 Td [(n)]TJ/F22 8.2889 Tf 7.384 1.434 Td [(denotes)-426(the)-426(index)-427(set)]TJ/F179 9.5641 Tf 89.319 0 Td [(f)]TJ/F22 8.2889 Tf 3.538 0 Td [(1)]TJ/F185 9.5641 Tf 4.8 0 Td [(;)]TJ/F22 8.2889 Tf 4.759 0 Td [(2)]TJ/F185 9.5641 Tf 4.8 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.191 0 Td [(n)]TJ/F179 9.5641 Tf 4.791 0 Td [(g)]TJ/F22 8.2889 Tf 3.539 0 Td [(;)]TJ ET 1 0 0 1 32.706 218.997 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -218.997 cm BT /F41 8.2889 Tf 32.706 208.599 Td [(I)]TJ/F41 5.8022 Tf 2.495 -1.435 Td [(N)]TJ/F22 8.2889 Tf 8.57 1.435 Td [(is)-420(the)]TJ/F41 8.2889 Tf 25.629 0 Td [(N)]TJ/F179 9.5641 Tf 10.127 0 Td [(\002)]TJ/F41 8.2889 Tf 11.072 0 Td [(N)]TJ/F22 8.2889 Tf 10.038 0 Td [(identity)-420(matrix;)-421(and)]TJ/F179 9.5641 Tf 83.193 0 Td [(\012)]TJ/F22 8.2889 Tf 11.137 0 Td [(denotes)-420(the)-421(Kronecker)]TJ ET 1 0 0 1 32.706 208.599 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -208.599 cm BT /F22 8.2889 Tf 32.706 198.201 Td [(product.)-292(If)]TJ/F41 8.2889 Tf 42.144 0 Td [(b)]TJ/F22 8.2889 Tf 6.918 0 Td [(is)-292(a)-291(vector,)-292(then)-291(diag)]TJ/F185 9.5641 Tf 79.801 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(b)]TJ/F185 9.5641 Tf 4.501 0 Td [(/)]TJ/F22 8.2889 Tf 5.985 0 Td [(denotes)-292(the)-291(diagonal)-292(matrix)]TJ ET 1 0 0 1 32.706 198.201 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -198.201 cm BT /F22 8.2889 Tf 32.706 187.803 Td [(with)-324(the)]TJ/F41 8.2889 Tf 35.575 0 Td [(i)]TJ/F22 8.2889 Tf 2.37 0 Td [(th)-324(diagonal)-325(entry)-324(being)-325(the)]TJ/F41 8.2889 Tf 108.312 0 Td [(i)]TJ/F22 8.2889 Tf 2.371 0 Td [(th)-324(element)-325(of)-324(vector)]TJ/F41 8.2889 Tf 81.701 0 Td [(b)]TJ/F22 8.2889 Tf 4.501 0 Td [(.)-325(Let)]TJ ET 1 0 0 1 32.706 187.803 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -187.803 cm BT /F22 8.2889 Tf 32.706 177.405 Td [(sig)]TJ/F185 9.5641 Tf 10.676 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(r)]TJ/F185 9.5641 Tf 4.04 0 Td [(/)]TJ/F185 6.6948 Tf 3.568 3.472 Td [(\013)]TJ/F179 9.5641 Tf 8.018 -3.472 Td [(D)]TJ/F22 8.2889 Tf 10.89 0 Td [(sign)]TJ/F185 9.5641 Tf 15.699 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(r)]TJ/F185 9.5641 Tf 4.041 0 Td [(/)]TJ/F179 9.5641 Tf 3.567 0 Td [(j)]TJ/F41 8.2889 Tf 2.736 0 Td [(r)]TJ/F179 9.5641 Tf 4.041 0 Td [(j)]TJ/F185 6.6948 Tf 2.735 3.472 Td [(\013)]TJ/F22 8.2889 Tf 4.589 -3.472 Td [(,)-286(where)]TJ/F185 9.5641 Tf 30.948 0 Td [(\013)-399(>)]TJ/F22 8.2889 Tf 20.163 0 Td [(0,)]TJ/F41 8.2889 Tf 9.113 0 Td [(r)]TJ/F179 9.5641 Tf 7.471 0 Td [(2)]TJ/F169 8.6077 Tf 9.445 0 Td [(R)]TJ/F22 8.2889 Tf 8.59 0 Td [(and)-286(sign)]TJ/F185 9.5641 Tf 32.322 0 Td [(.)]TJ/F179 9.5641 Tf 3.567 0 Td [(\001)]TJ/F185 9.5641 Tf 2.659 0 Td [(/)]TJ/F22 8.2889 Tf 5.941 0 Td [(is)-286(the)-287(sign)]TJ ET 1 0 0 1 32.706 177.405 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -177.405 cm BT /F22 8.2889 Tf 32.706 167.007 Td [(function.)