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)Tj 3.387 0 Td ( )Tj -20.996 -1.125 Td ( )Tj 1.104 0 Td ( )Tj 3.661 0 Td ( )Tj 1.826 0 Td ( )Tj 5.493 0 Td ( )Tj 3.55 0 Td ( )Tj 2.493 0 Td ( )Tj 2.549 0 Td ( )Tj 1.327 0 Td ( )Tj 1.826 0 Td ( )Tj -25.208 -1.125 Td ( )Tj 1.113 0 Td ( )Tj 1.504 0 Td ( )Tj 4.784 0 Td ( )Tj 2.393 0 Td ( )Tj 1.893 0 Td ( )Tj 2.504 0 Td ( )Tj 1.781 0 Td ( )Tj 3.503 0 Td ( )Tj 5.616 0 Td ( )Tj 2.06 0 Td ( )Tj -28.136 -1.125 Td ( )Tj 0.852 0 Td ( )Tj 5.131 0 Td ( )Tj 3.073 0 Td ( )Tj 1.186 0 Td ( )Tj 1.685 0 Td ( )Tj 4.186 0 Td ( )Tj 1.241 0 Td ( )Tj 0.852 0 Td ( )Tj 4.519 0 Td ( )Tj 3.297 0 Td ( )Tj ET Q BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 10 0 0 10 63 585.0001 Tm (tial)Tj 1.418 0 Td ( transition)Tj 4.475 0 Td ( and)Tj 1.919 0 Td ( is)Tj 0.974 0 Td ( called)Tj 2.807 0 Td ( a)Tj 0.807 0 Td ( )Tj /T1_1 1 Tf (free)Tj 1.917 0 Td ( wanderer)Tj /T1_0 1 Tf (.)Tj 4.641 0 Td ( In)Tj 1.195 0 Td ( Figure)Tj 3.031 0 Td ( 1\(a\),)Tj 2.307 0 Td ( right)Tj 2.363 0 Td ( in)Tj 1.141 0 Td ( the)Tj -28.989 -1.125 Td 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5.536 0 Td ( for)Tj 1.982 0 Td ( all)Tj 1.76 0 Td ( the)Tj 2.038 0 Td ( agents\222)Tj 3.705 0 Td ( velocities)Tj -26.378 -1.125 Td (\(principal)Tj 4.177 0 Td ( vector)Tj 2.953 0 Td ( in)Tj 1.121 0 Td ( our)Tj 1.788 0 Td ( model\).)Tj 3.564 0 Td ( Density)Tj 3.565 0 Td ( is)Tj 0.954 0 Td ( defined)Tj 3.454 0 Td ( by)Tj 1.343 0 Td ( the)Tj 1.62 0 Td ( average)Tj 3.564 0 Td ( num)Tj (-)Tj -28.104 -1.125 Td (ber)Tj 1.475 0 Td ( of)Tj 1.253 0 Td ( agents)Tj 3.086 0 Td ( located)Tj 3.475 0 Td ( in)Tj 1.198 0 Td ( the)Tj 1.697 0 Td ( neighborhood)Tj 6.423 0 Td ( of)Tj 1.253 0 Td ( each)Tj 2.308 0 Td ( agent.)Tj 2.975 0 Td ( In)Tj 1.252 0 Td ( Figure)Tj 3.088 0 Td ( 1,)Tj -29.488 -1.125 Td (polarization)Tj 5.402 0 Td ( and)Tj 2.068 0 Td ( density)Tj 3.513 0 Td ( are)Tj 1.79 0 Td ( normalized)Tj 5.29 0 Td ( by)Tj 1.512 0 Td ( maximal)Tj 4.232 0 Td ( polarization)Tj 5.681 0 Td ( in)Tj -29.488 -1.125 Td (\(a\))Tj 1.303 0 Td ( and)Tj 2.027 0 Td ( maximal)Tj 4.191 0 Td ( density)Tj 3.471 0 Td ( 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365.648 9.889 10.265 re f* q 1 0 0 1 101.7999 375.9123 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 111.6885 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 111.6885 375.9123 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 101.7999 365.6157 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 101.7999 355.351 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 111.689 355.351 9.889 10.265 re f* q 1 0 0 1 111.6885 365.6157 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 111.6885 355.351 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 375.9123 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 365.6157 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 355.351 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 107.4653 372.9894 cm 0 0 m 8.432 7.555 l S Q 1 0.298 0 scn q 1 0 0 1 114.9738 375.9126 cm 0 0 m 2.33 5.892 l -3.782 4.221 l h f* Q q 1 0 0 1 107.4653 372.9894 cm 0 0 m 0 8.343 l S Q q 1 0 0 1 110.2987 377.5544 cm 0 0 m -2.833 5.667 l -5.667 0 l h f* Q q 1 0 0 1 107.4653 372.9894 cm 0 0 m 7.97 -1.19 l S Q q 1 0 0 1 112.1174 375.1595 cm 0 0 m 5.186 -3.639 l -0.837 -5.605 l h f* Q q 1 0 0 1 115.9194 359.7507 cm 0 0 m 0 9.865 l S Q q 1 0 0 1 118.7528 365.8374 cm 0 0 m -2.834 5.667 l -5.667 0 l h f* Q q 1 0 0 1 115.9194 361.1765 cm 0 0 m 9.796 7.7 l S Q q 1 0 0 1 124.4965 364.3143 cm 0 0 m 2.704 5.73 l -3.502 4.456 l h f* Q q 1 0 0 1 115.9194 361.1765 cm 0 0 m 8.002 0 l S Q q 1 0 0 1 120.1433 364.0099 cm 0 0 m 5.667 -2.833 l 0 -5.667 l h f* Q q 1 0 0 1 97.569 361.1765 cm 0 0 m 1.214 9.931 l S Q q 1 0 0 1 101.1371 367.0138 cm 0 0 m -2.125 5.969 l -5.625 0.688 l h f* Q q 1 0 0 1 97.569 361.1765 cm 0 0 m 7.252 8.874 l S Q q 1 0 0 1 104.6248 365.3324 cm 0 0 m 1.392 6.181 l -4.388 3.586 l h f* Q q 1 0 0 1 97.569 361.1765 cm 0 0 m 5.208 1.084 l S Q q 1 0 0 1 99.656 358.7166 cm 0 0 m 4.97 3.929 l -1.155 5.548 l h f* Q /CS1 CS 0 SCN 0.321 w 0 j q 1 0 0 1 144.862 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 144.862 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 154.751 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 154.751 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 144.862 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 1 1 1 scn 144.862 395.852 9.889 10.265 re f* q 1 0 0 1 144.862 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 0.478 0.506 1 scn 154.751 406.116 9.889 10.265 re f* q 1 0 0 1 154.751 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 154.751 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 164.6086 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 164.609 416.413 9.889 10.265 re f* q 1 0 0 1 164.6086 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 174.4972 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 174.4972 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 164.6086 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 164.6086 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 174.497 406.116 9.889 10.265 re f* q 1 0 0 1 174.4972 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 174.4972 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 170.2682 423.731 cm 0 0 m 8.456 7.557 l S Q 1 0.298 0 scn q 1 0 0 1 177.7952 426.6575 cm 0 0 m 2.338 5.889 l -3.776 4.225 l h f* Q q 1 0 0 1 178.7266 411.9769 cm 0 0 m 9.793 7.652 l S Q q 1 0 0 1 187.2873 415.0703 cm 0 0 m 2.721 5.722 l -3.49 4.465 l h f* Q q 1 0 0 1 160.3795 411.9769 cm 0 0 m 7.297 8.829 l S Q q 1 0 0 1 167.4535 416.0883 cm 0 0 m 1.426 6.173 l -4.368 3.611 l h f* Q /CS1 CS 0 SCN 0.321 w 0 j q 1 0 0 1 82.7493 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 82.7493 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 92.6384 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 92.6384 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 82.7493 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 1 1 1 scn 82.749 395.852 9.889 10.265 re f* q 1 0 0 1 82.7493 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 0.478 0.506 1 scn 92.638 406.116 9.889 10.265 re f* q 1 0 0 1 92.6384 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 92.6384 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 102.4959 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 102.496 416.413 9.889 10.265 re f* q 1 0 0 1 102.4959 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 112.3845 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 112.3845 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 102.4959 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 102.4959 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 112.385 406.116 9.889 10.265 re f* q 1 0 0 1 112.3845 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 112.3845 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 122.2425 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 122.2425 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 122.2425 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 122.2425 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 108.1556 423.731 cm 0 0 m 10.982 5.06 l S Q 1 0.298 0 scn q 1 0 0 1 116.8925 424.6369 cm 0 0 m 3.962 4.944 l -2.371 5.147 l h f* Q q 1 0 0 1 116.614 411.9769 cm 0 0 m 3.584 9.95 l S Q q 1 0 0 1 121.5834 417.4126 cm 0 0 m -0.745 6.292 l -5.331 1.921 l h f* Q q 1 0 0 1 98.2668 411.9769 cm 0 0 m 2.39 9.891 l S Q q 1 0 0 1 102.5237 417.5305 cm 0 0 m -1.423 6.174 l -5.509 1.331 l h f* Q 1 1 1 scn q 1 0 0 1 133.5734 417.8607 cm 0 0 m 6.34 0 l 6.34 2.941 l 8.454 -2.94 l 6.34 -8.821 l 6.34 -5.881 l 0 -5.881 l h f* Q /CS1 CS 0 SCN 0.321 w 0 j q 1 0 0 1 133.5734 417.8609 cm 0 0 m 6.34 0 l 6.34 2.941 l 8.454 -2.94 l 6.34 -8.821 l 6.34 -5.881 l 0 -5.881 l 0 0 l h S Q q 1 0 0 1 133.9713 369.336 cm 0 0 m 5.296 0 l 5.296 2.941 l 7.061 -2.94 l 5.296 -8.822 l 5.296 -5.881 l 0 -5.881 l h f* Q q 1 0 0 1 133.9713 369.336 cm 0 0 m 5.296 0 l 5.296 2.941 l 7.061 -2.941 l 5.296 -8.822 l 5.296 -5.881 l 0 -5.881 l 0 0 l h S Q q 1 0 0 1 145.2599 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 145.2599 375.8997 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 155.1486 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 155.1486 375.8997 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 145.2599 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 145.26 345.035 9.889 10.277 re f* q 1 0 0 1 145.2599 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 0.478 0.506 1 scn 155.148 355.313 9.889 10.277 re f* q 1 0 0 1 155.1486 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 155.1486 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 165.0065 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 165.007 365.622 9.889 10.277 re f* q 1 0 0 1 165.0065 375.8997 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 174.8951 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 1 0.686 1 scn 174.895 365.622 9.889 10.277 re f* q 1 0 0 1 174.8951 375.8997 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 165.0065 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 165.0065 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 0.478 0.506 1 scn 174.895 355.313 9.889 10.277 re f* q 1 0 0 1 174.8951 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 174.8951 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 375.8997 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 170.672 372.9894 cm 0 0 m 8.432 7.555 l S Q 1 0.298 0 scn q 1 0 0 1 178.1805 375.9126 cm 0 0 m 2.33 5.892 l -3.782 4.221 l h f* Q q 1 0 0 1 170.672 372.9894 cm 0 0 m 0 8.396 l S Q q 1 0 0 1 173.5054 377.6069 cm 0 0 m -2.833 5.667 l -5.667 0 l h f* Q q 1 0 0 1 170.672 372.9894 cm 0 0 m 7.97 -1.19 l S Q q 1 0 0 1 175.3241 375.1595 cm 0 0 m 5.186 -3.639 l -0.837 -5.605 l h f* Q q 1 0 0 1 179.1261 359.6999 cm 0 0 m 0 9.917 l S Q q 1 0 0 1 181.9595 365.8391 cm 0 0 m -2.833 5.667 l -5.667 0 l h f* Q q 1 0 0 1 179.1261 361.1765 cm 0 0 m 9.843 7.655 l S Q q 1 0 0 1 187.7263 364.276 cm 0 0 m 2.734 5.716 l -3.48 4.473 l h f* Q q 1 0 0 1 179.1261 361.1765 cm 0 0 m 8.002 0 l S Q q 1 0 0 1 183.35 364.0099 cm 0 0 m 5.667 -2.833 l 0 -5.667 l h f* Q q 1 0 0 1 160.7757 361.1765 cm 0 0 m 1.214 9.931 l S Q q 1 0 0 1 164.3436 367.0138 cm 0 0 m -2.125 5.969 l -5.625 0.688 l h f* Q q 1 0 0 1 160.7757 361.1765 cm 0 0 m 7.301 8.878 l S Q q 1 0 0 1 167.8651 365.3365 cm 0 0 m 1.411 6.177 l -4.377 3.6 l h f* Q q 1 0 0 1 160.7757 361.1765 cm 0 0 m 5.208 1.084 l S Q q 1 0 0 1 162.8625 358.7166 cm 0 0 m 4.97 3.929 l -1.155 5.548 l h f* Q /CS1 CS 0 SCN 0.321 w 0 j q 1 0 0 1 82.5508 335.3609 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 82.5508 325.0836 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 92.4394 335.3609 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 92.4394 325.0836 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 82.5508 314.7739 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 1 1 1 scn 82.551 294.219 9.889 10.277 re f* q 1 0 0 1 82.5508 304.4966 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 0.478 0.506 1 scn 92.439 304.497 9.889 10.277 re f* q 1 0 0 1 92.4394 314.7739 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 92.4394 304.4966 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 102.297 335.3609 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 0.839 0.843 1 scn 102.297 314.806 9.889 10.277 re f* q 1 0 0 1 102.297 325.0836 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 112.186 335.3609 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 0.478 0.506 1 scn 112.186 314.806 9.889 10.277 re f* q 1 0 0 1 112.186 325.0836 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 102.297 314.7739 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 102.297 304.4966 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 112.186 304.497 9.889 10.277 re f* q 1 0 0 1 112.186 314.7739 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 112.186 304.4966 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 122.0435 335.3609 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 122.0435 325.0836 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 122.0435 314.7739 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 122.0435 304.4966 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q 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each)Tj 2.344 0 Td ( agent)Tj 2.733 0 Td ( has)Tj 1.845 0 Td ( two)Tj 2.067 0 Td ( potential)Tj 4.234 0 Td ( transitions.)Tj 5.391 0 Td (Although)Tj 4.178 0 Td ( it)Tj 1.011 0 Td ( is)Tj 1.067 0 Td ( possi)Tj (-)Tj ET q 0 60.6 432 68.4 re W n BT /T1_0 1 Tf 10 0 0 10 76.3178 51.6147 Tm ( )Tj 2.054 0 Td ( )Tj 4.166 0 Td ( )Tj 4.889 0 Td ( )Tj 1.832 0 Td ( )Tj 4.777 0 Td ( )Tj 1.221 0 Td ( )Tj 4.832 0 Td ( )Tj 1.665 0 Td ( )Tj -24.722 -1.124 Td ( )Tj 1.321 0 Td ( )Tj 4.266 0 Td ( )Tj 4.6 0 Td ( )Tj 3.32 0 Td ( )Tj 1.099 0 Td ( )Tj 1.877 0 Td ( )Tj 3.821 0 Td ( )Tj 1.321 0 Td ( )Tj 3.598 0 Td ( )Tj -21.736 -1.124 Td ( )Tj 2.029 0 Td ( )Tj 2.694 0 Td ( )Tj 1.252 0 Td ( )Tj 3.918 0 Td ( )Tj 4.92 0 Td ( )Tj 3.141 0 Td ( )Tj 2.253 0 Td ( )Tj 1.197 0 Td ( )Tj -24.124 -1.125 Td ( )Tj 1.254 0 Td ( )Tj 4.199 0 Td ( )Tj 4.922 0 Td ( )Tj 1.643 0 Td ( )Tj 2.309 0 Td ( )Tj 2.976 0 Td ( )Tj 2.81 0 Td ( )Tj 2.366 0 Td ( )Tj 3.421 0 Td ( )Tj -23.252 -1.125 Td ( )Tj 1.845 0 Td ( )Tj 2.345 0 Td ( )Tj 