A Simple Model of Ostracism Formation

We study formation of ostracism in a society from a game theoretical perspective. The dynamics of group formation is complicated in that the choices of the individuals and the form of the groups mutually affect each other in the process. A suggested simple model shows that individual efforts to increase his/her own sense of belonging is responsible for both growth of groups and creation of an outcast. Once a person happens to get behind in synchronizing with others, tendency to alienate him may grow among others, possibly making him left out in the end. Alienating minority occurs even when there is a penalty for disliking and people are encouraged to favor others. Considering that the target is accidentally picked, we can understand ostracism as an inherent part of the group formation, rather than a result of specific discrepancy among people. Another finding is that a single individual who seeks for unconditional unification of the society ("philanthropist'') likely invites his/her own isolation from the society, while the existence of such person generally promotes coalition of others.open0

Marginalized ordering and adaptive reaction time in bird flocks

We develop a model for a rich dynamics of a flock in a marginalized ordering state. The aim is to present an inter-individual coordination mechanism that keeps a flock constantly ready to respond to perturbations naturally present in biological systems. We extend the generalized Cucker-Smale model with the coupling of acceleration and introduce adaptive reaction times of each bird. We regard two key factors in the reaction times: (1) the local ordering state of each bird and (2) reaction sensitivity of a flock to the neighbor's momentum change with $\kappa^{-1}$. We show that our model displays innate fluctuations and rich dynamics as a reminiscent of natural flocks due to the adaptive reaction delay. This happens without relying on stochastic variables. We compute the correlation lengths of the fluctuations and find that the correlation of velocity and speed is scale-free, indicating some criticality of a flock. It is dynamically in a marginalized ordering states, rather than in either an ordered or a disordered state. Surprisingly, at a large value of $\kappa^{-1}$ (i.e., reaction sensitivity is high), the transition occurs from the standard diffusion to the super-diffusive Levy flights by increasing the strength of the velocity alignment. Our results indicate that the emergence of the long-term behaviors such as Levy flights can also be explained in terms of the inter-individual interaction that makes the system in a marginalized ordering state

Isolation and exploitation of minority: Game theoretical analysis

We investigate various group-size distributions occurring in a situation where each group???s resource is exposed to appropriation by other groups. The amount of appropriation depends on the size difference between groups. Our work focuses on the cases where the entire community isolates a small group or even an individual to maximize its gain. While people???s basic motivation to form a group can be understood based on the group-size effect on multiplying a collective asset, sensitive factors that induce a asymmetric group distribution are the group efficiency and the ratio of secured assets to assets pending in a competition. We show that social rejection to a minor group may occur when the group efficiency is relatively low and their asset is severely exposed to possible appropriation

A probability generating function method for stochastic reaction networks

In this paper we present a probability generating function (PGF) approach for analyzing stochastic reaction networks. The master equation of the network can be converted to a partial differential equation for PGF. Using power series expansion of PGF and Pade approximation, we develop numerical schemes for finding probability distributions as well as first and second moments. We show numerical accuracy of the method by simulating chemical reaction examples such as a binding-unbinding reaction, an enzyme-substrate model, Goldbeter-Koshland ultrasensitive switch model, and G(2)/M transition model.open1

Epidemic Spreading in Complex Networks with Resilient Nodes: Applications to FMD

At the outbreak of the animal epidemic disease, farms that recover quickly from partially infected state can delay or even suppress the wide spreading of the infection over farm networks. In this work, we focus on how the spatial transmission of the infection is affected by both factors, the topology of networks and the internal resilience mechanism of nodes. We first develop an individual farm model to examine the influence of initial number of infected individuals and vaccination rate on the transmission in a single farm. Based on such intrafarm model, the farm network is constructed which reflects disease transmission between farms at various stages. We explore the impact of the farms vaccinated at low rates on the disease transmission into entire farm network and investigate the effect of the control on hub farms on the transmission over the farm network. It is shown that intensive control on the farms vaccinated at low rates and hub farms effectively reduces the potential risk of foot-and-mouth disease (FMD) outbreak on the farm network

Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

This paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. We are especially interested in the quasilinear equation u(t) + au(x). = f(x)u + g(x)u(n) and the wave equation u(tt) = f(x)u(xx) that have a highly oscillating term like f(x) = sin(x/epsilon), epsilon << 1. It also applies to the equations involving rapidly changing or even discontinuous coefficients. The method is based on the solution interpolation and the underlying idea is to establish a numerical scheme by interpolating numerical data with a parameterized solution of the equation. While the constructed numerical schemes retain the same stability condition, they carry both quantitatively and qualitatively better performances than the standard method.open0

Evolution of Cooperation through Power Law Distributed Conflicts

At an individual level, cooperation can be seen as a behaviour that uses personal resource to support others or the groups which one belongs to. In a conflict between two individuals, a selfish person gains an advantage over a cooperative opponent, while in a group-group conflict the group with more cooperators wins. In this work, we develop a population model with continual conflicts at various scales and show cooperation can be sustained even when interpersonal conflicts dominate, as long as the conflict size follows a power law. The power law assumption has been met in several observations from real-world conflicts. Specifically if the population is structured on a scale-free network, both the power law distribution of conflicts and the survival of cooperation can be naturally induced without assuming a homogeneous population or frequent relocation of members. On the scale-free network, even when most people become selfish from continual person-person conflicts, people on the hubs tend to remain unselfish and play a role as ???repositories??? of cooperation.clos

Reservoir Computing based on Quenched Chaos

Reservoir computing (RC) is a brain-inspired computing framework that employs a transient dynamical system whose reaction to an input signal is transformed to a target output. One of the central problems in RC is to find a reliable reservoir with a large criticality, since computing performance of a reservoir is maximized near the phase transition. In this work, we propose a continuous reservoir that utilizes transient dynamics of coupled chaotic oscillators in a critical regime where sudden amplitude death occurs. This "explosive death" not only brings the system a large criticality which provides a variety of orbits for computing, but also stabilizes them which otherwise diverge soon in chaotic units. The proposed framework shows better results in tasks for signal reconstructions than RC based on explosive synchronization of regular phase oscillators. We also show that the information capacity of the reservoirs can be used as a predictive measure for computational capability of a reservoir at a critical point. (c) 2020 Elsevier Ltd. All rights reserved