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Di Paolo) Tj 183 3 TD 0 Tc 0 Tw ( ) Tj -183 -16.8 TD ( ) Tj 231.36 -11.16 TD /F0 9 Tf 0.03 Tw ( ) Tj -231.36 -12.96 TD /F0 12 Tf 0.0028 Tc -0.0028 Tw (Centre for Computational Neuroscience and Robotics \(CCNR\)) Tj 301.32 0 TD 0 Tc 0 Tw ( ) Tj -301.32 -13.8 TD -0.012 Tc (Centre) Tj 31.92 0 TD 0 Tc ( ) Tj 3 0 TD 0.001 Tc -0.001 Tw (for Research in Cognitive Science \(COGS\)) Tj 207 0 TD 0 Tc 0 Tw ( ) Tj -241.92 -13.8 TD -0.0012 Tc 0.0212 Tw (Dept. of Informatics, 5XƵ, UK) Tj 227.04 0 TD 0 Tc 0 Tw ( ) Tj -227.04 -13.8 TD -0.0132 Tc 0.0132 Tw ({t.froese, ) Tj 47.28 0 TD 0.0044 Tc 0 Tw (ezequiel}@sussex.ac.uk) Tj 116.88 0 TD 0 Tc ( ) Tj -135.84 -41.16 TD /F0 9 Tf 0.03 Tw ( ) Tj -28.32 -18.96 TD /F1 12 Tf -0.0147 Tc 0 Tw (Abstract.) Tj 47.52 0 TD /F0 12 Tf 0 Tc ( ) Tj 5.52 0 TD -0.002 Tc 2.582 Tw (We used an evolutionary robotics methodology to generate pairs of simulated) Tj 0 Tc 0.12 Tw ( ) Tj -53.04 -13.8 TD -0.0047 Tc 1.8266 Tw (agents capable of reliably establishing and maintaining a coordination pattern under no) Tj 437.28 0 TD 0.012 Tc -0.252 Tw (isy ) Tj -437.28 -13.8 TD -0.0009 Tc 0.0009 Tw (conditions. Unlike previous related work, agents were only evolved for this ability and not for ) Tj 0 -13.8 TD -0.0065 Tc 1.5865 Tw (their capacity to discriminate social contingency \(i.e., a live responsive partner\) from non) Tj 447.36 0 TD -0.036 Tc 0 Tw (-) Tj -447.36 -13.8 TD -0.0086 Tc 0.4286 Tw (contingent engagements \(i.e) Tj 135.6 0 TD 0 Tc 0 Tw (.) Tj 3 0 TD -0.0091 Tc 0.3691 Tw (, a recording\). However, when they) Tj 0 Tc -0.24 Tw ( ) Tj 174.84 0 TD -0.0094 Tc 0.2894 Tw (were made to interact with a ) Tj -313.44 -13.8 TD -0.0044 Tc 2.1644 Tw (recording of their partner made during a successful previous interaction, the coordination) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0088 Tc 1.2088 Tw (pattern could not be established. An analysis of the system\222s underlying dynamics revealed) Tj 0 Tc 0 Tw ( ) Tj T* -0.0105 Tc 0.4905 Tw (\(i\) that stability of the coordination patter) Tj 201.12 0 TD -0.0102 Tc 0.4902 Tw (n requires ongoing mutuality of interaction, and \(ii\)) Tj 0 Tc -0.12 Tw ( ) Tj -201.12 -13.8 TD -0.0053 Tc 2.1653 Tw (that the interaction process is not only constituted by, but also constitutive of, individual) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.012 Tc 0 Tw (behavior.) Tj 44.88 0 TD 0 Tc ( ) Tj 6 0 TD 0 Tc 0.0317 Tw (We suggest that this stability of coordination is a general property of a certain class ) Tj -50.88 -13.8 TD -0.015 Tc 0.615 Tw (of intera) Tj 40.92 0 TD 0.002 Tc 0.6247 Tw (ctively coupled dynamical systems, and conclude that psychological explanations of) Tj 0 Tc 0 Tw ( ) Tj -40.92 -13.8 TD -0.0129 Tc 2.1815 Tw (an individual\222s sensitivity to social contingency need to take into account the role of the) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0038 Tc 0.0038 Tw (interaction process.) Tj 93.36 0 TD 0 Tc 0 Tw ( ) Tj -93.36 -14.04 TD /F1 12 Tf ( ) Tj 0 -13.56 TD -0.008 Tc 0.008 Tw (Keywords: ) Tj 58.92 0 TD /F0 12 Tf -0.0041 Tc 0.0281 Tw (evolutionary robotics, social cognition, social c) Tj 226.92 0 TD -0.0262 Tc 0 Tw (ontingency.) Tj 56.4 0 TD 0 Tc ( ) Tj -342.24 -14.04 TD /F1 12 Tf ( ) Tj 0 -13.8 TD ( ) Tj 0 -11.76 TD /F0 9.96 Tf 0.03 Tw ( ) Tj 0 -13.56 TD /F1 12 Tf 0 Tw ( ) Tj T* /F0 12 Tf -0.0131 Tc 0.2531 Tw (To appear in: ) Tj 67.92 0 TD -0.0137 Tc 0.1937 Tw (M. Asada ) Tj 50.28 0 TD /F2 12 Tf 0 Tc 0.36 Tw (et al.) Tj 24.36 0 TD /F0 12 Tf 0 Tw ( ) Tj 3.36 0 TD -0.0154 Tc 0.0154 Tw (\(eds.\), ) Tj 33.24 0 TD /F2 12 Tf -0.0089 Tc 0.2969 Tw (From animals to animats 10: ) Tj 144.6 0 TD -0.014 Tc 0.374 Tw (Proc. of the 10) Tj 72.24 5.52 TD /F2 8.04 Tf -0.0676 Tc 0 Tw (th) Tj 6.24 -5.52 TD /F2 12 Tf 0 Tc ( ) Tj 3.36 0 TD -0.0347 Tc 0.1547 Tw (Int. Conf. ) Tj -405.6 -13.8 TD 0 Tc 0 Tw (o) Tj 6 0 TD 0.0074 Tc -0.0074 Tw (n Simulation of ) Tj 76.44 0 TD -0.0158 Tc 0.0158 Tw (Adaptive Behavior) Tj 89.4 0 TD /F0 12 Tf 0.0035 Tc 0.0365 Tw (, Berlin, Germany: Springer) Tj 134.4 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD 0.009 Tc -0.009 Tw (Verlag, pp. 52) Tj 68.76 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD 0 Tc (61) Tj 12 0 TD ( ) Tj ET endstream endobj 18 0 obj 4844 endobj 16 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 19 0 R /F2 21 0 R >> /ProcSet 2 0 R >> /Contents 17 0 R >> endobj 26 0 obj << /Length 27 0 R >> stream BT 518.28 59.4 TD 0 0 0 rg /F0 9.96 Tf 0.06 Tc 0 Tw (3) Tj 5.04 0 TD 0 Tc 0.03 Tw ( ) Tj -439.92 -11.52 TD ( ) Tj -11.4 711.36 TD /F0 12 Tf 0 Tw ( ) Tj 0 -14.04 TD /F1 12 Tf (1) Tj 6 0 TD /F3 12 Tf 0.024 Tw ( ) Tj 16.68 0 TD /F1 12 Tf 0.005 Tc 0 Tw (Introduction) Tj 65.4 0 TD 0 Tc ( ) Tj -88.08 -11.76 TD /F0 9.96 Tf 0.03 Tw ( ) Tj 0 -13.32 TD /F0 12 Tf -0.002 Tc 1.682 Tw (Evolutionary robotics is typically employed to investigate simulation models of minimally) Tj 0 Tc -0.24 Tw ( ) Tj 0 -13.8 TD -0.0042 Tc 2.7642 Tw (cognitive behavior, namely the simplest behavior that raises issues of genuine cognitive) Tj 0 Tc 0 Tw ( ) Tj T* -0.006 Tc 0.006 Tw (interest ) Tj 39.36 0 TD -0.036 Tc 0 Tw (\() Tj 3.96 0 TD 0.018 Tc 0.102 Tw (e.g. ) Tj 21.48 0 TD 0.0008 Tc 1.0792 Tw (Beer 1997; Harvey) Tj 0 Tc -0.24 Tw ( ) Tj 97.56 0 TD /F2 12 Tf 1.08 Tw (et al.) Tj 25.08 0 TD /F0 12 Tf 0 Tw ( ) Tj 4.08 0 TD -0.0028 Tc 1.1428 Tw (2005; Harvey 2001\).) Tj 101.88 0 TD 0 Tc 0 Tw ( ) Tj 4.08 0 TD 0.0091 Tc 1.0709 Tw (Recently there have been some) Tj 153.84 0 TD 0 Tc 0 Tw ( ) Tj -451.32 -13.8 TD -0.0023 Tc 0.8423 Tw (initial efforts to extend this methodology into the domain of social cognition) Tj 0 Tc 0 Tw ( ) Tj 379.92 0 TD -0.036 Tc (\() Tj 3.96 0 TD -0.012 Tc 0.012 Tw (e.g. ) Tj 21.12 0 TD 0.018 Tc 0.822 Tw (Di Paolo,) Tj 0 Tc 0.12 Tw ( ) Tj -405 -13.8 TD -0.0159 Tc 1.2596 Tw (Rohde & Iizuka 2008; Iizuka & Di Paolo 2007; Iizuka & Ikegam) Tj 325.32 0 TD -0.018 Tc 1.278 Tw (i 2004; Ikegami & Iizuka) Tj 0 Tc 0 Tw ( ) Tj -325.32 -13.8 TD -0.0076 Tc 1.3276 Tw (2007; Di Paolo 2000; Quinn 2001\)) Tj 173.4 0 TD -0.0096 Tc 1.3467 Tw (. 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Tj 0 Tc 0 Tw ( ) Tj -368.88 -13.8 TD 0.0024 Tc 1.4576 Tw (Moreover, an analysis of the resulting dynamics suggests that the interaction process itself) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0098 Tc 0.2273 Tw (plays an important role in enabling this behavior. Similar results were also found by the other ) Tj T* 0.0064 Tc 1.3136 Tw (simulation studies) Tj 0 Tc 0 Tw ( ) Tj 92.76 0 TD -0.0193 Tc 1.4093 Tw (\(e.g. Di Paolo, Rohde & Iizuka 2008; Ikegami & Iizuka 2007; Iizuka &) Tj 0 Tc -0.12 Tw ( ) Tj -92.76 -13.8 TD -0.01 Tc 0.01 Tw (Ikegami 2004\)) Tj 70.2 0 TD 0 Tc 0 Tw (.) 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We address this issue by testing) Tj 0 Tc 0 Tw ( ) Tj 332.4 0 TD /F2 12 Tf 0.0018 Tc 4.4382 Tw (whether termination of) Tj 0 Tc -0.12 Tw ( ) Tj -332.4 -13.8 TD 0.0024 Tc 0.9576 Tw (interaction emerges under more general conditions.) Tj 254.88 0 TD /F0 12 Tf 0 Tc 0 Tw ( ) Tj 3.96 0 TD 0 Tc 0.9596 Tw (Answering this question is important if) Tj 0 Tc -0.12 Tw ( ) Tj -258.84 -13.8 TD 0.0018 Tc 1.9382 Tw (the argument is made that these findings) Tj 0 Tc 0.12 Tw ( ) Tj 210.6 0 TD 0.0144 Tc 0.1056 Tw (might ) Tj 33 0 TD 0.0046 Tc 1.9754 Tw (apply more gene) Tj 83.88 0 TD 0.0027 Tc 1.9473 Tw (rally and in particular to) Tj 0 Tc 0 Tw ( ) Tj -327.48 -13.8 TD -0.0111 Tc 0.6196 Tw (human interactions. By changing the simulation setup in this manner we thus move closer to) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0028 Tc 0.612 Tw (the original double TV monitor experiment: the infants presumably did not have the specific) Tj 0 Tc 0 Tw ( ) Tj T* -0.0019 Tc 0.0319 Tw (goal to detect whether they were dealing with ) Tj 222.12 0 TD -0 Tc 0 Tw (a live video or just a recording. It is more likely ) Tj -222.12 -13.8 TD -0.0069 Tc 0.4869 Tw (that they were simply attempting to establish social coordination with their mothers but were) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0028 Tc 0.0028 Tw (unable to do so. ) Tj 78.96 0 TD 0 Tc 0 Tw ( ) Tj -78.96 -13.8 TD ( ) Tj 0 -13.8 TD ( ) Tj T* ( ) Tj ET endstream endobj 27 0 obj 8841 endobj 23 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 19 0 R /F2 21 0 R /F3 24 0 R >> /ProcSet 2 0 R >> /Contents 26 0 R >> endobj 29 0 obj << /Length 30 0 R >> stream BT 518.28 59.4 TD 0 0 0 rg /F0 9.96 Tf 0.06 Tc 0 Tw (4) Tj 5.04 0 TD 0 Tc 0.03 Tw ( ) Tj -439.92 -11.52 TD ( ) Tj -11.4 711.12 TD /F1 12 Tf 0 Tw (2) Tj 6 0 TD /F3 12 Tf 0.024 Tw ( ) Tj 16.68 0 TD /F1 12 Tf -0.0034 Tc 0 Tw (Methods) Tj 44.64 0 TD 0 Tc ( ) Tj -67.32 -11.76 TD /F0 9.96 Tf 0.03 Tw ( ) Tj 0 -13.32 TD /F0 12 Tf 0.006 Tc 0.714 Tw (We implemented a minimal simulation model analogous to Murray and Trevarthen\222s) Tj 0 Tc 0 Tw ( ) Tj 419.4 0 TD -0.012 Tc (\(1985\)) Tj 31.92 0 TD 0 Tc ( ) Tj -451.32 -13.8 TD 0.0009 Tc 2.6391 Tw (double TV monito) Tj 93.96 0 TD 0.0125 Tc 2.6275 Tw (r experiment by building on) Tj 0 Tc 0.12 Tw ( ) Tj 150.48 0 TD -0.0033 Tc 2.7153 Tw (work by Iizuka and Di Paolo) Tj 0 Tc 0 Tw ( ) Tj 157.44 0 TD -0.012 Tc (\(2007\)) Tj 31.92 0 TD 0.108 Tc 2.532 Tw (. A) Tj 0 Tc 0.12 Tw ( ) Tj -433.8 -13.8 TD -0.0065 Tc 0.0065 Tw (schematic of this simulat) Tj 119.64 0 TD -0.0058 Tc 0.0058 Tw (ion model is illustrated in Figure) Tj 156.84 0 TD 0 Tc 0 Tw ( ) Tj 3 0 TD (1.) Tj 9.12 0 TD ( ) Tj -277.2 -12 TD /F0 9.96 Tf 0.03 Tw ( ) Tj 0 -13.32 TD /F0 12 Tf 0 Tw ( ) Tj 286.2 -74.88 TD ( ) Tj -72 -10.8 TD ( ) Tj -225.6 -19.8 TD /F1 12 Tf -0.036 Tc (Fig) Tj 16.56 0 TD -0.016 Tc (ure) Tj 17.28 0 TD 0 Tc ( ) Tj 3.48 0 TD (1.) Tj 9 0 TD /F0 12 Tf ( ) Tj 3.48 0 TD -0.0176 Tc 0.5086 Tw (A schematic view of the model adapted from Iizuka and Di Paolo) Tj 319.56 0 TD 0 Tc 0 Tw ( ) Tj 3.48 0 TD -0.012 Tc (\(2007\)) Tj 31.92 0 TD -0.01 Tc 0.49 Tw (. The tw) Tj 40.56 0 TD 0 Tc 0 Tw (o ) Tj -445.32 -13.8 TD -0.0069 Tc 0.7349 Tw (identical agents are 40 units wide, only able to move in a horizontal direction, and equipped) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0.0052 Tc 0.2348 Tw (with a single on/off sensor) Tj 128.4 0 TD 0 Tc 0 Tw ( ) Tj 3.24 0 TD 0.0018 Tc 0.2382 Tw (at their centre) Tj 66.48 0 TD 0.0137 Tc 0.2396 Tw (. They