3.067 0 Td ( )Tj 1.622 0 Td ( )Tj 1.845 0 Td ( )Tj 4.068 0 Td ( )Tj 5.958 0 Td ( )Tj -22.914 -1.125 Td ( )Tj 4.352 0 Td ( )Tj 2.131 0 Td ( )Tj 5.743 0 Td ( )Tj 4.796 0 Td ( )Tj 2.687 0 Td ( )Tj 3.575 0 Td ( )Tj 2.131 0 Td ( )Tj -23.131 -1.125 Td ( )Tj 1.966 0 Td ( )Tj 5.466 0 Td ( )Tj 3.244 0 Td ( )Tj 4.189 0 Td ( )Tj 6.079 0 Td ( )Tj 1.3 0 Td ( )Tj /C2_1 1 Tf -25.877 -1.124 Td <0001>Tj /T1_0 1 Tf 1.918 0 Td ( )Tj ET Q BT /T1_4 1 Tf 8 0 0 8 63 612.0001 Tm (Robust)Tj ( Soldier)Tj ( Crab)Tj ( Ball)Tj ( Gate)Tj /T1_5 1 Tf 37.138 0 Td (95)Tj /T1_6 1 Tf 7 0 0 7 169.7103 31.6251 Tm (Complex)Tj ( Systems,)Tj ( )Tj /T1_7 1 Tf (2)Tj (0)Tj /T1_8 1 Tf ( \251)Tj ( 2011)Tj ( Complex)Tj ( Systems)Tj ( Publications,)Tj ( Inc.)Tj ET endstream endobj 5 0 obj <>stream ����Adobed���C �� ���� s!1AQa"q�2���B#�R��3b�$r��%C4S���cs�5D'���6Tdt���&� 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5.51 0 Td ( breaks)Tj 3.12 0 Td ( the)Tj 1.619 0 Td ( )Tj (c)Tj (o)Tj (h)Tj (e)Tj (r)Tj (-)Tj -27.829 -1.125 Td (e)Tj (n)Tj (c)Tj (e)Tj 1.988 0 Td ( of)Tj 1.267 0 Td ( a)Tj 0.878 0 Td ( flock.)Tj 2.823 0 Td ( The)Tj 2.044 0 Td ( velocity)Tj 3.711 0 Td ( matching)Tj 4.377 0 Td ( is)Tj 1.045 0 Td ( linearly)Tj 3.601 0 Td ( coupled)Tj 3.768 0 Td ( with)Tj 2.323 0 Td ( )Tj (e)Tj (x)Tj (t)Tj (e)Tj (r)Tj (-)Tj -27.823 -1.125 Td (n)Tj (a)Tj (l)Tj 1.676 0 Td ( perturbation)Tj 6.066 0 Td ( in)Tj 1.454 0 Td ( )Tj (b)Tj (o)Tj (i)Tj (d)Tj (s)Tj 2.955 0 Td ( and)Tj 2.232 0 Td ( SPP.)Tj 2.51 0 Td ( If)Tj 1.285 0 Td ( the)Tj 1.953 0 Td ( polarization)Tj 5.844 0 Td ( is)Tj 1.287 0 Td ( plotted)Tj -27.266 -1.124 Td (against)Tj 3.367 0 Td ( external)Tj 4.089 0 Td ( perturbation,)Tj 6.313 0 Td ( it)Tj 1.2 0 Td ( decreases)Tj 4.588 0 Td ( as)Tj 1.478 0 Td ( the)Tj 1.922 0 Td ( perturbation)Tj 6.035 0 Td ( de)Tj (-)Tj -28.989 -1.124 Td (creases.)Tj 3.405 0 Td ( Because)Tj 3.794 0 Td ( polarization)Tj 5.63 0 Td ( shows)Tj 3.074 0 Td ( a)Tj 0.906 0 Td ( phase)Tj 2.851 0 Td ( transition)Tj 4.574 0 Td ( that)Tj 2.128 0 Td ( is)Tj 1.073 0 Td ( depen)Tj (-)Tj -27.433 -1.124 Td (dent)Tj 2.029 0 Td ( on)Tj 1.53 0 Td ( the)Tj 1.751 0 Td ( external)Tj 3.918 0 Td ( perturbation,)Tj 6.142 0 Td ( it)Tj 1.029 0 Td ( is)Tj 1.085 0 Td ( regarded)Tj 4.196 0 Td ( as)Tj 1.307 0 Td ( an)Tj 1.474 0 Td ( order)Tj 2.752 0 Td ( )Tj (p)Tj (a)Tj (r)Tj (a)Tj (m)Tj (-)Tj -27.212 -1.124 Td (e)Tj (t)Tj (e)Tj (r)Tj (.)Tj 2.114 0 Td ( Thus,)Tj 2.949 0 Td ( the)Tj 1.837 0 Td ( density)Tj 3.56 0 Td ( of)Tj 1.393 0 Td ( a)Tj 1.004 0 Td ( flock)Tj 2.671 0 Td ( is)Tj 1.171 0 Td ( also)Tj 2.227 0 Td ( decreased)Tj 4.67 0 Td ( as)Tj 1.393 0 Td ( the)Tj 1.837 0 Td ( external)Tj -26.822 -1.125 Td (p)Tj (e)Tj (r)Tj (t)Tj (u)Tj (r)Tj (b)Tj (a)Tj (t)Tj (i)Tj (o)Tj (n)Tj 5.798 0 Td ( decreases.)Tj 4.907 0 Td ( In)Tj 1.518 0 Td ( this)Tj 2.186 0 Td ( framework,)Tj 5.685 0 Td ( the)Tj 1.963 0 Td ( noise)Tj 2.853 0 Td ( disturbs)Tj 4.076 0 Td ( the)Tj -28.989 -1.124 Td (c)Tj (o)Tj (h)Tj (e)Tj (r)Tj (e)Tj (n)Tj (c)Tj (e)Tj 4.284 0 Td ( of)Tj 1.174 0 Td ( a)Tj 0.785 0 Td ( flock,)Tj 2.73 0 Td ( which)Tj 2.897 0 Td ( reveals)Tj 3.229 0 Td ( a)Tj 0.785 0 Td ( flock)Tj 2.452 0 Td ( that)Tj 2.007 0 Td ( is)Tj 0.952 0 Td ( not)Tj 1.73 0 Td ( robust)Tj 3.064 0 Td ( but)Tj 1.73 0 Td ( is)Tj 0.952 0 Td ( sta)Tj (-)Tj -28.773 -1.125 Td (ble.)Tj 2.033 0 Td ( By)Tj 1.866 0 Td ( contrast,)Tj 4.533 0 Td ( in)Tj 1.589 0 Td ( our)Tj 2.256 0 Td ( model)Tj 3.421 0 Td ( inherent)Tj 4.311 0 Td ( perturbation)Tj 6.201 0 Td ( positively)Tj -26.21 -1.125 Td (c)Tj (o)Tj (n)Tj (t)Tj (r)Tj (i)Tj (b)Tj (u)Tj (t)Tj (e)Tj (s)Tj 4.899 0 Td ( to)Tj 1.232 0 Td ( generating)Tj 4.843 0 Td ( a)Tj 0.843 0 Td ( coherent)Tj 4.065 0 Td ( and)Tj 1.955 0 Td ( dense)Tj 2.732 0 Td ( swarm)Tj 3.231 0 Td ( and)Tj 1.955 0 Td ( can)Tj 1.843 0 Td ( imple)Tj (-)Tj -27.601 -1.125 Td (ment)Tj 2.234 0 Td ( robust)Tj 3.126 0 Td ( swarms,)Tj 3.902 0 Td ( which)Tj 2.959 0 Td ( can)Tj 1.847 0 Td ( be)Tj 1.347 0 Td ( used)Tj 2.292 0 Td ( analogous)Tj 4.738 0 Td ( to)Tj 1.236 0 Td ( billiard)Tj 3.46 0 Td ( balls)Tj 2.348 0 Td ( in)Tj -29.488 -1.125 Td (collision)Tj (-)Tj (based)Tj ( circuitry.)Tj ( )Tj ET q 72 293.04 9 10.56 re W n BT /T1_1 1 Tf 9 0 0 9 72 295.461 Tm (3)Tj (.)Tj ET Q q 0 291 432 12.96 re W n BT /T1_1 1 Tf 9 0 0 9 85.506 295.461 Tm (Collision)Tj ( Computing)Tj ( by)Tj ( Crab)Tj ( Swarm)Tj ( )Tj ( )Tj ET Q /CS0 CS 0 0 0 SCN 3 w 2 J q 1 0 0 1 64.006 293.0469 cm 0 0 m 0 9 l S Q 0.5 w q 1 0 0 1 62.756 291.7969 cm 0 0 m 305.994 0 l S Q q 74.04 273.72 13.92 9.84 re W n BT /T1_1 1 Tf 9 0 0 9 74 275.461 Tm (3)Tj (.)Tj (1)Tj ET Q BT /T1_1 1 Tf 9 0 0 9 92.51 275.461 Tm (Simulation)Tj ( Model)Tj ( )Tj ( )Tj ET 3 w q 1 0 0 1 65.01 275.1641 cm 0 0 m 0 6.883 l S Q BT /T1_0 1 Tf 10 0 0 10 63 262.6641 Tm (When)Tj 2.622 0 Td ( a)Tj 0.844 0 Td ( swarm)Tj 3.232 0 Td ( of)Tj 1.233 0 Td ( soldier)Tj 3.234 0 Td ( crabs)Tj 2.622 0 Td ( is)Tj 1.011 0 Td ( set)Tj 1.51 0 Td ( in)Tj 1.178 0 Td ( a)Tj 0.844 0 Td ( corridor,)Tj 4.179 0 Td ( it)Tj 0.955 0 Td ( is)Tj 1.011 0 Td ( expected)Tj 4.121 0 Td ( that)Tj -28.6 -1.1 Td (a)Tj 0.593 0 Td ( swarm)Tj 3.259 0 Td ( acts)Tj 2.037 0 Td ( as)Tj 1.26 0 Td ( a)Tj 0.871 0 Td ( robust)Tj 3.15 0 Td ( ball)Tj 1.983 0 Td ( and)Tj 1.983 0 Td ( goes)Tj 2.26 0 Td ( straight,)Tj 3.927 0 Td ( and)Tj 1.983 0 Td ( that)Tj 2.093 0 Td ( two)Tj 2.038 0 Td ( swarm)Tj -27.434 -1.1 Td (balls)Tj 2.327 0 Td ( are)Tj 1.937 0 Td ( united)Tj 3.327 0 Td ( into)Tj 2.327 0 Td ( one)Tj 2.16 0 Td ( ball)Tj 2.216 0 Td ( after)Tj 2.603 0 Td ( colliding.)Tj 4.606 0 Td ( Because)Tj 3.992 0 Td ( of)Tj 1.493 0 Td ( velocity)Tj -26.989 -1.1 Td (m)Tj (a)Tj (t)Tj (c)Tj (h)Tj (i)Tj (n)Tj (g)Tj (,)Tj 4.415 0 Td ( a)Tj 0.916 0 Td ( swarm)Tj 3.304 0 Td ( ball)Tj 2.028 0 Td ( resulting)Tj 4.139 0 Td ( from)Tj 2.526 0 Td ( the)Tj 1.749 0 Td ( fusion)Tj 3.084 0 Td ( of)Tj 1.305 0 Td ( two)Tj 2.083 0 Td ( balls)Tj 2.417 0 Td ( has)Tj 1.861 0 Td ( a)Tj -29.822 -1.1 Td (summary)Tj ( velocity)Tj ( of)Tj ( two)Tj ( colliding)Tj ( balls.)Tj ( )Tj ( )Tj ET q 0 95.04 432 121.92 re W n BT /T1_0 1 Tf 10 0 0 10 75 207.6641 Tm (Figure)Tj 2.785 0 Td ( 2)Tj 0.895 0 Td ( shows)Tj 3.007 0 Td ( an)Tj 1.395 0 Td ( OR)Tj 1.894 0 Td ( gate)Tj 2.116 0 Td ( implemented)Tj 5.892 0 Td ( by)Tj 1.395 0 Td ( the)Tj 1.672 0 Td ( collision)Tj 3.952 0 Td ( of)Tj 1.228 0 Td ( swarm)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 63 196.6641 Tm (balls.)Tj 2.363 0 Td ( In)Tj 1.25 0 Td ( this)Tj 1.918 0 Td ( simulation,)Tj 5.196 0 Td ( black)Tj 2.696 0 Td ( regions)Tj 3.474 0 Td ( are)Tj 1.695 0 Td ( walls)Tj 2.585 0 Td ( that)Tj 2.084 0 Td ( an)Tj 1.418 0 Td ( agent)Tj 2.695 0 Td ( cannot)Tj -27.377 -1.1 Td (invade.)Tj 3.161 0 Td ( Agents)Tj 3.27 0 Td ( can)Tj 1.827 0 Td ( move)Tj 2.659 0 Td ( in)Tj 1.161 0 Td ( the)Tj 1.66 0 Td ( white)Tj 2.716 0 Td ( area.)Tj 2.438 0 Td ( An)Tj 1.604 0 Td ( agent)Tj 2.66 0 Td ( moves)Tj 3.048 0 Td ( following)Tj -26.209 -1.1 Td (the)Tj 1.433 0 Td ( rule)Tj 2.045 0 Td ( mentioned)Tj 4.933 0 Td ( before,)Tj 3.378 0 Td ( where)Tj 2.989 0 Td ( each)Tj 2.322 0 Td ( agent)Tj 2.711 0 Td ( has)Tj 1.823 0 Td ( a)Tj 0.878 0 Td ( tendency)Tj 4.211 0 Td ( to)Tj 1.267 0 Td ( move)Tj -27.99 -1.1 Td (along)Tj 2.577 0 Td ( the)Tj 1.798 0 Td ( wall)Tj 2.299 0 Td ( if)Tj 1.076 0 Td ( it)Tj 1.076 0 Td ( is)Tj 1.132 0 Td ( close)Tj 2.576 0 Td ( to)Tj 1.354 0 Td ( the)Tj 1.798 0 Td ( wall.)Tj 2.577 0 Td ( This)Tj 2.354 0 Td ( tendency)Tj 4.298 0 Td ( is)Tj 1.132 0 Td ( consistent)Tj -26.044 -1.1 Td (with)Tj 2.029 0 Td ( our)Tj 1.863 0 Td ( observation)Tj 5.419 0 Td ( of)Tj 1.251 0 Td ( soldier)Tj 3.252 0 Td ( crabs.)Tj 2.918 0 Td ( In)Tj 1.25 0 Td ( a)Tj 0.862 0 Td ( corridor,)Tj 4.197 0 Td ( they)Tj 2.195 0 Td ( move)Tj 2.694 0 Td ( along)Tj -27.932 -1.1 Td (the)Tj 1.524 0 Td ( wall.)Tj 2.581 0 Td ( Because)Tj 3.857 0 Td ( they)Tj 2.302 0 Td ( have)Tj 2.469 0 Td ( a)Tj 0.969 0 Td ( tendency)Tj 4.302 0 Td ( to)Tj 1.358 0 Td ( move)Tj 2.801 0 Td ( together,)Tj 4.302 0 Td ( a)Tj 0.969 0 Td ( swarm)Tj -27.434 -1.1 Td (g)Tj (e)Tj (n)Tj (e)Tj (r)Tj (a)Tj (t)Tj (e)Tj (d)Tj 4.245 0 Td ( close)Tj 2.468 0 Td ( to)Tj 1.246 0 Td ( the)Tj 1.69 0 Td ( wall)Tj 2.191 0 Td ( of)Tj 1.246 0 Td ( the)Tj 1.69 0 Td ( corridor)Tj 3.914 0 Td ( propagates)Tj 5.08 0 Td ( along)Tj 2.747 0 Td ( the)Tj 1.69 0 Td ( wall.)Tj -28.21 -1.1 Td (If)Tj 0.794 0 Td ( a)Tj 0.907 0 Td ( soldier)Tj 3.297 0 Td ( crab)Tj 2.296 0 Td ( is)Tj 1.074 0 Td ( not)Tj 1.852 0 Td ( close)Tj 2.518 0 Td ( to)Tj 1.296 0 Td ( the)Tj 1.74 0 Td ( wall,)Tj 2.519 0 Td ( it)Tj 1.018 0 Td ( moves)Tj 3.128 0 Td ( freely.)Tj 3.073 0 Td ( In)Tj 1.295 0 Td ( this)Tj 1.963 0 Td ( OR)Tj -28.767 -1.1 Td (gate)Tj 1.853 0 Td ( an)Tj 1.41 0 Td ( agent)Tj 2.687 0 Td ( is)Tj 1.021 0 Td ( assumed)Tj 4.02 0 Td ( to)Tj 1.243 0 Td ( move)Tj 2.686 0 Td ( upward)Tj 3.689 0 Td ( along)Tj 2.744 0 Td ( the)Tj 1.687 0 Td ( wall)Tj 2.188 0 Td ( in)Tj 1.188 0 Td ( Figure)Tj 3.078 0 Td ( 2,)Tj -29.488 -1.1 Td (if)Tj ( it)Tj ( is)Tj ( close)Tj ( to)Tj ( the)Tj ( wall.)Tj ( )Tj 1.2 -1.1 Td (When)Tj 2.597 0 Td ( agents)Tj 3.041 0 Td ( are)Tj 1.652 0 Td ( set)Tj 1.485 0 Td ( in)Tj 1.153 0 Td ( their)Tj 2.319 0 Td ( input)Tj 2.598 0 Td ( position,)Tj 4.099 0 Td ( they)Tj 2.152 0 Td ( aggregate)Tj 4.429 0 Td ( into)Tj 2.042 0 Td ( one)Tj -28.766 -1.1 Td (swarm)Tj 2.938 0 Td ( moving)Tj 3.55 0 Td ( along)Tj 2.718 0 Td ( the)Tj 1.661 0 Td ( wall.)Tj 2.44 0 Td ( In)Tj 1.216 0 Td ( this)Tj 1.884 0 Td ( gate,)Tj 2.383 0 Td ( a)Tj 0.828 0 Td ( swarm)Tj 3.216 0 Td ( initiated)Tj 3.884 0 Td ( at)Tj 1.161 0 Td ( either)Tj -27.878 -1.1 Td (the)Tj 1.401 0 Td ( )Tj /T1_2 1 Tf (x)Tj /T1_0 1 Tf 0.902 0 Td ( or)Tj 1.291 0 Td ( )Tj /T1_2 1 Tf (y)Tj /T1_0 1 Tf 0.846 0 Td ( position)Tj 3.848 0 Td ( moves)Tj 3.067 0 Td ( upward)Tj 3.681 0 Td ( along)Tj 2.736 0 Td ( the)Tj 1.679 0 Td ( central)Tj 3.29 0 Td ( corridor)Tj 3.903 0 Td ( after)Tj 2.345 0 Td ( the)Tj ET q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 96.98 51.6641 Tm ( )Tj 5.455 0 Td ( )Tj 2.121 0 Td ( )Tj 3.732 0 Td ( )Tj 4.623 0 Td ( )Tj 1.453 0 Td ( )Tj 1.455 0 Td ( )Tj 2.621 0 Td ( )Tj 1.677 0 Td ( )Tj 2.065 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 123.865 40.6641 Tm ( )Tj 2.54 0 Td ( )Tj 1.262 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 171.184 40.6641 Tm ( )Tj 1.928 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 218.6 40.6641 Tm ( )Tj 1.985 0 Td ( )Tj 2.095 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 323.051 40.6641 Tm ( )Tj 1.985 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 82.485 27.6641 Tm ( )Tj 1.337 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 105.905 27.6641 Tm ( )Tj 2.004 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 157.605 27.6641 Tm ( )Tj 3.06 0 Td ( )Tj 1.782 0 Td ( )Tj 4.114 0 Td ( )Tj 1.337 0 Td ( )Tj 3.171 0 Td ( )Tj 4.782 0 Td ( )Tj 1.004 0 Td ( )Tj -26.656 -1.3 Td ( )Tj 3.665 0 Td ( )Tj 4.665 0 Td ( )Tj 1.166 0 Td ( )Tj 3.056 0 Td ( )Tj 0.888 0 Td ( )Tj 3 0 Td ( )Tj 0.832 0 Td ( )Tj 2.665 0 Td ( )Tj 1.221 0 Td ( )Tj 4.556 0 Td ( )Tj 1.221 0 Td ( )Tj -27.344 -1.1 Td ( )Tj 2.145 0 Td ( )Tj 4.147 0 Td ( )Tj 2.702 0 Td ( )Tj 2.035 0 Td ( )Tj 3.256 0 Td ( )Tj 2.369 0 Td ( )Tj 1.701 0 Td ( )Tj 1.534 0 Td ( )Tj 1.201 0 Td ( )Tj 1.701 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 316.6171 3.6641 Tm ( )Tj 1.98 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 345.1 3.6641 Tm ( )Tj -25.82 -1.3 Td ( )Tj 0.943 0 Td ( )Tj 2.946 0 Td ( )Tj 2 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 208.4819 -9.3359 Tm ( )Tj 2.445 0 Td ( )Tj 1.167 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 252.9418 -9.3359 Tm ( )Tj 1.833 0 Td ( )Tj ET Q q 0 60.72 432 35.28 re W n BT /T1_0 1 Tf 10 0 0 10 301.2318 -9.3359 Tm ( )Tj ET Q BT /T1_3 1 Tf 8 0 0 8 63 612.0001 Tm (96)Tj /T1_4 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positively)Tj 4.416 0 Td ( contribute)Tj 4.749 0 Td ( to)Tj 1.193 0 Td ( generating)Tj 4.804 0 Td ( and)Tj 1.916 0 Td ( main)Tj (-)Tj -27.823 -1.125 Td (taining)Tj 3.105 0 Td ( a)Tj 0.882 0 Td ( robust)Tj 3.161 0 Td ( swarm.)Tj 3.548 0 Td ( Inherent)Tj 3.992 0 Td ( noise)Tj 2.605 0 Td ( in)Tj 1.216 0 Td ( our)Tj 1.883 0 Td ( model)Tj 3.048 0 Td ( reveals)Tj 3.326 0 Td ( multiple)Tj -26.767 -1.125 Td (potential)Tj 3.938 0 Td ( transitions,)Tj 5.217 0 Td ( and)Tj 1.994 0 Td ( one)Tj 1.938 0 Td ( of)Tj 1.271 0 Td ( them)Tj 2.547 0 Td ( is)Tj 1.049 0 Td ( always)Tj 3.327 0 Td ( chosen)Tj 3.327 0 Td ( in)Tj 1.216 0 Td ( the)Tj 1.715 0 Td ( transi)Tj (-)Tj -27.544 -1.125 Td (tion)Tj 1.788 0 Td ( of)Tj 1.232 0 Td ( each)Tj 2.287 0 Td ( agent\222s)Tj 3.343 0 Td ( location.)Tj 4.122 0 Td ( The)Tj 2.009 0 Td ( inherent)Tj 3.899 0 Td ( noise,)Tj 2.844 0 Td ( therefore,)Tj 4.509 0 Td ( cannot)Tj 3.288 0 Td ( be)Tj -29.322 -1.125 Td (distinguished)Tj 5.754 0 Td ( from)Tj 2.473 0 Td ( external)Tj 3.863 0 Td ( noise.)Tj 2.864 0 Td ( This)Tj 2.252 0 Td ( means)Tj 3.084 0 Td ( that)Tj 2.085 0 Td ( external)Tj 3.863 0 Td ( noise)Tj 2.586 0 Td ( can)Tj -28.822 -1.125 Td (contribute)Tj 4.733 0 Td ( to)Tj 1.455 0 Td ( generating)Tj 5.066 0 Td ( robust)Tj 3.345 0 Td ( swarm)Tj 3.454 0 Td ( balls)Tj 2.567 0 Td ( while)Tj 2.9 0 Td ( the)Tj 1.899 0 Td ( direction)Tj 4.4 0 Td ( a)Tj -29.822 -1.125 Td (swarm)Tj 2.991 0 Td ( ball)Tj 1.993 0 Td ( moves)Tj 3.102 0 Td ( cannot)Tj 3.326 0 Td ( be)Tj 1.381 0 Td ( controlled.)Tj 5.049 0 Td ( However)Tj 4.326 0 Td ( unstable)Tj 3.993 0 Td ( the)Tj 