The progressive advent of artificial intelligence machines may represent both an opportunity or a threat. In order to have an idea of what is coming we propose a model that simulate a Human-AI ecosystem. In particular we consider systems where agents present biases, peer-to-peer interactions and also three body interactions that are crucial and describe two humans interacting with an artificial agent and two artificial intelligence agents interacting with a human. We focus our analysis by exploring how the relative fraction of artificial intelligence agents affect that ecosystem. We find evidence that for suitable values of the interaction parameters, arbitrarily small changes in such percentage may trigger dramatic changes for the system that can be either in one of the two polarised states or in an undecided state.

In this paper we use a statistical mechanical model as a paradigm for educational choices when the reference population is partitioned according to the socioeconomic attributes of gender and residence. We study how educational attainment is influenced by socioeconomic attributes of gender and residence for five selected developing countries. The model has a social and a private incentive part with coefficients measuring the influence individuals have on each other and the external influence on individuals, respectively. The methods of partial least squares and the ordinary least squares are, respectively, used to estimate the parameters of the interacting and the noninteracting models. This work differs from the previous work that motivated this work in the following sense: (a) the reference population is divided into subgroups with unequal subgroup sizes, (b) the proportion of individuals in each of the subgroups may depend on the population size N, and (c) the method of partial least squares is used for estimating the parameters of the model with social interaction as opposed to the least squares method used in the earlier work.

We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. We prove that the central limit theorem holds for a suitably rescaled magnetization, while its violation with the typical quartic behavior appears at the critical point.

This paper studies large deviations properties of vectors of empirical means and measures generated as follows. Consider a sequence X1,X2,…,Xn of independent and identically distributed random variables partitioned into d-subgroups with sizes n1,…,nd. Further, consider a d-dimensional vector mn whose coordinates are made up of the empirical means of the subgroups. We prove the following. (1) The sequence of vector of empirical means mn satisfies large deviations principle with rate n and rate function I, when the sequence X1,X2,…,Xn is Rl valued, with l≥1. (2) Similar large deviations results hold for the corresponding sequence of vector of empirical measures Ln if Xi’s, i=1,2,…,n, take on finitely many values. (3) The rate functions for the above large deviations principles are convex combinations of the corresponding rate functions arising from the large deviations principles of the coordinates of mn and Ln. The probability distributions used in the convex combinations are given by α=(α1,…,αd)=limn→∞1/n(n1,…,nd). These results are consequently used to derive variational formula for the thermodynamic limit for the pressure of multipopulation Curie-Weiss (I. Gallo and P. Contucci (2008), and I. Gallo (2009)) and mean-field Pott’s models, via a version of Varadhan’s integral lemma for an equicontinuous family of functions. These multipopulation models serve as a paradigm for decision-making context where social interaction and other socioeconomic attributes of individuals play a crucial role.

This paper proposes a statistical mechanical model for the energy conservation behaviour of energy users. The model was inspired by the multipopulation Curie-Weiss model and the discrete choice with social interaction model. We demonstrate that the model integrates the sociopsychological, the economic, and the energy technologist viewpoints to energy management, allowing us to subject these perspectives to an empirical study.

In this paper, we solve the inverse problem for the cubic mean-field Ising model. Starting from configuration data generated according to the distribution of the model, we reconstruct the free parameters of the system. We test the robustness of this inversion procedure both in the region of uniqueness of the solutions and in the region where multiple thermodynamics phases are present.