face each other in an unlimited continuous 1) Tj 249.24 0 TD -0.036 Tc 0 Tw (-) Tj -447.36 -13.8 TD -0.0223 Tc 0.0223 Tw (D space.) Tj 41.28 0 TD 0 Tc 0 Tw ( ) Tj -41.28 -25.8 TD ( ) Tj 0 -13.8 TD 0.0008 Tc 1.3519 Tw (The goal of the agents is to cross their sensors as far) Tj 0 Tc 0 Tw ( ) Tj 269.52 0 TD 0.003 Tc 1.341 Tw (away from their starting positions as) Tj 0 Tc 0 Tw ( ) Tj -269.52 -13.8 TD -0.0053 Tc 1.6853 Tw (possible, a task which requires mutual localization, convergence on a target direction, and) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0063 Tc 0.4948 Tw (movement in that direction while not losing track of each other. This task is non) Tj 390.72 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.014 Tc 0.194 Tw (trivial since ) Tj -394.68 -13.8 TD 0.0053 Tc 0.5947 Tw (sensory stimulation only corre) Tj 147.48 0 TD 0.0104 Tc 0.5896 Tw (lates with the overlapping of position \(when the centers of the) Tj 0 Tc 0 Tw ( ) Tj -147.48 -13.8 TD -0.0117 Tc 1.8117 Tw (agents are less than 20 units of space apart\); it does not convey the direction or speed of) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.009 Tc 0.033 Tw (movement of the other agent. ) Tj 144 0 TD 0 Tc 0 Tw ( ) Tj -144 -13.8 TD ( ) Tj 0 -13.8 TD -0.0023 Tc 4.2366 Tw (The agents are controlled by two identical continuous) Tj 287.16 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD 0.0028 Tc 4.1972 Tw (time recurrent) Tj 0 Tc 0 Tw ( ) Tj 79.08 0 TD -0.0043 Tc 4.2043 Tw (neural networks) Tj 0 Tc 0 Tw ( ) Tj -370.2 -13.8 TD -0.006 Tc (\(CTRNNs\)) Tj 53.28 0 TD -0.0087 Tc 1.4787 Tw (, as described by Beer) Tj 0 Tc 0 Tw ( ) Tj 115.8 0 TD -0.012 Tc (\(1997\)) Tj 31.92 0 TD -0.0101 Tc 1.5034 Tw (. They were chosen to be clones because work by) Tj 0 Tc -0.24 Tw ( ) Tj -201 -13.8 TD -0.0075 Tc 2.7075 Tw (Iizuka and Ikegami) Tj 0 Tc 0 Tw ( ) Tj 103.56 0 TD 0.008 Tc (\(2004\)) Tj 32.04 0 TD 0 Tc ( ) Tj 5.64 0 TD 0.0067 Tc 2.6333 Tw (on a relate) Tj 55.2 0 TD 0 Tc 0 Tw (d) Tj 6 0 TD ( ) Tj 5.64 0 TD -0 Tc 2.6606 Tw (task suggests that genetically similar agents are) Tj 0 Tc 0 Tw ( ) Tj -208.08 -13.8 TD -0.0108 Tc 0.5148 Tw (potentially better at coordination. They face each other in an unlimite) Tj 337.2 0 TD 0.041 Tc 0.439 Tw (d continuous 1) Tj 71.64 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.046 Tc 0.226 Tw (D space ) Tj -412.8 -13.8 TD -0.0128 Tc 1.9328 Tw (\(i.e. one agent faces \221up\222 and one agent faces \221down\222\). Distance and time units are of an) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0.0034 Tc 1.3166 Tw (arbitrary scale. Each agent can only move horizontally. One on/off sensor is located in the) Tj 0 Tc 0 Tw ( ) Tj T* -0.0071 Tc 1.9271 Tw (centre of each agent. The sensor is activated \(set) Tj 0 Tc 0 Tw ( ) Tj 252.24 0 TD -0.0098 Tc 1.9298 Tw (to 1\) when the agents cross each other,) Tj 0 Tc 0.12 Tw ( ) Tj -252.24 -13.8 TD 0 Tw (otherwise it is set to 0. ) Tj 111 0 TD ( ) Tj -111 -13.8 TD ( ) Tj 0 -13.8 TD -0.0018 Tc 0.9698 Tw (Noise is introduced into the simulation for 2 main reasons: \(i\) since the agents are identical) Tj 0 Tc 0.12 Tw ( ) Tj T* -0.0078 Tc 0.8478 Tw (they will need to make use of noise in order to break the symmetry of their movements and) Tj 0 Tc 0 Tw ( ) Tj T* -0.016 Tc (con) Tj 17.28 0 TD -0.0018 Tc 0.3803 Tw (verge on a common target direction, and \(ii\) robustness against noise increases the ability) Tj 0 Tc -0.24 Tw ( ) Tj -17.28 -13.8 TD 0.0051 Tc 1.332 Tw (of \221live\222 agents to cope with playback situations) Tj 0 Tc 0 Tw ( ) Tj 244.2 0 TD -0.012 Tc 1.452 Tw (\(Iizuka & Ikegami 2004\)) Tj 123.72 0 TD 0.0072 Tc 1.3128 Tw (. Accordingly, at) Tj 0 Tc 0.12 Tw ( ) Tj -367.92 -13.8 TD 0.0036 Tc 0.4764 Tw (each Euler time step there is a 5% probability that the current sensory state is flipped int) Tj 430.56 0 TD -0.015 Tc 0.195 Tw (o its ) Tj -430.56 -13.8 TD -0.0083 Tc 0.1 Tw (opposite state. We add a small perturbation to the motor outputs at each time step drawn from ) Tj 0 -13.8 TD -0.0011 Tc 1.9611 Tw (a Gaussian distribution ) Tj 2.004 Tc 0 Tw (\() Tj 123.48 0 TD /F2 12 Tf 0.048 Tc (\265) Tj 6 0 TD /F0 12 Tf 0 Tc ( ) Tj 4.92 0 TD -0.008 Tc 1.928 Tw (= 0;) Tj 0 Tc 0 Tw ( ) Tj 25.92 0 TD /F2 12 Tf 0.012 Tc (s) Tj 5.88 5.52 TD /F2 8.04 Tf 0.06 Tc (2) Tj 4.08 -5.52 TD /F0 12 Tf 0 Tc ( ) Tj 4.92 0 TD 0.0013 Tc 1.9307 Tw (= 0.05\). The noise is applied to the outputs before the) Tj 0 Tc 0.12 Tw ( ) Tj -175.2 -13.8 TD -0.0035 Tc 0.0435 Tw (application of motor gains.) Tj 129.36 0 TD 0 Tc 0 Tw ( ) Tj -129.36 -13.8 TD ( ) Tj 0 -13.8 TD -0.0092 Tc 2.1892 Tw (In order to further increase the rob) Tj 178.08 0 TD 0 Tc 2.1794 Tw (ustness of the behavioral strategies, the initial) Tj 0 Tc 0 Tw ( ) Tj 237.24 0 TD 0.0015 Tc 0.1185 Tw (relative ) Tj -415.32 -13.8 TD 0.0026 Tc 0.4774 Tw (displacement between the agents varies \(range [) Tj 232.56 0 TD -0.036 Tc 0 Tw (-) Tj 4.08 0 TD -0.0085 Tc 0.4285 Tw (25, 25]\). Starting from any of these possible ) Tj -236.64 -13.8 TD -0.0135 Tc 0.0135 Tw (relative ) Tj 39.72 0 TD 0.0105 Tc 0.8381 Tw (positions, the task for the agents is to coordinate their behavior such that they cross) Tj 0 Tc 0 Tw ( ) Tj -39.72 -13.8 TD -0.036 Tc 1.236 Tw (each ) Tj 1.2 Tc 0 Tw (o) Tj 32.04 0 TD -0.0015 Tc 1.2095 Tw (ther as far away from position 0 as possible. Since the agents are started in opposite) Tj 0 Tc 0 Tw ( ) Tj -32.04 -13.8 TD -0.01 Tc 1.45 Tw (orientation \(\221up\222 vs. \221down\222\), it is not possible for the evolutionary algorithm to hard code) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0041 Tc 0.0212 Tw (any trivial solution \(e.g. \221always move left\222\). ) Tj 218.04 0 TD 0 Tc 0 Tw ( ) Tj ET 235.2 671.64 m 235.44 671.52 l 235.56 671.28 l 235.44 671.04 l 235.2 670.92 l 234.96 671.04 l 234.84 671.28 l 234.96 671.52 l 235.2 671.64 l 236.64 671.64 m 236.76 671.64 l 237 671.52 l 237.12 671.28 l 237 671.04 l 236.76 670.92 l 236.64 670.92 l 236.4 671.04 l 236.28 671.28 l 236.4 671.52 l 236.64 671.64 l 238.2 671.64 m 238.44 671.52 l 238.56 671.28 l 238.44 671.04 l 238.2 670.92 l 237.96 671.04 l 237.84 671.28 l 237.96 671.52 l 238.2 671.64 l 239.76 671.64 m 240 671.52 l 240.12 671.28 l 240 671.04 l 239.76 670.92 l 239.4 671.04 l 239.28 671.28 l 239.4 671.52 l 239.76 671.64 l 241.2 671.64 m 241.44 671.52 l 241.56 671.28 l 241.44 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274.56 671.28 l 274.44 671.04 l 274.2 670.92 l 273.96 671.04 l 273.84 671.28 l 273.96 671.52 l 274.2 671.64 l 275.76 671.64 m 276 671.52 l 276.12 671.28 l 276 671.04 l 275.76 670.92 l 275.4 671.04 l 275.4 671.52 l 275.76 671.64 l 277.2 671.64 m 277.44 671.52 l 277.56 671.28 l 277.44 671.04 l 277.2 670.92 l 276.96 671.04 l 276.84 671.28 l 276.96 671.52 l 277.2 671.64 l 278.76 671.64 m 279 671.52 l 279.12 671.28 l 279 671.04 l 278.76 670.92 l 278.4 671.04 l 278.4 671.52 l 278.76 671.64 l 280.2 671.64 m 280.44 671.52 l 280.56 671.28 l 280.44 671.04 l 280.2 670.92 l 279.96 671.04 l 279.84 671.28 l 279.96 671.52 l 280.2 671.64 l 281.76 671.64 m 282 671.52 l 282.12 671.28 l 282 671.04 l 281.76 670.92 l 281.4 671.04 l 281.4 671.52 l 281.76 671.64 l 283.2 671.64 m 283.44 671.52 l 283.56 671.28 l 283.44 671.04 l 283.2 670.92 l 282.96 671.04 l 282.84 671.28 l 282.96 671.52 l 283.2 671.64 l 284.76 671.64 m 285 671.52 l 285.12 671.28 l 285 671.04 l 284.76 670.92 l 284.4 671.04 l 284.4 671.52 l 284.76 671.64 l 286.2 671.64 m 286.44 671.52 l 286.56 671.28 l 286.44 671.04 l 286.2 670.92 l 285.96 671.04 l 285.84 671.28 l 285.96 671.52 l 286.2 671.64 l 287.76 671.64 m 288 671.52 l 288.12 671.28 l 288 671.04 l 287.76 670.92 l 287.4 671.04 l 287.4 671.52 l 287.76 671.64 l 289.2 671.64 m 289.44 671.52 l 289.56 671.28 l 289.44 671.04 l 289.2 670.92 l 288.96 671.04 l 288.84 671.28 l 288.96 671.52 l 289.2 671.64 l 290.76 671.64 m 291 671.52 l 291.12 671.28 l 291 671.04 l 290.76 670.92 l 290.4 671.04 l 290.4 671.52 l 290.76 671.64 l 292.2 671.64 m 292.44 671.52 l 292.56 671.28 l 292.44 671.04 l 292.2 670.92 l 291.96 671.04 l 291.84 671.28 l 291.96 671.52 l 292.2 671.64 l 293.76 671.64 m 294 671.52 l 294.12 671.28 l 294 671.04 l 293.76 670.92 l 293.52 671.04 l 293.4 671.28 l 293.52 671.52 l 293.76 671.64 l 295.2 671.64 m 295.44 671.52 l 295.56 671.28 l 295.44 670.92 l 294.96 670.92 l 294.84 671.28 l 294.96 671.52 l 295.2 671.64 l 296.76 671.64 m 297 671.52 l 297.12 671.28 l 297 670.92 l 296.52 670.92 l 296.4 671.28 l 296.52 671.52 l 296.76 671.64 l 236.16 668.28 m 230.16 671.28 l 236.16 674.28 l 236.16 668.28 l 297 674.28 m 303 671.28 l 297 668.28 l 297 674.28 l h f 283.92 614.64 m 284.16 614.52 l 284.28 614.28 l 284.16 613.92 l 283.68 613.92 l 283.56 614.28 l 283.68 614.52 l 283.92 614.64 l 285.48 614.64 m 285.72 614.52 l 285.84 614.28 l 285.72 613.92 l 285.48 613.8 l 285.24 613.92 l 285.12 614.28 l 285.24 614.52 l 285.48 614.64 l 286.92 614.64 m 287.16 614.52 l 287.28 614.16 l 287.16 613.92 l 286.92 613.8 l 286.68 613.92 l 286.56 614.16 l 286.68 614.52 l 286.92 614.64 l 288.48 614.52 m 288.72 614.4 l 288.84 614.16 l 288.72 613.92 l 288.48 613.8 l 288.24 613.92 l 288.12 614.16 l 288.24 614.4 l 288.48 614.52 l 289.92 614.52 m 290.16 614.4 l 290.28 614.16 l 290.16 613.92 l 289.92 613.8 l 289.68 613.92 l 289.56 614.16 l 289.68 614.4 l 289.92 614.52 l 291.48 614.52 m 291.72 614.4 l 291.84 614.16 l 291.72 613.92 l 291.48 613.8 l 291.24 613.92 l 291.12 614.16 l 291.24 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h f endstream endobj 30 0 obj 26572 endobj 28 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 19 0 R /F2 21 0 R /F3 24 0 R >> /ProcSet 2 0 R >> /Contents 29 0 R >> endobj 34 0 obj << /Length 35 0 R >> stream BT 518.28 59.4 TD 0 0 0 rg /F0 9.96 Tf 0.06 Tc 0 Tw (5) Tj 5.04 0 TD 0 Tc 0.03 Tw ( ) Tj -439.92 -11.52 TD ( ) Tj -11.4 711.36 TD /F0 12 Tf 0 Tw ( ) Tj 0 -12 TD /F0 9.96 Tf 0.03 Tw ( ) Tj 0 -13.32 TD /F0 12 Tf 0 Tw (2.1) Tj 15 0 TD /F4 12 Tf 0.024 Tw ( ) Tj 10.56 0 TD /F0 12 Tf -0.006 Tc 0 Tw (Agents) Tj 33.96 0 TD 0 Tc ( ) Tj -17.52 -12 TD /F0 9.96 Tf 0.03 Tw ( ) Tj -42 -13.32 TD /F0 12 Tf -0.0094 Tc 0.4094 Tw (The agents are 40) Tj 86.04 0 TD 0 Tc 0 Tw ( ) Tj 3.36 0 TD 0.0008 Tc 0.3592 Tw (units wide, have an on/off sensor at their center, and can only move left or ) Tj -89.4 -13.8 TD 0.0011 Tc 0.8665 Tw (right by controlling the output