1.714 0 Td ( direc)Tj (-)Tj -27.878 -1.125 Td (tion)Tj 1.87 0 Td ( of)Tj 1.314 0 Td ( a)Tj 0.925 0 Td ( swam)Tj 2.924 0 Td ( ball)Tj 2.037 0 Td ( is,)Tj 1.37 0 Td ( the)Tj 1.758 0 Td ( corridor)Tj 3.982 0 Td ( of)Tj 1.314 0 Td ( the)Tj 1.758 0 Td ( OR)Tj 1.98 0 Td ( gate)Tj 2.202 0 Td ( is)Tj 1.092 0 Td ( one)Tj 1.981 0 Td ( way)Tj 2.203 0 Td ( and)Tj -28.71 -1.125 Td (then)Tj ( the)Tj ( output)Tj ( 1)Tj ( resulting)Tj ( from)Tj ( a)Tj ( swarm)Tj ( ball)Tj ( is)Tj ( robust.)Tj ( )Tj 1.2 -1.124 Td (Figure)Tj 2.746 0 Td ( 3)Tj 0.856 0 Td ( shows)Tj 2.968 0 Td ( an)Tj 1.356 0 Td ( AND)Tj 2.632 0 Td ( gate)Tj 2.077 0 Td ( of)Tj 1.189 0 Td ( swarm)Tj 3.188 0 Td ( balls.)Tj 2.579 0 Td ( Given)Tj 2.856 0 Td ( a)Tj 0.8 0 Td ( pair)Tj 2.023 0 Td ( of)Tj 1.189 0 Td ( inputs)Tj /T1_1 1 Tf -27.654 -1.1 Td (x)Tj /T1_0 1 Tf 0.596 0 Td ( and)Tj 1.93 0 Td ( )Tj /T1_1 1 Tf (y)Tj /T1_0 1 Tf 0.818 0 Td ( located)Tj 3.429 0 Td ( below,)Tj 3.208 0 Td ( the)Tj 1.651 0 Td ( left,)Tj 1.984 0 Td ( central,)Tj 3.54 0 Td ( and)Tj 1.93 0 Td ( right)Tj 2.374 0 Td ( corridors)Tj 4.264 0 Td ( above)Tj 2.874 0 Td ( rep)Tj (-)Tj -28.6 -1.3 Td (resent)Tj 2.59 0 Td ( the)Tj 1.646 0 Td ( output)Tj 3.203 0 Td ( as)Tj 1.202 0 Td ( NOT)Tj ET q 174.96 146.04 13.08 12 re W n BT /TT0 1 Tf 10 0 0 10 175.4922 148.9389 Tm (H)Tj ET Q BT /T1_1 1 Tf 10 0 0 10 178.7002 148.9389 Tm (x)Tj ET q 174.96 146.04 13.08 12 re W n BT /TT0 1 Tf 10 0 0 10 184.2602 148.9389 Tm (L)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 187.8138 148.9389 Tm ( AND)Tj 2.645 0 Td ( )Tj /T1_1 1 Tf (y)Tj /T1_0 1 Tf (,)Tj 1.091 0 Td ( )Tj /T1_1 1 Tf (x)Tj /T1_0 1 Tf 0.869 0 Td ( AND)Tj 2.645 0 Td ( )Tj /T1_1 1 Tf (y)Tj /T1_0 1 Tf (,)Tj 1.091 0 Td ( and)Tj 1.925 0 Td ( )Tj /T1_1 1 Tf (x)Tj /T1_0 1 Tf 0.869 0 Td ( AND)Tj 2.645 0 Td ( NOT)Tj 2.645 0 Td ( )Tj ET q 354 144 12.96 14.04 re W n BT /TT0 1 Tf 10 0 0 10 354.804 148.9389 Tm (H)Tj ET Q BT /T1_1 1 Tf 10 0 0 10 358.012 148.9389 Tm (y)Tj ET q 354 144 12.96 14.04 re W n BT /TT0 1 Tf 10 0 0 10 363.012 148.9389 Tm (L)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 366.22 148.9389 Tm (,)Tj -30.322 -1.3 Td (respectively.)Tj 5.653 0 Td ( Figure)Tj 3.378 0 Td ( 3)Tj 1.21 0 Td ( shows)Tj 3.322 0 Td ( a)Tj 1.154 0 Td ( series)Tj 2.987 0 Td ( of)Tj 1.543 0 Td ( snapshots)Tj 4.878 0 Td ( for)Tj 1.932 0 Td ( the)Tj 1.987 0 Td ( input)Tj ET q 63 120 60 14.04 re W n BT /TT0 1 Tf 10 0 0 10 63 124.9389 Tm (H)Tj ET Q BT /T1_1 1 Tf 10 0 0 10 66.208 124.9389 Tm (x)Tj /T1_0 1 Tf (,)Tj /T1_1 1 Tf 1.134 0 Td (y)Tj ET q 63 120 60 14.04 re W n BT /TT0 1 Tf 10 0 0 10 82.548 124.9389 Tm (L)Tj /C2_0 1 Tf 0.621 0 Td <0001>Tj /TT0 1 Tf 1.084 0 Td (H)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 102.804 124.9389 Tm (1)Tj (,)Tj 1.134 0 Td (1)Tj ET q 63 120 60 14.04 re W n BT /TT0 1 Tf 10 0 0 10 119.704 124.9389 Tm (L)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 122.912 124.9389 Tm (.)Tj 0.358 0 Td ( Two)Tj 2.358 0 Td ( swarm)Tj 3.246 0 Td ( balls)Tj 2.359 0 Td ( initiated)Tj 3.914 0 Td ( at)Tj 1.191 0 Td ( the)Tj 1.691 0 Td ( input)Tj 2.637 0 Td ( locations)Tj 4.248 0 Td ( move)Tj -27.99 -1.3 Td (along)Tj 2.569 0 Td ( their)Tj 2.457 0 Td ( walls,)Tj 2.958 0 Td ( leftward)Tj 4.068 0 Td ( and)Tj 2.069 0 Td ( rightward,)Tj 5.014 0 Td ( respectively.)Tj 5.734 0 Td ( Each)Tj 2.568 0 Td ( swarm)Tj -27.434 -1.1 Td (ball)Tj 1.732 0 Td ( consists)Tj 3.732 0 Td ( of)Tj 1.287 0 Td ( 40)Tj 1.51 0 Td ( agents.)Tj 3.398 0 Td ( After)Tj 2.618 0 Td ( the)Tj 1.731 0 Td ( collision,)Tj 4.289 0 Td ( a)Tj 0.898 0 Td ( united)Tj 3.121 0 Td ( swarm)Tj 3.286 0 Td ( moves)Tj -27.601 -1.1 Td (upward)Tj 3.621 0 Td ( due)Tj 2.12 0 Td ( to)Tj 1.453 0 Td ( the)Tj 1.897 0 Td ( integration)Tj 5.287 0 Td ( of)Tj 1.453 0 Td ( their)Tj 2.564 0 Td ( velocities)Tj 4.508 0 Td ( and)Tj 2.176 0 Td ( results)Tj 3.342 0 Td ( in)Tj 1.398 0 Td ( a)Tj -29.822 -1.1 Td (united)Tj 2.813 0 Td ( swarm)Tj 3.256 0 Td ( moving)Tj 3.59 0 Td ( to)Tj 1.257 0 Td ( the)Tj 1.701 0 Td ( central)Tj 3.312 0 Td ( corridor,)Tj 4.203 0 Td ( showing)Tj 3.981 0 Td ( that)Tj 2.09 0 Td ( )Tj ET q 327 75.96 6.96 12 re W n BT /T1_1 1 Tf 10 0 0 10 327.769 78.9389 Tm (x)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 334.2245 78.9389 Tm ( AND)Tj 2.7 0 Td ( )Tj ET q 363.96 74.04 5.04 13.92 re W n BT /T1_1 1 Tf 10 0 0 10 364 78.9389 Tm (y)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 63 65.9389 Tm (is)Tj 0.729 0 Td ( 1.)Tj 1.39 0 Td (As)Tj 1.172 0 Td ( well)Tj 2.118 0 Td ( as)Tj 1.229 0 Td ( the)Tj 1.673 0 Td ( behavior)Tj 4.119 0 Td ( of)Tj 1.229 0 Td ( an)Tj 1.396 0 Td ( OR)Tj 1.895 0 Td ( gate,)Tj 2.395 0 Td ( a)Tj 0.84 0 Td ( united)Tj 3.063 0 Td ( swarm)Tj 3.228 0 Td ( ball)Tj 1.952 0 Td ( con)Tj (-)Tj ET q 0 62.88 432 119.16 re W n BT /T1_0 1 Tf 10 0 0 10 81.0883 53.9389 Tm ( )Tj 1.198 0 Td ( )Tj 1.421 0 Td ( )Tj 3.031 0 Td ( )Tj 1.921 0 Td ( )Tj 4.532 0 Td ( )Tj 1.198 0 Td ( )Tj 4.866 0 Td ( )Tj 1.198 0 Td ( )Tj 3.031 0 Td ( )Tj 1.642 0 Td ( )Tj 1.754 0 Td ( )Tj -25.197 -1.1 Td ( )Tj 1.122 0 Td ( )Tj 3.289 0 Td ( )Tj 2.013 0 Td ( )Tj 5.959 0 Td ( )Tj 4.013 0 Td ( )Tj 3.735 0 Td ( )Tj 5.235 0 Td ( )Tj -21.459 -1.1 Td ( )Tj 1.251 0 Td ( )Tj 3.084 0 Td ( )Tj 1.196 0 Td ( )Tj 2.528 0 Td ( )Tj 2.528 0 Td ( )Tj 1.695 0 Td ( )Tj 4.529 0 Td ( )Tj 2.64 0 Td ( )Tj 1.196 0 Td ( )Tj 0.862 0 Td ( )Tj -25.288 -1.1 Td ( )Tj 2.256 0 Td ( )Tj 1.257 0 Td ( )Tj 1.756 0 Td ( )Tj 2.702 0 Td ( )Tj 4.203 0 Td ( )Tj 3.034 0 Td ( )Tj 1.535 0 Td ( )Tj 3.923 0 Td ( )Tj 2.646 0 Td ( )Tj 1.09 0 Td ( )Tj -24.907 -1.1 Td ( )Tj 1.691 0 Td ( )Tj 4.526 0 Td ( )Tj 2.025 0 Td ( )Tj 1.636 0 Td ( )Tj 1.691 0 Td ( )Tj 2.969 0 Td ( )Tj 2.024 0 Td ( )Tj 5.801 0 Td ( )Tj 1.247 0 Td ( )Tj 2.524 0 Td ( )Tj -27.42 -1.1 Td ( )Tj 2.015 0 Td ( )Tj 3.513 0 Td ( )Tj 1.625 0 Td ( )Tj 2.18 0 Td ( )Tj 2.957 0 Td ( )Tj 1.959 0 Td ( )Tj 2.679 0 Td ( )Tj 2.791 0 Td ( )Tj 3.735 0 Td ( )Tj 1.569 0 Td ( )Tj 1.847 0 Td ( )Tj -25.337 -1.1 Td ( )Tj 2.21 0 Td ( )Tj 2.987 0 Td ( )Tj 1.989 0 Td ( )Tj 2.709 0 Td ( )Tj 2.821 0 Td ( )Tj 1.599 0 Td ( )Tj 1.877 0 Td ( )Tj 4.154 0 Td ( )Tj 1.933 0 Td ( )Tj -22.485 -1.1 Td ( )Tj 4.166 0 Td ( )Tj ET Q BT /T1_5 1 Tf 8 0 0 8 63 612.0001 Tm (Robust)Tj ( Soldier)Tj ( Crab)Tj ( Ball)Tj ( Gate)Tj /T1_6 1 Tf 37.138 0 Td (97)Tj /T1_7 1 Tf 7 0 0 7 169.7103 31.6251 Tm (Complex)Tj ( Systems,)Tj ( )Tj /T1_8 1 Tf (2)Tj (0)Tj /T1_9 1 Tf ( \251)Tj ( 2011)Tj ( Complex)Tj ( Systems)Tj ( Publications,)Tj ( Inc.)Tj ET endstream endobj 11 0 obj <>stream ����Adobed���C �� HX��� s!1AQa"q�2���B#�R��3b�$r��%C4S���cs�5D'���6Tdt���&� 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1.396 0 Td ( )Tj 1.895 0 Td ( )Tj 2.395 0 Td ( )Tj 0.84 0 Td ( )Tj 3.063 0 Td ( )Tj 3.228 0 Td ( )Tj 1.952 0 Td ( )Tj ET Q BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 10 0 0 10 63 585.0001 Tm (sists)Tj 1.809 0 Td ( of)Tj 1.198 0 Td ( 80)Tj 1.421 0 Td ( agents)Tj 3.031 0 Td ( and)Tj 1.921 0 Td ( directions)Tj 4.532 0 Td ( of)Tj 1.198 0 Td ( transitions)Tj 4.866 0 Td ( of)Tj 1.198 0 Td ( agents)Tj 3.031 0 Td ( are)Tj 1.642 0 Td ( not)Tj 1.754 0 Td ( analo)Tj (-)Tj -27.599 -1.1 Td (gous.)Tj 2.402 0 Td ( A)Tj 1.122 0 Td ( swarm)Tj 3.289 0 Td ( ball)Tj 2.013 0 Td ( continuously)Tj 5.959 0 Td ( contains)Tj 4.013 0 Td ( internal)Tj 3.735 0 Td ( turbulence.)Tj 5.235 0 Td ( Initial)Tj -27.767 -1.1 Td (configurations)Tj 6.308 0 Td ( of)Tj 1.251 0 Td ( agents)Tj 3.084 0 Td ( in)Tj 1.196 0 Td ( these)Tj 2.528 0 Td ( gates)Tj 2.528 0 Td ( are)Tj 1.695 0 Td ( randomly)Tj 4.529 0 Td ( given)Tj 2.64 0 Td ( in)Tj 1.196 0 Td ( a)Tj 0.862 0 Td ( desig)Tj (-)Tj -27.822 -1.1 Td (nated)Tj 2.534 0 Td ( area)Tj 2.256 0 Td ( in)Tj 1.257 0 Td ( the)Tj 1.756 0 Td ( input)Tj 2.702 0 Td ( position,)Tj 4.203 0 Td ( where)Tj 3.034 0 Td ( no)Tj 1.535 0 Td ( external)Tj 3.923 0 Td ( noise)Tj 2.646 0 Td ( is)Tj 1.09 0 Td ( coupled)Tj -26.932 -1.1 Td (with)Tj 2.025 0 Td ( the)Tj 1.691 0 Td ( transition)Tj 4.526 0 Td ( rule)Tj 2.025 0 Td ( for)Tj 1.636 0 Td ( the)Tj 1.691 0 Td ( agent.)Tj 2.969 0 Td ( The)Tj 2.024 0 Td ( performance)Tj 5.801 0 Td ( of)Tj 1.247 0 Td ( these)Tj 2.524 0 Td ( gates)Tj -28.156 -1.1 Td (is)Tj 0.736 0 Td ( 100)Tj 2.015 0 Td ( percent)Tj 3.513 0 Td ( for)Tj 1.625 0 Td ( OR,)Tj 2.18 0 Td ( AND,)Tj 2.957 0 Td ( and)Tj 1.959 0 Td ( NOT)Tj 2.679 0 Td ( gates.)Tj 2.791 0 Td ( Because)Tj 3.735 0 Td ( we)Tj 1.569 0 Td ( can)Tj 1.847 0 Td ( imple)Tj (-)Tj -27.601 -1.1 Td (ment)Tj 2.264 0 Td ( OR,)Tj 2.21 0 Td ( AND,)Tj 2.987 0 Td ( and)Tj 1.989 0 Td ( NOT)Tj 2.709 0 Td ( gates,)Tj 2.821 0 Td ( we)Tj 1.599 0 Td ( can)Tj 1.877 0 Td ( calculate)Tj 4.154 0 Td ( any)Tj 1.933 0 Td ( propositional)Tj ET q 0 506.04 432 87.96 re W n BT /T1_0 1 Tf 10 0 0 10 63 508.0001 Tm (logic)Tj ( sentence.)Tj ( )Tj ET Q q 228.0959015 0 0 -157.6109924 100 493 cm /Im0 Do Q /CS0 CS 1 0.298 0 SCN 1.98 w 3.25 M 1 j 2 J q 1 0 0 1 140.2522 439.4191 cm 0 0 m 6.036 6.002 l S Q 1 0.298 0 scn q 1 0 0 1 145.5821 440.5777 cm 0 0 m 2.094 6.224 l -4.142 4.165 l h f* Q q 1 0 0 1 168.03 439.4191 cm 0 0 m -6.036 6.002 l S Q q 1 0 0 1 162.7001 440.5777 cm 0 0 m -2.094 6.224 l 4.142 4.165 l h f* Q q 1 0 0 1 269.8003 457.9376 cm 0 0 m 6.035 6.002 l S Q q 1 0 0 1 275.13 459.0963 cm 0 0 m 2.094 6.224 l -4.142 4.165 l h f* Q q 1 0 0 1 264.2529 457.9376 cm 0 0 m -6.036 6.002 l S Q q 1 0 0 1 258.9228 459.0963 cm 0 0 m -2.094 6.224 l 4.142 4.165 l h f* Q q 1 0 0 1 155.0997 391.2873 cm 0 0 m -0.032 7.301 l S Q q 1 0 0 1 152.148 394.66 cm 0 0 m 2.911 5.886 l 5.874 0.026 l h f* Q q 1 0 0 1 266.1293 406.0939 cm 0 0 m -0.032 7.301 l S Q q 1 0 0 1 263.1774 409.4666 cm 0 0 m 2.911 5.886 l 5.874 0.026 l h f* Q q 95.16 327.84 238.08 170.04 re W n 1 1 1 scn q 1 0 0 1 204.3364 433.5846 cm 0 0 m 0 0.88 l 0.402 0.88 0.682 0.897 0.842 0.934 c 1.098 0.99 1.307 1.103 1.468 1.272 c 1.578 1.388 1.661 1.543 1.717 1.736 c 1.75 1.85 1.766 1.935 1.766 1.992 c 2.824 1.992 l 2.824 -4.477 l 1.52 -4.477 l 1.52 0 l h f* Q q 1 0 0 1 216.9124 429.1075 cm 0 0 m 0 0.464 0.102 0.887 0.306 1.271 c 0.487 1.7 0.915 2.155 1.588 2.635 c 2.168 3.052 2.544 3.351 2.714 3.532 c 2.976 3.814 3.107 4.123 3.107 4.459 c 3.107 4.733 3.031 4.96 2.88 5.141 c 2.729 5.322 2.513 5.412 2.231 5.412 c 1.846 5.412 1.584 5.268 1.445 4.98 c 1.364 4.813 1.324 4.548 1.324 4.186 c 0.091 4.186 l 0.091 4.736 0.18 5.18 0.358 5.519 c 0.698 6.165 1.301 6.487 2.166 6.487 c 2.85 6.487 3.395 6.298 3.799 5.919 c 4.204 5.54 4.406 5.039 4.406 4.416 c 4.406 3.938 4.263 3.513 3.977 3.142 c 3.79 2.896 3.482 2.622 3.054 2.32 c 2.55 1.959 l 2.236 1.734 2.02 1.571 1.903 1.47 c 1.787 1.37 1.689 1.252 1.61 1.119 c 4.421 1.119 l 4.421 0 l h f* Q q 1 0 0 1 205.1744 405.1689 cm 0 0 m 0 -0.259 0.042 -0.473 0.126 -0.643 c 0.282 -0.955 0.565 -1.111 0.977 -1.111 c 1.228 -1.111 1.447 -1.025 1.635 -0.854 c 1.822 -0.682 1.916 -0.434 1.916 -0.111 c 1.916 0.317 1.749 0.603 1.415 0.747 c 1.224 0.827 0.918 0.868 0.5 0.868 c 0.5 1.782 l 0.909 1.782 1.195 1.819 1.358 1.894 c 1.638 2.019 1.777 2.272 1.777 2.654 c 1.777 2.9 1.704 3.101 1.556 3.255 c 1.41 3.41 1.203 3.488 0.935 3.488 c 0.629 3.488 0.403 3.391 0.258 3.196 c 0.115 3.003 0.043 2.745 0.043 2.421 c -1.131 2.421 l -1.131 2.748 -1.078 3.058 -0.974 3.352 c -0.869 3.606 -0.704 3.84 -0.48 4.054 c -0.311 4.206 -0.111 4.321 0.12 4.401 c 0.351 4.482 0.635 4.523 0.972 4.523 c 1.597 4.523 2.1 4.361 2.483 4.037 c 2.866 3.715 3.058 3.282 3.058 2.74 c 3.058 2.355 2.943 2.031 2.713 1.766 c 2.568 1.6 2.417 1.484 2.26 1.416 c 2.378 1.416 2.547 1.324 2.768 1.141 c 3.083 0.841 3.241 0.432 3.241 -0.087 c 3.241 -0.633 3.049 -1.114 2.667 -1.528 c 2.285 -1.941 1.72 -2.147 0.971 -2.147 c 0.048 -2.147 -0.593 -1.848 -0.952 -1.249 c -1.142 -0.931 -1.236 -0.515 -1.236 0 c h f* Q q 1 0 0 1 221.4809 404.575 cm 0 0 m -0.767 0 l -0.767 -1.392 l -2.01 -1.392 l -2.01 0 l -4.571 0 l -4.571 1.111 l -2.193 5.037 l -0.767 5.037 l -0.767 0.995 l 0 0.995 l h -2.01 0.995 m -2.01 3.787 l -3.63 0.995 l h f* Q 143.964 401.974 22.067 7.832 re f* /CS2 cs 0 scn q 1 0 0 1 146.3707 404.0627 cm 0 0 m 1.069 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 151.3708 405.3147 cm 0 0 m 0.834 0 l 0.424 1.293 l h 0.042 2.045 m 0.819 2.045 l 1.983 -1.252 l 1.238 -1.252 l 1.026 -0.567 l -0.185 -0.567 l -0.413 -1.252 l -1.131 -1.252 l h 0.426 2.036 m h 2.371 2.036 m 3.091 2.036 l 4.381 -0.259 l 4.381 2.036 l 5.021 2.036 l 5.021 -1.252 l 4.335 -1.252 l 3.011 1.084 l 3.011 -1.252 l 2.371 -1.252 l h 3.749 2.043 m h 6.382 1.468 m 6.382 -0.681 l 7.018 -0.681 l 7.343 -0.681 7.57 -0.521 7.698 -0.201 c 7.769 -0.025 7.804 0.185 7.804 0.428 c 7.804 0.763 7.751 1.02 7.646 1.199 c 7.541 1.379 7.331 1.468 7.018 1.468 c h 7.134 2.037 m 7.339 2.037 7.508 2.015 7.644 1.97 c 7.875 1.894 8.062 1.755 8.205 1.552 c 8.32 1.388 8.398 1.211 8.439 1.02 c 8.481 0.829 8.502 0.647 8.502 0.475 c 8.502 0.036 8.414 -0.335 8.239 -0.639 c 8 -1.048 7.632 -1.252 7.134 -1.252 c 5.715 -1.252 l 5.715 2.037 l h f* Q q 1 0 0 1 161.5774 403.6108 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.034 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.216 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.647 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q /CS0 cs 1 1 1 scn q 1 0 0 1 185.2437 391.134 cm 0 0 m 1.068 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 190.2437 392.386 cm 0 0 m 0.834 0 l 0.424 1.293 l h 0.042 2.045 m 0.819 2.045 l 1.983 -1.252 l 1.238 -1.252 l 1.026 -0.567 l -0.185 -0.567 l -0.413 -1.252 l -1.131 -1.252 l h 0.426 2.036 m