-281(If)]TJ/F41 8.2889 Tf 43.974 0 Td [(r)]TJ/F22 8.2889 Tf 6.37 0 Td [(is)-281(a)-281(vector,)-281(sig)]TJ/F185 9.5641 Tf 54.094 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(r)]TJ/F185 9.5641 Tf 4.041 0 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.472 Td [(\013)]TJ/F22 8.2889 Tf 6.918 -3.472 Td [(denotes)-281(the)-281(vector)-281(with)-281(the)-281(same)]TJ ET 1 0 0 1 32.706 167.007 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -167.007 cm BT /F22 8.2889 Tf 32.706 156.609 Td [(dimensions)-250(as)]TJ/F41 8.2889 Tf 56.223 0 Td [(r)]TJ/F22 8.2889 Tf 4.041 0 Td [(,)-250(obtained)-250(by)-250(operating)-250(sig)]TJ/F185 9.5641 Tf 100.734 0 Td [(.)]TJ/F179 9.5641 Tf 3.568 0 Td [(\001)]TJ/F185 9.5641 Tf 2.659 0 Td [(/)]TJ/F185 6.6948 Tf 3.567 3.472 Td [(\013)]TJ/F22 8.2889 Tf 6.661 -3.472 Td [(on)-250(each)-250(entry)-250(of)]TJ/F41 8.2889 Tf 63.534 0 Td [(r)]TJ/F22 8.2889 Tf 4.041 0 Td [(.)]TJ ET 1 0 0 1 32.706 156.609 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -156.609 cm BT /F153 8.2889 Tf 32.706 133.849 Td [(2.)-500(Preliminaries)]TJ ET 1 0 0 1 32.706 133.849 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -133.849 cm BT /F22 8.2889 Tf 44.661 113.147 Td [(Directed)-188(graph)-189(is)-188(used)-188(to)-188(model)-189(the)-188(interaction)-188(topology)-188(among)]TJ ET 1 0 0 1 32.706 113.147 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -113.147 cm BT /F22 8.2889 Tf 32.706 102.749 Td [(agents.)-236(A)-237(directed)-236(graph)]TJ/F181 8.9265 Tf 93.906 0 Td [(G)]TJ/F22 8.2889 Tf 7.69 0 Td [(consists)-236(of)-237(a)-236(vertex)-236(set)]TJ/F181 8.9265 Tf 87.36 0 Td [(V)]TJ/F185 9.5641 Tf 7.123 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)-278(f)]TJ/F185 9.5641 Tf 13.656 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F179 9.5641 Tf 4.814 1.435 Td [(V)]TJ/F41 8.2889 Tf 5.287 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(2)]TJ ET 1 0 0 1 32.706 102.749 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -102.749 cm BT /F181 8.9265 Tf 32.706 92.351 Td [(I)]TJ/F41 5.8022 Tf 5.133 -1.435 Td [(n)]TJ/F179 9.5641 Tf 3.852 1.435 Td [(g)]TJ/F22 8.2889 Tf 5.304 0 Td [(and)-213(an)-213(edge)-213(set)]TJ/F181 8.9265 Tf 59.921 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(\032)-278(f)]TJ/F185 9.5641 Tf 13.655 0 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(V)]TJ/F185 9.5641 Tf 5.287 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.418 -1.435 Td [(j)]TJ/F179 9.5641 Tf 4.831 1.435 Td [(2)]TJ/F181 8.9265 Tf 8.673 0 Td [(V)]TJ/F185 9.5641 Tf 7.123 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(/)]TJ/F179 9.5641 Tf 3.568 0 Td [(g)]TJ/F22 8.2889 Tf 3.539 0 Td [(.)-213(Edges)-213(such)-213(as)]TJ ET 1 0 0 1 32.706 92.351 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -92.351 cm BT /F185 9.5641 Tf 32.706 81.953 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(/)]TJ/F22 8.2889 Tf 5.396 0 Td [(are)-221(called)]TJ/F41 8.2889 Tf 38.221 0 Td [(self-loops)]TJ/F22 8.2889 Tf 34.598 0 Td [(.)-221(If)]TJ/F185 9.5641 Tf 10.936 0 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.418 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(V)]TJ/F185 9.5641 Tf 7.124 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)]TJ/F185 9.5641 Tf 3.769 0 Td [(v)]TJ/F41 5.8022 Tf 4.657 -1.435 Td [(i)]TJ/F22 8.2889 Tf 3.986 1.435 Td [(is)-221(called)-220(the)]TJ/F41 8.2889 Tf 46.657 0 Td [(parent)]TJ ET 1 0 0 1 32.706 81.953 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -81.953 cm BT /F22 8.2889 Tf 32.706 71.555 Td [(vertex)-233(of)]TJ/F185 9.5641 Tf 35.624 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(j)]TJ/F22 8.2889 Tf 2.175 1.435 Td [(.)