of their left and right motor nodes \(see Fig) Tj 362.88 0 TD -0.028 Tc 0 Tw (ure) Tj 15.24 0 TD 0 Tc ( ) Tj 3.84 0 TD -0.007 Tc 0.907 Tw (1\). Agents are) Tj 0 Tc 0 Tw ( ) Tj -381.96 -13.8 TD 0.0013 Tc 2.0387 Tw (controlled by a CTRNN consisting of 3 fully) Tj 228.96 0 TD -0.036 Tc 0 Tw (-) Tj 4.08 0 TD 0 Tc 2.0395 Tw (connected nodes with self) Tj 130.44 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.0069 Tc 2.0469 Tw (connections. Th) Tj 78.6 0 TD -0.048 Tc 0.048 Tw (e ) Tj -446.04 -13.8 TD -0.0021 Tc 0.0021 Tw (time evolution of the node activation follows:) Tj 219.36 0 TD 0 Tc 0 Tw ( ) Tj -207.96 -12 TD /F0 9.96 Tf 0.03 Tw ( ) Tj 146.76 -25.2 TD /F5 18.0206 Tf -0.0087 Tc 0 Tw (\345) Tj 5.16 -8.76 TD /F5 7.008 Tf -0.0074 Tc (=) Tj 58.92 11.52 TD /F5 12.0137 Tf 0.0045 Tc (+) Tj -73.32 0 TD (+) Tj -20.16 0 TD (-) Tj -9.84 0 TD (=) Tj 43.2 12.24 TD /F2 7.008 Tf 0.0057 Tc (N) Tj -1.44 -23.76 TD -0.0282 Tc (j) Tj 82.2 8.52 TD (i) Tj -31.2 0 TD (j) Tj -16.8 0 TD (j) Tj -12.6 0 TD (ji) Tj -39.6 0 TD (i) Tj -30.96 0 TD (i) Tj -10.08 0 TD (i) Tj 130.08 3 TD /F2 12.0137 Tf -0.0237 Tc (SI) Tj -27.36 0 TD -0.0541 Tc (y) Tj -16.32 0 TD 0.0067 Tc (z) Tj -15.12 0 TD 0.0269 Tc (w) Tj -36.12 0 TD -0.0541 Tc (y) Tj -30.84 0 TD (y) Tj 60.96 -11.52 TD /F0 7.008 Tf -0.024 Tc (1) Tj 48.84 11.52 TD /F0 12.0137 Tf -0.0406 Tc (\)) Tj -16.8 0 TD (\() Tj -92.16 0.6 TD /F6 12.0137 Tf (&) Tj -12.12 -0.6 TD /F7 12.0137 Tf 0.006 Tc (t) Tj 154.56 0 TD /F0 12 Tf 0 Tc ( ) Tj 3 0 TD (, ) Tj 6 0 TD ( ) Tj 1.8 0 TD ( ) Tj 6 0 TD ( ) Tj 96.24 -0.72 TD /F0 12.348 Tf -0.0319 Tc (\)) Tj -38.4 0 TD -0.054 Tc (1) Tj -6.6 0 TD 0.0677 Tc (/\() Tj -6.72 0 TD -0.054 Tc (1) Tj -14.64 0 TD -0.0319 Tc (\)) Tj -10.92 0 TD (\() Tj 73.92 4.2 TD /F2 4.41 Tf -0.026 Tc (i) Tj -2.64 1.44 TD /F2 6.174 Tf 0.033 Tc (b) Tj -6.48 0 TD 0.0187 Tc (x) Tj -68.04 -8.76 TD -0.0364 Tc (i) Tj 57.96 3.12 TD /F2 12.348 Tf 0.0375 Tc (e) Tj -49.68 0 TD (x) Tj -12.96 0 TD -0.0034 Tc (z) Tj 75.84 5.64 TD /F5 6.174 Tf -0.0295 Tc (-) Tj -7.32 0 TD (-) Tj ET q 402.96 629.28 6.84 15.12 re h W n BT 402.96 632.04 TD /F5 12.348 Tf -0.0591 Tc (+) Tj ET Q q 374.52 629.28 6.84 15.12 re h W n BT 374.52 632.04 TD /F5 12.348 Tf -0.0591 Tc (=) Tj ET Q BT 439.56 632.76 TD /F0 12 Tf 0 Tc ( ) Tj 34.32 0 TD ( ) Tj 35.4 0 TD -0.024 Tc (\(1\)) Tj 14.04 0 TD 0 Tc ( ) Tj -451.32 -25.8 TD ( ) Tj 0 -13.8 TD -0.0103 Tc 0.8503 Tw (In this equation) Tj 0 Tc 0 Tw ( ) Tj 80.04 0 TD /F2 12 Tf -0.048 Tc (y) Tj 5.28 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.84 0 TD -0.0139 Tc 0.8299 Tw (represents the cell potential of node) Tj 0 Tc 0 Tw ( ) Tj 178.44 0 TD /F2 12 Tf 0.024 Tc (i) Tj 3.36 0 TD /F0 12 Tf 0 Tc (, ) Tj 6.84 0 TD /F2 12 Tf 0.012 Tc (z) Tj 4.68 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.84 0 TD -0.0153 Tc 0.8553 Tw (is the firing rate as calculated by) Tj 0 Tc -0.12 Tw ( ) Tj -290.76 -13.8 TD 0.0018 Tc 1.1982 Tw (the standard sigmoid function,) Tj 0 Tc 0 Tw ( ) Tj 153.84 0 TD /F2 12 Tf 0.024 Tc (t) Tj 4.32 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 4.2 0 TD 0.0015 Tc 1.1985 Tw (\(range [1, 100]\) is its time constant,) Tj 0 Tc 0 Tw ( ) Tj 182.76 0 TD /F2 12 Tf (b) Tj 6 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 4.2 0 TD -0.048 Tc 1.248 Tw (\(range ) Tj 1.164 Tc 0 Tw ([) Tj 38.64 0 TD -0.036 Tc (-) Tj 3.96 0 TD -0.0105 Tc 1.2105 Tw (3, 3]\) is a) Tj 0 Tc -0.12 Tw ( ) Tj -402.48 -13.8 TD -0.008 Tc 1.328 Tw (bias term, and) Tj 0 Tc 0 Tw ( ) Tj 74.52 0 TD /F2 12 Tf 0.036 Tc (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.0449 Tc (ji) Tj 4.56 0 TD /F0 8.04 Tf 0 Tc 0.03 Tw ( ) Tj 3.24 1.56 TD /F0 12 Tf -0.008 Tc 1.328 Tw (\(range ) Tj 1.284 Tc 0 Tw ([) Tj 39 0 TD -0.036 Tc (-) Tj 3.96 0 TD 0 Tc (8,) Tj 9 0 TD ( ) Tj 4.32 0 TD -0.0145 Tc 1.3478 Tw (8]\) is the strength of the connection from the neuron) Tj 262.32 0 TD /F2 12 Tf 0 Tc 0 Tw ( ) Tj 4.32 0 TD 0.024 Tc (j) Tj 3.36 0 TD /F0 12 Tf 0 Tc ( ) Tj 4.32 0 TD 0.012 Tc (to) Tj 9.36 0 TD /F2 12 Tf 0 Tc ( ) Tj 4.32 0 TD 0.024 Tc (i) Tj 3.36 0 TD /F0 12 Tf 0 Tc (. ) Tj 7.32 0 TD /F2 12 Tf -0.036 Tc (I) Tj 3.84 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj -451.32 -13.8 TD 0 Tc 0.0996 Tw (represents the sensory input to node ) Tj 176.04 0 TD /F2 12 Tf -0.036 Tc 0 Tw (I) Tj 3.96 0 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD -0.016 Tc 0.016 Tw (and ) Tj 20.4 0 TD /F2 12 Tf 0 Tc 0 Tw (S) Tj 6 0 TD /F0 12 Tf ( ) Tj 3.12 0 TD -0.0032 Tc 0.1099 Tw (is the sensor gain. The total number of nodes ) Tj 219.6 0 TD /F2 12 Tf 0.036 Tc 0 Tw (N) Tj 8.04 0 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD 0.024 Tc (i) Tj 3.36 0 TD -0.108 Tc -0.012 Tw (s ) Tj -446.76 -13.8 TD 0.0013 Tc 1.5587 Tw (set to 3; there are no hidden nodes \(all nodes receive sensory input\). The sensory input is) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0124 Tc 0.1324 Tw (calculated by multiplying 1/0 \(on/off\) by an sensor gain parameter ) Tj 322.56 0 TD /F2 12 Tf 0 Tc 0 Tw (S) Tj 6 0 TD /F0 12 Tf ( ) Tj 3.12 0 TD -0.012 Tc 0.108 Tw (\(range [1, 100]\), and this ) Tj -331.68 -13.8 TD 0.0056 Tc 1.2244 Tw (is applied to all nodes. There is one node, which only receives in) Tj 325.68 0 TD 0.0096 Tc 1.1904 Tw (put and does not produce) Tj 0 Tc 0 Tw ( ) Tj -325.68 -13.8 TD 0.0056 Tc 2.0436 Tw (motor output and two actuator nodes for controlling movement; one for leftward and the) Tj 0 Tc 0.12 Tw ( ) Tj 0 -13.8 TD 0.0045 Tc 0.4847 Tw (other for rightward velocity. Each velocity is calculated by mapping the actuator output onto) Tj 0 Tc -0.12 Tw ( ) Tj T* -0.0195 Tc 1.6995 Tw (the range ) Tj 1.644 Tc 0 Tw ([) Tj 54.6 0 TD -0.036 Tc (-) Tj 3.96 0 TD -0.0108 Tc 1.7058 Tw (1, 1] and then multiplying it by an ou) Tj 192.24 0 TD -0.0049 Tc 1.6849 Tw (tput gain parameter \(range [1, 50]\). The) Tj 0 Tc -0.12 Tw ( ) Tj -250.8 -13.8 TD -0.0075 Tc 0.2635 Tw (overall agent velocity is calculated as the difference between the left and right velocities. The ) Tj 0 -13.8 TD -0.0012 Tc 4.223 Tw (time evolution of the simulation environment and each agent\222s CTRNN controller is) Tj 0 Tc 0 Tw ( ) Tj T* -0 Tc 0 Tw (calculated by using Euler integrati) Tj 164.64 0 TD -0.0023 Tc 0.0023 Tw (on with a time step of 0.1. ) Tj 128.4 0 TD 0 Tc 0 Tw ( ) Tj -293.04 -13.8 TD ( ) Tj 0 -13.8 TD -0.0041 Tc 2.0987 Tw (Similar settings have already been successfully used by Iizuka and Di Paolo) Tj 0 Tc 0 Tw ( ) Tj 392.76 0 TD -0.012 Tc (\(2007\)) Tj 31.92 0 TD -0.015 Tc 2.055 Tw (. The) Tj 0 Tc 0 Tw ( ) Tj -424.68 -13.8 TD 0.0069 Tc 0.132 Tw (main differences are that \(i\) the agents of the current study only have 3 nodes, \(ii\) the input is ) Tj 0 -13.8 TD -0 Tc 1.3543 Tw (fed to all nodes instead of one dedicated) Tj 0 Tc 0 Tw ( ) Tj 206.76 0 TD 0 Tc 1.3644 Tw (sensory node, \(iii\) and each actuator node has its) Tj 0 Tc 0 Tw ( ) Tj -206.76 -13.8 TD -0.0021 Tc 0.1301 Tw (own gain parameter. The first difference was chosen to further minimize the conditions of the ) Tj 0 -13.8 TD -0.0034 Tc 2.6434 Tw (model and facilitate analysis; differences \(ii\) and \(iii\) were implemented to increase the) Tj 0 Tc 0 Tw ( ) Tj T* -0.0092 Tc 0.0092 Tw (evolvability of the ) Tj 90.84 0 TD 0.0096 Tc 0 Tw (solutions.) Tj 46.44 0 TD 0 Tc ( ) Tj -137.28 -13.8 TD ( ) Tj 0 -13.8 TD (2.2) Tj 15 0 TD /F4 12 Tf 0.024 Tw ( ) Tj 10.56 0 TD /F0 12 Tf -0.0063 Tc 0.1263 Tw (Evolutionary algorithm) Tj 112.32 0 TD 0 Tc 0 Tw ( ) Tj -137.88 -13.8 TD ( ) Tj 0 -13.8 TD -0.02 Tc 1.46 Tw (The ) Tj 1.392 Tc 0 Tw (a) Tj 28.44 0 TD -0.018 Tc 1.458 Tw (gents are) Tj 0 Tc 0 Tw ( ) Tj 48.72 0 TD -0.0133 Tc (optimized) Tj 48 0 TD 0 Tc ( ) Tj 4.44 0 TD -0.0129 Tc 1.4748 Tw (by using a simple genetic algorithm \(GA\) which is based on the) Tj 321.72 0 TD 0 Tc 0 Tw ( ) Tj -451.32 -13.8 TD 0.0025 Tc 3.1175 Tw (microbial GA, a steady) Tj 120.48 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.006 Tc 3.126 Tw (state GA with tournament selection) Tj 0 Tc 0 Tw ( ) Tj 188.4 0 TD -0.009 Tc 3.129 Tw (\(Harvey 2001\)) Tj 73.32 0 TD -0.0084 Tc 3.1284 Tw (. Until some) Tj 0 Tc 0 Tw ( ) Tj -386.16 -13.8 TD -0.001 Tc 0.961 Tw (termination criterion is reached, two members of the popul) Tj 289.92 0 TD -0.0013 Tc 0.9613 Tw (ation are chosen at random, both) Tj 0 Tc 0.12 Tw ( ) Tj -289.92 -13.8 TD -0.0078 Tc 0.7278 Tw (have their fitness evaluated, and while the \221winner\222 of the tournament remains unchanged in) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD 0.001 Tc 2.6647 Tw (the population, the \221loser\222 is replaced by a slightly mutated copy of the \221winner\222. Each) Tj 0 Tc 0.12 Tw ( ) Tj T* 0.0019 Tc 1.9181 Tw (member is a clonal pair) Tj 120.36 0 TD 0 Tc 0 Tw ( ) Tj 4.92 0 TD -0.012 Tc 1.932 Tw (of agents) Tj 45.48 0 TD -0.0051 Tc 1.9251 Tw (. We defi) Tj 48.12 0 TD 0.0013 Tc 1.9187 Tw (ne a generation as the number of tournaments) Tj 0 Tc 0 Tw ( ) Tj -218.88 -13.8 TD 0.0076 Tc -0 Tw (required to generate a number of offspring equal to the population size. The population size is ) Tj 0 -13.8 TD -0.0022 Tc 0.0022 Tw (40 and the run terminates at 5000 generations.) Tj 221.88 0 TD 0 Tc 0 Tw ( ) Tj -221.88 -13.8 TD ( ) Tj 0 -13.8 TD -0.0162 Tc 1.2522 Tw (All CTRNN parameters and gains are genetically encoded by a real) Tj 335.52 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.024 Tc (va) Tj 11.28 0 TD -0.0014 Tc 1.2014 Tw (lued vector which is) Tj 0 Tc 0 Tw ( ) Tj -350.76 -13.8 TD -0.0117 Tc 2.0617 Tw (initialized randomly. The mutation operator changes each gene by a random value drawn) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0.0143 Tc 0.3457 Tw (from a Gaussian distribution \() Tj 145.44 0 TD /F2 12 Tf 0.048 Tc 0 Tw (\265) Tj 6 0 TD /F0 12 Tf 0 Tc ( ) Tj 3.36 0 TD -0.008 Tc 0.188 Tw (= 0; ) Tj 22.8 0 TD /F2 12 Tf 0.012 Tc 0 Tw (s) Tj 5.88 5.52 TD /F2 8.04 Tf 0.06 Tc (2) Tj 4.08 -5.52 TD /F0 12 Tf 0 Tc ( ) Tj 3.36 0 TD -0.0021 Tc 0.3488 Tw (= 0.05\) with reflection at the gene boundaries. Before ) Tj -190.92 -13.8 TD -0.001 Tc 0.886 Tw (evaluation, each gene is decoded linearly to the corre) Tj 261.96 0 TD 0.0022 Tc 0.8618 Tw (sponding range \(except gains and time) Tj 0 Tc -0.12 Tw ( ) Tj -261.96 -13.8 TD -0.0041 Tc 0.0041 Tw (constants which are exponentially scaled\). ) Tj 205.92 0 TD 0 Tc 0 Tw ( ) Tj -205.92 -13.8 TD ( ) Tj ET endstream