h 2.371 2.036 m 3.091 2.036 l 4.381 -0.259 l 4.381 2.036 l 5.022 2.036 l 5.022 -1.252 l 4.335 -1.252 l 3.011 1.084 l 3.011 -1.252 l 2.371 -1.252 l h 3.749 2.043 m h 6.382 1.468 m 6.382 -0.681 l 7.018 -0.681 l 7.344 -0.681 7.57 -0.521 7.698 -0.201 c 7.769 -0.024 7.804 0.185 7.804 0.428 c 7.804 0.763 7.751 1.02 7.646 1.199 c 7.541 1.379 7.332 1.468 7.018 1.468 c h 7.134 2.037 m 7.339 2.037 7.508 2.015 7.644 1.97 c 7.875 1.894 8.062 1.755 8.205 1.553 c 8.32 1.388 8.398 1.211 8.439 1.02 c 8.481 0.829 8.502 0.647 8.502 0.475 c 8.502 0.036 8.414 -0.335 8.239 -0.639 c 8 -1.048 7.632 -1.252 7.134 -1.252 c 5.715 -1.252 l 5.715 2.037 l h f* Q q 1 0 0 1 200.4503 390.6821 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.035 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.216 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.647 -0.452 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q 1 1 1 SCN 0.742 w q 1 0 0 1 199.5197 395.7333 cm 0 0 m 3.671 0 l S Q q 1 0 0 1 109.3745 391.1324 cm 0 0 m 1.069 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 114.3745 392.3844 cm 0 0 m 0.835 0 l 0.424 1.293 l h 0.042 2.045 m 0.819 2.045 l 1.983 -1.252 l 1.238 -1.252 l 1.026 -0.567 l -0.185 -0.567 l -0.413 -1.252 l -1.131 -1.252 l h 0.426 2.036 m h 2.371 2.036 m 3.091 2.036 l 4.381 -0.259 l 4.381 2.036 l 5.022 2.036 l 5.022 -1.252 l 4.335 -1.252 l 3.012 1.084 l 3.012 -1.252 l 2.371 -1.252 l h 3.749 2.043 m h 6.382 1.468 m 6.382 -0.681 l 7.018 -0.681 l 7.344 -0.681 7.57 -0.521 7.698 -0.201 c 7.769 -0.025 7.804 0.185 7.804 0.428 c 7.804 0.763 7.751 1.02 7.646 1.199 c 7.541 1.379 7.332 1.468 7.018 1.468 c h 7.134 2.037 m 7.339 2.037 7.508 2.015 7.644 1.97 c 7.875 1.894 8.062 1.755 8.205 1.552 c 8.32 1.388 8.398 1.211 8.439 1.02 c 8.481 0.829 8.502 0.647 8.502 0.475 c 8.502 0.036 8.414 -0.335 8.239 -0.639 c 8 -1.048 7.632 -1.252 7.134 -1.252 c 5.715 -1.252 l 5.715 2.037 l h f* Q q 1 0 0 1 124.5811 390.6805 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.034 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.216 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.648 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q q 1 0 0 1 108.8442 396.3043 cm 0 0 m 3.671 0 l S Q /CS2 cs 0 scn q 1 0 0 1 118.6337 333.782 cm 0 0 m 1.069 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 189.146 333.3302 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.034 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.215 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.647 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q Q BT 0 0 0 scn /T1_1 1 Tf 8 0 0 8 63 310.653 Tm (F)Tj (i)Tj (g)Tj (u)Tj (r)Tj (e)Tj 3.368 0 Td (3)Tj (.)Tj ET q 0 279 432 39 re W n BT /T1_2 1 Tf 9 0 0 9 99.5537 310.653 Tm (A)Tj 0.919 0 Td ( series)Tj 2.809 0 Td ( of)Tj 1.365 0 Td ( snapshots)Tj 4.7 0 Td ( \(1,)Tj 1.643 0 Td ( 2,)Tj 1.31 0 Td ( 3,)Tj 1.31 0 Td ( and)Tj 2.088 0 Td ( 4\))Tj 1.365 0 Td ( in)Tj 1.31 0 Td ( an)Tj 1.532 0 Td ( AND)Tj 2.808 0 Td ( gate)Tj 2.253 0 Td ( of)Tj 1.365 0 Td ( swarm)Tj ET Q BT /T1_2 1 Tf 9 0 0 9 63 301.153 Tm (balls.)Tj 2.346 0 Td ( Swarm)Tj 3.344 0 Td ( balls)Tj 2.346 0 Td ( located)Tj 3.456 0 Td ( at)Tj 1.178 0 Td ( the)Tj 1.678 0 Td ( )Tj /T1_3 1 Tf 0.279 0 Td (x)Tj /T1_2 1 Tf 0.623 0 Td ( and)Tj 1.957 0 Td ( )Tj /T1_3 1 Tf (y)Tj /T1_2 1 Tf 0.845 0 Td ( positions)Tj 4.236 0 Td ( consist)Tj 3.29 0 Td ( of)Tj 1.234 0 Td ( 40)Tj 1.457 0 Td ( agents.)Tj 3.345 0 Td ( Each)Tj -31.611 -1.056 Td (agent)Tj 2.421 0 Td ( is)Tj 1.033 0 Td ( represented)Tj 5.31 0 Td ( by)Tj 1.422 0 Td ( a)Tj 0.866 0 Td ( square)Tj 3.2 0 Td ( with)Tj 2.311 0 Td ( its)Tj 1.366 0 Td ( 5)Tj (-)Tj (step)Tj 2.977 0 Td ( trajectory.)Tj 4.81 0 Td ( Red)Tj 2.088 0 Td ( arrows)Tj 3.367 0 Td ( repre)Tj (-)Tj -31.167 -1.056 Td (sent)Tj ( the)Tj ( direction)Tj ( a)Tj ( swarm)Tj ( ball)Tj ( is)Tj ( moving)Tj ( toward.)Tj ( )Tj ( )Tj ET q 0 99 432 162.96 re W n BT /T1_0 1 Tf 10 0 0 10 75 252.653 Tm (Finally,)Tj 3.387 0 Td ( we)Tj 1.662 0 Td ( discuss)Tj 3.441 0 Td ( the)Tj 1.773 0 Td ( robustness)Tj 4.997 0 Td ( of)Tj 1.329 0 Td ( the)Tj 1.773 0 Td ( gates.)Tj 2.884 0 Td ( As)Tj 1.55 0 Td ( mentioned)Tj 4.995 0 Td ( be)Tj (-)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 63 241.653 Tm (fore,)Tj 2.121 0 Td ( the)Tj 1.732 0 Td ( OR)Tj 1.954 0 Td ( gate)Tj 2.176 0 Td ( acts)Tj 2.065 0 Td ( very)Tj 2.232 0 Td ( well)Tj 2.177 0 Td ( against)Tj 3.455 0 Td ( external)Tj 3.899 0 Td ( perturbation.)Tj 6.123 0 Td ( Here,)Tj -27.933 -1.1 Td (we)Tj 1.247 0 Td ( estimate)Tj 3.856 0 Td ( the)Tj 1.636 0 Td ( performance)Tj 5.746 0 Td ( of)Tj 1.192 0 Td ( the)Tj 1.636 0 Td ( AND)Tj 2.635 0 Td ( gate)Tj 2.08 0 Td ( under)Tj 2.804 0 Td ( a)Tj 0.803 0 Td ( high)Tj 2.193 0 Td ( rate)Tj 1.969 0 Td ( of)Tj 1.192 0 Td ( ex)Tj (-)Tj -28.989 -1.1 Td (ternal)Tj 2.564 0 Td ( noise.)Tj 2.843 0 Td ( In)Tj 1.23 0 Td ( the)Tj 1.675 0 Td ( simulation,)Tj 5.176 0 Td ( the)Tj 1.675 0 Td ( external)Tj 3.842 0 Td ( noise)Tj 2.565 0 Td ( that)Tj 2.064 0 Td ( is)Tj 1.009 0 Td ( coupled)Tj 3.732 0 Td ( with)Tj -28.377 -1.1 Td (the)Tj 1.417 0 Td ( operation)Tj 4.53 0 Td ( of)Tj 1.251 0 Td ( velocity)Tj 3.695 0 Td ( matching)Tj 4.361 0 Td ( is)Tj 1.029 0 Td ( defined)Tj 3.529 0 Td ( as)Tj 1.251 0 Td ( a)Tj 0.862 0 Td ( random)Tj 3.751 0 Td ( value)Tj 2.64 0 Td ( )Tj /TT0 1 Tf 0.284 0 Td (x)Tj /T1_0 1 Tf 0.553 0 Td ( se)Tj (-)Tj -29.156 -1.1 Td (lected)Tj 2.579 0 Td ( with)Tj 2.303 0 Td ( equal)Tj 2.692 0 Td ( probability)Tj 5.138 0 Td ( from)Tj 2.468 0 Td ( )Tj ET q 216.96 195 31.08 12 re W n BT /TT1 1 Tf 10 0 0 10 217.5931 197.653 Tm (@)Tj ET Q BT /TT0 1 Tf 10 0 0 10 220.9232 197.653 Tm (-)Tj 0.744 0 Td (l)Tj /T1_0 1 Tf (,)Tj /TT0 1 Tf 1.092 0 Td (l)Tj ET q 216.96 195 31.08 12 re W n BT /TT1 1 Tf 10 0 0 10 244.4268 197.653 Tm (D)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 247.7569 197.653 Tm (.)Tj 0.358 0 Td ( When)Tj 2.914 0 Td ( the)Tj 1.691 0 Td ( velocity)Tj 3.691 0 Td ( of)Tj 1.247 0 Td ( each)Tj -28.378 -1.1 Td (agent)Tj 2.413 0 Td ( in)Tj 1.192 0 Td ( a)Tj 0.858 0 Td ( two-dimensional)Tj 7.581 0 Td ( space)Tj 2.691 0 Td ( )Tj /T1_4 1 Tf (v)Tj /T1_0 1 Tf 0.858 0 Td ( is)Tj 1.025 0 Td ( projected)Tj 4.358 0 Td ( in)Tj 1.192 0 Td ( the)Tj 1.691 0 Td ( )Tj /T1_4 1 Tf (x)Tj /T1_0 1 Tf 0.914 0 Td ( and)Tj 1.97 0 Td ( )Tj /T1_4 1 Tf (y)Tj /T1_0 1 Tf 0.858 0 Td ( planes)Tj -27.599 -1.3 Td (denoted)Tj 3.664 0 Td ( by)Tj 1.553 0 Td ( )Tj /T1_4 1 Tf (v)Tj ET q 117 171 11.04 12 re W n BT /T1_5 1 Tf 8 0 0 8 122.9717 171.8122 Tm (x)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 130.111 173.653 Tm ( and)Tj 2.109 0 Td ( )Tj /T1_4 1 Tf (v)Tj /T1_5 1 Tf 8 0 0 8 158.9822 171.8122 Tm (y)Tj /T1_0 1 Tf 10 0 0 10 163.4822 173.653 Tm (,)Tj 0.497 0 Td ( the)Tj 1.83 0 Td ( external)Tj 3.997 0 Td ( noise)Tj 2.72 0 Td ( is)Tj 1.164 0 Td ( coupled)Tj 3.887 0 Td ( by)Tj 1.553 0 Td ( )Tj /T1_4 1 Tf (v)Tj ET q 321.96 171 26.04 12 re W n BT /T1_5 1 Tf 8 0 0 8 327.7703 171.8122 Tm (x)Tj ET Q BT /TT0 1 Tf 10 0 0 10 334.7183 173.653 Tm (+)Tj 0.85 0 Td (x)Tj /T1_0 1 Tf 0.688 0 Td ( and)Tj ET q 63 153.96 24.96 15 re W n BT /T1_4 1 Tf 10 0 0 10 63 159.8122 Tm (v)Tj ET Q BT /T1_5 1 Tf 8 0 0 8 68 157.9714 Tm (y)Tj ET q 63 153.96 24.96 15 re W n BT /TT0 1 Tf 10 0 0 10 74.5 159.8122 Tm (+)Tj 0.85 0 Td (x)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 89.2329 159.8122 Tm ( and)Tj 2.044 0 Td ( then)Tj 2.321 0 Td ( normalized)Tj 5.265 0 Td ( to)Tj 1.321 0 Td ( make)Tj 2.764 0 Td ( the)Tj 1.765 0 Td ( length)Tj 3.099 0 Td ( of)Tj 1.321 0 Td ( the)Tj 1.765 0 Td ( velocity)Tj 3.765 0 Td ( be)Tj 1.432 0 Td ( 1.)Tj -29.488 -1.384 Td (We)Tj 1.588 0 Td ( estimate)Tj 3.975 0 Td ( performance)Tj 5.865 0 Td ( within)Tj 3.201 0 Td ( the)Tj 1.755 0 Td ( range)Tj 2.811 0 Td ( )Tj (0.0)Tj /TT0 1 Tf 1.968 0 Td (\247)Tj 0.944 0 Td (l)Tj 0.814 0 Td (\247)Tj /T1_0 1 Tf 0.944 0 Td (0.2)Tj 1.534 0 Td ( when)Tj 2.756 0 Td ( )Tj (c)Tj (o)Tj (m)Tj (-)Tj -28.157 -1.1 Td (p)Tj (a)Tj (r)Tj (i)Tj (n)Tj (g)Tj 2.844 0 Td ( our)Tj 1.844 0 Td ( model)Tj 3.009 0 Td ( of)Tj 1.232 0 Td ( )Tj /T1_4 1 Tf (P)Tj ET q 155.04 132 31.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 164.1982 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 175.0382 134.9714 Tm (20)Tj 1.177 0 Td ( with)Tj 2.288 0 Td ( one)Tj 1.899 0 Td ( with)Tj 2.288 0 Td ( )Tj /T1_4 1 Tf (P)Tj ET q 254.04 132 25.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 263.4664 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 274.3064 134.9714 Tm (1)Tj (.)Tj 0.899 0 Td ( If)Tj 1.008 0 Td ( )Tj /T1_4 1 Tf (P)Tj ET q 296.04 132 31.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 305.2755 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 316.1154 134.9714 Tm (20)Tj (,)Tj 1.455 0 Td ( multiple)Tj -26.767 -1.1 Td (potential)Tj 3.96 0 Td ( transitions)Tj 4.961 0 Td ( play)Tj 2.238 0 Td ( a)Tj 0.904 0 Td ( role)Tj 2.071 0 Td ( in)Tj 1.238 0 Td ( mutual)Tj 3.459 0 Td ( anticipation)Tj 5.572 0 Td ( that)Tj 2.126 0 Td ( can)Tj 1.904 0 Td ( con)Tj (-)Tj -28.433 -1.1 Td (tribute)Tj 3.104 0 Td ( to)Tj 1.382 0 Td ( collective)Tj 4.492 0 Td ( behavior.)Tj 4.55 0 Td ( If)Tj 1.158 0 Td ( )Tj /T1_4 1 Tf (P)Tj ET q 212.04 110.04 27 12 re W n BT /C2_0 1 Tf 10 0 0 10 221.7667 112.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 232.6066 112.9714 Tm (1)Tj (,)Tj 1.049 0 Td ( coherence)Tj 4.77 0 Td ( of)Tj 1.382 0 Td ( swarm)Tj 3.381 0 Td ( results)Tj -27.544 -1.1 Td (only)Tj ( from)Tj ( velocity)Tj ( matching.)Tj ( )Tj ET q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 75 90.9714 Tm (Figure)Tj 2.83 0 Td ( 4)Tj 0.941 0 Td ( shows)Tj 3.053 0 Td ( performance)Tj 5.827 0 Td ( of)Tj 1.274 0 Td ( an)Tj 1.44 0 Td ( AND)Tj 2.717 0 Td ( gate)Tj 2.162 0 Td ( implemented)Tj 5.937 0 Td ( by)Tj 1.44 0 Td ( our)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 63 79.7214 Tm (swarm)Tj 3.09 0 Td ( model)Tj 3.146 0 Td ( under)Tj 2.981 0 Td ( a)Tj 0.98 0 Td ( perturbed)Tj 4.703 0 Td ( condition.)Tj 4.871 0 Td ( The)Tj 2.146 0 Td ( performance)Tj 5.923 0 Td ( is)Tj 1.147 0 Td ( de)Tj (-)Tj -28.989 -1.125 Td (fined)Tj 2.333 0 Td ( by)Tj 1.5 0 Td ( the)Tj 1.777 0 Td ( success)Tj 3.499 0 Td ( rate)Tj 2.11 0 Td ( of)Tj 1.333 0 Td ( the)Tj 1.777 0 Td ( gate.)Tj 2.611 0 Td (In)Tj 1.054 0 Td ( each)Tj 2.388 0 Td ( experiment,)Tj 5.554 0 Td ( we)Tj 1.666 0 Td ( set)Tj 1.61 0 Td ( 40)Tj ET q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 90.5643 56.4714 Tm ( )Tj 1.146 0 Td ( )Tj 1.645 0 Td ( )Tj 2.591 0 Td ( )Tj 4.203 0 Td ( )Tj ET Q q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 195.1157 56.4714 Tm ( )Tj 1.924 0 Td ( )Tj ET Q q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 225.2643 56.4714 Tm ( )Tj 0.977 0 Td ( )Tj 2.424 0 Td ( )Tj 1.201 0 Td ( )Tj 1.645 0 Td ( )Tj 3.034 0 Td ( )Tj 1.757 0 Td ( )Tj -26.293 -1.3 Td ( )Tj 0.918 0 Td ( )Tj 3.141 0 Td ( )Tj 3.306 0 Td ( )Tj 2.751 0 Td ( )Tj 1.751 0 Td ( )Tj 3.308 0 Td ( )Tj 2.029 0 Td ( )Tj 1.307 0 Td ( )Tj ET Q q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 267.5977 43.4714 Tm ( )Tj 2.75 0 Td ( )Tj ET Q q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 307.0593 43.4714 Tm ( )Tj 1.64 0 Td ( )Tj -24.65 -1.3 Td ( )Tj 2.73 0 Td ( )Tj 1.619 0 Td ( )Tj 1.674 0 Td ( )Tj 5.173 0 Td ( )Tj 1.23 0 Td ( )Tj 1.341 0 Td ( )Tj 0.841 0 Td ( )Tj 3.674 0 Td ( )Tj 4.786 0 Td ( )Tj 0.952 0 Td ( )Tj 1.008 0 Td ( )Tj 0.841 0 Td ( )Tj -25.478 -1.125 Td ( )Tj 5.843 0 Td ( )Tj 1.067 0 Td ( )Tj 3.567 0 Td ( )Tj 1.456 0 Td ( )Tj 1.733 0 Td ( )Tj 3.733 0 Td ( )Tj 1.289 0 Td ( )Tj 4.622 0 Td ( )Tj -21.817 -1.125 Td ( )Tj 1.45 0 Td ( )Tj 1.727 0 Td ( )Tj 2.394 0 Td ( )Tj 3.727 0 Td ( )Tj 1.283 0 Td ( )Tj 5.615 0 Td ( )Tj 2.395 0 Td ( )Tj 6.226 0 Td ( )Tj -26.565 -1.125 Td ( )Tj 3.368 0 Td ( )Tj 3.146 0 Td ( )Tj 2.425 0 Td ( )Tj ET Q q 0 65.52 432 34.44 re W n BT /T1_0 1 Tf 10 0 0 10 198.0667 -3.2786 Tm ( )Tj 5.704 0 Td ( )Tj 1.369 0 Td ( )Tj 1.813 0 Td ( )Tj 5.593 0 Td ( )Tj -24.919 -1.125 Td ( )Tj 1.734 0 Td ( )Tj 3.902 0 Td ( )Tj 5.847 0 Td ( )Tj 3.624 0 Td ( )Tj 4.679 0 Td ( )Tj 1.734 0 Td ( )Tj 4.4 0 Td ( )Tj -25.86 -1.125 Td ( )Tj 1.517 0 Td ( )Tj 4.183 0 Td ( )Tj 5.127 0 Td ( )Tj 1.517 0 Td ( )Tj 1.961 0 Td ( )Tj 4.128 0 Td ( )Tj 1.517 0 Td ( )Tj 6.074 0 Td ( )Tj -25.878 -1.125 Td ( )Tj 1.611 0 Td ( )Tj 5.721 0 Td ( )Tj 3.335 0 Td ( )Tj 4.555 0 Td ( )Tj ET Q BT /T1_6 1 Tf 8 0 0 8 63 612.0001 Tm (98)Tj /T1_5 1 Tf 18.19 0 Td (Y.