## 5 Results
### Experiment B: Borderline Identification
Horizontal black bars denote frontier robots and horizontal blank bars represent interior agents. (**d**) Temporal evolution of LED actions of the robots as time elapses. Horizontal black bars denote activated LED. (**a**) Swarm topology graph, alpha shape highlighted. (**b**) Swarm graph, successes and errors highlighted. (**c**) Alpha shape. (**d**) LED actions. **Scalability**: In Figure 13, the scalability of the system is evaluated. The results are presented using a sample of size 50 with independent simulation executions. For each swarm size, it shows the accuracy of each time step, defined as the number of agents correctly identified as frontier or interior divided by the swarm size. The curves represent the time dependent median of the accuracy using all the collected samples. Alternatively, the shadow areas indicate, at each time instant, the first and third quantiles of the accuracies. It can be observed that the solution scales utterly well as swarm size increases. Indeed, there is no statistically significant degradation in accuracy as the number of robots grows, up to 50 agents. Consequently, the scalability of the system is clearly fulfilled. Figure 11: Temporal evolution of true positive and negative rates in the borderline identification experiment with 30 robots. Darker curves represent median TPR and TNR and contours of the shadow areas are the first and third quantiles, using a sample of size 50. Figure 12: (**a–e**) snapshots of the borderline identification experiment at different simulation time steps. The balls represent the robots in the swarm. Robots colored in red indicate that the LED is turned on at the corresponding time step. Similarly, blue balls denote robots with the LED deactivated. Swarm topology and robot distances are preserved in the graphs. (**f**) Actual alpha shape, in purple, used as target, Note that at time step 50, once the decisions are settled, there are only 2 errors. Moreover, both errors correspond to false negatives. **Robustness**: The robustness capabilities are evaluated by reinitializing the robots spatial graph, defining their positions, every 200 time steps. However, the states of the CTRNNs of all the robots are maintained untouched regardless of the position resampling. This causes an abrupt change in the swarm topology, leading to agents being forced to reconsider if they are in the borderline subset. Figure 14 displays both target borderline temporal evolution (left) and robots LED actions (right). Although there are several erroneous decisions, robots are generally able to respond successfully to topological alterations. Figure 15 represents the accuracy distributions for different swarm sizes under the above mentioned topology alterations. Evidently, there is a short transient period of time required by the agents to notice the swarm changes and alter its neural states as a consequence. The resampling of robot positions result in discontinuous accuracy drop as the alpha shape and, thus, the robots in the borderline, change. Agents are able to detect the changes and almost correctly solve the task for the unexpected swarm redistribution. **Communication**: With the aim of studying the communication that emerges as a result of evolution, Figure 16 analyzes the importance of the communication variables in solving the task. Specifically, in the figure, it can be observed the accuracy comparison among a scenario with no inhibition and when different communication variables are inhibited. Each inhibition is performed one by one and consists in replacing the value of the corresponding variable with zeros at the input of the CTRNN. The comparison of the figure reveals that the information about the orientation from where the message was sensed is a highly relevant context variable, whose deletion causes system breakdown. On the contrary, provided that the system accuracy is not significantly decreased, the results indicate that the message is not harnessed in this experiment.