-233(A)]TJ/F41 8.2889 Tf 11.281 0 Td [(path)]TJ/F22 8.2889 Tf 18.566 0 Td [(in)-233(directed)-233(graph)]TJ/F181 8.9265 Tf 66.997 0 Td [(G)]TJ/F22 8.2889 Tf 7.661 0 Td [(from)]TJ/F185 9.5641 Tf 20.473 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F22 4.9734 Tf 1.659 -1.353 Td [(1)]TJ/F22 8.2889 Tf 5.807 2.788 Td [(to)]TJ/F185 9.5641 Tf 9.722 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F41 4.9734 Tf 1.659 -1.352 Td [(k)]TJ/F22 8.2889 Tf 5.513 2.787 Td [(is)-233(a)-233(sequence)]TJ ET 1 0 0 1 32.706 71.555 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -71.555 cm BT /F185 9.5641 Tf 32.706 61.157 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F22 4.9734 Tf 1.659 -1.353 Td [(1)]TJ/F185 9.5641 Tf 3.876 2.788 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(i)]TJ/F22 4.9734 Tf 1.66 -1.353 Td [(2)]TJ/F185 9.5641 Tf 3.876 2.788 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(v)]TJ/F41 5.8022 Tf 26.849 -1.435 Td [(i)]TJ/F41 4.9734 Tf 1.66 -1.352 Td [(k)]TJ/F22 8.2889 Tf 6.558 2.787 Td [(of)-359(finite)-359(vertices)-359(such)-359(that)]TJ/F185 9.5641 Tf 105.576 0 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.435 Td [(i)]TJ/F41 4.9734 Tf 1.659 -1.352 Td [(j)]TJ/F185 9.5641 Tf 2.434 2.787 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(i)]TJ/F41 4.9734 Tf 1.66 -1.353 Td [(j)]TJ/F179 5.7385 Tf 1.437 0 Td [(C)]TJ/F22 4.9734 Tf 4.476 0 Td [(1)]TJ/F185 9.5641 Tf 3.876 2.788 Td [(/)]TJ/F179 9.5641 Tf 8.541 0 Td [(2)]TJ/F181 8.9265 Tf 10.989 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(/)]TJ/F22 8.2889 Tf 6.543 0 Td [(for)]TJ ET 1 0 0 1 32.706 61.157 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -61.157 cm BT /F41 8.2889 Tf 32.706 50.759 Td [(j)]TJ/F179 9.5641 Tf 8.474 0 Td [(D)]TJ/F22 8.2889 Tf 13.539 0 Td [(1)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)]TJ/F22 8.2889 Tf 4.76 0 Td [(2)]TJ/F185 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F41 8.2889 Tf 22.192 0 Td [(k)]TJ/F179 9.5641 Tf 7.804 0 Td [(\000)]TJ/F22 8.2889 Tf 10.954 0 Td [(1.)-412(If)]TJ/F41 8.2889 Tf 18.899 0 Td [(i)]TJ/F22 5.8022 Tf 2.37 -1.435 Td [(1)]TJ/F179 9.5641 Tf 9.936 1.435 Td [(D)]TJ/F41 8.2889 Tf 13.539 0 Td [(i)]TJ/F41 5.8022 Tf 2.371 -1.435 Td [(k)]TJ/F22 8.2889 Tf 3.515 1.435 Td [(,)-411(then)-411(this)-411(path)-411(is)-411(also)-411(called)-411(a)]TJ ET 1 0 0 1 32.706 50.759 cm 0 g 0 G 0 g 0 G 1 0 0 1 -32.706 -50.759 cm BT /F41 8.2889 Tf 32.706 40.361 Td [(loop)]TJ/F22 8.2889 Tf 15.716 0 Td [(.)-308(Directed)-307(graph)]TJ/F181 8.9265 Tf 64.298 0 Td [(G)]TJ/F22 8.2889 Tf 8.278 0 Td [(is)]TJ/F41 8.2889 Tf 8.731 0 Td [(strongly)-307(connected)]TJ/F22 8.2889 Tf 71.745 0 Td [(if)-307(between)-308(every)-307(pair)]TJ ET 1 0 0 1 32.706 40.361 cm 0 g 0 G 0 g 0 G 1 0 0 1 260.025 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -292.731 -40.361 cm BT /F22 8.2889 Tf 301.697 720.809 Td [(of)-322(distinct)-321(vertices)]TJ/F185 9.5641 Tf 74.092 0 Td [(v)]TJ/F41 5.8022 Tf 4.657 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(j)]TJ/F22 8.2889 Tf 2.175 1.435 Td [(,)-322(there)-321(exists)-322(a)-321(path)-322(that)-321(begins)-322(at)]TJ/F185 9.5641 Tf 134.831 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F22 8.2889 Tf 4.822 1.435 Td [(and)]TJ ET 1 0 0 1 301.697 720.809 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -720.809 cm BT /F22 8.2889 Tf 301.697 710.394 Td [(ends)-278(at)]TJ/F185 9.5641 Tf 29.999 0 Td [(v)]TJ/F41 5.8022 Tf 4.657 -1.435 Td [(j)]TJ/F22 8.2889 Tf 2.175 1.435 Td [(.)