Maximizing Activity in Ising Networks via the TAP Approximation

A wide array of complex biological, social, and physical systems have recently been shown to be quantitatively described by Ising models, which lie at the intersection of statistical physics and machine learning. Here, we study the fundamental question of how to optimize the state of a networked Ising system given a budget of external influence. In the continuous setting where one can tune the influence applied to each node, we propose a series of approximate gradient ascent algorithms based on the Plefka expansion, which generalizes the na\"{i}ve mean field and TAP approximations. In the discrete setting where one chooses a small set of influential nodes, the problem is equivalent to the famous influence maximization problem in social networks with an additional stochastic noise term. In this case, we provide sufficient conditions for when the objective is submodular, allowing a greedy algorithm to achieve an approximation ratio of $1-1/e$. Additionally, we compare the Ising-based algorithms with traditional influence maximization algorithms, demonstrating the practical importance of accurately modeling stochastic fluctuations in the system

Effects of Anticipation in Individually Motivated Behaviour on Control and Survival in a Multi-Agent Scenario with Resource Constraints

This is an open access article distributed under the Creative Commons Attribution License CC BY 3.0 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Self-organization and survival are inextricably bound to an agent’s ability to control and anticipate its environment. Here we assess both skills when multiple agents compete for a scarce resource. Drawing on insights from psychology, microsociology and control theory, we examine how different assumptions about the behaviour of an agent’s peers in the anticipation process affect subjective control and survival strategies. To quantify control and drive behaviour, we use the recently developed information-theoretic quantity of empowerment with the principle of empowerment maximization. In two experiments involving extensive simulations, we show that agents develop risk-seeking, risk-averse and mixed strategies, which correspond to greedy, parsimonious and mixed behaviour. Although the principle of empowerment maximization is highly generic, the emerging strategies are consistent with what one would expect from rational individuals with dedicated utility models. Our results support empowerment maximization as a universal drive for guided self-organization in collective agent systemsPeer reviewedFinal Published versio