A multiscale view of nonlinear diffusion in biology: From cells to tissues

This paper presents a review on the mathematical tools for the derivation of macroscopic models in biology from the underlying description at the scale of cells as it is delivered by a kinetic theory model. The survey is followed by an overview of research perspectives. The derivation is inspired by the Hilbert’s method, known in classic kinetic theory, which is here applied to a broad class of kinetic equations modeling multicellular dynamics. The main difference between this class of equations with respect to the classical kinetic theory consists in the modeling of cell interactions which is developed by theoretical tools of stochastic game theory rather than by laws of classical mechanics. The survey is focused on the study of nonlinear diffusion and source terms.

Provoking the Adversary by Detecting Eavesdropping and Jamming Attacks: A Game-Theoretical Framework

This paper investigates the secrecy and reliability of a communication where the user is assisting an Intrusion Detection System (IDS) in detecting the adversary’s attack. The adversary is assumed to be sophisticated such that it can conduct eavesdropping and jamming attacks. The IDS is equipped with the capability of detecting both of those attacks. Two scenarios were considered; the first scenario is that the user is trying to detect the adversary by assisting the IDS, and the second scenario is that the user is equipped with a silent time slot in its communication protocol besides assisting the IDS, in order to provoke the adversary into jamming the channel, thus detecting it with a higher probability. Interestingly, adding the capability of detecting eavesdropping attacks pushed the adversary into conducting jamming attacks much more, thus aiding in detecting the adversary earlier. All of that was modeled by means of stochastic game theory, in order to analyze and study the behavior and the interactions between the user and the adversary. Results show a major improvement in the first scenario by 188% and an improvement by 294% in the second scenario in the game value when the probability of detecting eavesdropping attacks was 0.3, which represents the payoff that the user gains in terms of secrecy and reliability.

A quest toward a mathematical theory of the dynamics of swarms

This paper addresses some preliminary steps toward the modeling and qualitative analysis of swarms viewed as living complex systems. The approach is based on the methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlocal, nonlinearly additive and modeled by theoretical tools of stochastic game theory. Collective learning theory can play an important role in the modeling approach. We present a kinetic equation incorporating the Cucker–Smale flocking force and stochastic game theoretic interactions in collision operators. We also present a sufficient framework leading to the asymptotic velocity alignment and global existence of smooth solutions for the proposed kinetic model with a special kernel. Analytic results on the global existence and flocking dynamics are presented, while the last part of the paper looks ahead to research perspectives.

Vulnerability Analysis of CSP Based on Stochastic Game Theory

With the development of industrial informatization, the industrial control network has gradually become much accessible for attackers. A series of vulnerabilities will therefore be exposed, especially the vulnerability of exclusive industrial communication protocols (ICPs), which has not yet been attached with enough emphasis. In this paper, stochastic game theory is applied on the vulnerability analysis of clock synchronization protocol (CSP), one of the pivotal ICPs. The stochastic game model is built strictly according to the protocol with both Man-in-the-Middle (MIM) attack and dependability failures being taken into account. The situation of multiple attack routes is considered for depicting the practical attack scenarios, and the introduction of time aspect characterizes the success probabilities of attackers actions. The vulnerability analysis is then realized through determining the optimal strategies of attacker under different states of system, respectively.