-278(Directed)-277(graph)]TJ/F181 8.9265 Tf 63.558 0 Td [(G)]TJ/F22 8.2889 Tf 8.031 0 Td [(is)-278(said)-277(to)]TJ/F41 8.2889 Tf 36.286 0 Td [(have)-278(a)-277(spanning)-278(tree)]TJ/F22 8.2889 Tf 78.572 0 Td [(if)-278(there)]TJ ET 1 0 0 1 301.697 710.394 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -710.394 cm BT /F22 8.2889 Tf 301.697 699.979 Td [(exists)-194(a)-195(vertex)-194(that)-194(is)-195(called)-194(the)]TJ/F41 8.2889 Tf 118.475 0 Td [(root)]TJ/F22 8.2889 Tf 17.38 0 Td [(which)-194(can)-195(be)-194(connected)-194(to)-195(any)]TJ ET 1 0 0 1 301.697 699.979 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -699.979 cm BT /F22 8.2889 Tf 301.697 689.563 Td [(others)-250(through)-250(paths.)]TJ ET 1 0 0 1 301.697 689.563 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -689.563 cm BT /F22 8.2889 Tf 313.653 679.171 Td [(A)]TJ/F41 8.2889 Tf 7.71 0 Td [(subgraph)]TJ/F181 8.9265 Tf 36.166 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(s)]TJ/F22 8.2889 Tf 5.106 1.435 Td [(of)-270(directed)-270(graph)]TJ/F181 8.9265 Tf 67.875 0 Td [(G)]TJ/F22 8.2889 Tf 7.971 0 Td [(is)-270(a)-270(directed)-271(graph)-270(such)-270(that)]TJ ET 1 0 0 1 301.697 679.171 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -679.171 cm BT /F181 8.9265 Tf 301.697 668.756 Td [(V)]TJ/F185 9.5641 Tf 7.124 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(s)]TJ/F185 9.5641 Tf 2.865 1.435 Td [(/)]TJ/F179 9.5641 Tf 9.719 0 Td [(\032)]TJ/F181 8.9265 Tf 13.611 0 Td [(V)]TJ/F185 9.5641 Tf 7.124 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(/)]TJ/F22 8.2889 Tf 7.002 0 Td [(and)]TJ/F181 8.9265 Tf 17.684 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(s)]TJ/F185 9.5641 Tf 2.865 1.435 Td [(/)]TJ/F179 9.5641 Tf 9.719 0 Td [(\032)]TJ/F181 8.9265 Tf 13.611 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(.)-415(If)-415(for)-414(any)]TJ/F185 9.5641 Tf 45.743 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.418 -1.435 Td [(j)]TJ/F179 9.5641 Tf 8.326 1.435 Td [(2)]TJ/F181 8.9265 Tf 12.167 0 Td [(V)]TJ/F185 9.5641 Tf 7.123 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(s)]TJ/F185 9.5641 Tf 2.865 1.435 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)]TJ ET 1 0 0 1 301.697 668.756 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -668.756 cm BT /F185 9.5641 Tf 301.697 658.341 Td [(.v)]TJ/F41 5.8022 Tf 8.226 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 10.723 0 Td [(2)]TJ/F181 8.9265 Tf 13.171 0 Td [(E)]TJ/F185 9.5641 Tf 5.855 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(s)]TJ/F185 9.5641 Tf 2.865 1.435 Td [(/)]TJ/F179 9.5641 Tf 17.877 0 Td [(\050)167(\051)]TJ/F185 9.5641 Tf 32.667 0 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 10.722 0 Td [(2)]TJ/F181 8.9265 Tf 13.171 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(/)]TJ/F22 8.2889 Tf 3.567 0 Td [(,)-462(then)]TJ/F181 8.9265 Tf 27.093 0 Td [(G)]TJ/F41 5.8022 Tf 5.73 -1.435 Td [(s)]TJ/F22 8.2889 Tf 6.692 1.435 Td [(is)-462(called)]TJ ET 1 0 0 1 301.697 658.341 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -658.341 cm BT /F22 8.2889 Tf 301.697 647.926 Td [(an)]TJ/F41 8.2889 Tf 12.97 0 Td [(induced)-441(subgraph)]TJ/F22 8.2889 Tf 66.457 0 Td [(.)-442(In)-441(this)-440(case,)]TJ/F181 8.9265 Tf 56.722 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(s)]TJ/F22 8.2889 Tf 6.518 1.435 Td [(is)-441(also)-440(said)-441(to)-441(be)-440(induced)]TJ ET 1 0 0 1 301.697 647.926 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -647.926 cm BT /F22 8.2889 Tf 301.697 637.51 Td [(by)]TJ/F181 8.9265 Tf 11.722 0 Td [(V)]TJ/F185 9.5641 Tf 7.124 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.434 Td [(s)]TJ/F185 9.5641 Tf 2.865 1.434 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(.)