endobj 35 0 obj 11488 endobj 31 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font 42 0 R /ProcSet 2 0 R >> /Contents 34 0 R >> endobj 42 0 obj << /F0 6 0 R /F2 21 0 R /F4 32 0 R /F5 36 0 R /F6 38 0 R /F7 40 0 R >> endobj 44 0 obj << /Length 45 0 R >> stream BT 518.28 59.4 TD 0 0 0 rg /F0 9.96 Tf 0.06 Tc 0 Tw (6) Tj 5.04 0 TD 0 Tc 0.03 Tw ( ) Tj -439.92 -11.52 TD ( ) Tj -11.4 711.36 TD /F0 12 Tf -0.0072 Tc 0.8712 Tw (During each fitness evaluation an agent is tested in 15 trials runs; to increase the robustness) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0057 Tc 1.4457 Tw (of the evolving solutions to noise and variations in initial conditions only) Tj 0 Tc -0.24 Tw ( ) Tj 371.04 0 TD 0.006 Tc 1.434 Tw (the lowest score) Tj 0 Tc 0.12 Tw ( ) Tj -371.04 -13.8 TD 0.0008 Tc 0.4992 Tw (achieved in any of the trials is chosen as the overall score. Each trial run consists of 50 units) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0075 Tc 2.4 Tw (of time \(500 Euler time steps\). At the start of each trial agents have their internal node) Tj 0 Tc 0 Tw ( ) Tj T* -0 Tc 2.2634 Tw (activations set to small random values drawn from) Tj 0 Tc 0 Tw ( ) Tj 263.4 0 TD -0.0055 Tc 2.2855 Tw (a standard Gaussian distribution. The) Tj 0 Tc -0.12 Tw ( ) Tj -263.4 -13.8 TD -0.002 Tc 2.0697 Tw (initial distance between the agents varies; agent \221down\222 always gets placed at position 0,) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0106 Tc 2.1706 Tw (while agent \221up\222 starts at a different position for each trial \(15 different positions evenly) Tj 0 Tc -0.36 Tw ( ) Tj T* -0.0057 Tc 0.0057 Tw (distributed across range [) Tj 120.96 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD 0 Tc (25, 25) Tj 30 0 TD 0.016 Tc -0.016 Tw (]\). ) Tj 14.04 0 TD 0 Tc 0 Tw ( ) Tj -168.96 -13.8 TD ( ) Tj 0 -13.8 TD -0.0105 Tc 2.5305 Tw (The fitness score of a trial run is calculated on the basis of a single factor, namely the) Tj 0 Tc 0.12 Tw ( ) Tj T* 0.0013 Tc 0.1258 Tw (absolute value of the final crossing position of the two agents divided by a factor of 10. ) Tj 424.32 0 TD 0 Tc 0 Tw (Thus, ) Tj -424.32 -13.8 TD -0.0041 Tc 0.3532 Tw (in contrast to the work done by Iizuka and Di Paolo ) Tj 255 0 TD -0.012 Tc 0 Tw (\(2007\)) Tj 31.92 0 TD 0.01 Tc 0.35 Tw (, these) Tj 30.96 0 TD 0 Tc 0 Tw ( ) Tj 3.36 0 TD -0 Tc 0.288 Tw (agents were not evolved to ) Tj -321.24 -13.8 TD -0.0087 Tc 2.0487 Tw (break off the interaction) Tj 0 Tc 0 Tw ( ) Tj 126.6 0 TD -0.012 Tc 0.012 Tw (pattern ) Tj 38.28 0 TD -0.0177 Tc 2.0748 Tw (when detecting a lack of social contingency. In) Tj 239.76 0 TD -0.012 Tc 0 Tw (stead) Tj 24.6 0 TD 0.016 Tc 2.024 Tw (, we) Tj 0 Tc 0.12 Tw ( ) Tj -429.24 -13.8 TD -0.0034 Tc 1.3234 Tw (aimed to) Tj 0 Tc 0 Tw ( ) Tj 47.4 0 TD 0.0046 Tc 1.3263 Tw (generate a simulation model that under normal circumstances results in highly fit) Tj 0 Tc 0 Tw ( ) Tj -47.4 -13.8 TD -0.0014 Tc 0.0014 Tw (coordination behavior. Presumably, such behavi) Tj 231.24 0 TD -0 Tc 0.0267 Tw (or should be more robust when faced with the ) Tj -231.24 -13.8 TD -0.0024 Tc 0.0024 Tw (\221playback\222 condition. ) Tj 105.6 0 TD 0 Tc 0 Tw ( ) Tj -105.6 -13.8 TD ( ) Tj 0 -14.04 TD /F1 12 Tf -0.0015 Tc 0.0015 Tw (3 Results) Tj 52.32 0 TD 0 Tc 0 Tw ( ) Tj -52.32 -13.56 TD /F0 12 Tf ( ) Tj 0 -13.8 TD -0.0012 Tc 0.1878 Tw (The GA was run 4 times. The fittest agent, with a score of 244.8, was produced during the 4) Tj 445.08 5.52 TD /F0 8.04 Tf 0.0524 Tc 0 Tw (th) Tj 6.24 -5.52 TD /F0 12 Tf 0 Tc ( ) Tj -451.32 -13.8 TD -0.0018 Tc 0.8854 Tw (run in generation 3477. This solution was then tested extensively; agent \221down\222) Tj 0 Tc 0 Tw ( ) Tj 395.4 0 TD 0.0107 Tc 0.8293 Tw (was always) Tj 0 Tc 0 Tw ( ) Tj -395.4 -13.8 TD -0.0095 Tc 0.2284 Tw (placed at position 0, while agent \221up\222 starts at a different position for each trial \(101 positions ) Tj 0 -13.8 TD -0.006 Tc 1.086 Tw (evenly distributed across range ) Tj 1.044 Tc 0 Tw ([) Tj 160.2 0 TD -0.036 Tc (-) Tj 3.96 0 TD -0.012 Tc 1.092 Tw (50, 50]\). Each trial is repeated 150 times. The mean score) Tj 0 Tc 0 Tw ( ) Tj -164.16 -13.8 TD 0.0045 Tc 2.0355 Tw (across this range of initial conditions is plotted ) Tj 2.064 Tc 0 Tw (i) Tj 247.2 0 TD 0.048 Tc 1.992 Tw (n Fig) Tj 27 0 TD -0.028 Tc 0 Tw (ure) Tj 15.36 0 TD 0 Tc ( ) Tj 5.04 0 TD 2.04 Tw (2 ) Tj 2.004 Tc 0 Tw (\() Tj 15 0 TD 0.021 Tc (left) Tj 16.08 0 TD -0.018 Tc 0.018 Tw (\). ) Tj 12 0 TD -0.012 Tc 0 Tw (T) Tj 7.32 0 TD 0.0042 Tc 2.0658 Tw (he agents are able to) Tj 0 Tc 0 Tw ( ) Tj -345 -13.8 TD -0.0057 Tc 1.8149 Tw (generalize their behavior well beyond the range that they were originally evolved to cope) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0112 Tc 1.0842 Tw (with. On average the best initial position for agent \221up\222 turned out to be at 11 \(mean score:) Tj 0 Tc 0 Tw ( ) Tj T* -0.0051 Tc (292.9\).) Tj 33.96 0 TD 0 Tc ( ) Tj -33.96 -13.8 TD ( ) Tj 0 -13.8 TD ( ) Tj ET q 85.68 263.64 217.44 106.2 re h W n 1 1 1 rg 85.68 262.8 218.28 107.04 re f* Q 1 1 1 rg 130.56 298.8 m 130.56 362.04 l 282.48 362.04 l 282.48 298.8 l h f* 0.12 w 1 J 1 j 1 1 1 RG 130.56 298.8 m 130.56 362.04 l 282.48 362.04 l 282.48 298.8 l 130.56 298.8 l S 130.56 298.68 0.24 0.24 re f 0.298 0.298 0.298 RG 130.56 298.8 m 282.48 298.8 l S 0.302 0.302 0.302 rg 282.48 298.68 0.24 0.24 re f 130.56 298.8 m 130.56 362.04 l S 130.56 361.92 0.24 0.24 re f 137.28 298.8 m 137.28 295.92 l S 137.28 295.8 0.24 0.24 re f BT 0.9942 0 0 1 130.56 285 Tm /F4 8.7559 Tf 0.0471 Tc (-50) Tj ET 171.48 298.8 m 171.48 295.92 l S 171.48 295.8 0.24 0.24 re f BT 0.9942 0 0 1 164.64 285 Tm (-25) Tj ET 206.52 298.8 m 206.52 295.92 l S 206.52 295.8 0.24 0.24 re f BT 0.9942 0 0 1 204.6 285 Tm -0.0405 Tc (0) Tj ET 240.6 298.8 m 240.6 295.92 l S 240.6 295.8 0.24 0.24 re f BT 0.9942 0 0 1 235.8 285 Tm (25) Tj ET 274.68 298.8 m 274.68 295.92 l S 274.68 295.8 0.24 0.24 re f BT 0.9942 0 0 1 269.88 285 Tm (50) Tj ET 130.56 298.8 m 126.6 298.8 l S 126.6 298.68 0.24 0.24 re f BT 0.9942 0 0 1 118.8 296.76 Tm (0) Tj ET 130.56 315.36 m 126.6 315.36 l S 126.6 315.24 0.24 0.24 re f BT 0.9942 0 0 1 109.08 313.32 Tm -0 Tc (100) Tj ET 130.56 330.96 m 126.6 330.96 l S 126.6 330.84 0.24 0.24 re f BT 0.9942 0 0 1 109.08 328.8 Tm (200) Tj ET 130.56 346.44 m 126.6 346.44 l S 126.6 346.32 0.24 0.24 re f BT 0.9942 0 0 1 109.08 344.4 Tm (300) Tj ET 130.56 362.04 m 126.6 362.04 l S 126.6 361.92 0.24 0.24 re f BT 0.9942 0 0 1 109.08 360 Tm (400) Tj 0.6 0.6 0.6 RG ET 137.28 345.48 m 137.28 303.72 l S 135.36 345.48 m 138.36 345.48 l S 135.36 303.72 m 138.36 303.72 l S 138.36 345.48 m 138.36 304.68 l S 137.28 345.48 m 139.32 345.48 l S 137.28 304.68 m 139.32 304.68 l S 139.32 345.48 m 139.32 303.72 l S 138.36 345.48 m 141.24 345.48 l S 138.36 303.72 m 141.24 303.72 l S 141.24 348.48 m 141.24 307.56 l S 139.32 348.48 m 142.2 348.48 l S 139.32 307.56 m 142.2 307.56 l S 142.2 348.48 m 142.2 309.48 l S 141.24 348.48 m 144.12 348.48 l S 141.24 309.48 m 144.12 309.48 l S 144.12 348.48 m 144.12 308.52 l S 142.2 348.48 m 145.08 348.48 l S 142.2 308.52 m 145.08 308.52 l S 145.08 348.48 m 145.08 306.6 l S 144.12 348.48 m 147.12 348.48 l S 144.12 306.6 m 147.12 306.6 l S 147.12 347.52 m 147.12 305.64 l S 145.08 347.52 m 148.08 347.52 l S 145.08 305.64 m 148.08 305.64 l S 148.08 350.4 m 148.08 312.48 l S 147.12 350.4 m 149.04 350.4 l S 147.12 312.48 m 149.04 312.48 l S 149.04 350.4 m 149.04 313.44 l S 148.08 350.4 m 150.96 350.4 l S 148.08 313.44 m 150.96 313.44 l S 150.96 350.4 m 150.96 311.52 l S 149.04 350.4 m 151.92 350.4 l S 149.04 311.52 m 151.92 311.52 l S 151.92 348.48 m 151.92 307.56 l S 150.96 348.48 m 153.84 348.48 l S 150.96 307.56 m 153.84 307.56 l S 153.84 352.32 m 153.84 316.32 l S 151.92 352.32 m 154.92 352.32 l S 151.92 316.32 m 154.92 316.32 l S 154.92 350.4 m 154.92 310.44 l S 153.84 350.4 m 155.88 350.4 l S 153.84 310.44 m 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305.76 l S 487.56 299.88 m 490.56 299.88 l S 490.56 305.76 m 490.56 299.88 l S 488.52 305.76 m 491.52 305.76 l S 488.52 299.88 m 491.52 299.88 l S 491.52 304.68 m 491.52 299.88 l S 490.56 304.68 m 492.48 304.68 l S 490.56 299.88 m 492.48 299.88 l S 492.48 305.76 m 492.48 299.88 l S 491.52 305.76 m 494.4 305.76 l S 491.52 299.88 m 494.4 299.88 l S 354.84 301.8 m 364.56 301.8 l 365.64 302.76 l 366.6 301.8 l 388.08 301.8 l 389.04 302.76 l 390 301.8 l 424.2 301.8 l 425.16 302.76 l 426.12 301.8 l 428.04 302.76 l 429 302.76 l 431.04 301.8 l 432 301.8 l 432.96 302.76 l 434.88 301.8 l 435.84 302.76 l 437.76 301.8 l 440.76 301.8 l 441.72 302.76 l 442.68 302.76 l 444.6 301.8 l 445.68 302.76 l 449.52 302.76 l 451.44 301.8 l 452.4 302.76 l 464.16 302.76 l 465.12 301.8 l 466.08 302.76 l 468.12 301.8 l 469.08 302.76 l 492.48 302.76 l S 0 0 0 RG 354.84 301.8 m 364.56 301.8 l 365.64 302.76 l 366.6 301.8 l 388.08 301.8 l 389.04 302.76 l 390 301.8 l 424.2 301.8 l 425.16 302.76 l 426.12 301.8 l 428.04 302.76 l 429 302.76 l 431.04 301.8 l 432 301.8 l 432.96 302.76 l 434.88 301.8 l 435.84 302.76 l 437.76 301.8 l 440.76 301.8 l 441.72 302.76 l 442.68 302.76 l 444.6 301.8 l 445.68 302.76 l 449.52 302.76 l 451.44 301.8 l 452.4 302.76 l 464.16 302.76 l 465.12 301.8 l 466.08 302.76 l 468.12 301.8 l 469.08 302.76 l 492.48 302.76 l S 0 0 0 rg 492.48 302.64 0.24 0.24 re f BT 0.9933 0 0 1 372.48 270.72 Tm /F4 10.7298 Tf -0.3223 Tc (Relati) Tj 0.1543 Tc -0.2372 Tw (ve d) Tj -0.0067 Tc 0 Tw (isplace) Tj -0.3151 Tc (ment) Tj ET BT 0 0.9933 -1 0 315.96 298.92 Tm -0.1197 Tc 0.1559 Tw (Mean fitne) Tj 0.5512 Tc 0 Tw (ss) Tj ET BT 520.92 263.64 TD /F0 12 Tf 0 Tc ( ) Tj 12 0 TD ( ) Tj -460.92 -16.8 TD /F1 12 Tf -0.036 Tc (Fig) Tj 16.56 0 TD -0.016 Tc (ure) Tj 17.4 0 TD 0 Tc ( ) Tj 6.72 0 TD (2.) Tj 9 0 TD /F0 12 Tf ( ) Tj 6.72 0 TD /F2 12 Tf 0.0264 Tc (Left:) Tj 22.68 0 TD /F0 12 Tf 0 Tc ( ) Tj 6.72 0 TD 0 Tc 3.7558 Tw (Mean score achieved by the fittest agent starting from various initial) Tj 0 Tc -0.12 Tw ( ) Tj -85.8 -13.8 TD 0.0037 Tc 2.9962 Tw (positions, with standard deviation.) Tj 0 Tc 0 Tw ( ) Tj 180.12 0 TD /F2 12 Tf 0.02 Tc (Right:) Tj 30.12 0 TD /F0 12 Tf 0 Tc ( ) Tj 6 0 TD 0.0084 Tc 3.0066 Tw (Mean score by the fittest agent but this time) Tj 0 Tc 0 Tw ( ) Tj -216.24 -13.8 TD -0.0033 Tc 0.0033 Tw (interacting with non) Tj 96.6 