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The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a…

Understanding the emergence of inequality in complex systems requires attention to both structural dynamics and intrinsic heterogeneity. In the context of opinion dynamics, traditional models relied on static snapshots or assumed…

In this paper, we mathematically formulate the interaction and dynamics of a hierarchical complex social system where each agent is seen as an array of many variables. The formation of identities and modifications can be studied by using…

The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models…

We present a simple dynamical model for describing trading interactions between agents in a social network by considering only two dynamical variables, namely money and goods or services, that are assumed conserved over the whole time span…

We analyze the dynamics of a forecasting game which exhibits the phenomenon of information cascades. Each agent aims at correctly predicting a binary variable and he/she can either look for independent information or herd on the choice of…

In social networks, bursts of activity often result from the imitative behavior between interacting agents. The Ising model, along with its variants in the social sciences, serves as a foundational framework to explain these phenomena…

In this paper, we propose a statistical aggregation method for agent-based models with heterogeneous agents that interact both locally on a complex adaptive network and globally on a market. The method combines three approaches from…

Empirical distributions of wealth and income can be reproduced using simplified agent-based models of economic interactions, analogous to microscopic collisions of gas particles. Building upon these models of freely interacting agents, we…

There are numerous examples of societies with extremely stable mix of contrasting opinions. We argue that this stability is a result of an interplay between society network topology adjustment and opinion changing processes. To support this…

A simple computer simulation model of a closed market on a fixed network with free flow of goods and money is introduced. The model contains only two variables : the amount of goods and money beside the size of the system. An initially flat…

We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…

This short review presents a selected history of the mutual fertilization between physics and economics, from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial…

In this paper, we present the possibility of using the Ising like models to explain by Statistical Physics means the connection between the financial discontinuities (herd behavior, bubbles, crashes) and "critical points" in physical of…

This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities…

We propose a simple statistical-physics-inspired model for the effect of intrinsic fluctuations on supply and demand in markets. The model consists of agents that trade in two types of goods of which the total number is separately…

We investigate, at the fundamental level, the questions of `why', `when' and `how' one could or should reach out to poor and vulnerable people to support them in the absence of governmental institutions. We provide a simple and new approach…

This paper studies a novel stochastic compartmental model that describes the dynamics of trust in society. The population is split into three compartments representing levels of trust in society: trusters, skeptics and doubters. The focus…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model…