-P.)Tj ( Gunji,)Tj ( Y.)Tj ( Nishiyama,)Tj ( and)Tj ( A.)Tj ( Adamatzky)Tj /T1_7 1 Tf 7 0 0 7 63 31.6251 Tm (Complex)Tj ( Systems,)Tj ( )Tj /T1_8 1 Tf (2)Tj (0)Tj /T1_9 1 Tf ( \251)Tj ( 2011)Tj ( Complex)Tj ( Systems)Tj ( Publications,)Tj ( Inc.)Tj ET endstream endobj 15 0 obj <>stream ����Adobed���C �� ����� s!1AQa"q�2���B#�R��3b�$r��%C4S���cs�5D'���6Tdt���&� 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an)Tj 1.351 0 Td ( AND)Tj 2.627 0 Td ( gate)Tj 2.072 0 Td ( implemented)Tj 5.848 0 Td ( by)Tj 1.351 0 Td ( the)Tj 1.628 0 Td ( swarm)Tj 3.183 0 Td ( model.)Tj 3.239 0 Td ( Per)Tj (-)Tj -32 -1.056 Td (formance)Tj 4.237 0 Td ( is)Tj 1.128 0 Td ( plotted)Tj 3.517 0 Td ( against)Tj 3.517 0 Td ( the)Tj 1.794 0 Td ( strength)Tj 3.961 0 Td ( of)Tj 1.35 0 Td ( external)Tj 3.961 0 Td ( perturbation.)Tj 6.185 0 Td ( A)Tj 1.182 0 Td ( swarm)Tj -30.834 -1.056 Td (model)Tj 2.812 0 Td ( with)Tj 2.369 0 Td ( )Tj ET q 111.96 230.04 29.04 10.92 re W n BT /T1_4 1 Tf 9 0 0 9 112.1355 233.183 Tm (P)Tj /C2_1 1 Tf 0.944 0 Td <0001>Tj /T1_3 1 Tf 1.117 0 Td (20)Tj ET Q BT /T1_3 1 Tf 9 0 0 9 142.0147 233.183 Tm ( is)Tj 1.091 0 Td ( compared)Tj 4.701 0 Td ( to)Tj 1.313 0 Td ( one)Tj 1.98 0 Td ( with)Tj 2.369 0 Td ( )Tj ET q 246.96 230.04 25.08 10.92 re W n BT /T1_4 1 Tf 9 0 0 9 247.614 233.183 Tm (P)Tj /C2_1 1 Tf 0.944 0 Td <0001>Tj /T1_3 1 Tf 1.117 0 Td (1)Tj ET Q BT /T1_3 1 Tf 9 0 0 9 271.173 233.183 Tm (.)Tj 0.424 0 Td ( The)Tj 2.09 0 Td ( model)Tj 3.09 0 Td ( with)Tj 2.369 0 Td ( )Tj ET q 345 230.04 24 10.92 re W n BT /T1_4 1 Tf 9 0 0 9 345.441 233.183 Tm (P)Tj /C2_1 1 Tf 0.944 0 Td <0001>Tj /T1_3 1 Tf 1.117 0 Td (1)Tj ET Q BT /T1_3 1 Tf 9 0 0 9 63 223.683 Tm (can)Tj ( correspond)Tj ( to)Tj ( )Tj (b)Tj (o)Tj (i)Tj (d)Tj (s)Tj (.)Tj ( )Tj ( )Tj /T1_0 1 Tf 10 0 0 10 75 194.183 Tm (In)Tj 1.161 0 Td ( contrast,)Tj 4.329 0 Td ( the)Tj 1.884 0 Td ( performance)Tj 5.994 0 Td ( of)Tj 1.44 0 Td ( our)Tj 2.052 0 Td ( swarm)Tj 3.439 0 Td ( model)Tj 3.217 0 Td ( with)Tj 2.496 0 Td ( )Tj ET q 336.96 192 32.04 12 re W n BT /T1_1 1 Tf 10 0 0 10 337.93 194.183 Tm (P)Tj /C2_0 1 Tf 0.911 0 Td <0001>Tj /T1_0 1 Tf 1.084 0 Td (20)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 63 183.183 Tm (does)Tj 1.999 0 Td ( not)Tj 1.777 0 Td ( decrease)Tj 3.942 0 Td ( drastically)Tj 4.777 0 Td ( as)Tj 1.221 0 Td ( the)Tj 1.665 0 Td ( strength)Tj 3.832 0 Td ( of)Tj 1.221 0 Td ( perturbation)Tj 5.778 0 Td ( increases.)Tj -26.211 -1.1 Td (A)Tj 0.908 0 Td ( large)Tj 2.576 0 Td ( possibility)Tj 4.856 0 Td ( of)Tj 1.354 0 Td ( transitions)Tj 5.022 0 Td ( can)Tj 1.965 0 Td ( increase)Tj 3.909 0 Td ( the)Tj 1.798 0 Td ( probability)Tj 5.245 0 Td ( of)Tj 1.354 0 Td ( the)Tj -28.989 -1.1 Td (presence)Tj 3.698 0 Td ( of)Tj 1.199 0 Td ( highly)Tj 2.978 0 Td ( popular)Tj 3.701 0 Td ( sites,)Tj 2.421 0 Td ( which)Tj 2.922 0 Td ( increases)Tj 4.143 0 Td ( the)Tj 1.643 0 Td ( possibility)Tj 4.701 0 Td ( of)Tj 1.199 0 Td ( mu)Tj (-)Tj -28.601 -1.1 Td (tual)Tj 1.826 0 Td ( anticipation)Tj 5.605 0 Td ( that)Tj 2.159 0 Td ( results)Tj 3.215 0 Td ( in)Tj 1.271 0 Td ( the)Tj 1.77 0 Td ( collective)Tj 4.436 0 Td ( behavior)Tj 4.216 0 Td ( of)Tj 1.326 0 Td ( swarming.)Tj -25.822 -1.1 Td (External)Tj 3.762 0 Td ( perturbation)Tj 5.819 0 Td ( also)Tj 2.096 0 Td ( increases)Tj 4.206 0 Td ( the)Tj 1.706 0 Td ( possibilities)Tj 5.375 0 Td ( of)Tj 1.262 0 Td ( transitions.)Tj 5.208 0 Td ( In)Tj -29.434 -1.1 Td (this)Tj 1.653 0 Td ( sense)Tj 2.597 0 Td ( the)Tj 1.708 0 Td ( external)Tj 3.875 0 Td ( perturbation)Tj 5.821 0 Td ( cannot)Tj 3.32 0 Td ( be)Tj 1.375 0 Td ( distinguished)Tj 6.044 0 Td ( from)Tj 2.485 0 Td ( po)Tj (-)Tj -28.877 -1.1 Td (tential)Tj 2.813 0 Td ( transitions,)Tj 5.204 0 Td ( and)Tj 1.981 0 Td ( can)Tj 1.869 0 Td ( produce)Tj 3.87 0 Td ( the)Tj 1.702 0 Td ( same)Tj 2.534 0 Td ( contribution)Tj 5.76 0 Td ( as)Tj 1.258 0 Td ( increas)Tj (-)Tj -26.989 -1.1 Td (ing)Tj 1.61 0 Td ( the)Tj 1.887 0 Td ( number)Tj 3.887 0 Td ( of)Tj 1.443 0 Td ( potential)Tj 4.388 0 Td ( transitions.)Tj 5.389 0 Td ( The)Tj 2.22 0 Td ( external)Tj 4.054 0 Td ( perturbation)Tj -24.876 -1.1 Td (plays)Tj 2.263 0 Td ( a)Tj 0.818 0 Td ( role)Tj 1.985 0 Td ( in)Tj 1.152 0 Td ( generating)Tj 4.818 0 Td ( and)Tj 1.93 0 Td ( keeping)Tj 3.652 0 Td ( a)Tj 0.818 0 Td ( swarm)Tj 3.206 0 Td ( ball.)Tj 2.208 0 Td ( The)Tj 1.984 0 Td ( directed)Tj 3.762 0 Td ( mo)Tj (-)Tj -28.601 -1.1 Td (tion)Tj 1.819 0 Td ( of)Tj 1.263 0 Td ( a)Tj 0.874 0 Td ( swarm)Tj 3.262 0 Td ( along)Tj 2.764 0 Td ( the)Tj 1.707 0 Td ( wall,)Tj 2.486 0 Td ( however,)Tj 4.319 0 Td ( depends)Tj 3.875 0 Td ( on)Tj 1.486 0 Td ( the)Tj 1.707 0 Td ( strength)Tj 3.874 0 Td ( of)Tj -29.433 -1.1 Td (velocity)Tj 3.582 0 Td ( matching.)Tj 4.804 0 Td ( That)Tj 2.582 0 Td ( is)Tj 1.194 0 Td ( the)Tj 1.86 0 Td ( reason)Tj 3.361 0 Td ( why)Tj 2.361 0 Td ( the)Tj 1.86 0 Td ( performance)Tj 5.97 0 Td ( of)Tj 1.416 0 Td ( the)Tj -28.989 -1.1 Td (AND)Tj 2.436 0 Td ( gate)Tj 2.159 0 Td ( implemented)Tj 6.109 0 Td (by)Tj 1.16 0 Td ( swarms)Tj 3.659 0 Td ( with)Tj 2.326 0 Td ( )Tj ET q 243.96 60 32.04 12 re W n BT /T1_1 1 Tf 10 0 0 10 244.255 62.1831 Tm (P)Tj /C2_0 1 Tf 0.911 0 Td <0001>Tj /T1_0 1 Tf 1.084 0 Td (20)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 276.36 62.1831 Tm ( is)Tj 1.048 0 Td ( slightly)Tj 3.494 0 Td ( decreased.)Tj ET q 0 59.16 432 144.84 re W n BT /T1_0 1 Tf 10 0 0 10 86.645 50.1831 Tm ( )Tj 2.199 0 Td ( )Tj 1.81 0 Td ( )Tj 4.088 0 Td ( )Tj 3.2 0 Td ( )Tj 2.422 0 Td ( )Tj 1.921 0 Td ( )Tj 3.755 0 Td ( )Tj 3.477 0 Td ( )Tj 2.088 0 Td ( )Tj -24.268 -1.1 Td ( )Tj ET Q BT /T1_5 1 Tf 8 0 0 8 63 612.0001 Tm (Robust)Tj ( Soldier)Tj ( Crab)Tj ( Ball)Tj ( Gate)Tj /T1_6 1 Tf 37.138 0 Td (99)Tj /T1_7 1 Tf 7 0 0 7 169.7103 31.6251 Tm (Complex)Tj ( Systems,)Tj ( )Tj /T1_8 1 Tf (2)Tj (0)Tj /T1_9 1 Tf ( \251)Tj ( 2011)Tj ( Complex)Tj ( Systems)Tj ( Publications,)Tj ( Inc.)Tj ET endstream endobj 19 0 obj [52 0 R] endobj 20 0 obj <>stream H�\�Mj�0 ��>��3��I�!P���&�[I �lg�ۏ�)T`���'����{K>��s�&<9�9,lz=���mڻ|��D���9���T]�~�8'^���B�G�o�=�p�:wG���NH hp8Ƞ��W3!茝Z'�O�I�?���ܗ�alp8Gc� ���B���C�QHS�`� gw)����7N��Pva�>stream ����Adobed���C �� f^��� s!1AQa"q�2���B#�R��3b�$r��%C4S���cs�5D'���6Tdt���&� 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( )Tj 1.586 0 Td ( )Tj 2.641 0 Td ( )Tj 1.363 0 Td ( )Tj 1.807 0 Td ( )Tj 2.806 0 Td ( )Tj 2.251 0 Td ( )Tj 5.584 0 Td ( )Tj 5.917 0 Td ( )Tj 1.363 0 Td ( )Tj -26.581 -1.1 Td ( )Tj 2.131 0 Td ( )Tj 1.632 0 Td ( )Tj 3.022 0 Td ( )Tj ET Q Q q 0 648 m 0 648 l 432 648 l h W n q 0 54.84 432 539.16 re W n BT /T1_3 1 Tf 10 0 0 10 184.5552 12.7931 Tm ( )Tj ET Q Q q 0 648 m 0 648 l 432 648 l h W n q 0 54.84 432 539.16 re W n BT /T1_3 1 Tf 10 0 0 10 214.1891 12.7931 Tm ( )Tj 1.299 0 Td ( )Tj ET Q Q q 0 648 m 0 648 l 432 648 l h W n q 0 54.84 432 539.16 re W n BT /T1_3 1 Tf 10 0 0 10 254.0308 12.7931 Tm ( )Tj 1.021 0 Td ( )Tj 2.578 0 Td ( )Tj 2.578 0 Td ( )Tj 1.299 0 Td ( )Tj 2.578 0 Td ( )Tj -24.712 -1.1 Td ( )Tj ET Q Q BT /T1_4 1 Tf 8 0 0 8 63 612.0001 Tm (Robust)Tj ( Soldier)Tj ( Crab)Tj ( Ball)Tj ( Gate)Tj /T1_5 1 Tf 36.582 0 Td (101)Tj /T1_6 1 Tf 7 0 0 7 169.7103 31.6251 Tm (Complex)Tj ( Systems,)Tj ( )Tj /T1_7 1 Tf (2)Tj (0)Tj /T1_8 1 Tf ( \251)Tj ( 2011)Tj ( Complex)Tj ( Systems)Tj ( 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2.095 0 Td ( required)Tj 4.04 0 Td ( for)Tj 1.706 0 Td ( this)Tj 1.984 0 Td ( work.)Tj 2.985 0 Td ( The)Tj 2.094 0 Td ( duration)Tj 4.152 0 Td ( of)Tj 1.317 0 Td ( any)Tj -28.766 -1.1 Td (s)Tj (i)Tj (n)Tj (g)Tj (l)Tj (e)Tj 2.479 0 Td ( experiment)Tj 5.144 0 Td ( was)Tj 1.979 0 Td ( so)Tj 1.257 0 Td ( short)Tj 2.535 0 Td ( that)Tj 2.034 0 Td ( no)Tj 1.424 0 Td ( crab)Tj 2.201 0 Td ( was)Tj 1.979 0 Td ( ever)Tj 2.089 0 Td ( endangered.)Tj 5.535 0 Td ( The)Tj -28.656 -1.1 Td (crabs)Tj 2.437 0 Td ( were)Tj 2.492 0 Td ( kept)Tj 2.326 0 Td ( in)Tj 1.271 0 Td ( comfortable)Tj 5.658 0 Td ( conditions)Tj 4.939 0 Td ( and)Tj 2.049 0 Td ( after)Tj 2.436 0 Td ( all)Tj 1.493 0 Td ( experiments)Tj -25.101 -1.1 Td (were)Tj 2.158 0 Td ( released)Tj 3.825 0 Td ( to)Tj 1.27 0 Td ( their)Tj 2.381 0 Td ( natural)Tj 3.493 0 Td ( habitat.)Tj 3.715 0 Td ( Furthermore,)Tj 6.104 0 Td ( on)Tj 1.493 0 Td ( visual)Tj 2.882 0 Td ( inspec)Tj (-)Tj -27.322 -1.1 Td (tion,)Tj 2.08 0 Td ( no)Tj 1.469 0 Td ( crabs)Tj 2.635 0 Td ( appeared)Tj 4.302 0 Td ( to)Tj 1.246 0 Td ( have)Tj 2.357 0 Td ( been)Tj 2.357 0 Td ( injured)Tj 3.414 0 Td ( or)Tj 1.302 0 Td ( adversely)Tj 4.357 0 Td ( affected)Tj 3.744 0 Td ( by)Tj -29.266 -1.1 Td (the)Tj ( experiments.)Tj ( )Tj /T1_2 1 Tf 8 0 0 8 63 612.0001 Tm (102)Tj /T1_3 1 Tf 18.19 0 Td (Y.-P.)Tj ( Gunji,)Tj ( Y.)Tj ( Nishiyama,)Tj ( and)Tj ( A.)Tj ( Adamatzky)Tj /T1_4 1 Tf 7 0 0 7 63 31.6251 Tm (Complex)Tj ( Systems,)Tj ( )Tj /T1_5 1 Tf (2)Tj (0)Tj /T1_6 1 Tf ( \251)Tj ( 2011)Tj ( Complex)Tj ( Systems)Tj ( Publications,)Tj ( Inc.)Tj ET endstream endobj 34 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]>>/Rotate 0/Type/Page>> endobj 35 0 obj <>stream q 0 0 432 648 re W n /CS0 CS 1 1 1 SCN 0.12 w /GS0 gs q 1 0 0 1 0 648.0001 cm 0 0 m 0 0 l S Q Q BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 9 0 0 9 72 585.9141 Tm (References)Tj ( )Tj ( )Tj ET q 0 54 432 540 re W n /CS0 CS 0 0 0 SCN 3 w 2 J q 1 0 0 1 64.5 583.5001 cm 0 0 m 0 9 l S Q Q /CS0 CS 0 0 0 SCN 0.5 w 2 J q 1 0 0 1 63.25 582.2501 cm 0 0 m 305.5 0 l S Q q 48 560.04 30 9.96 re W n BT /T1_1 1 Tf 9 0 0 9 67.002 563.0001 Tm ([)Tj (1)Tj (])Tj ET Q q 0 531.96 432 38.04 re W n BT /T1_1 1 Tf 9 0 0 9 84 563.0001 Tm (A.)Tj 1.264 0 Td ( Adamatzky)Tj 5.485 0 Td ( and)Tj 2.155 0 Td ( B.)Tj 1.432 0 Td ( De)Tj 1.765 0 Td ( Lacy)Tj 2.598 0 Td ( Costello,)Tj 4.377 0 Td ( \223Binary)Tj 3.933 0 Td ( Collisions)Tj 4.823 0 Td ( between)Tj ET Q BT /T1_1 1 Tf 9 0 0 9 84 553.5001 Tm (Wave-Fragments)Tj 7.543 0 Td ( in)Tj 1.378 0 Td ( a)Tj 1.044 0 Td ( Sub-Excitable)Tj 6.489 0 Td ( Belousov\226Zhabotinsky)Tj 10.436 0 Td ( Medium,\224)Tj /T1_2 1 Tf -26.889 -1.056 Td (Chaos,)Tj ( Solitons)Tj ( &)Tj ( Fractals)Tj /T1_1 1 Tf (,)Tj ( )Tj /T1_3 1 Tf (3)Tj (4)Tj /T1_1 1 Tf (\(2\),)Tj ( 2007)Tj ( pp.)Tj ( 307\226315.)Tj 0 -1.056 TD (d)Tj (o)Tj (i)Tj (:)Tj (1)Tj (0)Tj (.)Tj (1)Tj (0)Tj (1)Tj (6)Tj (/)Tj (j)Tj (.)Tj (c)Tj (h)Tj (a)Tj (o)Tj (s)Tj (.)Tj (2)Tj (0)Tj (0)Tj (6)Tj (.)Tj (0)Tj (3)Tj (.)Tj (0)Tj (9)Tj (5)Tj (.)Tj ET q 48 518.04 30 9.96 re W n BT /T1_1 1 Tf 9 0 0 9 67.002 521.0001 Tm ([)Tj (2)Tj (])Tj ET Q q 0 509.04 432 18.96 re W n BT /T1_1 1 Tf 9 0 0 9 84 521.0001 Tm (A.)Tj 1.277 0 Td ( Adamatzky.)Tj 5.776 0 Td ( \223Slime)Tj 3.444 0 Td ( Mould)Tj 3.502 0 Td ( Logical)Tj 3.723 0 Td ( Gates:)Tj 3.278 0 Td ( Exploring)Tj 4.836 0 Td ( Ballistic)Tj 3.945 0 Td ( Ap)Tj (-)Tj ET Q BT /T1_1 1 Tf 9 0 0 9 84 511.5001 Tm (proach.\224)Tj ( \(May)Tj ( 13,)Tj ( 2010\))Tj ( arXiv:1005.2301v1.)Tj ( )Tj ET q 48 495 30 9.96 re W n BT /T1_1 1 Tf 9 0 0 9 67.002 498.0001 Tm ([)Tj (3)Tj (])Tj ET Q q 0 486 432 18.96 re W n BT /T1_1 1 Tf 9 0 0 9 84 498.0001 Tm (A.)Tj 1.215 0 Td ( Adamatzky,)Tj 5.714 0 Td ( B.)Tj 1.383 0 Td ( De)Tj 1.716 0 Td ( Lacy)Tj 2.549 0 Td ( Costello,)Tj 4.328 0 Td ( and)Tj 2.106 0 Td ( T.)Tj 1.438 0 Td ( Asai,)Tj 2.66 0 Td ( )Tj /T1_2 1 Tf (R)Tj (e)Tj (a)Tj (c)Tj (t)Tj (i)Tj (o)Tj (n)Tj (-)Tj (D)Tj (i)Tj (f)Tj (f)Tj (u)Tj (s)Tj (i)Tj (o)Tj (n)Tj ET Q BT /T1_2 1 Tf 9 0 0 9 84 488.5001 Tm (C)Tj (o)Tj (m)Tj (p)Tj (u)Tj (t)Tj (e)Tj (r)Tj (s)Tj /T1_1 1 Tf (,)Tj ( Boston:)Tj ( Elsevier,)Tj ( 2005.)Tj ( )Tj ET q 48 471.96 30 10.08 re W n BT /T1_1 1 Tf 9 0 0 9 67.002 475.0001 Tm ([)Tj (4)Tj (])Tj ET Q q 0 443.04 432 39 re W n BT /T1_1 1 Tf 9 0 0 9 84 475.0001 Tm (K.)Tj 1.211 0 Td ( Yoshikawa,)Tj 5.602 0 Td ( I.)Tj 1.099 0 Td ( M.)Tj 1.767 0 Td ( Motoike,)Tj 4.49 0 Td ( T.)Tj 1.433 0 Td ( Ichino,)Tj 3.489 0 Td ( T.)Tj 1.433 0 Td ( Yamaguchi,)Tj 5.655 0 Td ( Y.)Tj 1.489 0 Td ( Igarashi,)Tj ET Q BT /T1_1 1 Tf 9 0 0 9 84 464.5001 Tm (J)Tj (.)Tj /TT0 1 Tf 0.88 0 Td ( )Tj /T1_1 1 Tf (Gorecki,)Tj 4.186 0 Td ( and)Tj 2.103 0 Td ( J.)Tj 1.158 0 Td ( N.)Tj 1.602 0 Td ( Gorecka,)Tj 4.436 0 Td ( \223Basic)Tj 3.269 0 Td ( Information)Tj 5.712 0 Td ( Processing)Tj 4.992 0 Td ( Opera)Tj (-)Tj -28.334 -1.056 Td (tions)Tj 2.142 0 Td ( with)Tj 2.253 0 Td ( Pulses)Tj 2.92 0 Td ( of)Tj 1.197 0 Td ( Excitation)Tj 4.753 0 Td ( in)Tj 1.142 0 Td ( a)Tj 0.808 0 Td ( Reaction-Diffusion)Tj 8.531 0 Td ( System,\224)Tj 4.14 0 Td ( )Tj /T1_2 1 Tf (I)Tj (n)Tj (t)Tj (e)Tj (r)Tj (n)Tj (a)Tj (-)Tj -27.889 -1.056 Td (tional)Tj ( Journal)Tj ( of)Tj ( Unconventional)Tj ( Computing)Tj /T1_1 1 Tf (,)Tj ( )Tj /T1_3 1 Tf (5)Tj /T1_1 1 Tf (\(1\),)Tj ( 2009)Tj ( pp.)Tj ( 3\22637.)Tj ( )Tj ET q 48 429 30 9.96 re W n BT /T1_1 1 Tf 9 0 0 9 67.002 432.0001 Tm ([)Tj (5)Tj (])Tj ET Q q 0 401.04 432 37.92 re W n BT /T1_1 1 Tf 9 0 0 9 84 432.0001 Tm (A.)Tj 1.093 0 Td ( Toth,)Tj 2.761 0 Td ( V.)Tj 1.373 0 Td ( Gaspar,)Tj 3.762 0 Td ( and)Tj 1.984 0 Td ( K.)Tj 1.372 0 Td ( Showalter,)Tj 4.984 0 Td ( \223Signal)Tj 3.54 0 Td ( Transmission)Tj 6.15 0 Td ( in)Tj 1.206 0 Td ( Chemi)Tj (-)Tj ET Q BT /T1_1 1 Tf 9 0 0 9 84 422.5001 Tm (cal)Tj 1.298 0 Td ( Systems:)Tj 4.019 0 Td ( Propagation)Tj 5.634 0 Td ( of)Tj 1.243 0 Td ( Chemical)Tj 4.408 0 Td ( Waves)Tj 3.187 0 Td ( through)Tj 3.8 0 Td ( Capillary)Tj 4.355 0 Td ( Tubes,\224)Tj /T1_2 1 Tf -27.944 -1.056 Td (Journal)Tj ( of)Tj ( Physical)Tj ( Chemistry)Tj ( B)Tj /T1_1 1 Tf (,)Tj ( )Tj /T1_3 1 Tf (9)Tj (8)Tj /T1_1 1 Tf (\()Tj (2)Tj (\))Tj (,)Tj ( 1994)Tj ( pp.)Tj ( 522\226531.)Tj T* (d)Tj (o)Tj (i)Tj (:)Tj (1)Tj (0)Tj (.)Tj (1)Tj (0)Tj (2)Tj (1)Tj (/)Tj (j)Tj (1)Tj (0)Tj (0)Tj (0)Tj (5)Tj (3)Tj (a)Tj (0)Tj (2)Tj (9)Tj (.)Tj ET q 48 387 30 9.96 re W n BT /T1_1 1 Tf 9 0 0 9 67.002 390.0001 Tm ([)Tj (6)Tj (])Tj ET Q q 0 378 432 18.96 re W n BT /T1_1 1 Tf 9 0 0 9 84 390.0001 Tm (A.)Tj 1.071 0 Td ( Toth)Tj 2.461 0 Td ( and)Tj 1.962 0 Td ( K.)Tj 1.35 0 Td ( Showalter,)Tj 4.962 0 Td ( \223Logical)Tj 4.073 0 Td ( Gates)Tj 2.794 0 Td ( in)Tj 1.184 0 Td ( Excitable)Tj 4.35 0 Td ( Media,\224)Tj 3.962 0 Td ( )Tj /T1_2 1 Tf (J)Tj (o)Tj (u)Tj (r)Tj (n)Tj (a)Tj (l)Tj ET Q BT /T1_2 1 Tf 9 0 0 9 84 380.5001 Tm (of)Tj ( Chemical)Tj ( Physics)Tj /T1_1 1 Tf (,)Tj ( )Tj /T1_3 1 Tf (1)Tj (0)Tj (3)Tj /T1_1 1 Tf (\(6\),)Tj ( 1995)Tj ( p.)Tj ( 2058.)Tj ( doi:)Tj (1)Tj (0)Tj (.)Tj (1)Tj (0)Tj (6)Tj (3)Tj (/)Tj (1)Tj (.)Tj (4)Tj (6)Tj (9)Tj (7)Tj (3)Tj (2)Tj (.)Tj ET q 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10 293.5885 271.629 Tm (H)Tj ET Q BT /T1_2 1 Tf 10 0 0 10 296.7965 271.629 Tm (x)Tj /T1_0 1 Tf (,)Tj /T1_2 1 Tf 1.134 0 Td (y)Tj ET q 293.04 267 60.96 14.04 re W n BT /TT0 1 Tf 10 0 0 10 313.1365 271.629 Tm (L)Tj /C2_0 1 Tf 0.621 0 Td <0001>Tj /TT0 1 Tf 1.084 0 Td (H)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 333.3925 271.629 Tm [(1,)-300 (0)]TJ ET q 293.04 267 60.96 14.04 re W n BT /TT0 1 Tf 10 0 0 10 350.2924 271.629 Tm (L)Tj ET Q BT 10 0 0 10 356.77 271.629 Tm ( or)Tj ET q 63 255.96 24 12 re W n BT /TT0 1 Tf 10 0 0 10 63 258.629 Tm (H)Tj /T1_0 1 Tf [(0,)-300 (1)]TJ /TT0 1 Tf (L)Tj ET Q BT 10 0 0 10 86.316 258.629 Tm [(,)-142 ( 40)-142 ( individuals)-142 ( are)-142 ( set)-142 ( for)-142 ( input)-142 ( space)-142 ( A)-142 ( or)-142 ( B,)-142 ( respectively.)-142 ( In)]TJ -2.336 -1.1 Td [(any)-65 ( input)-65 ( case,)-65 ( both)-65 ( intimidation)-65 ( plates)-65 ( are)-65 ( unfolded)-65 ( and)-65 ( stood)-65 ( verti-)]TJ 0.002 -1.1 Td [(cally)-23 ( soon)-23 ( after)-23 ( the)-23 ( gate)-23 ( 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144.84 re W n BT 10 0 0 10 86.645 50.1831 Tm [( )-1921 ( )-1532 ( )-3810 ( )-2922 ( )-2144 ( )-1643 ( )-3477 ( )-3199 ( )-1810 ( )]TJ 0.692 -1.1 Td ( )Tj ET Q BT /T1_5 1 Tf 8 0 0 8 63 612.0001 Tm (Robust Soldier Crab Ball Gate)Tj /T1_6 1 Tf 37.138 0 Td (99)Tj /T1_7 1 Tf 7 0 0 7 169.7103 31.6251 Tm (Complex Systems, )Tj /T1_8 1 Tf (20)Tj /T1_9 1 Tf ( \251 2011 Complex Systems Publications, Inc.)Tj ET /Artifact <>BDC q 1 0 0 1 236.4914246 34.6799164 cm 0 g /GS1 gs /Fm0 Do Q EMC endstream endobj 151 0 obj <>>>/Resources 152 0 R/Subtype/Form>>stream 0 g 0 G 0 i 0 J []0 d 0 j 1 w 10 M 0 Tc 0 Tw 100 Tz 0 TL 0 Tr 0 Ts BT /SabonLTStd-Roman 6 Tf 0 g 130.71 -4.584 Td ( ) Tj -130.709 -7.2 Td (https://doi.org/10.25088/ComplexSystems.20.2.93) Tj ET endstream endobj 152 0 obj <> endobj 153 0 obj <> endobj 154 0 obj <>stream /
