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Pairwise interactions are fundamental drivers of collective behavior-responsible for group cohesion. The abiding question is how each individual influences the collective. However, time-delayed mutual information and transfer entropy, commonly used to quantify mutual influence in aggregated individuals, can result in misleading interpretations. Here, we show that these information measures have substantial pitfalls in measuring information flow between agents from their trajectories. We decompose the information measures into three distinct modes of information flow to expose the role of individual and group memory in collective behavior. It is found that decomposed information modes between a single pair of agents reveal the nature of mutual influence involving many-body nonadditive interactions without conditioning on additional agents. The pairwise decomposed modes of information flow facilitate an improved diagnosis of mutual influence in collectives.

In collective systems, influence of individuals can permeate an entire group through indirect interactionscomplicating any scheme to understand individual roles from observations. A typical approach to understand an individuals influence on another involves consideration of confounding factors, for example, by conditioning on other individuals outside of the pair. This becomes unfeasible in many cases as the number of individuals increases. In this article, we review some of the unforeseen problems that arise in understanding individual influence in a collective such as single cells, as well as some of the recent works which address these issues using tools from information theory. [ABSTRACT FROM AUTHOR]

The (3 + 1)-dimensional Kadomtsev–Petviashvili equation has significant applications that emerge in the study of fluids and multi-component plasmas. The main object of our study is to investigate stable and efficient solitary solutions to the stated wave equations through two different schemes that provide generic solutions like exponential functions, trigonometric functions, hyperbolic functions, etc. The graphical illustrations for different values of the corresponding parameters of the attained solutions are explained in order to expose the intimate structure of the substantial phenomena. In particular, changes in wave position and category with respect to time are deliberated extensively through 2D figures. It has been found that wave velocity depends on some free parameters associated with the methods used to solve the equation. It has been demonstrated that for different values of the free parameters, the obtained solutions of the KP model exhibit dark soliton, peakon shape soliton, dark soliton-type wave, bright soliton, bell-shaped soliton, etc. Moreover, the direction and position of the solitons for the variation of other parameters are measured, from which a simple and comprehensive interpretation of the various aspects of water waves can be obtained. We think the obtained solution could be highly useful for studying nonlinear events in fluid dynamics, wind waves, and wind-generated waves. [ABSTRACT FROM AUTHOR]

Transfer entropy in information theory was recently demonstrated [Basak et al., Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. Therefore, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to the noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes the identification of the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy difficult. A measure to quantify the degree of strong convexity at the coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of the global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change in transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories. [ABSTRACT FROM AUTHOR]