-287(A)]TJ/F41 8.2889 Tf 12.181 0 Td [(strongly)-287(connected)-287(component)]TJ/F22 8.2889 Tf 115.332 0 Td [(is)-287(an)-287(induced)-288(subgraph)]TJ ET 1 0 0 1 301.697 637.51 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -637.51 cm BT /F22 8.2889 Tf 301.697 627.095 Td [(that)-493(is)-493(maximal,)-494(subject)-493(to)-493(being)-493(strongly)-493(connected.)-495(Suppose)]TJ ET 1 0 0 1 301.697 627.095 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -627.095 cm BT /F22 8.2889 Tf 301.697 616.68 Td [(that)-379(all)-380(strongly)-379(connected)-379(components)-379(of)]TJ/F181 8.9265 Tf 169.132 0 Td [(G)]TJ/F22 8.2889 Tf 8.875 0 Td [(are)]TJ/F181 8.9265 Tf 15.196 0 Td [(G)]TJ/F22 5.8022 Tf 5.731 -1.435 Td [(1)]TJ/F22 8.2889 Tf 3.857 1.435 Td [(,)]TJ/F181 8.9265 Tf 5.085 0 Td [(G)]TJ/F22 5.8022 Tf 5.731 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F181 8.9265 Tf 22.192 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(p)]TJ/F22 8.2889 Tf 3.724 1.435 Td [(.)]TJ ET 1 0 0 1 301.697 616.68 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -616.68 cm BT /F22 8.2889 Tf 301.697 606.265 Td [(We)-304(define)-304(another)-303(directed)-304(graph)]TJ/F181 8.9265 Tf 133.093 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.472 Td [(c)]TJ/F22 8.2889 Tf 6.036 -3.472 Td [(related)-304(to)]TJ/F181 8.9265 Tf 39.741 0 Td [(G)]TJ/F22 8.2889 Tf 8.249 0 Td [(with)-304(vertex)-304(set)]TJ ET 1 0 0 1 301.697 606.265 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -606.265 cm BT /F179 9.5641 Tf 301.697 595.85 Td [(f)]TJ/F181 8.9265 Tf 3.539 0 Td [(G)]TJ/F22 5.8022 Tf 5.731 -1.435 Td [(1)]TJ/F185 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F181 8.9265 Tf 4.76 0 Td [(G)]TJ/F22 5.8022 Tf 5.731 -1.435 Td [(2)]TJ/F185 9.5641 Tf 3.858 1.435 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F181 8.9265 Tf 22.191 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(p)]TJ/F179 9.5641 Tf 3.724 1.435 Td [(g)]TJ/F22 8.2889 Tf 3.539 0 Td [(,)-209(satisfying)-208(the)-209(assumption)-209(that)-209(no)-208(self-loop)-209(exists)]TJ ET 1 0 0 1 301.697 595.85 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -595.85 cm BT /F22 8.2889 Tf 301.697 585.434 Td [(in)]TJ/F181 8.9265 Tf 9.175 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 3.472 Td [(c)]TJ/F22 8.2889 Tf 5.183 -3.472 Td [(and)-201(satisfying)-201(the)-200(property)-201(that)-201(for)-201(any)]TJ/F41 8.2889 Tf 148.568 0 Td [(i)]TJ/F179 9.5641 Tf 5.028 0 Td [(6)1(D)]TJ/F41 8.2889 Tf 10.116 0 Td [(j)]TJ/F22 8.2889 Tf 2.396 0 Td [(,)]TJ/F185 9.5641 Tf 3.605 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.157 1.434 Td [(;)]TJ/F181 8.9265 Tf 4.76 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.434 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.434 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F41 5.8022 Tf 5.73 3.472 Td [(c)]TJ/F185 9.5641 Tf 3.519 -3.472 Td [(/)]TJ ET 1 0 0 1 301.697 585.434 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -585.434 cm BT /F22 8.2889 Tf 301.697 575.019 Td [(if)-341(and)-342(only)-341(if)-341(there)-342(exist)-341(a)-341(vertex)]TJ/F185 9.5641 Tf 131.184 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.479 Td [(i)]TJ/F179 5.7385 Tf 1.659 1.935 Td [(0)]TJ/F179 9.5641 Tf 7.143 -0.456 Td [(2)]TJ/F181 8.9265 Tf 10.613 0 Td [(V)]TJ/F185 9.5641 Tf 7.124 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.434 