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0.216 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.648 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q q 1 0 0 1 108.8442 396.3043 cm 0 0 m 3.671 0 l S Q /CS2 cs 0 scn q 1 0 0 1 118.6337 333.782 cm 0 0 m 1.069 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 189.146 333.3302 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.034 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.215 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.647 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q Q BT 0 0 0 scn /T1_1 1 Tf 8 0 0 8 63 310.653 Tm [(Figure)-367 (3.)]TJ ET q 0 279 432 39 re W n BT /T1_2 1 Tf 9 0 0 9 99.5537 310.653 Tm [(A)-198 ( series)-198 ( of)-198 ( snapshots)-198 ( \(1,)-198 ( 2,)-198 ( 3,)-198 ( and)-198 ( 4\))-198 ( in)-198 ( an)-198 ( AND)-198 ( gate)-198 ( of)-198 ( swarm)]TJ ET Q BT /T1_2 1 Tf 9 0 0 9 63 301.153 Tm [(balls.)-67 ( Swarm)-67 ( balls)-67 ( located)-67 ( at)-67 ( the)-67 ( )]TJ /T1_3 1 Tf 14.627 0 Td (x)Tj /T1_2 1 Tf 0.623 0 Td [( and)-67 ( )]TJ /T1_3 1 Tf (y)Tj /T1_2 1 Tf 2.802 0 Td [( positions)-67 ( consist)-67 ( of)-67 ( 40)-67 ( agents.)-67 ( Each)]TJ -18.049 -1.056 Td [(agent)-88 ( is)-88 ( represented)-88 ( by)-88 ( a)-88 ( square)-88 ( with)-88 ( its)-88 ( 5-step)-88 ( trajectory.)-88 ( Red)-88 ( arrows)-88 ( repre-)]TJ 0.004 -1.056 Td (sent the direction a swarm ball is moving toward. )Tj ET q 0 99 432 162.96 re W n BT /T1_0 1 Tf 10 0 0 10 75 252.653 Tm [(Finally,)-162 ( we)-162 ( discuss)-162 ( the)-162 ( robustness)-162 ( of)-162 ( the)-162 ( gates.)-162 ( As)-162 ( mentioned)-162 ( be-)]TJ ET Q BT /T1_0 1 Tf 10 0 0 10 63 241.653 Tm [(fore,)-121 ( the)-121 ( OR)-121 ( gate)-121 ( acts)-121 ( very)-121 ( well)-121 ( against)-121 ( external)-121 ( perturbation.)-121 ( Here,)]TJ 0.001 -1.1 Td [(we)-25 ( estimate)-25 ( the)-25 ( performance)-25 ( of)-25 ( the)-25 ( AND)-25 ( gate)-25 ( under)-25 ( a)-25 ( high)-25 ( rate)-25 ( of)-25 ( ex-)]TJ 0 -1.1 TD [(ternal)-64 ( noise.)-64 ( In)-64 ( the)-64 ( simulation,)-64 ( the)-64 ( external)-64 ( noise)-64 ( that)-64 ( is)-64 ( coupled)-64 ( with)]TJ -0.002 -1.1 Td [(the)-84 ( operation)-84 ( of)-84 ( velocity)-84 ( matching)-84 ( is)-84 ( defined)-84 ( as)-84 ( a)-84 ( random)-84 ( value)-84 ( )]TJ /TT0 1 Tf 28.6 0 Td (x)Tj /T1_0 1 Tf 0.553 0 Td ( se-)Tj -29.156 -1.1 Td [(lected)-80 ( with)-80 ( equal)-80 ( probability)-80 ( from)-80 ( )]TJ ET q 216.96 195 31.08 12 re W n BT /TT1 1 Tf 10 0 0 10 217.5931 197.653 Tm (@)Tj ET Q BT /TT0 1 Tf 10 0 0 10 220.9232 197.653 Tm [(-)-100 (l)]TJ /T1_0 1 Tf (,)Tj /TT0 1 Tf 1.836 0 Td (l)Tj ET q 216.96 195 31.08 12 re W n BT /TT1 1 Tf 10 0 0 10 244.4268 197.653 Tm (D)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 247.7569 197.653 Tm [(.)-80 ( When)-80 ( the)-80 ( velocity)-80 ( of)-80 ( each)]TJ -18.477 -1.1 Td [(agent)-80 ( in)-80 ( a)-80 ( two-dimensional)-80 ( space)-80 ( )]TJ /T1_4 1 Tf (v)Tj /T1_0 1 Tf 15.593 0 Td [( is)-80 ( projected)-80 ( in)-80 ( the)-80 ( )]TJ /T1_4 1 Tf (x)Tj /T1_0 1 Tf 9.18 0 Td [( and)-80 ( )]TJ /T1_4 1 Tf (y)Tj /T1_0 1 Tf 2.828 0 Td ( planes)Tj -27.599 -1.3 Td [(denoted)-219 ( by)-219 ( )]TJ /T1_4 1 Tf (v)Tj ET q 117 171 11.04 12 re W n BT /T1_5 1 Tf 8 0 0 8 122.9717 171.8122 Tm (x)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 130.111 173.653 Tm [( and)-219 ( )]TJ /T1_4 1 Tf (v)Tj /T1_5 1 Tf 8 0 0 8 158.9822 171.8122 Tm (y)Tj /T1_0 1 Tf 10 0 0 10 163.4822 173.653 Tm [(,)-219 ( the)-219 ( external)-219 ( noise)-219 ( is)-219 ( coupled)-219 ( by)-219 ( )]TJ /T1_4 1 Tf (v)Tj ET q 321.96 171 26.04 12 re W n BT /T1_5 1 Tf 8 0 0 8 327.7703 171.8122 Tm (x)Tj ET Q BT /TT0 1 Tf 10 0 0 10 334.7183 173.653 Tm [(+)-206 (x)]TJ /T1_0 1 Tf 1.538 0 Td ( and)Tj ET q 63 153.96 24.96 15 re W n BT /T1_4 1 Tf 10 0 0 10 63 159.8122 Tm (v)Tj ET Q BT /T1_5 1 Tf 8 0 0 8 68 157.9714 Tm (y)Tj ET q 63 153.96 24.96 15 re W n BT /TT0 1 Tf 10 0 0 10 74.5 159.8122 Tm [(+)-206 (x)]TJ ET Q BT /T1_0 1 Tf 10 0 0 10 89.2329 159.8122 Tm [( and)-154 ( then)-154 ( normalized)-154 ( to)-154 ( make)-154 ( the)-154 ( length)-154 ( of)-154 ( the)-154 ( velocity)-154 ( be)-154 ( 1.)]TJ -2.626 -1.384 Td [(We)-144 ( estimate)-144 ( performance)-144 ( within)-144 ( the)-144 ( range)-144 ( 0.0)]TJ /TT0 1 Tf 21.163 0 Td [(\247)-300 (l)-300 (\247)]TJ /T1_0 1 Tf 2.702 0 Td [(0.2)-144 ( when)-144 ( com-)]TJ -23.867 -1.1 Td [(paring)-65 ( our)-65 ( model)-65 ( of)-65 ( )]TJ /T1_4 1 Tf (P)Tj ET q 155.04 132 31.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 164.1982 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 175.0382 134.9714 Tm [(20)-65 ( with)-65 ( one)-65 ( with)-65 ( )]TJ /T1_4 1 Tf (P)Tj ET q 254.04 132 25.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 263.4664 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 274.3064 134.9714 Tm [(1.)-65 ( If)-65 ( )]TJ /T1_4 1 Tf (P)Tj ET q 296.04 132 31.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 305.2755 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 316.1154 134.9714 Tm [(20,)-65 ( multiple)]TJ -25.312 -1.1 Td [(potential)-126 ( transitions)-126 ( play)-126 ( a)-126 ( role)-126 ( in)-126 ( mutual)-126 ( anticipation)-126 ( that)-126 ( can)-126 ( con-)]TJ T* [(tribute)-215 ( to)-215 ( collective)-215 ( behavior.)-215 ( If)-215 ( )]TJ /T1_4 1 Tf (P)Tj ET q 212.04 110.04 27 12 re W n BT /C2_0 1 Tf 10 0 0 10 221.7667 112.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 232.6066 112.9714 Tm [(1,)-215 ( coherence)-215 ( of)-215 ( swarm)-215 ( results)]TJ -16.962 -1.1 Td (only from velocity matching. )Tj ET q 0 65.52 432 34.44 re W n BT 10 0 0 10 75 90.9714 Tm [(Figure)-106 ( 4)-107 ( shows)-107 ( performance)-106 ( of)-107 ( an)-106 ( AND)-107 ( gate)-107 ( implemented)-106 ( by)-106 ( our)]TJ ET Q BT 10 0 0 10 63 79.7214 Tm [(swarm)-202 ( model)-202 ( under)-202 ( a)-202 ( perturbed)-202 ( condition.)-202 ( The)-202 ( performance)-202 ( is)-202 ( de-)]TJ -0.002 -1.125 Td [(fined)-166 ( by)-166 ( the)-166 ( success)-166 ( rate)-166 ( of)-166 ( the)-166 ( gate.)-278 (In)-166 ( each)-166 ( experiment,)-166 ( we)-166 ( set)-166 ( 40)]TJ ET q 0 65.52 432 34.44 re W n BT 10 0 0 10 90.5643 56.4714 Tm [( )-868 ( )-1367 ( )-2313 ( )-3925 ( )]TJ ET Q q 0 65.52 432 34.44 re W n BT 10 0 0 10 195.1157 56.4714 Tm [( )-1646 ( )]TJ ET Q q 0 65.52 432 34.44 re W n BT 10 0 0 10 225.2643 56.4714 Tm [( )-699 ( )-2146 ( )-923 ( )-1367 ( )-2756 ( )-1479 ( )]TJ -15.255 -1.3 Td [( )-640 ( )-2863 ( )-3028 ( )-2473 ( )-1473 ( )-3030 ( )-1751 ( )-1029 ( )]TJ ET Q q 0 65.52 432 34.44 re W n BT 10 0 0 10 267.5977 43.4714 Tm [( )-2472 ( )]TJ ET Q q 0 65.52 432 34.44 re W n BT 10 0 0 10 307.0593 43.4714 Tm [( )-1362 ( )]TJ -23.01 -1.3 Td [( )-2452 ( )-1341 ( )-1396 ( )-4895 ( )-952 ( )-1063 ( )-563 ( )-3396 ( )-4508 ( )-674 ( )-730 ( )-563 ( )]TJ 0.391 -1.125 Td ( )Tj 5.843 0 Td [( )-789 ( )-3289 ( )-1178 ( )-1455 ( )-3455 ( )-1011 ( )-4344 ( )]TJ -4.35 -1.125 Td [( )-1172 ( )-1449 ( )-2116 ( )-3449 ( )-1005 ( )]TJ 16.196 0 Td [( )-2117 ( )]TJ 8.621 0 Td ( )Tj -26.565 -1.125 Td [( )-3090 ( )-2868 ( )-2147 ( )]TJ ET Q q 0 65.52 432 34.44 re W n BT 10 0 0 10 198.0667 -3.2786 Tm ( )Tj 5.704 0 Td [( )-1091 ( )-1535 ( )]TJ 8.775 0 Td ( )Tj -24.919 -1.125 Td [( )-1456 ( )-3624 ( )]TJ 11.483 0 Td [( )-3346 ( )-4401 ( )-1456 ( )-4122 ( )]TJ -11.423 -1.125 Td [( )-1239 ( )-3905 ( )-4849 ( )-1239 ( )-1683 ( )-3850 ( )-1239 ( )]TJ 26.024 0 Td ( )Tj -25.878 -1.125 Td [( )-1333 ( )]TJ 7.332 0 Td [( )-3057 ( )-4277 ( )]TJ ET Q BT /T1_6 1 Tf 8 0 0 8 63 612.0001 Tm (98)Tj /T1_5 1 Tf 18.19 0 Td (Y.-P. 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6.447 0.109 l 6.447 -0.094 6.455 -0.233 6.471 -0.305 c 6.495 -0.421 6.551 -0.505 6.638 -0.559 c 6.638 -0.671 l 5.609 -0.671 l 5.578 -0.572 5.555 -0.493 5.542 -0.432 c 5.515 -0.307 5.502 -0.179 5.502 -0.048 c 5.502 0.366 l 5.502 0.651 5.451 0.84 5.35 0.934 c 5.249 1.029 5.059 1.077 4.782 1.077 c 3.806 1.077 l 3.806 -0.671 l 2.889 -0.671 l 2.889 3.787 l h f* Q q 1 0 0 1 148.0027 431.3796 cm 0 0 m 0.108 0 l 0.19 0 0.269 0.005 0.346 0.015 c 0.424 0.024 0.493 0.047 0.553 0.083 c 0.611 0.117 0.673 0.187 0.738 0.295 c 0.804 0.402 0.835 0.467 0.831 0.492 c 0.359 3.926 l 1.306 3.926 l 1.506 1.5 l 2.689 3.926 l 3.594 3.926 l 1.796 0.692 l 1.449 0.068 1.197 -0.319 1.041 -0.468 c 0.885 -0.618 0.618 -0.694 0.242 -0.694 c 0.059 -0.694 l -0.143 -0.694 l h f* Q Q BT 0 0 0 scn /T1_2 1 Tf 8 0 0 8 63 354.6831 Tm [(Figure)-367 (2.)]TJ ET q 0 323.04 432 39 re W n BT /T1_3 1 Tf 9 0 0 9 99.9528 354.6831 Tm [( A)-44 ( series)-44 ( of)-44 ( snapshots)-44 ( \(1,)-44 ( 2,)-44 ( 3,)-44 ( and)-44 ( 4\))-44 ( in)-44 ( an)-44 ( OR)-44 ( gate)-44 ( of)-44 ( swarm)-44 ( balls.)]TJ ET Q BT /T1_3 1 Tf 9 0 0 9 63 345.1831 Tm [(Swarm)-63 ( balls)-63 ( located)-63 ( at)-63 ( the)-63 ( )]TJ /T1_4 1 Tf 11.983 0 Td (x)Tj /T1_3 1 Tf 0.619 0 Td [( and)-63 ( )]TJ /T1_4 1 Tf (y)Tj /T1_3 1 Tf 2.794 0 Td [( positions)-63 ( consist)-63 ( of)-63 ( 40)-63 ( agents.)-63 ( Each)-63 ( agent)]TJ -15.395 -1.056 Td [(is)-55 ( represented)-55 ( by)-55 ( a)-55 ( square)-55 ( with)-55 ( its)-55 ( 5-step)-55 ( trajectory.)-55 ( Red)-55 ( arrows)-55 ( represent)-55 ( the)]TJ -0.003 -1.056 Td (direction of motion of a swarm ball. )Tj /T1_0 1 Tf 10 0 0 10 75 296.6831 Tm [(We)-168 ( can)-168 ( estimate)-168 ( the)-168 ( effect)-168 ( of)-168 ( external)-168 ( perturbation)-168 ( if)-168 ( the)-168 ( agents\222)]TJ -1.2 -1.125 Td [(transition)-31 ( rule)-31 ( is)-31 ( coupled)-31 ( with)-31 ( external)-31 ( perturbation.)-31 ( As)-31 ( shown)-31 ( in)-31 ( Fig-)]TJ -0.002 -1.125 Td [(ure)-26 ( 2,)-26 ( inherent)-26 ( noise)-26 ( can)-26 ( positively)-26 ( contribute)-26 ( to)-26 ( generating)-26 ( and)-26 ( main-)]TJ -0.001 -1.125 Td [(taining)-104 ( a)-104 ( robust)-104 ( swarm.)-104 ( Inherent)-104 ( noise)-104 ( in)-104 ( our)-104 ( model)-104 ( reveals)-104 ( multiple)]TJ -0.001 -1.125 Td [(potential)-104 ( transitions,)-104 ( and)-104 ( one)-104 ( of)-104 ( them)-104 ( is)-104 ( always)-104 ( chosen)-104 ( in)-104 ( the)-104 ( transi-)]TJ -0.005 -1.125 Td [(tion)-65 ( of)-65 ( each)-65 ( agent\222s)-65 ( location.)-65 ( The)-65 ( inherent)-65 ( noise,)-65 ( therefore,)-65 ( cannot)-65 ( be)]TJ -0.001 -1.125 Td [(distinguished)-85 ( from)-85 ( external)-85 ( noise.)-85 ( This)-85 ( means)-85 ( that)-85 ( external)-85 ( noise)-85 ( can)]TJ 0.002 -1.125 Td [(contribute)-288 ( to)-288 ( generating)-288 ( robust)-288 ( swarm)-288 ( balls)-288 ( while)-288 ( the)-288 ( direction)-288 ( a)]TJ -0.003 -1.125 Td [(swarm)-103 ( ball)-103 ( moves)-103 ( cannot)-103 ( be)-103 ( controlled.)-103 ( However)-103 ( unstable)-103 ( the)-103 ( direc-)]TJ -0.003 -1.125 Td [(tion)-147 ( of)-147 ( a)-147 ( swam)-147 ( ball)-147 ( is,)-147 ( the)-147 ( corridor)-147 ( of)-147 ( the)-147 ( OR)-147 ( gate)-147 ( is)-147 ( one)-147 ( way)-147 ( and)]TJ 0 -1.125 TD (then the output 1 resulting from a swarm ball is robust. )Tj 1.2 -1.124 Td [(Figure)-22 ( 3)-22 ( shows)-22 ( an)-22 ( AND)-22 ( gate)-22 ( of)-22 ( swarm)-22 ( balls.)