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.0014 Tc 0.0014 Tw (responsive, recorded movements obtained from the original trials.) Tj 316.32 0 TD 0 Tc 0 Tw ( ) Tj -416.88 -25.8 TD ( ) Tj 0 -13.8 TD 0 Tc 3.2581 Tw (In order to demonstrate the general robustness of the evolved agents under this initial) Tj 0 Tc 0 Tw ( ) Tj T* -0.0087 Tc 0.3387 Tw (condition, we ran another set of trials with agent \221up\222 starting from position 11 while varying ) Tj T* 0.0046 Tc 3.3554 Tw (noise levels. The motor noise was varied while ) Tj 3.384 Tc 0 Tw (t) Tj 258.72 0 TD 0.0015 Tc 3.3825 Tw (he sensor noise remained constant at) Tj 0 Tc 0 Tw ( ) Tj -258.72 -13.8 TD 0 Tc 0.1379 Tw (evolutionary strength \(5%\), and sensor noise was varied while motor noise remained constant ) Tj 0 -13.8 TD -0.036 Tc 0 Tw (\() Tj 3.96 0 TD /F2 12 Tf 0.012 Tc (s) Tj 5.88 5.52 TD /F2 8.04 Tf 0.06 Tc (2) Tj 4.08 -5.52 TD /F0 12 Tf 0 Tc ( ) Tj 3.36 0 TD 0.012 Tc 0.324 Tw (= 0.05\). At each noise level we tested the agents ) Tj 238.92 0 TD 0.0056 Tc 0.3544 Tw (for 150 trials. As shown in Figure) Tj 164.64 0 TD 0 Tc 0 Tw ( ) Tj 3.36 0 TD 0.0192 Tc 0.1608 Tw (3, the ) Tj -424.2 -13.8 TD 0.0047 Tc 0.4753 Tw (agents are able to cope with a wide range of perturbations. Indeed, their overall performance ) Tj 0 -13.8 TD -0.001 Tc 0.8543 Tw (degrades gracefully until the sensor and motor signals are completely) Tj 340.2 0 TD 0 Tc 0 Tw ( ) Tj 3.84 0 TD -0 Tc 0.8807 Tw (swamped by noise. In) Tj 0 Tc 0.12 Tw ( ) Tj -344.04 -13.8 TD -0.0053 Tc 1.8145 Tw (the case of sensor noise, for example, average performance only approaches 0 just before) Tj 0 Tc -0.12 Tw ( ) Tj ET endstream endobj 45 0 obj 37074 endobj 43 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 19 0 R /F2 21 0 R /F4 32 0 R >> /ProcSet 2 0 R >> /Contents 44 0 R >> endobj 48 0 obj << /Length 49 0 R >> stream BT 518.28 59.4 TD 0 0 0 rg /F0 9.96 Tf 0.06 Tc 0 Tw (7) Tj 5.04 0 TD 0 Tc 0.03 Tw ( ) Tj -439.92 -11.52 TD ( ) Tj -11.4 711.36 TD /F0 12 Tf 0 Tc 1.9412 Tw (reaching the 50% mark \(at which point sensory activation becomes completely arbitrary\).) Tj 0 Tc 0.12 Tw ( ) Tj 0 -13.8 TD 0.0035 Tc -0.0035 Tw (This demonstrates that the agents are able to produce hig) Tj 272.88 0 TD -0.0048 Tc 0.0448 Tw (hly robust coordination behavior.) 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137.4 673.92 l S 138.36 698.28 m 138.36 672.96 l S 137.4 698.28 m 140.28 698.28 l S 137.4 672.96 m 140.28 672.96 l S 141.24 695.4 m 141.24 679.8 l S 140.28 695.4 m 143.16 695.4 l S 140.28 679.8 m 143.16 679.8 l S 144.24 696.36 m 144.24 672 l S 143.16 696.36 m 146.16 696.36 l S 143.16 672 m 146.16 672 l S 147.12 695.4 m 147.12 675 l S 146.16 695.4 m 149.04 695.4 l S 146.16 675 m 149.04 675 l S 150 694.44 m 150 675 l S 149.04 694.44 m 151.92 694.44 l S 149.04 675 m 151.92 675 l S 153 694.44 m 153 666.24 l S 151.92 694.44 m 154.92 694.44 l S 151.92 666.24 m 154.92 666.24 l S 155.88 692.4 m 155.88 672 l S 154.92 692.4 m 157.8 692.4 l S 154.92 672 m 157.8 672 l S 158.76 692.4 m 158.76 671.04 l S 157.8 692.4 m 159.72 692.4 l S 157.8 671.04 m 159.72 671.04 l S 161.76 691.44 m 161.76 664.2 l S 159.72 691.44 m 162.72 691.44 l S 159.72 664.2 m 162.72 664.2 l S 164.64 692.4 m 164.64 662.28 l S 162.72 692.4 m 165.6 692.4 l S 162.72 662.28 m 165.6 662.28 l S 167.52 689.52 m 167.52 660.36 l S 165.6 689.52 m 168.48 689.52 l S 165.6 660.36 m 168.48 660.36 l S 170.52 689.52 m 170.52 656.52 l S 168.48 689.52 m 171.48 689.52 l S 168.48 656.52 m 171.48 656.52 l S 173.4 686.64 m 173.4 654.48 l S 171.48 686.64 m 174.36 686.64 l S 171.48 654.48 m 174.36 654.48 l S 176.28 685.68 m 176.28 653.52 l S 174.36 685.68 m 177.24 685.68 l S 174.36 653.52 m 177.24 653.52 l S 179.28 680.76 m 179.28 647.76 l S 177.24 680.76 m 180.24 680.76 l S 177.24 647.76 m 180.24 647.76 l S 182.16 679.8 m 182.16 646.68 l S 180.24 679.8 m 183.12 679.8 l S 180.24 646.68 m 183.12 646.68 l S 184.08 673.92 m 184.08 642.84 l S 183.12 673.92 m 186 673.92 l S 183.12 642.84 m 186 642.84 l S 187.08 672.96 m 187.08 642.84 l S 186 672.96 m 189 672.96 l S 186 642.84 m 189 642.84 l S q 189.84 641.88 0.24 26.28 re h W n 189.96 668.16 m 189.96 641.88 l S Q 189 668.16 m 191.88 668.16 l S 192.84 672 m 192.84 643.8 l S 191.88 672 m 194.76 672 l S 191.88 643.8 m 194.76 643.8 l S q 195.72 641.88 0.24 26.28 re h W n 195.84 668.16 m 195.84 641.88 l S Q 194.76 668.16 m 197.76 668.16 l S q 198.6 641.88 0.24 23.4 re h W n 198.72 665.16 m 198.72 641.88 l S Q 197.76 665.16 m 200.64 665.16 l S q 201.6 641.88 0.24 22.44 re h W n 201.6 664.2 m 201.6 641.88 l S Q 200.64 664.2 m 203.52 664.2 l S q 204.48 641.88 0.24 20.52 re h W n 204.6 662.28 m 204.6 641.88 l S Q 203.52 662.28 m 206.52 662.28 l S q 207.36 641.88 0.24 16.56 re h W n 207.48 658.44 m 207.48 641.88 l S Q 206.52 658.44 m 208.44 658.44 l S q 210.36 641.88 0.24 14.64 re h W n 210.36 656.52 m 210.36 641.88 l S Q 208.44 656.52 m 211.32 656.52 l S q 213.24 641.88 0.24 14.64 re h W n 213.36 656.52 m 213.36 641.88 l S Q 211.32 656.52 m 214.32 656.52 l S q 216.12 641.88 0.24 15.6 re h W n 216.24 657.48 m 216.24 641.88 l S Q 214.32 657.48 m 217.2 657.48 l S q 219.12 641.88 0.24 11.76 re h W n 219.12 653.52 m 219.12 641.88 l S Q 217.2 653.52 m 220.08 653.52 l S q 222 641.88 0.24 14.64 re h W n 222.12 656.52 m 222.12 641.88 l S Q 220.08 656.52 m 223.08 656.52 l S q 224.88 641.88 0.24 13.68 re h W n 225 655.44 m 225 641.88 l S Q 223.08 655.44 m 225.96 655.44 l S q 227.88 641.88 0.24 11.76 re h W n 227.88 653.52 m 227.88 641.88 l S Q 225.96 653.52 m 228.84 653.52 l S q 230.76 641.88 0.24 12.72 re h W n 230.88 654.48 m 230.88 641.88 l S Q 228.84 654.48 m 231.84 654.48 l S q 232.68 641.88 0.24 13.68 re h W n 232.8 655.44 m 232.8 641.88 l S Q 231.84 655.44 m 234.72 655.44 l S 235.68 650.64 m 235.68 642.84 l S 234.72 650.64 m 237.6 650.64 l S 234.72 642.84 m 237.6 642.84 l S q 238.56 641.88 0.24 10.8 re h W n 238.68 652.56 m 238.68 641.88 l S Q 237.6 652.56 m 240.6 652.56 l S q 241.44 641.88 0.24 10.8 re h W n 241.56 652.56 m 241.56 641.88 l S Q 240.6 652.56 m 243.48 652.56 l S 244.44 648.72 m 244.44 642.84 l S 243.48 648.72 m 246.36 648.72 l S 243.48 642.84 m 246.36 642.84 l S q 247.32 641.88 0.24 8.76 re h W n 247.44 650.64 m 247.44 641.88 l S Q 246.36 650.64 m 249.36 650.64 l S q 250.2 641.88 0.24 9.72 re h W n 250.32 651.6 m 250.32 641.88 l S Q 249.36 651.6 m 252.24 651.6 l S 253.2 649.68 m 253.2 642.84 l S 252.24 649.68 m 255.24 649.68 l S 252.24 642.84 m 255.24 642.84 l S q 256.08 641.88 0.24 11.76 re h W n 256.2 653.52 m 256.2 641.88 l S Q 255.24 653.52 m 257.16 653.52 l S q 258.96 641.88 0.24 8.76 re h W n 259.08 650.64 m 259.08 641.88 l S Q 257.16 650.64 m 260.04 650.64 l S 261.96 649.68 m 261.96 642.84 l S 260.04 649.68 m 262.92 649.68 l S 260.04 642.84 m 262.92 642.84 l S q 264.84 641.88 0.24 9.72 re h W n 264.96 651.6 m 264.96 641.88 l S Q 262.92 651.6 m 265.92 651.6 l S q 267.72 641.88 0.24 8.76 re h W n 267.84 650.64 m 267.84 641.88 l S Q 265.92 650.64 m 268.8 650.64 l S q 270.72 641.88 0.24 6.84 re h W n 270.72 648.72 m 270.72 641.88 l S Q 268.8 648.72 m 271.68 648.72 l S 273.72 649.68 m 273.72 642.84 l S 271.68 649.68 m 274.68 649.68 l S 271.68 642.84 m 274.68 642.84 l S q 276.6 641.88 0.24 3.96 re h W n 276.6 645.72 m 276.6 641.88 l S Q 274.68 645.72 m 277.56 645.72 l S 133.44 687.6 m 135.36 686.64 l 138.36 685.68 l 141.24 687.6 l 144.24 684.72 l 150 684.72 l 153 680.76 l 155.88 682.68 l 158.76 681.72 l 161.76 677.88 l 164.64 676.92 l 167.52 675 l 170.52 672.96 l 173.4 670.08 l 176.28 669.12 l 179.28 664.2 l 182.16 663.24 l 184.08 658.44 l 187.08 657.48 l 189.96 654.48 l 192.84 657.48 l 195.84 654.48 l 198.72 652.56 l 201.6 652.56 l 204.6 651.6 l 207.48 649.68 l 210.36 648.72 l 213.36 648.72 l 216.24 649.68 l 219.12 647.76 l 222.12 648.72 l 225 647.76 l 232.8 647.76 l 235.68 646.68 l 241.56 646.68 l 244.44 645.72 l 247.44 646.68 l 256.2 646.68 l 259.08 645.72 l 261.96 645.72 l 264.96 646.68 l 267.84 646.68 l 270.72 645.72 l 273.72 646.68 l 276.6 643.8 l S 0 0 0 RG 133.44 687.6 m 135.36 686.64 l 138.36 685.68 l 141.24 687.6 l 144.24 684.72 l 150 684.72 l 153 680.76 l 155.88 682.68 l 158.76 681.72 l 161.76 677.88 l 164.64 676.92 l 167.52 675 l 170.52 672.96 l 173.4 670.08 l 176.28 669.12 l 179.28 664.2 l 182.16 663.24 l 184.08 658.44 l 187.08 657.48 l 189.96 654.48 l 192.84 657.48 l 195.84 654.48 l 198.72 652.56 l 201.6 652.56 l 204.6 651.6 l 207.48 649.68 l 210.36 648.72 l 213.36 648.72 l 216.24 649.68 l 219.12 647.76 l 222.12 648.72 l 225 647.76 l 232.8 647.76 l 235.68 646.68 l 241.56 646.68 l 244.44 645.72 l 247.44 646.68 l 256.2 646.68 l 259.08 645.72 l 261.96 645.72 l 264.96 646.68 l 267.84 646.68 l 270.72 645.72 l 273.72 646.68 l 276.6 643.8 l S 0 0 0 rg 276.6 643.68 0.24 0.24 re f BT 0.9934 0 0 1 165.6 614.76 Tm /F4 10.7017 Tf -0.0753 Tc 0.0597 Tw (Motor noise level) Tj ET BT 0 0.9934 -1 0 101.52 643.8 Tm -0.0937 Tc 0.018 Tw (Mean fitne) Tj 0.4442 Tc 0 Tw (ss) Tj ET BT 300.12 607.68 TD /F0 12 Tf 0 Tc ( ) Tj ET q 306.12 607.68 211.8 106.44 re h W n 1 1 1 rg 306.12 606.84 212.64 107.28 re f* Q 1 1 1 rg 351 642.96 m 351 706.32 l 497.28 706.32 l 497.28 642.96 l h f* 1 1 1 RG 351 642.96 m 351 706.32 l 497.28 706.32 l 497.28 642.96 l 351 642.96 l S 351 642.84 0.24 0.24 re f 0.298 0.298 0.298 RG 351 642.96 m 497.28 642.96 l S 0.302 0.302 0.302 rg 497.28 642.84 0.24 0.24 re f 351 642.96 m 351 706.32 l S 351 706.2 0.24 0.24 re f 351 642.96 m 351 639.96 l S 351 639.84 0.24 0.24 re f BT 0.9929 0 0 1 349.08 629.16 Tm /F4 8.7757 Tf -0.045 Tc (0) Tj ET 377.28 642.96 m 377.28 639.96 l S 377.28 639.84 0.24 0.24 re f BT 0.9929 0 0 1 372.48 629.16 Tm (10) Tj ET 403.68 642.96 m 403.68 639.96 l S 403.68 639.84 0.24 0.24 re f BT 0.9929 0 0 1 398.76 629.16 Tm 0.0759 Tc (20) Tj ET 429.96 642.96 m 429.96 639.96 l S 429.96 639.84 0.24 0.24 re f BT 0.9929 0 0 1 425.16 629.16 Tm -0.045 Tc (30) Tj ET 457.32 642.96 m 457.32 639.96 l S 457.32 639.84 0.24 0.24 re f BT 0.9929 0 0 1 452.4 629.16 Tm 0.0759 Tc (40) Tj ET 483.6 642.96 m 483.6 639.96 l S 483.6 639.84 0.24 0.24 re f BT 0.9929 0 0 1 478.8 629.16 Tm -0.045 Tc (50) Tj ET 351 642.96 m 348.12 642.96 l S 348 642.84 0.24 0.24 re f BT 0.9929 0 0 1 339.24 640.92 Tm (0) Tj ET 351 659.52 m 348.12 659.52 l S 348 659.4 0.24 0.24 re f BT 0.9929 0 0 1 329.52 657.48 Tm -0.0047 Tc (100) Tj ET 351 675.12 