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.434 Td [(/)]TJ/F22 8.2889 Tf 6.396 0 Td [(and)-341(a)-342(vertex)]TJ/F185 9.5641 Tf 51.332 0 Td [(v)]TJ/F41 5.8022 Tf 4.658 -1.479 Td [(j)]TJ/F179 5.7385 Tf 1.677 1.935 Td [(0)]TJ/F179 9.5641 Tf 7.143 -0.456 Td [(2)]TJ ET 1 0 0 1 301.697 575.019 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -575.019 cm BT /F181 8.9265 Tf 301.697 564.604 Td [(V)]TJ/F185 9.5641 Tf 7.124 0 Td [(.)]TJ/F181 8.9265 Tf 3.567 0 Td [(G)]TJ/F41 5.8022 Tf 5.731 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F22 8.2889 Tf 5.639 0 Td [(such)-250(that)]TJ/F185 9.5641 Tf 37.317 0 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.479 Td [(i)]TJ/F179 5.7385 Tf 1.659 1.934 Td [(0)]TJ/F185 9.5641 Tf 2.546 -0.455 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.479 Td [(j)]TJ/F179 5.7385 Tf 1.677 1.934 Td [(0)]TJ/F185 9.5641 Tf 2.546 -0.455 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(2)]TJ/F181 8.9265 Tf 8.672 0 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(.)]TJ ET 1 0 0 1 301.697 564.604 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -564.604 cm BT /F22 8.2889 Tf 313.653 554.212 Td [(A)]TJ/F41 8.2889 Tf 9.067 0 Td [(weighted)-434(directed)-434(graph)]TJ/F181 8.9265 Tf 95.034 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 7.166 0 Td [(is)-434(a)-434(directed)-434(graph)]TJ/F181 8.9265 Tf 78.565 0 Td [(G)]TJ/F22 8.2889 Tf 9.329 0 Td [(with)-434(a)]TJ ET 1 0 0 1 301.697 554.212 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -554.212 cm BT /F22 8.2889 Tf 301.697 543.797 Td [(nonnegative)-297(weight)-298(matrix)]TJ/F41 8.2889 Tf 106.871 0 Td [(A)]TJ/F179 9.5641 Tf 8.695 0 Td [(D)-383(T)]TJ/F41 8.2889 Tf 14.31 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(ij)]TJ/F179 9.5641 Tf 3.834 1.435 Td [(U)-383(2)]TJ/F169 8.6077 Tf 16.53 0 Td [(R)]TJ/F41 5.8022 Tf 6.216 3.471 Td [(n)]TJ/F179 6.6948 Tf 3.354 0 Td [(\002)]TJ/F41 5.8022 Tf 5.249 0 Td [(n)]TJ/F22 8.2889 Tf 3.851 -3.471 Td [(,)-298(such)-297(that)]TJ/F185 9.5641 Tf 42.508 0 Td [(.v)]TJ/F41 5.8022 Tf 8.225 -1.435 Td [(i)]TJ/F185 9.5641 Tf 2.158 1.435 Td [(;)-167(v)]TJ/F41 5.8022 Tf 9.417 -1.435 Td [(j)]TJ/F185 9.5641 Tf 2.175 1.435 Td [(/)]TJ/F179 9.5641 Tf 7.232 0 Td [(2)]TJ ET 1 0 0 1 301.697 543.797 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -543.797 cm BT /F181 8.9265 Tf 301.697 533.381 Td [(E)]TJ/F185 9.5641 Tf 5.856 0 Td [(.)]TJ/F181 8.9265 Tf 3.568 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(/)]TJ/F179 9.5641 Tf 8.72 0 Td [(,)]TJ/F41 8.2889 Tf 15.128 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.434 Td [(ji)]TJ/F185 9.5641 Tf 8.986 1.434 Td [(>)]TJ/F22 8.2889 Tf 12.613 0 Td [(0.)-368(In)-368(this)-367(paper,)-367(it)-368(is)-367(assumed)-368(that)-367(the)-368(diagonal)]TJ ET 1 0 0 1 301.697 533.381 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -533.381 cm BT /F22 8.2889 Tf 301.697 522.966 Td [(entries)-253(of)-253(mat)1(rix)]TJ/F41 8.2889 Tf 65.716 0 Td [(A)]TJ/F22 8.2889 Tf 7.126 0 Td [(are)-253(all)-253(zeros.)