-22 ( Given)-22 ( a)-22 ( pair)-22 ( of)-22 ( inputs)]TJ /T1_1 1 Tf -1.195 -1.1 Td (x)Tj /T1_0 1 Tf 0.596 0 Td [( and)-40 ( )]TJ /T1_1 1 Tf (y)Tj /T1_0 1 Tf 2.748 0 Td [( located)-40 ( below,)-40 ( the)-40 ( left,)-40 ( central,)-40 ( and)-40 ( right)-40 ( corridors)-40 ( above)-40 ( rep-)]TJ -3.346 -1.3 Td [(resent)-35 ( the)-35 ( output)-35 ( as)-35 ( NOT)]TJ ET q 174.96 146.04 13.08 12 re W n BT /TT0 1 Tf 10 0 0 10 175.4922 148.9389 Tm (H)Tj ET Q BT /T1_1 1 Tf 10 0 0 10 178.7002 148.9389 Tm (x)Tj ET q 174.96 146.04 13.08 12 re W n BT /TT0 1 Tf 10 0 0 10 184.2602 148.9389 Tm (L)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 187.8138 148.9389 Tm [( AND)-35 ( )]TJ /T1_1 1 Tf (y)Tj /T1_0 1 Tf [(,)-35 ( )]TJ /T1_1 1 Tf (x)Tj /T1_0 1 Tf 4.605 0 Td [( AND)-35 ( )]TJ /T1_1 1 Tf (y)Tj /T1_0 1 Tf [(,)-35 ( and)-35 ( )]TJ /T1_1 1 Tf (x)Tj /T1_0 1 Tf 6.53 0 Td [( AND)-35 ( NOT)-35 ( )]TJ ET q 354 144 12.96 14.04 re W n BT /TT0 1 Tf 10 0 0 10 354.804 148.9389 Tm (H)Tj ET Q BT /T1_1 1 Tf 10 0 0 10 358.012 148.9389 Tm (y)Tj ET q 354 144 12.96 14.04 re W n BT /TT0 1 Tf 10 0 0 10 363.012 148.9389 Tm (L)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 366.22 148.9389 Tm (,)Tj -30.322 -1.3 Td [(respectively.)-376 ( Figure)-376 ( 3)-376 ( shows)-376 ( a)-376 ( series)-376 ( of)-376 ( snapshots)-376 ( for)-376 ( the)-376 ( input)]TJ ET q 63 120 60 14.04 re W n BT /TT0 1 Tf 10 0 0 10 63 124.9389 Tm (H)Tj ET Q BT /T1_1 1 Tf 10 0 0 10 66.208 124.9389 Tm (x)Tj /T1_0 1 Tf (,)Tj /T1_1 1 Tf 1.134 0 Td (y)Tj ET q 63 120 60 14.04 re W n BT /TT0 1 Tf 10 0 0 10 82.548 124.9389 Tm (L)Tj /C2_0 1 Tf 0.621 0 Td <0001>Tj /TT0 1 Tf 1.084 0 Td (H)Tj ET Q BT /T1_0 1 Tf 10 0 0 10 102.804 124.9389 Tm [(1,)-300 (1)]TJ ET q 63 120 60 14.04 re W n BT /TT0 1 Tf 10 0 0 10 119.704 124.9389 Tm (L)Tj ET Q BT 10 0 0 10 122.912 124.9389 Tm [(.)-80 ( Two)-80 ( swarm)-80 ( balls)-80 ( initiated)-80 ( at)-80 ( the)-80 ( input)-80 ( locations)-80 ( move)]TJ -5.988 -1.3 Td [(along)-179 ( their)-179 ( walls,)-179 ( leftward)-179 ( and)-179 ( rightward,)-179 ( respectively.)-179 ( Each)-179 ( swarm)]TJ 0.003 -1.1 Td [(ball)-120 ( consists)-120 ( of)-120 ( 40)-120 ( agents.)-120 ( After)-120 ( the)-120 ( collision,)-120 ( a)-120 ( united)-120 ( swarm)-120 ( moves)]TJ 0.001 -1.1 Td [(upward)-286 ( due)-286 ( to)-286 ( the)-286 ( integration)-286 ( of)-286 ( their)-286 ( velocities)-286 ( and)-286 ( results)-286 ( in)-286 ( a)]TJ -0.003 -1.1 Td [(united)-90 ( swarm)-90 ( moving)-90 ( to)-90 ( the)-90 ( central)-90 ( corridor,)-90 ( showing)-90 ( that)-90 ( )]TJ ET q 327 75.96 6.96 12 re W n BT /T1_1 1 Tf 10 0 0 10 327.769 78.9389 Tm (x)Tj ET Q BT 10 0 0 10 334.2245 78.9389 Tm [( AND)-90 ( )]TJ ET q 363.96 74.04 5.04 13.92 re W n BT /T1_1 1 Tf 10 0 0 10 364 78.9389 Tm (y)Tj ET Q BT 10 0 0 10 63 65.9389 Tm [(is)-62 ( 1.)-278 (As)-62 ( well)-62 ( as)-62 ( the)-62 ( behavior)-62 ( of)-62 ( an)-62 ( OR)-62 ( gate,)-62 ( a)-62 ( united)-62 ( swarm)-62 ( ball)-62 ( con-)]TJ ET q 0 62.88 432 119.16 re W n BT 10 0 0 10 81.0883 53.9389 Tm [( )-920 ( )-1143 ( )-2753 ( )-1643 ( )-4254 ( )-920 ( )-4588 ( )-920 ( )-2753 ( )-1364 ( )-1476 ( )]TJ 0.595 -1.1 Td [( )-844 ( )-3011 ( )-1735 ( )]TJ 12.383 0 Td [( )-3735 ( )-3457 ( )-4957 ( )]TJ -8.476 -1.1 Td [( )-973 ( )-2806 ( )-918 ( )-2250 ( )-2250 ( )-1417 ( )-4251 ( )-2362 ( )-918 ( )-584 ( )]TJ -3.779 -1.1 Td [( )-1978 ( )-979 ( )-1478 ( )-2424 ( )-3925 ( )-2756 ( )-1257 ( )-3645 ( )-2368 ( )-812 ( )]TJ -0.505 -1.1 Td [( )-1413 ( )-4248 ( )-1747 ( )-1358 ( )-1413 ( )-2691 ( )-1746 ( )]TJ 22.363 0 Td [( )-969 ( )-2246 ( )]TJ -23.649 -1.1 Td [( )-1737 ( )-3235 ( )-1347 ( )-1902 ( )-2679 ( )-1681 ( )-2401 ( )-2513 ( )-3457 ( )-1291 ( )-1569 ( )]TJ 1.533 -1.1 Td [( )-1932 ( )-2709 ( )-1711 ( )-2431 ( )-2543 ( )-1321 ( )-1599 ( )-3876 ( )-1655 ( )]TJ -0.206 -1.1 Td [( )-3888 ( )]TJ ET Q BT /T1_5 1 Tf 8 0 0 8 63 612.0001 Tm (Robust Soldier Crab Ball Gate)Tj /T1_6 1 Tf 37.138 0 Td (97)Tj /T1_7 1 Tf 7 0 0 7 169.7103 31.6251 Tm (Complex Systems, )Tj /T1_8 1 Tf (20)Tj /T1_9 1 Tf ( \251 2011 Complex Systems Publications, Inc.)Tj ET /Artifact <>BDC q 1 0 0 1 236.4914246 34.6799164 cm 0 g 0 G 1 w 10 M 0 j 0 J /GS1 gs /Fm0 Do Q EMC endstream endobj 163 0 obj <>>>/Resources 164 0 R/Subtype/Form>>stream 0 g 0 G 0 i 0 J []0 d 0 j 1 w 10 M 0 Tc 0 Tw 100 Tz 0 TL 0 Tr 0 Ts BT /SabonLTStd-Roman 6 Tf 0 g 130.71 -4.584 Td ( ) Tj -130.709 -7.2 Td (https://doi.org/10.25088/ComplexSystems.20.2.93) Tj ET endstream endobj 164 0 obj <> endobj 165 0 obj <> endobj 166 0 obj <>stream /
endstream endobj 167 0 obj <> endobj 168 0 obj <>stream q 0 0 432 648 re W n /CS0 CS 1 1 1 SCN 0.12 w /GS0 gs q 1 0 0 1 0 648.0001 cm 0 0 m 0 0 l S Q Q q 0 504 432 90 re W n BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 10 0 0 10 81.7611 653.2501 Tm ( )Tj ET Q q 0 504 432 90 re W n BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 10 0 0 10 110.1621 653.2501 Tm [( )-1900 ( )-3567 ( )]TJ 11.758 0 Td [( )-678 ( )-2012 ( )-3066 ( )]TJ 12.047 0 Td ( )Tj -26.986 -1.125 Td [( )-1091 ( )-3259 ( )-980 ( )-2035 ( )-2702 ( )-1703 ( )-1424 ( )-2757 ( )-3144 ( )-1424 ( )-3759 ( )]TJ 0.366 -1.125 Td [( )-3021 ( )-908 ( )-2354 ( )-2075 ( )-2296 ( )-2741 ( )-1352 ( )-4685 ( )-1075 ( )-2186 ( )]TJ -0.23 -1.125 Td [( )-3397 ( )-4063 ( )-2785 ( )-564 ( )-2732 ( )-4065 ( )-2231 ( )-1786 ( )-2785 ( )-953 ( )]TJ 0.989 -1.125 Td [( )-2727 ( )-893 ( )-3226 ( )-2283 ( )-2172 ( )]TJ 18.475 0 Td [( )-1894 ( )-2172 ( )-3616 ( )]TJ ET Q q 0 504 432 90 re W n BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 10 0 0 10 92.51 597.0001 Tm [( )-2066 ( )-2455 ( )-1567 ( )-1789 ( )-3956 ( )]TJ 22.792 0 Td [( )-733 ( )-789 ( )]TJ ET Q BT /CS0 cs 0 0 0 scn /GS0 gs /T1_0 1 Tf 10 0 0 10 63 585.0001 Tm [(ble)-54 ( that)-54 ( potential)-54 ( transitions)-54 ( can)-54 ( contribute)-54 ( to)-54 ( swarming,)-54 ( the)-54 ( overlap-)]TJ 0.002 -1.124 Td [(ping)-154 ( of)-154 ( potential)-154 ( transition)-154 ( targets)-154 ( is)-154 ( too)-154 ( difficult)-154 ( to)-154 ( achieve)-154 ( mutual)]TJ 0 -1.124 TD [(anticipation.)-85 ( The)-85 ( effect)-85 ( of)-85 ( multiple)-85 ( transitions)-85 ( results)-85 ( only)-85 ( in)-85 ( random)]TJ 0.002 -1.125 Td [(choice)-87 ( of)-87 ( potential)-87 ( transitions)-87 ( for)-87 ( each)-87 ( agent.)-87 ( Thus,)-87 ( both)-87 ( density)-87 ( and)]TJ -0.001 -1.125 Td [(polarization)-234 ( are)-234 ( very)-234 ( small.)-234 ( As)-234 ( the)-234 ( inherent)-234 ( perturbation)-234 ( increases,)]TJ -0.003 -1.125 Td [(density)-241 ( increases)-241 ( and)-241 ( polarization)-241 ( decreases.)-241 ( High)-241 ( density)-241 ( and)-241 ( low)]TJ 0.002 -1.125 Td [(polarization)-355 ( are)-355 ( maintained)-355 ( where)-355 ( inherent)-355 ( perturbation)-355 ( is)-355 ( larger)]TJ ET q 0 504 432 90 re W n BT 10 0 0 10 63 506.2676 Tm (than)Tj /C2_0 1 Tf <0001>Tj /T1_0 1 Tf (0.5. )Tj ET Q BT 10 0 0 10 75 495.2676 Tm [(In)-78 ( boids)-78 ( and)-78 ( self-propelling)-78 ( particles)-78 ( \(SPP\))-78 ( [14],)-78 ( a)-78 ( very)-78 ( dense)-78 ( flock)]TJ -1.203 -1.125 Td [(is)-204 ( achieved)-204 ( only)-204 ( by)-204 ( high)-204 ( polarization.)-204 ( The)-204 ( more)-204 ( highly)-204 ( polarized)-204 ( a)]TJ 0.003 -1.125 Td [(flock)-8 ( is,)-8 ( the)-8 ( denser)-8 ( it)-8 ( is.)-8 ( By)-8 ( contrast,)-8 ( low)-8 ( polarization)-8 ( breaks)-8 ( the)-8 ( coher-)]TJ -0.004 -1.125 Td [(ence)-100 ( of)-100 ( a)-100 ( flock.)-100 ( The)-100 ( velocity)-100 ( matching)-100 ( is)-100 ( linearly)-100 ( coupled)-100 ( with)-100 ( exter-)]TJ 0.002 -1.125 Td [(nal)-342 ( perturbation)-342 ( in)-342 ( boids)-342 ( and)-342 ( SPP.)-342 ( If)-342 ( the)-342 ( polarization)-342 ( is)-342 ( plotted)]TJ -0.004 -1.124 Td [(against)-311 ( external)-311 ( perturbation,)-311 ( it)-311 ( decreases)-311 ( as)-311 ( the)-311 ( perturbation)-311 ( de-)]TJ 0.003 -1.124 Td [(creases.)-128 ( Because)-128 ( polarization)-128 ( shows)-128 ( a)-128 ( phase)-128 ( transition)-128 ( that)-128 ( is)-128 ( depen-)]TJ 0.002 -1.124 Td [(dent)-140 ( on)-140 ( the)-140 ( external)-140 ( perturbation,)-140 ( it)-140 ( is)-140 ( regarded)-140 ( as)-140 ( an)-140 ( order)-140 ( param-)]TJ 0.001 -1.124 Td [(eter.)-226 ( Thus,)-226 ( the)-226 ( density)-226 ( of)-226 ( a)-226 ( flock)-226 ( is)-226 ( also)-226 ( decreased)-226 ( as)-226 ( the)-226 ( external)]TJ 0.004 -1.125 Td [(perturbation)-352 ( decreases.)-352 ( In)-352 ( this)-352 ( framework,)-352 ( the)-352 ( noise)-352 ( disturbs)-352 ( the)]TJ -0.003 -1.124 Td [(coherence)-7 ( of)-7 ( a)-7 ( flock,)-7 ( which)-7 ( reveals)-7 ( a)-7 ( flock)-7 ( that)-7 ( is)-7 ( not)-7 ( robust)-7 ( but)-7 ( is)-7 ( sta-)]TJ -0.002 -1.125 Td [(ble.)-477 ( By)-477 ( contrast,)-477 ( in)-477 ( our)-477 ( model)-477 ( inherent)-477 ( perturbation)-477 ( positively)]TJ 0 -1.125 TD [(contributes)-65 ( to)-65 ( generating)-65 ( a)-65 ( coherent)-65 ( and)-65 ( dense)-65 ( swarm)-65 ( and)-65 ( can)-65 ( imple-)]TJ -0.003 -1.125 Td [(ment)-69 ( robust)-69 ( swarms,)-69 ( which)-69 ( can)-69 ( be)-69 ( used)-69 ( analogous)-69 ( to)-69 ( billiard)-69 ( balls)-69 ( in)]TJ 0.001 -1.125 Td (collision-based circuitry. )Tj ET q 72 293.04 9 10.56 re W n BT /T1_1 1 Tf 9 0 0 9 72 295.461 Tm (3.)Tj ET Q q 0 291 432 12.96 re W n BT /T1_1 1 Tf 9 0 0 9 85.506 295.461 Tm (Collision Computing by Crab Swarm )Tj ET Q /CS0 CS 0 0 0 SCN 3 w 2 J q 1 0 0 1 64.006 293.0469 cm 0 0 m 0 9 l S Q 0.5 w q 1 0 0 1 62.756 291.7969 cm 0 0 m 305.994 0 l S Q q 74.04 273.72 13.92 9.84 re W n BT /T1_1 1 Tf 9 0 0 9 74 275.461 Tm (3.1)Tj ET Q BT /T1_1 1 Tf 9 0 0 9 92.51 275.461 Tm (Simulation Model )Tj ET 3 w q 1 0 0 1 65.01 275.1641 cm 0 0 m 0 6.883 l S Q BT /T1_0 1 Tf 10 0 0 10 63 262.6641 Tm [(When)-66 ( a)-66 ( swarm)-66 ( of)-66 ( soldier)-66 ( crabs)-66 ( is)-66 ( set)-66 ( in)-66 ( a)-66 ( corridor,)-66 ( it)-66 ( is)-66 ( expected)-66 ( that)]TJ -0.004 -1.1 Td [(a)-93 ( swarm)-93 ( acts)-93 ( as)-93 ( a)-93 ( robust)-93 ( ball)-93 ( and)-93 ( goes)-93 ( straight,)-93 ( and)-93 ( that)-93 ( two)-93 ( swarm)]TJ 0.003 -1.1 Td [(balls)-326 ( are)-326 ( united)-326 ( into)-326 ( one)-326 ( ball)-326 ( after)-326 ( colliding.)-326 ( Because)-326 ( of)-326 ( velocity)]TJ -0.001 -1.1 Td [(matching,)-138 ( a)-138 ( swarm)-138 ( ball)-138 ( resulting)-138 ( from)-138 ( the)-138 ( fusion)-138 ( of)-138 ( two)-138 ( balls)-138 ( has)-138 ( a)]TJ 0.005 -1.1 Td (summary velocity of two colliding balls. )Tj ET q 0 95.04 432 121.92 re W n BT 10 0 0 10 75 207.6641 Tm [(Figure)-61 ( 2)-61 ( shows)-61 ( an)-61 ( OR)-61 ( gate)-61 ( implemented)-61 ( by)-61 ( the)-61 ( collision)-61 ( of)-61 ( swarm)]TJ ET Q BT 10 0 0 10 63 196.6641 Tm [(balls.)-84 ( In)-84 ( this)-84 ( simulation,)-84 ( black)-84 ( regions)-84 ( are)-84 ( walls)-84 ( that)-84 ( an)-84 ( agent)-84 ( cannot)]TJ -0.003 -1.1 Td [(invade.)-49 ( Agents)-49 ( can)-49 ( move)-49 ( in)-49 ( the)-49 ( white)-49 ( area.)-49 ( An)-49 ( agent)-49 ( moves)-49 ( following)]TJ -0.005 -1.1 Td [(the)-100 ( rule)-100 ( mentioned)-100 ( before,)-100 ( where)-100 ( each)-100 ( agent)-100 ( has)-100 ( a)-100 ( tendency)-100 ( to)-100 ( move)]TJ 0 -1.1 TD [(along)-187 ( the)-187 ( wall)-187 ( if)-187 ( it)-187 ( is)-187 ( close)-187 ( to)-187 ( the)-187 ( wall.)-187 ( This)-187 ( tendency)-187 ( is)-187 ( consistent)]TJ 0.003 -1.1 Td [(with)-84 ( our)-84 ( observation)-84 ( of)-84 ( soldier)-84 ( crabs.)-84 ( In)-84 ( a)-84 ( corridor,)-84 ( they)-84 ( move)-84 ( along)]TJ -0.002 -1.1 Td [(the)-191 ( wall.)-191 ( Because)-191 ( they)-191 ( have)-191 ( a)-191 ( tendency)-191 ( to)-191 ( move)-191 ( together,)-191 ( a)-191 ( swarm)]TJ T* [(generated)-79 ( close)-79 ( to)-79 ( the)-79 ( wall)-79 ( of)-79 ( the)-79 ( corridor)-79 ( propagates)-79 ( along)-79 ( the)-79 ( wall.)]TJ -0.003 -1.1 Td [(If)-129 ( a)-129 ( soldier)-129 ( crab)-129 ( is)-129 ( not)-129 ( close)-129 ( to)-129 ( the)-129 ( wall,)-129 ( it)-129 ( moves)-129 ( freely.)-129 ( In)-129 ( this)-129 ( OR)]TJ 0.003 -1.1 Td [(gate)-76 ( an)-76 ( agent)-76 ( is)-76 ( assumed)-76 ( to)-76 ( move)-76 ( upward)-76 ( along)-76 ( the)-76 ( wall)-76 ( in)-76 ( Figure)-76 ( 2,)]TJ 0.006 -1.1 Td (if it is close to the wall. )Tj 1.2 -1.1 Td [(When)-41 ( agents)-41 ( are)-41 ( set)-41 ( in)-41 ( their)-41 ( input)-41 ( position,)-41 ( they)-41 ( aggregate)-41 ( into)-41 ( one)]TJ -1.199 -1.1 Td [(swarm)-50 ( moving)-50 ( along)-50 ( the)-50 ( wall.)