Entation behavior consequently no parallel motion. (c) Dynamic parallel group: A-836339 site individuals align with each other and make the group more SIS3 web motile compared to two previous cases. (d) Highly parallel group: Individuals are in a highly aligned arrangement and the group is more motile compared to previous cases.In the next step, we estimate the transition probability matrix between the identified states (Fig. 1c) and based on these probabilities, we are able to construct the free energy landscape for the transitions between these states (see equations (6) and (7) in free energy landscape section in Methods). Our formalism generalizes the method of local equilibrium state analysis presented by Akinori Baba and his coworkers13,47 to construct the energy landscape of a one-dimensional single molecule time series. To further exploit this free energy landscape description, we develop an information theoretic framework for quantifying the degree of emergence, self-organization and complexity of a collective group motion. To analyze our framework, we first use a well-known agent-based model31 which captures different behavior of a collection of interactive agents in a three dimensional space (see the simulation section in the Methods for more details about the model). This model is based on simplified local interactions between the individuals and is able to mimic the spatial dynamics of a group of animals such as bird flocks or fish school. By varying the degree of local interactions among the agents in this model, we can observe different types of behavior from the group31. The motion of each individual in the group is the outcome of local repulsion, alignment and attraction tendencies depending on the location and orientation of the neighboring agents. The individuals tend to align themselves with the neighbors, while avoiding collision by keeping a minimum distance between them. Individuals avoid being isolated and keep the group to move as a single coherent entity by maintaining an attraction tendency between them.Scientific RepoRts | 6:27602 | DOI: 10.1038/srepwww.nature.com/scientificreports/Figure 3. Transition probabilities among the states identified in different collective behaviors of the simulated agent-based model. (a) Torus, the plot shows the transition probability between different states in this collective behavior. (b) Swarm, the group of agents has the highest number of states in this collective behavior and the landscape has more spikes and is less smooth compared to the other cases. (c) Dynamic parallel group, the transition probability looks similar to the torus phase, this similarity is due to preference of individuals to align their motion parallel to their neighbors. (d) Highly parallel group, the group has the lowest number of possible states in this phase and the landscape is less spiky due to high preference of individuals to move parallel with respect to each other. The dynamics of the group can change between four different common collective behaviors depending on the width of different zones around the individuals (Fig. 2). These four collective motion behaviors identified by Couzin and coworkers31 are: torus, swarm, dynamic parallel group and highly parallel group. The torus configuration emerges when the individuals rotate around an empty space. This happens when the zone of orientation is relatively small compared to zone of attraction. In this case individuals have a tiny zone of repulsion around them (Fig. 2a). O.Entation behavior consequently no parallel motion. (c) Dynamic parallel group: Individuals align with each other and make the group more motile compared to two previous cases. (d) Highly parallel group: Individuals are in a highly aligned arrangement and the group is more motile compared to previous cases.In the next step, we estimate the transition probability matrix between the identified states (Fig. 1c) and based on these probabilities, we are able to construct the free energy landscape for the transitions between these states (see equations (6) and (7) in free energy landscape section in Methods). Our formalism generalizes the method of local equilibrium state analysis presented by Akinori Baba and his coworkers13,47 to construct the energy landscape of a one-dimensional single molecule time series. To further exploit this free energy landscape description, we develop an information theoretic framework for quantifying the degree of emergence, self-organization and complexity of a collective group motion. To analyze our framework, we first use a well-known agent-based model31 which captures different behavior of a collection of interactive agents in a three dimensional space (see the simulation section in the Methods for more details about the model). This model is based on simplified local interactions between the individuals and is able to mimic the spatial dynamics of a group of animals such as bird flocks or fish school. By varying the degree of local interactions among the agents in this model, we can observe different types of behavior from the group31. The motion of each individual in the group is the outcome of local repulsion, alignment and attraction tendencies depending on the location and orientation of the neighboring agents. The individuals tend to align themselves with the neighbors, while avoiding collision by keeping a minimum distance between them. Individuals avoid being isolated and keep the group to move as a single coherent entity by maintaining an attraction tendency between them.Scientific RepoRts | 6:27602 | DOI: 10.1038/srepwww.nature.com/scientificreports/Figure 3. Transition probabilities among the states identified in different collective behaviors of the simulated agent-based model. (a) Torus, the plot shows the transition probability between different states in this collective behavior. (b) Swarm, the group of agents has the highest number of states in this collective behavior and the landscape has more spikes and is less smooth compared to the other cases. (c) Dynamic parallel group, the transition probability looks similar to the torus phase, this similarity is due to preference of individuals to align their motion parallel to their neighbors. (d) Highly parallel group, the group has the lowest number of possible states in this phase and the landscape is less spiky due to high preference of individuals to move parallel with respect to each other. The dynamics of the group can change between four different common collective behaviors depending on the width of different zones around the individuals (Fig. 2). These four collective motion behaviors identified by Couzin and coworkers31 are: torus, swarm, dynamic parallel group and highly parallel group. The torus configuration emerges when the individuals rotate around an empty space. This happens when the zone of orientation is relatively small compared to zone of attraction. In this case individuals have a tiny zone of repulsion around them (Fig. 2a). O.