-252(Let)]TJ/F41 8.2889 Tf 63.509 0 Td [(L)]TJ/F185 9.5641 Tf 3.929 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F179 9.5641 Tf 6.282 0 Td [(D)-284(T)]TJ/F41 8.2889 Tf 13.36 0 Td [(l)]TJ/F41 5.8022 Tf 2.271 -1.434 Td [(ij)]TJ/F179 9.5641 Tf 3.835 1.434 Td [(U)-284(2)]TJ/F169 8.6077 Tf 14.63 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(n)]TJ/F179 6.6948 Tf 3.353 0 Td [(\002)]TJ/F41 5.8022 Tf 5.249 0 Td [(n)]TJ/F22 8.2889 Tf 5.947 -3.472 Td [(denote)-253(the)]TJ ET 1 0 0 1 301.697 522.966 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -522.966 cm BT /F41 8.2889 Tf 301.697 512.551 Td [(graph)-250(Laplacian)]TJ/F22 8.2889 Tf 60.351 0 Td [(of)]TJ/F181 8.9265 Tf 9.533 0 Td [(G)]TJ/F185 9.5641 Tf 5.73 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F22 8.2889 Tf 3.568 0 Td [(,)-250(which)-250(is)-250(defined)-250(by)]TJ ET 1 0 0 1 301.697 512.551 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -512.551 cm BT /F41 8.2889 Tf 301.697 481.729 Td [(l)]TJ/F41 5.8022 Tf 2.272 -1.434 Td [(ij)]TJ/F179 9.5641 Tf 6.491 1.434 Td [(D)]TJ/F189 9.5641 Tf 10.116 22.476 Td [(8)]TJ 0 -8.608 Td [(>)]TJ 0 -2.869 Td [(<)]TJ 0 -17.215 Td [(>)]TJ 0 -2.869 Td [(:)]TJ/F41 5.8022 Tf 17.755 26.573 Td [(n)]TJ/F189 9.5641 Tf -5.09 -2.019 Td [(X)]TJ/F41 5.8022 Tf -5.09 -19.556 Td [(k)]TJ/F179 6.6948 Tf 3.017 0 Td [(D)]TJ/F22 5.8022 Tf 5.222 0 Td [(1)]TJ/F185 6.6948 Tf 3.359 0 Td [(;)]TJ/F41 5.8022 Tf 2.216 0 Td [(k)]TJ/F179 6.6948 Tf 3.018 0 Td [(6)1(D)]TJ/F41 5.8022 Tf 5.222 0 Td [(i)]TJ/F41 8.2889 Tf 3.253 10.47 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.435 Td [(ik)]TJ/F185 9.5641 Tf 5.175 1.435 Td [(;)]TJ/F41 8.2889 Tf 13.128 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(j)]TJ/F179 9.5641 Tf -63.172 -20.214 Td [(\000)]TJ/F41 8.2889 Tf 7.46 0 Td [(a)]TJ/F41 5.8022 Tf 4.418 -1.434 Td [(ij)]TJ/F185 9.5641 Tf 3.834 1.434 Td [(;)]TJ/F41 8.2889 Tf 32.316 0 Td [(i)]TJ/F179 9.5641 Tf 5.027 0 Td [(6)1(D)]TJ/F41 8.2889 Tf 10.117 0 Td [(j)]TJ/F185 9.5641 Tf 2.395 0 Td [(:)]TJ ET 1 0 0 1 301.697 481.729 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -481.729 cm BT /F22 8.2889 Tf 301.697 451.373 Td [(We)-250(have)]TJ ET 1 0 0 1 301.697 451.373 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -18.639 cm 0 g 0 G 1 0 0 1 -297.712 -432.734 cm BT /F153 8.2889 Tf 301.697 432.734 Td [(Lemma)-250(1)]TJ ET 1 0 0 1 338.284 432.734 cm 0 g 0 G 1 0 0 1 -338.284 -432.734 cm BT /F22 8.2889 Tf 342.269 432.734 Td [(\050)]TJ ET 1 0 0 1 345.336 432.734 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -345.336 -432.734 cm BT /F41 8.2889 Tf 345.336 432.734 Td [(Olfati-Saber)]TJ ET 1 0 0 1 389.101 432.734 cm 0 g 0 G 1 0 0 1 4.607 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -393.708 -432.734 cm BT /F41 8.2889 Tf 393.708 432.734 Td [(&)]TJ ET 1 0 0 1 400.074 432.734 cm 0 g 0 G 1 0 0 1 4.607 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -404.681 -432.734 cm BT /F41 8.2889 Tf 404.681 432.734 Td [(Murray,)]TJ ET 1 0 0 1 434.073 432.734 cm 0 g 0 G 1 0 0 1 4.609 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -438.682 -432.734 cm BT /F41 8.2889 Tf 438.682 432.734 Td [(2004)]TJ ET 1 0 0 1 457.017 432.734 cm 0 g 0 G 1 0 0 1 -457.017 -432.734 cm BT /F41 8.2889 Tf 457.017 432.734 Td [(;)]TJ ET 1 0 0 1 464.248 432.734 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -464.248 -432.734 cm BT /F41 8.2889 Tf 464.248 432.734 Td [(Ren)]TJ ET 1 0 0 1 477.883 432.734 cm 0 g 0 G 1 0 0 1 4.607 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -482.49 -432.734 cm BT /F41 8.2889 Tf 482.49 432.734 Td [(et)-556(al.)]TJ ET 1 0 0 1 502.596 432.734 cm 0 g 0 G 1 0 0 1 -502.596 -432.734 cm BT /F41 8.2889 Tf 502.596 432.734 Td [(,)]TJ ET 1 0 0 1 504.478 432.734 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 4.609 0 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -509.087 -432.734 cm BT /F41 8.2889 Tf 