Distribution of the number of overlaps allows calculating a bootstrapped P-value

Distribution of the number of overlaps allows calculating a bootstrapped P-value for the observed number of overlaps under the null (the observed number of overlaps is not larger than that expected by chance) and the CEP-37440 chemical information alternative (the observed number of overlaps is larger than that expected by chance) hypotheses.
www.nature.com/scientificreportsOPENreceived: 07 January 2016 Accepted: 20 May 2016 Published: 14 JuneA Statistical Physics Characterization of the Complex Systems Dynamics: Quantifying Complexity from Spatio-Temporal InteractionsHana Koorehdavoudi1 Paul BogdanBiological systems are frequently categorized as complex systems due to their capabilities of generating spatio-temporal structures from apparent random decisions. In spite of research on analyzing biological systems, we lack a quantifiable framework for measuring their complexity. To fill this gap, in this paper, we develop a new paradigm to study a collective group of N agents moving and interacting in a three-dimensional space. Our paradigm helps to identify the spatio-temporal states of the motion of the group and their associated transition probabilities. This framework enables the estimation of the free energy landscape corresponding to the identified states. Based on the energy landscape, we quantify missing information, emergence, self-organization and complexity for a collective motion. We show that the collective motion of the group of agents evolves to reach the most probable state with relatively lowest energy level and lowest missing information compared to other possible states. Our analysis demonstrates that the natural group of animals exhibit a higher degree of emergence, self-organization and complexity over time. Consequently, this algorithm can be integrated into new frameworks to engineer collective motions to achieve certain degrees of emergence, self-organization and complexity. A complex system refers to a system in which there is a lack of precise relation between the system’s outcomes and the original causes of those outcomes1?. The main characteristics of complex systems are their unpredictable and nonlinear dynamics. This complexity in a system is due to the intricate SIS3 dose heterogeneous coupling between the components of the system, which makes it impossible to analyze the components individually and isolated from the rest of the system5. The close coupling and interactions between the units of the complex system cause recognizable collective behavior at larger scales6. A group of agents or animals moving collectively is an example of a complex system. The collective characteristics between the agents of a group are regulated by behavioral tendencies, as well as short-range and long-range interactions among them. In such a complex system, the group with identical agents’ behavior evolves through different states (i.e., spatio-temporal arrangement/configuration of the agents moving in a collective group formation)7,8. We can encode the dynamics (evolution) of the group among different states by constructing a free energy landscape representation9?1. Different factors like the number of members, internal capabilities of the individuals (e.g., sensitivity to neighbors, motion speed of individuals, computational/processing capabilities of agents) and external properties (e.g., environmental and boundary condition) influence the overall collective behavior and the free energy landscape; further, these factors can contribute to various phase transitions.Distribution of the number of overlaps allows calculating a bootstrapped P-value for the observed number of overlaps under the null (the observed number of overlaps is not larger than that expected by chance) and the alternative (the observed number of overlaps is larger than that expected by chance) hypotheses.
www.nature.com/scientificreportsOPENreceived: 07 January 2016 Accepted: 20 May 2016 Published: 14 JuneA Statistical Physics Characterization of the Complex Systems Dynamics: Quantifying Complexity from Spatio-Temporal InteractionsHana Koorehdavoudi1 Paul BogdanBiological systems are frequently categorized as complex systems due to their capabilities of generating spatio-temporal structures from apparent random decisions. In spite of research on analyzing biological systems, we lack a quantifiable framework for measuring their complexity. To fill this gap, in this paper, we develop a new paradigm to study a collective group of N agents moving and interacting in a three-dimensional space. Our paradigm helps to identify the spatio-temporal states of the motion of the group and their associated transition probabilities. This framework enables the estimation of the free energy landscape corresponding to the identified states. Based on the energy landscape, we quantify missing information, emergence, self-organization and complexity for a collective motion. We show that the collective motion of the group of agents evolves to reach the most probable state with relatively lowest energy level and lowest missing information compared to other possible states. Our analysis demonstrates that the natural group of animals exhibit a higher degree of emergence, self-organization and complexity over time. Consequently, this algorithm can be integrated into new frameworks to engineer collective motions to achieve certain degrees of emergence, self-organization and complexity. A complex system refers to a system in which there is a lack of precise relation between the system’s outcomes and the original causes of those outcomes1?. The main characteristics of complex systems are their unpredictable and nonlinear dynamics. This complexity in a system is due to the intricate heterogeneous coupling between the components of the system, which makes it impossible to analyze the components individually and isolated from the rest of the system5. The close coupling and interactions between the units of the complex system cause recognizable collective behavior at larger scales6. A group of agents or animals moving collectively is an example of a complex system. The collective characteristics between the agents of a group are regulated by behavioral tendencies, as well as short-range and long-range interactions among them. In such a complex system, the group with identical agents’ behavior evolves through different states (i.e., spatio-temporal arrangement/configuration of the agents moving in a collective group formation)7,8. We can encode the dynamics (evolution) of the group among different states by constructing a free energy landscape representation9?1. Different factors like the number of members, internal capabilities of the individuals (e.g., sensitivity to neighbors, motion speed of individuals, computational/processing capabilities of agents) and external properties (e.g., environmental and boundary condition) influence the overall collective behavior and the free energy landscape; further, these factors can contribute to various phase transitions.

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