m 348.12 675.12 l S 348 675 0.24 0.24 re f BT 0.9929 0 0 1 329.52 673.08 Tm (200) Tj ET 351 690.72 m 348.12 690.72 l S 348 690.6 0.24 0.24 re f BT 0.9929 0 0 1 329.52 688.68 Tm (300) Tj ET 351 706.32 m 348.12 706.32 l S 348 706.2 0.24 0.24 re f BT 0.9929 0 0 1 329.52 704.28 Tm (400) Tj ET q 351 681.72 0.24 13.92 re h W n 0.6 0.6 0.6 RG 351 695.64 m 351 681.96 l S Q q 351 695.4 1.08 0.24 re h W n 0.6 0.6 0.6 RG 351 695.64 m 351.96 695.64 l S Q q 351 681.72 1.08 0.24 re h W n 0.6 0.6 0.6 RG 351 681.96 m 351.96 681.96 l S Q 0.6 0.6 0.6 RG 352.92 696.6 m 352.92 678.96 l S 351.96 696.6 m 354.84 696.6 l S 351.96 678.96 m 354.84 678.96 l S 355.92 696.6 m 355.92 680.04 l S 354.84 696.6 m 356.88 696.6 l S 354.84 680.04 m 356.88 680.04 l S 358.8 696.6 m 358.8 680.04 l S 356.88 696.6 m 359.76 696.6 l S 356.88 680.04 m 359.76 680.04 l S 360.72 699.48 m 360.72 669.24 l S 359.76 699.48 m 362.64 699.48 l S 359.76 669.24 m 362.64 669.24 l S 363.72 698.52 m 363.72 676.08 l S 362.64 698.52 m 365.64 698.52 l S 362.64 676.08 m 365.64 676.08 l S 366.6 698.52 m 366.6 673.2 l S 365.64 698.52 m 367.56 698.52 l S 365.64 673.2 m 367.56 673.2 l S 369.48 698.52 m 369.48 674.16 l S 367.56 698.52 m 370.44 698.52 l S 367.56 674.16 m 370.44 674.16 l S 371.52 698.52 m 371.52 672.24 l S 370.44 698.52 m 373.44 698.52 l S 370.44 672.24 m 373.44 672.24 l S 374.4 699.48 m 374.4 669.24 l S 373.44 699.48 m 375.36 699.48 l S 373.44 669.24 m 375.36 669.24 l S 377.28 698.52 m 377.28 671.16 l S 375.36 698.52 m 378.24 698.52 l S 375.36 671.16 m 378.24 671.16 l S 380.28 699.48 m 380.28 670.2 l S 378.24 699.48 m 381.24 699.48 l S 378.24 670.2 m 381.24 670.2 l S 382.2 699.48 m 382.2 666.36 l S 381.24 699.48 m 384.12 699.48 l S 381.24 666.36 m 384.12 666.36 l S 385.08 698.52 m 385.08 664.44 l S 384.12 698.52 m 386.16 698.52 l S 384.12 664.44 m 386.16 664.44 l S 388.08 698.52 m 388.08 668.28 l S 386.16 698.52 m 389.04 698.52 l S 386.16 668.28 m 389.04 668.28 l S 390 698.52 m 390 664.44 l S 389.04 698.52 m 391.92 698.52 l S 389.04 664.44 m 391.92 664.44 l S 392.88 698.52 m 392.88 662.4 l S 391.92 698.52 m 394.92 698.52 l S 391.92 662.4 m 394.92 662.4 l S 395.88 698.52 m 395.88 661.44 l S 394.92 698.52 m 396.84 698.52 l S 394.92 661.44 m 396.84 661.44 l S 398.76 698.52 m 398.76 661.44 l S 396.84 698.52 m 399.72 698.52 l S 396.84 661.44 m 399.72 661.44 l S 400.68 698.52 m 400.68 664.44 l S 399.72 698.52 m 402.72 698.52 l S 399.72 664.44 m 402.72 664.44 l S 403.68 697.56 m 403.68 659.52 l S 402.72 697.56 m 404.64 697.56 l S 402.72 659.52 m 404.64 659.52 l S 406.56 697.56 m 406.56 657.6 l S 404.64 697.56 m 407.52 697.56 l S 404.64 657.6 m 407.52 657.6 l S 409.56 697.56 m 409.56 655.56 l S 407.52 697.56 m 410.52 697.56 l S 407.52 655.56 m 410.52 655.56 l S 411.48 696.6 m 411.48 654.6 l S 410.52 696.6 m 413.4 696.6 l S 410.52 654.6 m 413.4 654.6 l S 414.36 695.64 m 414.36 651.72 l S 413.4 695.64 m 415.32 695.64 l S 413.4 651.72 m 415.32 651.72 l S 417.36 694.56 m 417.36 651.72 l S 415.32 694.56 m 418.32 694.56 l S 415.32 651.72 m 418.32 651.72 l S 419.28 694.56 m 419.28 651.72 l S 418.32 694.56 m 421.2 694.56 l S 418.32 651.72 m 421.2 651.72 l S 422.16 695.64 m 422.16 652.68 l S 421.2 695.64 m 424.08 695.64 l S 421.2 652.68 m 424.08 652.68 l S 425.16 692.64 m 425.16 647.76 l S 424.08 692.64 m 426.12 692.64 l S 424.08 647.76 m 426.12 647.76 l S 428.04 694.56 m 428.04 649.8 l S 426.12 694.56 m 429 694.56 l S 426.12 649.8 m 429 649.8 l S q 429.96 642 0.24 45.84 re h W n 429.96 687.84 m 429.96 642 l S Q 429 687.84 m 432 687.84 l S 432.96 692.64 m 432.96 645.84 l S 432 692.64 m 433.92 692.64 l S 432 645.84 m 433.92 645.84 l S q 435.84 642 0.24 45.84 re h W n 435.84 687.84 m 435.84 642 l S Q 433.92 687.84 m 436.8 687.84 l S q 438.72 642 0.24 38.04 re h W n 438.72 680.04 m 438.72 642 l S Q 436.8 680.04 m 439.8 680.04 l S q 440.64 642 0.24 39 re h W n 440.76 681 m 440.76 642 l S Q 439.8 681 m 442.68 681 l S q 443.64 642 0.24 38.04 re h W n 443.64 680.04 m 443.64 642 l S Q 442.68 680.04 m 444.6 680.04 l S q 446.52 642 0.24 30.24 re h W n 446.52 672.24 m 446.52 642 l S Q 444.6 672.24 m 447.6 672.24 l S q 448.44 642 0.24 35.16 re h W n 448.56 677.04 m 448.56 642 l S Q 447.6 677.04 m 450.48 677.04 l S q 451.44 642 0.24 28.32 re h W n 451.44 670.2 m 451.44 642 l S Q 450.48 670.2 m 453.36 670.2 l S q 454.32 642 0.24 28.32 re h W n 454.32 670.2 m 454.32 642 l S Q 453.36 670.2 m 455.4 670.2 l S q 457.2 642 0.24 16.56 re h W n 457.32 658.56 m 457.32 642 l S Q 455.4 658.56 m 458.28 658.56 l S q 459.24 642 0.24 21.48 re h W n 459.24 663.36 m 459.24 642 l S Q 458.28 663.36 m 461.16 663.36 l S q 462.12 642 0.24 14.64 re h W n 462.12 656.64 m 462.12 642 l S Q 461.16 656.64 m 463.2 656.64 l S q 465 642 0.24 12.72 re h W n 465.12 654.6 m 465.12 642 l S Q 463.2 654.6 m 466.08 654.6 l S q 468 642 0.24 8.76 re h W n 468 650.76 m 468 642 l S Q 466.08 650.76 m 468.96 650.76 l S q 469.92 642 0.24 9.72 re h W n 469.92 651.72 m 469.92 642 l S Q 468.96 651.72 m 471.96 651.72 l S q 472.8 642 0.24 7.8 re h W n 472.92 649.8 m 472.92 642 l S Q 471.96 649.8 m 473.88 649.8 l S q 475.8 642 0.24 4.92 re h W n 475.8 646.8 m 475.8 642 l S Q 473.88 646.8 m 476.76 646.8 l S q 477.72 642 0.24 5.88 re h W n 477.84 647.76 m 477.84 642 l S Q 476.76 647.76 m 479.76 647.76 l S q 480.6 642 0.24 7.8 re h W n 480.72 649.8 m 480.72 642 l S Q 479.76 649.8 m 482.64 649.8 l S q 483.6 642 0.24 6.84 re h W n 483.6 648.84 m 483.6 642 l S Q 482.64 648.84 m 484.56 648.84 l S q 351 643.68 132.84 45.12 re h W n 351 688.8 m 352.92 687.84 l 355.92 687.84 l 358.8 688.8 l 360.72 684.84 l 363.72 686.76 l 366.6 685.8 l 371.52 685.8 l 374.4 683.88 l 377.28 684.84 l 380.28 684.84 l 382.2 682.92 l 385.08 681.96 l 388.08 682.92 l 390 681 l 392.88 681 l 395.88 680.04 l 398.76 680.04 l 400.68 681 l 403.68 678 l 406.56 678 l 409.56 676.08 l 411.48 675.12 l 414.36 673.2 l 419.28 673.2 l 422.16 674.16 l 425.16 670.2 l 428.04 672.24 l 429.96 665.4 l 432.96 669.24 l 435.84 665.4 l 438.72 658.56 l 440.76 659.52 l 443.64 658.56 l 446.52 653.64 l 448.56 656.64 l 451.44 652.68 l 454.32 652.68 l 457.32 647.76 l 459.24 649.8 l 462.12 646.8 l 465.12 645.84 l 468 644.88 l 472.92 644.88 l 475.8 643.92 l 477.84 643.92 l 480.72 644.88 l 483.6 643.92 l S Q q 351 643.68 132.84 45.12 re h W n 0 0 0 RG 351 688.8 m 352.92 687.84 l 355.92 687.84 l 358.8 688.8 l 360.72 684.84 l 363.72 686.76 l 366.6 685.8 l 371.52 685.8 l 374.4 683.88 l 377.28 684.84 l 380.28 684.84 l 382.2 682.92 l 385.08 681.96 l 388.08 682.92 l 390 681 l 392.88 681 l 395.88 680.04 l 398.76 680.04 l 400.68 681 l 403.68 678 l 406.56 678 l 409.56 676.08 l 411.48 675.12 l 414.36 673.2 l 419.28 673.2 l 422.16 674.16 l 425.16 670.2 l 428.04 672.24 l 429.96 665.4 l 432.96 669.24 l 435.84 665.4 l 438.72 658.56 l 440.76 659.52 l 443.64 658.56 l 446.52 653.64 l 448.56 656.64 l 451.44 652.68 l 454.32 652.68 l 457.32 647.76 l 459.24 649.8 l 462.12 646.8 l 465.12 645.84 l 468 644.88 l 472.92 644.88 l 475.8 643.92 l 477.84 643.92 l 480.72 644.88 l 483.6 643.92 l S Q 0 0 0 rg 483.6 643.8 0.24 0.24 re f BT 0.9929 0 0 1 379.32 614.76 Tm /F4 10.7259 Tf -0.1564 Tc (Sen) Tj 0.1461 Tc -0.2267 Tw (sor no) Tj 0.0018 Tc -0.0824 Tw (ise level) Tj ET BT 0 0.9929 -1 0 318.96 643.92 Tm -0.1159 Tc 0.1541 Tw (Mean fitne) Tj 0.5551 Tc 0 Tw (ss) Tj ET BT 517.92 607.68 TD /F0 12 Tf 0 Tc ( ) Tj -445.92 -16.8 TD /F1 12 Tf -0.036 Tc (Fig) Tj 16.56 0 TD 0.048 Tc (u) Tj 6.72 0 TD -0.048 Tc (re) Tj 10.56 0 TD 0 Tc ( ) Tj 5.28 0 TD (3.) Tj 9 0 TD /F0 12 Tf ( ) Tj 5.28 0 TD -0.0109 Tc 2.2909 Tw (Robustness to noise: mean fitness score achieved over 150 trials by the fittest) Tj 0 Tc 0 Tw ( ) Tj -53.4 -13.8 TD -0.0023 Tc 0.9708 Tw (evolved agent starting from position 11 for a range of noise levels, with standard deviation.) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0065 Tc 2.1815 Tw (Original noise strength during evolution is 0.05 for motor) Tj 0 Tc 0 Tw ( ) Tj 298.56 0 TD -0.018 Tc 0.018 Tw (\(left\) ) Tj 29.04 0 TD -0.0195 Tc 2.1795 Tw (and 5% for) Tj 57.48 0 TD 0 Tc 0 Tw ( ) Tj 5.16 0 TD 0.0044 Tc 2.1556 Tw (sensor noise) Tj 61.08 0 TD 0 Tc 0 Tw ( ) Tj -451.32 -13.8 TD -0.0086 Tc (\(right\)) Tj 30.48 0 TD 0 Tc (. ) Tj 6.12 0 TD ( ) Tj -25.2 -24 TD /F0 9.96 Tf 0.03 Tw ( ) Tj -11.4 -13.32 TD /F0 12 Tf -0.0084 Tc 0.3444 Tw (Finally, another 150 trials were conducted with agent \221up\222 at position 11 \(under normal noise ) Tj 0 -13.8 TD -0.0041 Tc 1.2133 Tw (conditions\). The movement of agent \221down\222 during the best trial \(score: 321\) was recorded) Tj 0 Tc 0.12 Tw ( ) Tj T* -0.0097 Tc 3.9938 Tw (for playback. Another 150 trials were) Tj 199.56 0 TD 0 Tc 0 Tw ( ) Tj 6.96 0 TD -0.002 Tc 3.962 Tw (then run under) Tj 0 Tc 0 Tw ( ) Tj 84.84 0 TD /F2 12 Tf -0.015 Tc (playback) Tj 43.2 0 TD /F0 12 Tf 0 Tc ( ) Tj 6.96 0 TD -0.0063 Tc 3.9663 Tw (conditions: the initial) Tj 0 Tc -0.12 Tw ( ) Tj -341.52 -13.8 TD 0.0018 Tc 0.7262 Tw (conditions reflect those of the recorded best trial run \(agent \221up\222 always starts at position 11) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0.0042 Tc 1.565 Tw (and with the same initial internal activation\), and the movement of agent \221down\222 replicate) Tj 0 Tc 0 Tw ( ) Tj T* 0.0045 Tc 1.4355 Tw (those which it prod) Tj 96.72 0 TD 0.006 Tc 1.458 Tw (uced during the recording. While the sensorimotor noise for agent \221up\222) Tj 0 Tc 0.12 Tw ( ) Tj -96.72 -13.8 TD 0.0031 Tc 2.5341 Tw (was different during each of these trials, no additional noise was added to the recorded) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0 Tc -0 Tw (movement of agent \221down\222. ) Tj 136.32 0 TD 0 Tc 0 Tw ( ) Tj -136.32 -13.8 TD ( ) Tj 0 -13.8 TD -0 Tc 0.4922 Tw (The results are striking: whereas the original 150 trials of mutual) Tj 0 Tc 0 Tw ( ) Tj 319.68 0 TD -0.009 Tc (\(two) Tj 21.96 0 TD -0.036 Tc (-) Tj 4.08 0 TD 0 Tc 0.3194 Tw (way\) interaction were ) Tj -345.72 -13.8 TD -0.0037 Tc 0.7477 Tw (highly successful \(mean score: 268\), the 150 trials of playback \(one) Tj 332.16 0 TD -0.036 Tc 0 Tw (-) Tj 4.08 0 TD -0.0138 Tc 0.8138 Tw (way\) interaction were a) Tj 0 Tc -0.12 Tw ( ) Tj -336.24 -13.8 TD -0.0084 Tc 0.8484 Tw (drastic failure \(mean score: 19\). The severity of this failure is surprising since under normal) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0.0021 Tc 3.3579 Tw (conditions the active agent is robust ag) Tj 206.76 0 TD 0.0013 Tc 3.3587 Tw (ainst various forms of noise, and able to cope) Tj 0 Tc 0.12 Tw ( ) Tj -206.76 -13.8 TD -0.0032 Tc 0.9731 Tw (effectively with a wide range of initial conditions. Moreover, during the playback condition) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0027 Tc 1.3319 Tw (its \221partner\222 performs what had previously been a highly fit behavioral repertoire. Still, the) Tj 0 Tc -0.12 Tw ( ) Tj T* -0.0087 Tc 0.6087 Tw (active agent is unabl) Tj 99.96 0 TD -0.007 Tc 0.595 Tw (e to adapt to the situation of interacting with a non) Tj 247.56 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.003 Tc 0.303 Tw (responsive \221partner\222. ) Tj -351.48 -13.8 TD -0.0066 Tc 0.9596 Tw (It could be argued that this result is unique to the chosen situation. 