509.087 432.734 Td [(2007)]TJ ET 1 0 0 1 527.422 432.734 cm 0 g 0 G 1 0 0 1 -527.422 -432.734 cm BT /F41 8.2889 Tf 527.422 432.734 Td [(;)]TJ ET 1 0 0 1 534.653 432.734 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -534.653 -432.734 cm BT /F41 8.2889 Tf 534.653 432.734 Td [(Xiao)]TJ ET 1 0 0 1 550.874 432.734 cm 0 g 0 G 1 0 0 1 -550.874 -432.734 cm BT /F41 8.2889 Tf 550.874 432.734 Td [(,)]TJ ET 1 0 0 1 552.756 432.734 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -251.059 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.415 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -301.697 -422.319 cm BT /F41 8.2889 Tf 301.697 422.319 Td [(2008)]TJ ET 1 0 0 1 320.032 422.319 cm 0 g 0 G 1 0 0 1 -320.032 -422.319 cm BT /F22 8.2889 Tf 320.032 422.319 Td [(\051.)]TJ/F41 8.2889 Tf 7.079 0 Td [(Graph)-250(Laplacian)-250(L)]TJ/F185 9.5641 Tf 65.474 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F41 8.2889 Tf 5.64 0 Td [(of)]TJ/F181 8.9265 Tf 10.655 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.032 0 Td [(/)]TJ/F41 8.2889 Tf 5.639 0 Td [(has)-250(the)-250(following)-250(properties:)]TJ ET 1 0 0 1 301.697 422.319 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -15.032 cm 0 g 0 G 1 0 0 1 -301.697 -407.287 cm BT /F22 8.2889 Tf 301.697 407.287 Td [(\0501\051)]TJ ET 1 0 0 1 312.622 407.287 cm 0 g 0 G 1 0 0 1 -312.622 -407.287 cm BT /F41 8.2889 Tf 316.607 407.287 Td [(if)]TJ/F181 8.9265 Tf 9.811 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F41 8.2889 Tf 6.843 0 Td [(has)-395(a)-395(spanning)-395(tree,)-396(then)-395(eigenvalue)]TJ/F22 8.2889 Tf 141.522 0 Td [(0)]TJ/F41 8.2889 Tf 8.075 0 Td [(is)-395(algebraically)]TJ ET 1 0 0 1 301.697 407.287 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -407.287 cm BT /F41 8.2889 Tf 316.607 396.872 Td [(simple)-250(and)-250(all)-250(other)-250(eigenvalues)-250(are)-250(with)-250(positive)-250(real)-250(parts;)]TJ ET 1 0 0 1 301.697 396.872 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.324 cm 0 g 0 G 1 0 0 1 -301.697 -386.548 cm BT /F22 8.2889 Tf 301.697 386.548 Td [(\0502\051)]TJ ET 1 0 0 1 312.622 386.548 cm 0 g 0 G 1 0 0 1 -312.622 -386.548 cm BT /F41 8.2889 Tf 316.607 386.548 Td [(if)]TJ/F181 8.9265 Tf 8.751 0 Td [(G)]TJ/F185 9.5641 Tf 5.731 0 Td [(.)]TJ/F41 8.2889 Tf 3.567 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F41 8.2889 Tf 5.783 0 Td [(is)-267(strongly)-267(connected,)-268(then)-267(there)-267(exists)-267(a)-268(positive)-267(column)]TJ ET 1 0 0 1 301.697 386.548 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -386.548 cm BT /F41 8.2889 Tf 316.607 376.133 Td [(vector)]TJ/F185 9.5641 Tf 25.459 0 Td [(!)]TJ/F179 9.5641 Tf 9.113 0 Td [(2)]TJ/F169 8.6077 Tf 8.672 0 Td [(R)]TJ/F41 5.8022 Tf 6.217 3.472 Td [(n)]TJ/F41 8.2889 Tf 5.924 -3.472 Td [(such)-250(that)]TJ/F185 9.5641 Tf 36.392 0 Td [(!)]TJ/F22 5.8022 Tf 6.456 3.472 Td [(T)]TJ/F41 8.2889 Tf 3.736 -3.472 Td [(L)]TJ/F185 9.5641 Tf 3.928 0 Td [(.)]TJ/F41 8.2889 Tf 3.568 0 Td [(A)]TJ/F185 9.5641 Tf 5.031 0 Td [(/)]TJ/F179 9.5641 Tf 6.224 0 Td [(D)]TJ/F22 8.2889 Tf 10.117 0 Td [(0)]TJ/F41 8.2889 Tf 4.799 0 Td [(.)]TJ ET 1 0 0 1 301.697 376.133 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -376.133 cm BT /F153 8.2889 Tf 301.697 353.345 Td [(3.)-500(Problem)-250(formulation)]TJ ET 1 0 0 1 301.697 353.345 cm 0 g 0 G 0 g 0 G 1 0 0 1 -301.697 -353.345 cm BT /F22 8.2889 Tf 313.653 332.583 Td 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