-50 ( In)-50 ( this)-50 ( gate,)-50 ( a)-50 ( swarm)-50 ( initiated)-50 ( at)-50 ( either)]TJ 0.001 -1.1 Td [(the)-68 ( )]TJ /T1_2 1 Tf (x)Tj /T1_0 1 Tf 2.303 0 Td [( or)-68 ( )]TJ 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1 111.6885 365.6157 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 111.6885 355.351 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 375.9123 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 365.6157 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 121.5465 355.351 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 107.4653 372.9894 cm 0 0 m 8.432 7.555 l S Q 1 0.298 0 scn q 1 0 0 1 114.9738 375.9126 cm 0 0 m 2.33 5.892 l -3.782 4.221 l h f* Q q 1 0 0 1 107.4653 372.9894 cm 0 0 m 0 8.343 l S Q q 1 0 0 1 110.2987 377.5544 cm 0 0 m -2.833 5.667 l -5.667 0 l h f* Q q 1 0 0 1 107.4653 372.9894 cm 0 0 m 7.97 -1.19 l S Q q 1 0 0 1 112.1174 375.1595 cm 0 0 m 5.186 -3.639 l -0.837 -5.605 l h f* Q q 1 0 0 1 115.9194 359.7507 cm 0 0 m 0 9.865 l S Q q 1 0 0 1 118.7528 365.8374 cm 0 0 m -2.834 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0 1 144.862 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 1 1 1 scn 144.862 395.852 9.889 10.265 re f* q 1 0 0 1 144.862 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 0.478 0.506 1 scn 154.751 406.116 9.889 10.265 re f* q 1 0 0 1 154.751 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 154.751 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 164.6086 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 164.609 416.413 9.889 10.265 re f* q 1 0 0 1 164.6086 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 174.4972 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 174.4972 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 164.6086 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 164.6086 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q 174.497 406.116 9.889 10.265 re f* q 1 0 0 1 174.4972 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 174.4972 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 426.6776 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 416.381 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 184.3551 406.1159 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 170.2682 423.731 cm 0 0 m 8.456 7.557 l S Q 1 0.298 0 scn q 1 0 0 1 177.7952 426.6575 cm 0 0 m 2.338 5.889 l -3.776 4.225 l h f* Q q 1 0 0 1 178.7266 411.9769 cm 0 0 m 9.793 7.652 l S Q q 1 0 0 1 187.2873 415.0703 cm 0 0 m 2.721 5.722 l -3.49 4.465 l h f* Q q 1 0 0 1 160.3795 411.9769 cm 0 0 m 7.297 8.829 l S Q q 1 0 0 1 167.4535 416.0883 cm 0 0 m 1.426 6.173 l -4.368 3.611 l h f* Q /CS1 CS 0 SCN 0.321 w 0 j q 1 0 0 1 82.7493 436.9424 cm 0 0 m 9.889 0 l 9.889 -10.265 l 0 -10.265 l h S Q q 1 0 0 1 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f* q 1 0 0 1 174.8951 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 174.8951 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 386.1771 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 375.8997 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 365.5901 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q q 1 0 0 1 184.7527 355.3128 cm 0 0 m 9.889 0 l 9.889 -10.277 l 0 -10.277 l h S Q /CS0 CS 1 0.298 0 SCN 1.924 w 1 j q 1 0 0 1 170.672 372.9894 cm 0 0 m 8.432 7.555 l S Q 1 0.298 0 scn q 1 0 0 1 178.1805 375.9126 cm 0 0 m 2.33 5.892 l -3.782 4.221 l h f* Q q 1 0 0 1 170.672 372.9894 cm 0 0 m 0 8.396 l S Q q 1 0 0 1 173.5054 377.6069 cm 0 0 m -2.833 5.667 l -5.667 0 l h f* Q q 1 0 0 1 170.672 372.9894 cm 0 0 m 7.97 -1.19 l S Q q 1 0 0 1 175.3241 375.1595 cm 0 0 m 5.186 -3.639 l -0.837 -5.605 l h f* Q q 1 0 0 1 179.1261 359.6999 cm 0 0 m 0 9.917 l S Q q 1 0 0 1 181.9595 365.8391 cm 0 0 m 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7.804 0.428 c 7.804 0.763 7.751 1.02 7.646 1.199 c 7.541 1.379 7.332 1.468 7.018 1.468 c h 7.134 2.037 m 7.339 2.037 7.508 2.015 7.644 1.97 c 7.875 1.894 8.062 1.755 8.205 1.553 c 8.32 1.388 8.398 1.211 8.439 1.02 c 8.481 0.829 8.502 0.647 8.502 0.475 c 8.502 0.036 8.414 -0.335 8.239 -0.639 c 8 -1.048 7.632 -1.252 7.134 -1.252 c 5.715 -1.252 l 5.715 2.037 l h f* Q q 1 0 0 1 200.4503 390.6821 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.035 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.216 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.647 -0.452 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q 1 1 1 SCN 0.742 w q 1 0 0 1 199.5197 395.7333 cm 0 0 m 3.671 0 l S Q q 1 0 0 1 109.3745 391.1324 cm 0 0 m 1.069 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 114.3745 392.3844 cm 0 0 m 0.835 0 l 0.424 1.293 l h 0.042 2.045 m 0.819 2.045 l 1.983 -1.252 l 1.238 -1.252 l 1.026 -0.567 l -0.185 -0.567 l -0.413 -1.252 l -1.131 -1.252 l h 0.426 2.036 m h 2.371 2.036 m 3.091 2.036 l 4.381 -0.259 l 4.381 2.036 l 5.022 2.036 l 5.022 -1.252 l 4.335 -1.252 l 3.012 1.084 l 3.012 -1.252 l 2.371 -1.252 l h 3.749 2.043 m h 6.382 1.468 m 6.382 -0.681 l 7.018 -0.681 l 7.344 -0.681 7.57 -0.521 7.698 -0.201 c 7.769 -0.025 7.804 0.185 7.804 0.428 c 7.804 0.763 7.751 1.02 7.646 1.199 c 7.541 1.379 7.332 1.468 7.018 1.468 c h 7.134 2.037 m 7.339 2.037 7.508 2.015 7.644 1.97 c 7.875 1.894 8.062 1.755 8.205 1.552 c 8.32 1.388 8.398 1.211 8.439 1.02 c 8.481 0.829 8.502 0.647 8.502 0.475 c 8.502 0.036 8.414 -0.335 8.239 -0.639 c 8 -1.048 7.632 -1.252 7.134 -1.252 c 5.715 -1.252 l 5.715 2.037 l h f* Q q 1 0 0 1 124.5811 390.6805 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.034 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.216 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.648 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q q 1 0 0 1 108.8442 396.3043 cm 0 0 m 3.671 0 l S Q /CS2 cs 0 scn q 1 0 0 1 118.6337 333.782 cm 0 0 m 1.069 1.228 l 0.54 2.421 l 1.303 2.421 l 1.554 1.718 l 2.089 2.421 l 2.831 2.421 l 1.801 1.24 l 2.356 0 l 1.58 0 l 1.32 0.727 l 0.756 0 l h f* Q q 1 0 0 1 189.146 333.3302 cm 0 0 m 0.079 0 l 0.139 0 0.197 0.004 0.253 0.011 c 0.311 0.018 0.361 0.034 0.405 0.061 c 0.447 0.085 0.492 0.137 0.54 0.215 c 0.588 0.294 0.611 0.342 0.608 0.36 c 0.263 2.873 l 0.956 2.873 l 1.102 1.098 l 1.968 2.873 l 2.63 2.873 l 1.314 0.506 l 1.061 0.05 0.876 -0.233 0.762 -0.343 c 0.647 -0.453 0.453 -0.508 0.177 -0.508 c 0.044 -0.508 l -0.105 -0.508 l h f* Q Q BT 0 0 0 scn /T1_1 1 Tf 8 0 0 8 63 310.653 Tm [(Figure)-367 (3.)]TJ ET q 0 279 432 39 re W n BT /T1_2 1 Tf 9 0 0 9 99.5537 310.653 Tm [(A)-198 ( series)-198 ( of)-198 ( snapshots)-198 ( \(1,)-198 ( 2,)-198 ( 3,)-198 ( and)-198 ( 4\))-198 ( in)-198 ( an)-198 ( AND)-198 ( gate)-198 ( of)-198 ( swarm)]TJ ET Q BT /T1_2 1 Tf 9 0 0 9 63 301.153 Tm [(balls.)-67 ( Swarm)-67 ( balls)-67 ( located)-67 ( at)-67 ( the)-67 ( )]TJ /T1_3 1 Tf 14.627 0 Td (x)Tj /T1_2 1 Tf 0.623 0 Td [( and)-67 ( )]TJ /T1_3 1 Tf (y)Tj /T1_2 1 Tf 2.802 0 Td [( positions)-67 ( consist)-67 ( of)-67 ( 40)-67 ( agents.)-67 ( Each)]TJ -18.049 -1.056 Td [(agent)-88 ( is)-88 ( represented)-88 ( by)-88 ( a)-88 ( square)-88 ( with)-88 ( its)-88 ( 5-step)-88 ( trajectory.)-88 ( Red)-88 ( arrows)-88 ( repre-)]TJ 0.004 -1.056 Td (sent the direction a swarm ball is moving toward. )Tj ET q 0 99 432 162.96 re W n BT /T1_0 1 Tf 10 0 0 10 75 252.653 Tm [(Finally,)-162 ( we)-162 ( discuss)-162 ( the)-162 ( robustness)-162 ( of)-162 ( the)-162 ( gates.)-162 ( As)-162 ( mentioned)-162 ( be-)]TJ ET Q BT /T1_0 1 Tf 10 0 0 10 63 241.653 Tm [(fore,)-121 ( the)-121 ( OR)-121 ( gate)-121 ( acts)-121 ( very)-121 ( well)-121 ( against)-121 ( external)-121 ( perturbation.)-121 ( Here,)]TJ 0.001 -1.1 Td [(we)-25 ( estimate)-25 ( the)-25 ( performance)-25 ( of)-25 ( the)-25 ( AND)-25 ( gate)-25 ( under)-25 ( a)-25 ( high)-25 ( rate)-25 ( of)-25 ( ex-)]TJ 0 -1.1 TD [(ternal)-64 ( noise.)-64 ( In)-64 ( the)-64 ( simulation,)-64 ( the)-64 ( external)-64 ( noise)-64 ( that)-64 ( is)-64 ( coupled)-64 ( with)]TJ -0.002 -1.1 Td [(the)-84 ( operation)-84 ( of)-84 ( velocity)-84 ( matching)-84 ( is)-84 ( defined)-84 ( as)-84 ( a)-84 ( random)-84 ( value)-84 ( )]TJ /TT0 1 Tf 28.6 0 Td (x)Tj /T1_0 1 Tf 0.553 0 Td ( se-)Tj -29.156 -1.1 Td [(lected)-80 ( with)-80 ( equal)-80 ( probability)-80 ( from)-80 ( )]TJ ET q 216.96 195 31.08 12 re W n BT /TT1 1 Tf 10 0 0 10 217.5931 197.653 Tm (@)Tj ET Q BT /TT0 1 Tf 10 0 0 10 220.9232 197.653 Tm [(-)-100 (l)]TJ /T1_0 1 Tf (,)Tj /TT0 1 Tf 1.836 0 Td (l)Tj ET q 216.96 195 31.08 12 re W n BT /TT1 1 Tf 10 0 0 10 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Tf 1.538 0 Td ( and)Tj ET q 63 153.96 24.96 15 re W n BT /T1_4 1 Tf 10 0 0 10 63 159.8122 Tm (v)Tj ET Q BT /T1_5 1 Tf 8 0 0 8 68 157.9714 Tm (y)Tj ET q 63 153.96 24.96 15 re W n BT /TT0 1 Tf 10 0 0 10 74.5 159.8122 Tm [(+)-206 (x)]TJ ET Q BT /T1_0 1 Tf 10 0 0 10 89.2329 159.8122 Tm [( and)-154 ( then)-154 ( normalized)-154 ( to)-154 ( make)-154 ( the)-154 ( length)-154 ( of)-154 ( the)-154 ( velocity)-154 ( be)-154 ( 1.)]TJ -2.626 -1.384 Td [(We)-144 ( estimate)-144 ( performance)-144 ( within)-144 ( the)-144 ( range)-144 ( 0.0)]TJ /TT0 1 Tf 21.163 0 Td [(\247)-300 (l)-300 (\247)]TJ /T1_0 1 Tf 2.702 0 Td [(0.2)-144 ( when)-144 ( com-)]TJ -23.867 -1.1 Td [(paring)-65 ( our)-65 ( model)-65 ( of)-65 ( )]TJ /T1_4 1 Tf (P)Tj ET q 155.04 132 31.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 164.1982 134.9714 Tm <0001>Tj ET Q BT /T1_0 1 Tf 10 0 0 10 175.0382 134.9714 Tm [(20)-65 ( with)-65 ( one)-65 ( with)-65 ( )]TJ /T1_4 1 Tf (P)Tj ET q 254.04 132 25.92 12 re W n BT /C2_0 1 Tf 10 0 0 10 263.4664 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a)-134 ( number)-134 ( of)-134 ( poten-)]TJ -0.002 -1.1 Td [(tial)-121 ( transitions)-121 ( )]TJ ET q 129.96 383.04 7.08 12 re W n BT /T1_2 1 Tf 10 0 0 10 130.444 385.2618 Tm (P)Tj ET Q BT 10 0 0 10 137.7661 385.2618 Tm [( in)-121 ( a)-121 ( range)-121 ( restricted)-121 ( by)-121 ( angle)-121 ( )]TJ /TT0 1 Tf (a)Tj /T1_1 1 Tf [(.)-121 ( The)-121 ( neighborhood)]TJ -7.478 -1.1 Td [(has)-104 ( dual)-104 ( roles:)-104 ( the)-104 ( extended)-104 ( body)-104 ( of)-104 ( an)-104 ( individual)-104 ( for)-104 ( active)-104 ( interac-)]TJ -0.004 -1.1 Td (tion and the local space for passively monitoring other individuals. )Tj 1.2 -1.1 Td [(Figure)-127 ( 1)-127 ( shows)-127 ( a)-127 ( typical)-127 ( transition)-127 ( of)-127 ( our)-127 ( swarm)-127 ( model)-127 ( of)-127 ( which)]TJ -1.195 -1.125 Td [(individuals)-105 ( are)-105 ( numbered)-105 ( from)-105 ( 1)-105 ( to)-105 ( 3.)-105 ( First,)-105 ( velocity)-105 ( matching)-105 ( is)-105 ( ap-)]TJ 0.005 -1.125 Td [(plied)-132 ( to)-132 ( the)-132 ( principal)-132 ( vector)-132 ( by)-132 ( averaging)-132 ( all)-132 ( flock-mate)-132 ( velocities)-132 ( in)]TJ 0.001 -1.125 Td [(the)-126 ( neighborhood,)-126 ( NM,)-126 ( which)-126 ( is)-126 ( defined)-126 ( here)-126 ( as)-126 ( a)-126 ( Moore)-126 ( neighbor-)]TJ 0.002 -1.125 Td [(hood)-66 ( extended)-66 ( by)-66 ( next-nearest)-66 ( neighboring)-66 ( cells)-66 ( \(Figure)-66 ( 1\(a\),)-66 ( left)-66 ( and)]TJ 0.001 -1.125 Td [(center)-155 ( in)-155 ( top)-155 ( row\).)-155 ( If)-155 ( targets)-155 ( of)-155 ( some)-155 ( potential)-155 ( transitions)-155 ( are)-155 ( over-)]TJ -0.005 -1.125 Td [(lapped)-86 ( at)-86 ( a)-86 ( particular)-86 ( cell)-86 ( \(Figure)-86 ( 1\(a\))-86 ( right)-86 ( in)-86 ( top)-86 ( row\),)-86 ( the)-86 ( overlap-)]TJ -0.005 -1.125 Td [(ping)-210 ( is)-210 ( counted)-210 ( as)-210 ( \223popularity.\224)-210 ( In)-210 ( Figure)-210 ( 1\(a\),)-210 ( left)-210 ( in)-210 ( center)-210 ( row,)]TJ -0.004 -1.125 Td [(transitions)-140 ( from)-140 ( individuals)-140 ( 2)-140 ( and)-140 ( 3)-140 ( overlap)-140 ( at)-140 ( a)-140 ( pink)-140 ( cell,)-140 ( meaning)]TJ 0.004 -1.125 Td [(that)-114 ( the)-114 ( pink)-114 ( cell)-114 ( has)-114 ( a)-114 ( popularity)-114 ( of)-114 ( 2.)-114 ( If)-114 ( some)-114 ( potential)-114 ( transitions)]TJ -0.004 -1.125 Td [(reach)-47 ( highly)-47 ( popular)-47 ( sites)-47 ( beyond)-47 ( the)-47 ( threshold)-47 ( of)-47 ( popularity)-47 ( \(defined)]TJ -0.001 -1.125 Td [(here)-26 ( by)-26 ( 1\),)-26 ( an)-26 ( individual)-26 ( moves)-26 ( to)-26 ( the)-26 ( site)-26 ( with)-26 ( the)-26 ( highest)-26 ( popularity.)]TJ -0.003 -1.125 Td [(In)-202 ( Figure)-202 ( 1\(a\),)-202 ( center)-202 ( in)-202 ( center)-202 ( row,)-202 ( the)-202 ( individual)-202 ( 2)-202 ( moves)-202 ( to)-202 ( the)]TJ -0.005 -1.125 Td [(most)-150 ( popular)-150 ( cell.)-150 ( If)-150 ( several)-150 ( individuals)-150 ( intend)-150 ( to)-150 ( move)-150 ( to)-150 ( the)-150 ( same)]TJ -0.004 -1.125 Td [(site,)-130 ( one)-130 ( individual)-130 ( is)-130 ( randomly)-130 ( chosen,)-130 ( and)-130 ( others)-130 ( move)-130 ( to)-130 ( the)-130 ( sec-)]TJ 0.002 -1.125 Td [(ond-best)-33 ( site.)-33 ( In)-33 ( Figure)-33 ( 1\(a\),)-33 ( both)-33 ( individuals)-33 ( 2)-33 ( and)-33 ( 3)-33 ( can)-33 ( move)-33 ( to)-33 ( the)]TJ 0.004 -1.125 Td [(popular)-82 ( site.)-82 ( The)-82 ( individual)-81 ( 2)-82 ( was)-82 ( randomly)-82 ( chosen.)-82 ( This)-82 ( rule)-82 ( imple-)]TJ 0.004 -1.125 Td [(ments)-134 ( the)-134 ( individual\222s)-134 ( mutual)-134 ( anticipation.)-134 ( Even)-134 ( a)-134 ( human)-134 ( can)-134 ( avoid)]TJ 0 -1.125 TD [(collisions)-11 ( in)-11 ( crowded)-11 ( pedestrian)-11 ( traffic)-11 ( by)-11 ( anticipation)-11 ( [12].)-11 ( We)-11 ( imple-)]TJ -0.001 -1.125 Td [(ment)-119 ( this)-119 ( kind)-119 ( of)-119 ( behavior)-119 ( by)-119 ( the)-119 ( mutual)-119 ( anticipation.)-119 ( If)-119 ( there)-119 ( is)-119 ( no)]TJ -0.001 -1.125 Td [(popular)-23 ( site)-23 ( in)-23 ( any)-23 ( of)-23 ( the)-23 ( potential)-23 ( transition)-23 ( targets)-23 ( and)-23 ( another)-23 ( indi-)]TJ -0.005 -1.125 Td [(vidual)-53 ( in)-53 ( the)-53 ( neighborhood)-53 ( is)-53 ( following,)-53 ( NF,)-53 ( defined)-53 ( here)-53 ( as)-53 ( a)-53 ( Moore)]TJ -0.005 -1.125 Td [(neighborhood,)-171 ( moves)-171 ( due)-171 ( to)-171 ( mutual)-171 ( anticipation)-171 ( and)-171 ( the)-171 ( individual)]TJ -0.001 -1.125 Td [(moves)-54 ( to)-54 ( occupy)-54 ( the)-54 ( absent)-54 ( cell)-54 ( generated)-54 ( by)-54 ( the)-54 ( mutual)-54 ( anticipation.)]TJ -0.003 -1.125 Td [(Namely,)-215 ( it)-215 ( follows)-215 ( the)-215 ( predecessor)-215 ( \(Figure)-215 ( 1\(a\),)-215 ( right)-215 ( in)-215 ( the)-215 ( center)]TJ -0.003 -1.125 Td [(row\).)-170 ( If)-170 ( an)-170 ( individual)-170 ( does)-170 ( not)-170 ( obey)-170 ( the)-170 ( mutual)-170 ( anticipation)-170 ( and)-170 ( is)]TJ T* [(not)-74 ( a)-74 ( follower,)-278 (it)-74 ( moves)-74 ( in)-74 ( the)-74 ( direction)-74 ( of)-74 ( a)-74 ( randomly)-74 ( chosen)-74 ( poten-)]TJ ET q 0 56.76 432 305.28 re W n BT 10 0 0 10 77.1754 47.7617 Tm [( )-4197 ( )-1641 ( )-696 ( )-2529 ( )-529 ( )]TJ /T1_2 1 Tf 12.899 0 Td ( )Tj /T1_1 1 Tf 4.641 0 Td [( )-917 ( )-2753 ( )-2029 ( )-2085 ( )-863 ( )]TJ -16.342 -1.125 Td [( )-2001 ( )-1333 ( )-4336 ( )-556 ( )-667 ( )-500 ( )-1610 ( )-4334 ( )]TJ ET Q BT /T1_3 1 Tf 8 0 0 8 63 612.0001 Tm (94)Tj /T1_4 1 Tf 18.19 0 Td (Y.-P. 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