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Tj 200.52 0 TD 0 Tc 0 Tw ( ) Tj 4.56 0 TD -0.0113 Tc 1.5713 Tw (The activity during) Tj 0 Tc -0.12 Tw ( ) Tj 99.48 0 TD -0.001 Tc 1.561 Tw (the first time) Tj 0 Tc 0 Tw ( ) Tj -386.88 -13.8 TD -0.0051 Tc 0.0051 Tw (steps of ) Tj 39.96 0 TD -0.008 Tc 0 Tw (the) Tj 14.64 0 TD 0 Tc ( ) Tj 3 0 TD -0.0009 Tc 0.0209 Tw (best trial run is shown in Figure) Tj 152.64 0 TD 0 Tc 0 Tw ( ) Tj 3 0 TD (4.) 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Tj 9 0 TD /F0 12 Tf ( ) Tj 4.2 0 TD -0.0072 Tc 0.9672 Tw (Initial activity) Tj 0 Tc -0.12 Tw ( ) Tj 72.48 0 TD 0.96 Tw (of the two agents) Tj 0 Tw ( ) Tj 89.16 0 TD -0.0021 Tc 0.9754 Tw (during the best trial run. From top to bottom the) Tj 0 Tc -0.12 Tw ( ) Tj -212.64 -13.8 TD 0.0048 Tc 1.4352 Tw (traces show the evolution over time) Tj 178.2 0 TD 0 Tc 0 Tw ( ) Tj 4.44 0 TD 0.0015 Tc 1.4385 Tw (of \(i\) the) Tj 44.88 0 TD 0.054 Tc 0 Tw (ir) Tj 7.44 0 TD 0 Tc ( ) Tj 4.44 0 TD 0.0018 Tc 1.4382 Tw (relative displacement, \(ii\) their noisy input) Tj 0 Tc 0 Tw ( ) Tj -239.4 -13.8 TD -0.0082 Tc 1.4962 Tw (signal and actual sensory contact, \(iii\)) Tj 0 Tc 0 Tw ( ) Tj 193.56 0 TD -0.0074 Tc 1.4874 Tw (their velocity, and \(iv\)) Tj 0 Tc 0 Tw ( ) Tj 116.04 0 TD -0.0017 Tc 1.4417 Tw (the CTRNN node outputs of) Tj 0 Tc -0.12 Tw ( ) Tj -309.6 -13.8 TD -0.0144 Tc 0.0144 Tw (agent \221up\222.) Tj 51.96 0 TD 0 Tc 0 Tw ( ) Tj -40.56 -24 TD /F0 9.96 Tf 0.03 Tw ( ) Tj -11.4 -13.32 TD /F0 12 Tf 0.007 Tc 2.161 Tw (Initially the agents have no knowledge of how their own position relates to that of their) Tj 0 Tc 0.12 Tw ( ) Tj 0 -13.8 TD -0.024 Tc 0 Tw (pa) Tj 11.28 0 TD -0.0091 Tc 0.5076 Tw (rtner. Moreover, they have no way of gaining that information except when changing their) Tj 0 Tc 0 Tw ( ) Tj -11.28 -13.8 TD -0.0068 Tc 3.8268 Tw (sensory input by engaging in movement. However, it turns out that one stereotypical) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0037 Tc 0.7237 Tw (behavioral pattern is sufficient to solve the non) Tj 230.52 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.0157 Tc 0.7357 Tw (trivial problem of reliable local) Tj 152.52 0 TD -0.0051 Tc 0.7251 Tw (ization. First,) Tj 0 Tc -0.12 Tw ( ) Tj -387 -13.8 TD -0.0115 Tc 0.8515 Tw (each agent moves rightwards for a few units of time, and then starts moving leftwards. 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After separating again ) Tj 2.604 Tc 0 Tw (\() Tj 184.08 0 TD /F2 12 Tf -0.036 Tc (I) Tj 3.96 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 5.64 0 TD -0.0117 Tc 2.6517 Tw (= 0\) the firing of the left motor node goes down) Tj 0 Tc 0 Tw ( ) Tj -195.96 -13.8 TD -0 Tc 2.2899 Tw (followed by the right motor node which eventually leads to the behavioral pattern being) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0034 Tc 0.6034 Tw (reinitiated. According) Tj 105.72 0 TD -0.0046 Tc 0.6155 Tw (ly, agent \221up\222 should be able to engage with a playback recording.) Tj 0 Tc 0 Tw ( ) Tj 327 0 TD -0.02 Tc 0.02 Tw (The ) Tj -432.72 -13.8 TD -0.0092 Tc 0.0092 Tw (activity during the ) Tj 90.84 0 TD /F2 12 Tf -0 Tc 0 Tw (playback) Tj 43.32 0 TD /F0 12 Tf 0 Tc ( ) Tj 3 0 TD -0.0024 Tc 0.0264 Tw (trial run is shown in Fig) Tj 114.96 0 TD 0.012 Tc 0 Tw (ure) Tj 15.36 0 TD 0 Tc ( ) Tj 3 0 TD (5.) Tj 9.12 0 TD ( ) Tj -279.6 -13.8 TD ( ) Tj 0 -13.8 TD ( ) Tj ET q 466.32 0 0 -244.08 72 687.24 cm /im3 Do endstream endobj 61 0 obj 1263 endobj 63 0 obj << /Type /XObject /Subtype /Image /Name /im3 /Width 555 /Height 290 /BitsPerComponent 4 /ColorSpace [ /Indexed /DeviceRGB 15 62 0 R ] /Length 64 0 R >> stream """"!!""""!!"!!!""!!"!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!""""!"!!!!"!!!!!!!!!!!!!!!!"!!!!!!!!!!!""!"!!"!"""!""!!"!"!!!!!!DDDDDDDDDDDDDDDDDDDD!"!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUQ!!QUQUUUUQUUUUUUU!!UUUQQUUUUQUQDDA"UUUUUUQUUUQUUUUUUUUUQUQUQDDDDDUUQUUUUQQQDDDQUQQQQDDDDDAUQQUDQUUQQDDDAQUDDUUUUUUUUUUUUUUUUUUUUQQUQDQUQUQDAQQUUQDAQQUQDAQQUD"!!"QUA!!UQQA!QQQDA!"""QA""QUQA!UDAQAUQD"!"!DAUQAQDUUAADAUQQDDQAAAUQDDQAADAUAAAAADAUUUQAAAQADAADADAUDADDDAADDD@DADADDQDADDAADDD@ADDQDADDDA!UUQDADDD!DADDDDD!DDDDDDDDDDDDDDDDADDDDDDA!"""D@DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD!!!!!""""!!""""!!"!!!""!!"!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!""""!"!!!!!!!!"!!!!!!!!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!""!"!!"!"""!""!!"!!!"!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"!333133"3!!1!!1!!"""!!!!1!!"1333333333333333333331""!"!!1!!!1!!"" !!!1!!!!!!!""113"31!!1""!!!!!!"""11!!11!!331"!!3311"33113130""3131330!!!!3311111!!!!1133331!!!!"""113311111131""!!133331131111311!!!3331133333313113131133131333311311!!!!3133311133113331333331331311111131133131331331333331""3111333333333313331133113113333333133333113333333113313333311131331""""!!""""!!"!!!""!!"!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!""""!"!!!!!!!!"!!!!!!!!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!""!"!!"!"""!""!!"!!!"!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!"!!!!!!"""111!!11111111!!11111111!!11111111"1111111111331111111111111111111111111"!!"111111111!!111111111!111111111!"""111111111""11111111111!1111111111111111111111"!"!11111111111111113333333333333333333311111111111111111111111111111111111331111111!1111111!1111111!1111111!"" 1111!!!!!""""!!""""!!"!!!""!!"!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!""""!"!!!!!!!!"!!!!!!!!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!""!"!!"!"""!""!!"!!!"!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!"!""!!!!!!"""!!!!"!!"""!"!!"!!!!!!""#333333333333333333333333333333333330333333333333333333333333333333333333333333!!!!!!!!!!"""!!!!!!"""!!!!!!"""!"!!!!!!!""#333333333330033333333333333333333333333333333333333333333333333333333333333!!!!!!!!!!"""!!""!!!!!!"""!!!!"!!" endstream endobj 64 0 obj 80620 endobj 62 0 obj << /Length 65 0 R /Filter /ASCII85Decode >> stream !!!$!s8P>L5bOdG^qd`n@"84Wzzzzzzz~> endstream endobj 65 0 obj 34 endobj 66 0 obj << /Length 67 0 R >> stream Q BT 538.32 443.16 TD ( ) Tj -466.32 -11.04 TD /F1 12 Tf ( ) Tj 0 -19.56 TD -0.036 Tc (Fig) Tj 16.56 0 TD -0.016 Tc (ure) Tj 17.4 0 TD 0 Tc ( ) Tj 3.24 0 TD (5.) Tj 9 0 TD /F0 12 Tf ( ) Tj 3.36 0 TD -0.0131 Tc 0.2531 Tw (Initial activity during a ) Tj 114.24 0 TD /F2 12 Tf -0 Tc 0 Tw (playback) Tj 43.32 0 TD /F0 12 Tf 0 Tc ( ) Tj 3.24 0 TD 0.0112 Tc 0.1688 Tw (trial run in which ) Tj 87.12 0 TD 0.0048 Tc 0.2352 Tw (the movements of agent \221down\222 ) Tj -297.48 -13.8 TD -0.042 Tc 0 Tw (ar) Tj 9.24 0 TD -0.0128 Tc 0.2768 Tw (e the same as in Fig) Tj 96 0 TD 0.012 Tc 0 Tw (ure) Tj 15.48 0 TD 0 Tc ( ) Tj 3.24 0 TD -0.014 Tc 0.254 Tw (4. From) Tj 38.16 0 TD 0 Tc 0 Tw ( ) Tj 3.24 0 TD -0.0066 Tc 0.2266 Tw (top to bottom the traces show the evolution over time of \(i\) ) Tj -165.36 -13.8 TD 0.0065 Tc 2.5227 Tw (the relative displacement between the agents, \(ii\) their noisy input signal and the actual) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD 0.0052 Tc 0.4919 Tw (moments of sensory contact, \(iii\) their velocities, and \(iv\) the CTRNN node outputs of agent) Tj 0 Tc 0 Tw ( ) Tj T* -0.0144 Tc 0.0144 Tw (\221up\222. ) Tj 26.04 0 TD 0 Tc 0 Tw ( ) Tj -26.04 -25.8 TD ( ) Tj 0 -13.8 TD 0 Tc -0 Tw (At ) Tj 17.04 0 TD -0.0117 Tc 2.0517 Tw (first the \221live\222 agent aligns itself with the \221playback\222 agent as in the original situation) Tj 0 Tc -0.12 Tw ( ) Tj -17.04 -13.8 TD 0.039 Tc 0 Tw (\(Fig) Tj 19.92 0 TD -0.028 Tc (ure) Tj 15.24 0 TD 0 Tc ( ) Tj 5.76 0 TD 0.0019 Tc 2.7581 Tw (4\). During mutual \(two) Tj 119.64 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.0055 Tc 2.7826 Tw (way\) interaction agent \221down\222 would always respond to) Tj 0 Tc 0 Tw ( ) Tj -164.52 -13.8 TD -0.0064 Tc 1.9482 Tw (contact by moving away slightly. However, in the playback situation this co) Tj 385.92 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.012 Tc (regul) Tj 24.6 0 TD -0.012 Tc 1.932 Tw (ation is) Tj 0 Tc -0.12 Tw ( ) Tj -414.48 -13.8 TD -0.0069 Tc 3.4869 Tw (prevented from occurring. Accordingly, every encounter results in a slight decrease of) Tj 0 Tc 0.12 Tw ( ) Tj 0 -13.8 TD 0.0088 Tc 0.1032 Tw (relative displacement between the two agents, thereby in turn making it more likely that there ) Tj T* -0.0108 Tc 1.828 Tw (will be another sensory stimulation. Up to about) Tj 0 Tc -0.12 Tw ( ) Tj 248.4 0 TD /F2 12 Tf 0.024 Tc 0 Tw (t) Tj 3.36 0 TD /F0 12 Tf 0 Tc ( ) Tj 4.8 0 TD -0.036 Tc 1.836 Tw (= 3, agent \221up) Tj 71.76 0 TD -0.0146 Tc 1.8146 Tw (\222 is still able to partially) Tj 0 Tc -0.36 Tw ( ) Tj -328.32 -13.8 TD 0.0025 Tc 3.2461 Tw (regulate this displacement on its own by adjusting the output of its right motor node.) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.006 Tc 1.698 Tw (However, from that point onwards the right motor node saturates at) Tj 0 Tc 0 Tw ( ) Tj 344.88 0 TD /F2 12 Tf 0.012 Tc (z) Tj 4.68 -1.56 TD /F2 8.04 Tf 0.06 Tc (3) Tj 4.08 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 4.56 0 TD 0 Tc 1.6793 Tw (= 1, and thereafter) Tj 0 Tc 0.12 Tw ( ) Tj -358.2 -13.8 TD -0.0008 Tc 2.9048 Tw (remains unaffected by further sensory stimulation.) Tj 256.44 0 TD 0 Tc 0 Tw ( ) Tj 5.88 0 TD -0.0022 Tc 2.8822 Tw (Finally, at around) Tj 0 Tc 0 Tw ( ) Tj 96.6 0 TD /F2 12 Tf 0.024 Tc (t) Tj 3.48 0 TD /F0 12 Tf 0 Tc ( ) Tj 5.88 0 TD -0.0028 Tc 2.8828 Tw (= 6 the positive) Tj 0 Tc 0 Tw ( ) Tj -368.28 -13.8 TD 0 Tc 4.1994 Tw (feedback loop between) Tj 0 Tc 0.12 Tw ( ) Tj 126.24 0 TD -0.012 Tc -0.108 Tw (increasing ) Tj 56.4 0 TD 0 Tc 4.1995 Tw (sensory stimulation and mounting leftward velocity) Tj 0 Tc -0.12 Tw ( ) Tj -182.64 -13.8 TD -0 Tc 0.568 Tw (becomes unstable in such a way that recovery from breakdown is impossible. The live agent ) Tj 0 -13.8 TD -0.001 Tc 0.001 Tw (falls behind the playback agent, and heads ) Tj 205.92 0 TD 0.0031 Tc -0.0031 Tw (in the opposite direction.) Tj 119.4 0 TD 0 Tc 0 Tw ( ) Tj -325.32 -13.8 TD ( ) Tj 0 -13.8 TD 0.0057 Tc 2.7636 Tw (Why does this breakdown of coordination not occur when both agents engage in \221live\222) Tj 0 Tc 0.12 Tw ( ) Tj T* 0.0042 Tc 3.1158 Tw (interaction? The simple answer provided by this model is that) Tj 324.72 0 TD 0 Tc 0 Tw ( ) Tj 6.12 0 TD -0.008 Tc (the) Tj 14.64 0 TD 0 Tc ( ) Tj 6.12 0 TD /F2 12 Tf 0.0073 Tc 3.1127 Tw (stability of ongoing) Tj 0 Tc -0.12 Tw ( ) Tj -351.6 -13.8 TD 0.0014 Tc 3.5086 Tw (coordination requires mutuality of interaction) Tj 235.44 0 TD /F0 12 Tf -0.0027 Tc 3.4827 Tw (. After the) Tj 55.92 0 TD 0 Tc 0 Tw ( ) Tj 6.48 0 TD 0.0042 Tc 3.5058 Tw (initial alignment we find that) Tj 0 Tc 0 Tw ( ) Tj -297.84 -13.8 TD -0.005 Tc 4.1 Tw (coordinated movement in one direction consists of continuous co) Tj 345.12 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.0078 Tc 4.0878 Tw (regulated oscillatory) Tj 0 Tc -0.24 Tw ( ) Tj -349.08 -13.8 TD -0.0037 Tc 2.8937 Tw (behavior. Agents control their respective velocities such that they cross their sensors at) Tj 0 Tc -0.12 Tw ( ) Tj ET endstream endobj 67 0 obj 5140 endobj 59 0 obj << /Type /Page /Parent 47 0 R /Resources << /Font << /F0 6 0 R /F1 19 0 R /F2 21 0 R >> /XObject << /im3 63 0 R >> /ProcSet 2 0 R >> /Contents [ 60 0 R 66 0 R ] >> endobj 69 0 obj << /Length 70 0 R >> stream BT 513.36 59.4 TD 0 0 0 rg /F0 9.96 Tf 0.06 Tc 0 Tw (10) Tj 9.96 0 TD 0 Tc 0.03 Tw ( ) Tj -439.92 -11.52 TD ( ) Tj -11.4 711.36 TD /F0 12 Tf 0.0035 Tc 2.1565 Tw (relatively regular intervals. This) Tj 0 Tc 0 Tw ( ) Tj 165.72 0 TD -0.0093 Tc 0.0093 Tw (iterative ) Tj 44.52 0 TD -0.042 Tc 0 Tw (re) Tj 9.36 0 TD -0.0044 Tc 2.2044 Tw (action chain constitutes ) Tj 2.112 Tc 0 Tw (a) Tj 127.44 0 TD 0 Tc (n) Tj 6 0 TD ( ) Tj 5.28 0 TD -0.0137 Tc -0.1063 Tw (ongoing ) Tj 44.4 0 TD 0.0133 Tc 2.1467 Tw (pattern of) Tj 0 Tc 0.12 Tw ( ) Tj -402.72 -13.8 TD -0.003 Tc 0 Tw (turn) Tj 19.32 0 TD -0.036 Tc (-) Tj 3.96 0 TD 0.003 Tc 0.7497 Tw (taking; noise perturbations get amplified in a way that requires continuous co) Tj 379.44 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD -0.0013 Tc 0.0013 Tw (regulated ) Tj -406.68 -13.8 TD -0.042 Tc 0 Tw (re) Tj 9.24 0 TD -0.036 Tc (-) Tj 3.96 0 TD -0.0008 Tc 0.0008 Tw (establishment of the interaction ) Tj 153.96 0 TD -0.012 Tc 0.092 Tw (\(Ikegami & Iizuka 2007\)) Tj 119.64 0 TD 0 Tc 0 Tw (.) Tj 3.12 0 TD ( ) Tj -289.92 -13.8 TD ( ) Tj 0 -13.8 TD -0.006 Tc 0.006 Tw (3.2 Dynamical analysis) Tj 118.32 0 TD 0 Tc 0 Tw ( ) Tj -118.32 -13.8 TD ( ) Tj 0 -13.8 TD -0.0117 Tc 0.9888 Tw (Can we account for the oscillating pattern in) Tj 0 Tc 0 Tw ( ) Tj 223.32 0 TD -0.0023 Tc 0.9451 Tw (dynamical terms? Since the output of the non) Tj 224.16 0 TD -0.036 Tc 0 Tw (-) Tj -447.48 -13.8 TD -0.004 Tc 0.304 Tw (motor node ) Tj 59.16 0 TD /F2 12 Tf 0.012 Tc 0 Tw (z) Tj 4.68 -1.56 TD /F2 8.04 Tf 0.06 Tc (1) Tj 4.08 1.56 TD /F2 12 Tf -0.162 Tc (\(y) Tj 9.12 -1.56 TD /F2 8.04 Tf 0.06 Tc (1) Tj 4.2 1.56 TD /F2 12 Tf -0.036 Tc (\)) Tj 3.84 0 TD /F0 12 Tf 0 Tc ( ) Tj 3.72 0 TD -0.0041 Tc 0.6298 Tw (= 1 during coordination, it can be treated as a fixed parameter. The rest of) Tj 0 Tc 0.12 Tw ( ) Tj -88.8 -13.8 TD 0.0032 Tc 0.0368 Tw (the system consists only of the two motor nodes. The parameters are ) Tj 332.16 0 TD /F2 12 Tf 0.024 Tc 0 Tw (t) Tj 4.32 -1.56 TD /F2 8.04 Tf 0.06 Tc (2) Tj 4.08 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3 0 TD 0.0144 Tc -0.0144 Tw (= 1.6, ) Tj 30.84 0 TD /F2 12 Tf 0 Tc 0 Tw (b) Tj 6 -1.56 TD /F2 8.04 Tf 0.06 Tc (2) Tj 4.08 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3 0 TD 0.0144 Tc 0.0456 Tw (= 2.6, ) Tj 30.84 0 TD /F2 12 Tf 0.036 Tc 0 Tw (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.06 Tc (12) Tj 8.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3 0 TD -0.048 Tc 0.048 Tw (= ) Tj 9.72 0 TD -0.036 Tc 0 Tw (-) Tj -447.24 -13.8 TD 0 Tc (3.7, ) Tj 21.12 0 TD /F2 12 Tf 0.036 Tc (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.06 Tc (22) Tj 8.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD -0.0096 Tc 0.0696 Tw (= 1.0, ) Tj 30.96 0 TD /F2 12 Tf 0.036 Tc 0 Tw (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.06 Tc (32) Tj 8.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD -0.048 Tc (=) Tj 6.72 0 TD 0 Tc ( ) Tj 3.12 0 TD -0.036 Tc (-) Tj 3.96 0 TD -0.0069 Tc 0.0669 Tw (7.9, and ) Tj 41.52 0 TD /F2 12 Tf 0.024 Tc 0 Tw (t) Tj 4.32 -1.56 TD /F2 8.04 Tf 0.06 Tc (3) Tj 4.08 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD 0.0144 Tc 0.1056 Tw (= 1.1, ) Tj 31.08 0 TD /F2 12 Tf 0 Tc 0 Tw (b) Tj 6 -1.56 TD /F2 8.04 Tf 0.06 Tc (3) Tj 4.08 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD 0.0144 Tc 0.1056 Tw (= 2.9, ) Tj 31.08 0 TD /F2 12 Tf 0.036 Tc 0 Tw (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.06 Tc (13) Tj 8.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD -0.048 Tc 0.048 Tw (= ) Tj 9.84 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD 0 Tc (5.8, ) Tj 21.12 0 TD /F2 12 Tf 0.036 Tc (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.06 Tc (23) Tj 8.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD -0.048 Tc 0.048 Tw (= ) Tj 9.84 0 TD -0.036 Tc 0 Tw (-) Tj 3.96 0 TD 0 Tc (5.8, ) Tj 21.12 0 TD /F2 12 Tf 0.036 Tc (w) Tj 8.04 -1.56 TD /F2 8.04 Tf 0.06 Tc (33) Tj 8.16 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD -0.0096 Tc 0.0696 Tw (= 2.3. ) Tj 31.08 0 TD -0.0022 Tc 0.0822 Tw (If agents are ) Tj -391.8 -13.8 TD -0.0009 Tc 0.2609 Tw (not in contact with each other \() Tj 150.6 0 TD /F2 12 Tf -0.036 Tc 0 Tw (I) Tj 3.96 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.24 0 TD -0.0067 Tc 0.2248 Tw (= 0\), there is a globally attracting stable equilibrium point at ) Tj -160.08 -13.8 TD -0.036 Tc 0 Tw (\() Tj 3.96 0 TD (-) Tj 3.96 0 TD 0 Tc (3.4, ) Tj 21.36 0 TD -0.036 Tc (-) Tj 3.96 0 TD -0.013 Tc 0.373 Tw (7.5\). Being in this state effectively slows down rightward velocity.) Tj 322.68 0 TD 0 Tc 0 Tw ( ) Tj 3.48 0 TD -0.009 Tc 0.279 Tw (Because of this the ) Tj -359.4 -13.8 TD -0.0011 Tc 0.0251 Tw (agents eventually make contact. When ) Tj 188.04 0 TD /F2 12 Tf -0.036 Tc 0 Tw (I) Tj 3.96 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 3.12 0 TD 0.0104 Tc 0 Tw (= 1 the equilibrium point is shifted to \(0.3, 1.9\). This ) Tj -197.4 -13.8 TD -0.0084 Tc 0.0384 Tw (effectively speeds up the rightward velocity of the agent.) Tj 272.88 0 TD 0 Tc 0 Tw ( ) Tj -272.88 -13.8 TD ( ) Tj 0 -13.8 TD -0.003 Tc 1.923 Tw (Interestingly, under normal conditions the dynamical system never reaches eith) Tj 397.68 0 TD -0.02 Tc 1.94 Tw (er of these) Tj 0 Tc 0 Tw ( ) Tj -397.68 -13.8 TD 0.0051 Tc 3.2349 Tw (two equilibrium points, because their existence is made transitory through the ongoing) Tj 0 Tc 0 Tw ( ) Tj 0 -13.8 TD -0.0285 Tc (interact) Tj 35.88 0 TD -0.0008 Tc 1.5608 Tw (ion. This is illustrated in Figure) Tj 159.12 0 TD 0 Tc 0 Tw ( ) Tj 4.56 0 TD 0.0049 Tc 1.5551 Tw (6 \(left\) in terms of the motor node firing rates for) Tj 0 Tc 0.12 Tw ( ) Tj -199.56 -13.8 TD -0.0045 Tc 0.3754 Tw (agent \221up\222 over a whole run \(50 units of time\). The trajectory) Tj 0 Tc -0.24 Tw ( ) Tj 300.48 0 TD -0.0017 Tc 0.3917 Tw (settles down into an oscillatory) Tj 0 Tc -0.12 Tw ( ) Tj -300.48 -13.8 TD -0.0129 Tc 1.4529 Tw (pattern that traces the corner near point \(0, 1\), in the middle of the two equilibrium points) Tj 0 Tc -0.12 Tw ( ) Tj 0 -13.8 TD -0.0027 Tc 1.3527 Tw (\(located at \(0.95, 1\) when) Tj 0 Tc 0 Tw ( ) Tj 132.96 0 TD /F2 12 Tf -0.036 Tc (I) Tj 3.96 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 4.32 0 TD 0.0048 Tc 1.3152 Tw (= 1, and at \(0.30, 0\) when) Tj 0 Tc 0 Tw ( ) Tj 136.08 0 TD /F2 12 Tf -0.036 Tc (I) Tj 3.96 -1.56 TD /F2 8.04 Tf 0.0449 Tc (i) Tj 2.28 1.56 TD /F0 12 Tf 0 Tc ( ) Tj 4.32 0 TD 0.0021 Tc 1.3379 Tw (= 0\). The state trajectory for the) Tj 0 Tc 0.12 Tw ( ) Tj -290.16 -13.8 TD -0.0074 Tc 2.0474 Tw (playback situation of the same run) Tj 174.96 0 TD 0 Tc 0 Tw ( ) Tj 5.04 0 TD -0.012 Tc 2.052 Tw (is displayed in Figure) Tj 109.56 0 TD 0 Tc 0 Tw ( ) Tj 5.04 0 TD -0.0083 Tc 2.0723 Tw (6 \(right\). At first the trajectory) Tj 0 Tc -0.24 Tw ( ) Tj -294.6 -13.8 TD -0.0063 Tc 1.0863 Tw (moves into the same region of state space but then, during the period of prolonged contact,) Tj 0 Tc 0.12 Tw ( ) Tj 0 -13.8 TD 0.0042 Tc 1.4438 Tw (the left motor node gets saturated while the right motor node remains at 1. This continues) Tj 0 Tc 0 Tw ( ) Tj T* -0.0206 Tc 1.7006 Tw (until the system) Tj 79.2 0 TD 0 Tc 0 Tw ( ) Tj 4.68 0 TD -0.0053 Tc 1.6853 Tw (almost reaches the equilibrium point at \(0.95, 1\), but it eventually causes) Tj 0 Tc 0 Tw ( ) Tj -83.88 -13.8 TD -0.0042 Tc 0.0226 Tw (agent \221up\222 to slow down too much thereby breaking out of the coordination pattern.) Tj 400.56 0 TD 0 Tc 0 Tw ( ) Tj 3.12 0 TD ( ) Tj -392.28 -13.8 TD ( ) Tj 0 -13.8 TD ( ) Tj ET q 189.84 0 0 -93.48 101.04 383.64 cm /im4 Do endstream endobj 70 0 obj 7798 endobj 72 0 obj << /Type /XObject /Subtype /Image /Name /im4 /Width 244 /Height 120 /BitsPerComponent 4 /ColorSpace [ /Indexed /DeviceRGB 15 71 0 R ] /Length 73 0 R >> stream """""""""!"""!"""!!!!!!!!!!!!!"""!!!!!!!!!!!!!!!!!!"!!!!!!!!!"!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""!""!"""!"""!""!!!3!!!!!!331!!!!!!333!!!!""""""""""""""""""""""""""#333""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!333!!!!!!331!!!!!3!!""!!!!!!!!!!!!!!!!!!"!!""!!!!!!!!!!!!!!!!!!!!!!!"""!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!""!!!!!!!!!!!!!!!!!!!!"!""!!!!!!!!!!!!!"!!!!!!!!!!!!!!""!!!!!!!"""!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!"!""!!!!!!!!!!!!!"!!!!!!"!"!!!!!!!!!!!!!!!!!!"!!""!!!!!!!!!!!!!!!!!"""!"! 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