Ne of orientation while radii of zone of repulsion and attraction is fixed (red line) and in other case varying value of the radius of zone of attraction while radii of zone of repulsion and orientation is fixed (blue line).missing information has been defined as a way to quantify the number of possible different ways to arrange a specific system44,48. Therefore, it estimates the level of disorder in a system. For a collective motion, we consider it as a level of missing communicated information between the agents due to their interactions with each other. This can be interpreted as the amount of information needed to specify the exact physical state of the group forming a specific spatial arrangement. This also means how much internal order or uncertainty a group formation has in a specific state. Figure 4a compares the missing information of the swarm for different collective behaviors with different number of individuals (see missing information section in Methods). In our analysis, we consider the same initial conditions for the individuals’ location and speed. The radii of individuals’ interaction zones generating similar collective behavior are identical irrespective of the population size of the group. Figure 4a shows the transition from a swarm phase to torus, dynamic parallel group and then highly parallel group; corresponding to this transition, we observe that the missing information is decreasing due to more alignment among the neighbors and GS-4059 web increasing internal order of the group structure. To further investigate the effect of local interactions on missing information related to the group structure, we increase the group density to 100 individuals, we fix the radius of zone of repulsion and zone of orientation, and we change the zone of attraction. We consider the same initial condition for the individuals’ location and speed in all the cases. We perform the same analysis and quantify the missing information of the collective group. Figure 4b (blue line) shows that by increasing the radius of zone of attraction while maintaining the same initial condition it results in decreasing the missing information. Increasing the zone of attraction causes the individuals to interact more with each other rather than being isolated and as a result the group tends to show more collective arrangment. This means there is more structural order and less missing information about the group formation. Similarly, fixing the radius of zone of repulsion and zone of attraction and increasing the radius of zone of orientation contributes to a reduction in the missing information (red line in Fig. 4b). This means that the expansion of orientation zone makes the individuals to align with each other and move parallel, which implies an increasing degree of internal order within the group. Consequently, the missing information decreases.based on their simple behavioral rules. Different ways of communication and information transfer between them affects their individual behaviors and motion. To investigate and quantify the complexity of cellular groups, we study motion of S. marcescens bacteria with density of 108 (bacteria/cm3) moving in vitro. We consider the motion of 9 bacteria (our analysis can be extended to a higher number if we are able to track and extract long time trajectories of all the individuals) in the experiments and consider it as a collective group for our analysis (see S. marcescens dataset from GW 4064 web Methods for details). Next, we identify.Ne of orientation while radii of zone of repulsion and attraction is fixed (red line) and in other case varying value of the radius of zone of attraction while radii of zone of repulsion and orientation is fixed (blue line).missing information has been defined as a way to quantify the number of possible different ways to arrange a specific system44,48. Therefore, it estimates the level of disorder in a system. For a collective motion, we consider it as a level of missing communicated information between the agents due to their interactions with each other. This can be interpreted as the amount of information needed to specify the exact physical state of the group forming a specific spatial arrangement. This also means how much internal order or uncertainty a group formation has in a specific state. Figure 4a compares the missing information of the swarm for different collective behaviors with different number of individuals (see missing information section in Methods). In our analysis, we consider the same initial conditions for the individuals’ location and speed. The radii of individuals’ interaction zones generating similar collective behavior are identical irrespective of the population size of the group. Figure 4a shows the transition from a swarm phase to torus, dynamic parallel group and then highly parallel group; corresponding to this transition, we observe that the missing information is decreasing due to more alignment among the neighbors and increasing internal order of the group structure. To further investigate the effect of local interactions on missing information related to the group structure, we increase the group density to 100 individuals, we fix the radius of zone of repulsion and zone of orientation, and we change the zone of attraction. We consider the same initial condition for the individuals’ location and speed in all the cases. We perform the same analysis and quantify the missing information of the collective group. Figure 4b (blue line) shows that by increasing the radius of zone of attraction while maintaining the same initial condition it results in decreasing the missing information. Increasing the zone of attraction causes the individuals to interact more with each other rather than being isolated and as a result the group tends to show more collective arrangment. This means there is more structural order and less missing information about the group formation. Similarly, fixing the radius of zone of repulsion and zone of attraction and increasing the radius of zone of orientation contributes to a reduction in the missing information (red line in Fig. 4b). This means that the expansion of orientation zone makes the individuals to align with each other and move parallel, which implies an increasing degree of internal order within the group. Consequently, the missing information decreases.based on their simple behavioral rules. Different ways of communication and information transfer between them affects their individual behaviors and motion. To investigate and quantify the complexity of cellular groups, we study motion of S. marcescens bacteria with density of 108 (bacteria/cm3) moving in vitro. We consider the motion of 9 bacteria (our analysis can be extended to a higher number if we are able to track and extract long time trajectories of all the individuals) in the experiments and consider it as a collective group for our analysis (see S. marcescens dataset from Methods for details). Next, we identify.
