A stochastic model for the influence of social distancing on loneliness

Life and self-organization on the way to artificial intelligence for collective dynamics

This work is dedicated to the study, modeling, and simulation, of the collective dynamics of interacting living entities. The first perspective is to develop a mathematical theory of swarm intelligence for the above mentioned systems. The second perspective is to design the conceptual tools for a theory of artificial intelligence. The aim is to model a dynamics where interacting entities learn from other entities as well as from the environment and external actions. Then, out of this collective learning process, each entity develops a strategy to pursue specific goals through a decision making process that leads to the dynamic. The approach is based on developments of the kinetic theory of active particles. This paper does not naively state that the problem of artificial intelligence for collective dynamics has been exhaustively considered, but some hints are proposed to contribute to such a challenging perspective in view of further developments.

Data-driven mathematical modeling approaches for COVID-19: A survey

In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 260 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population. This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

The dynamics of casual groups can keep free-riders at bay

Understanding the conditions for maintaining cooperation in groups of unrelated individuals despite the presence of non-cooperative members is a major research topic in contemporary biological, sociological, and economic theory. The N-person snowdrift game models the type of social dilemma where cooperative actions are costly, but there is a reward for performing them. We study this game in a scenario where players move between play groups following the casual group dynamics, where groups grow by recruiting isolates and shrink by losing individuals who then become isolates. This describes the size distribution of spontaneous human groups and also the formation of sleeping groups in monkeys. We consider three scenarios according to the probability of isolates joining a group. We find that for appropriate choices of the cost-benefit ratio of cooperation and the aggregation-disaggregation ratio in the formation of casual groups, free-riders can be completely eliminated from the population. If individuals are more attracted to large groups, we find that cooperators persist in the population even when the mean group size diverges. We also point out the remarkable similarity between the replicator equation approach to public goods games and the trait group formulation of structured demes.

When expert predictions fail

We examine the opportunities and challenges of expert judgment in the social sciences, scrutinizing the way social scientists make predictions. While social scientists show above-chance accuracy in predicting laboratory-based phenomena, they often struggle to predict real-world societal changes. We argue that most causal models used in social sciences are oversimplified, confuse levels of analysis to which a model applies, misalign the nature of the model with the nature of the phenomena, and fail to consider factors beyond the scientist's pet theory. Taking cues from physical sciences and meteorology, we advocate an approach that integrates broad foundational models with context-specific time series data. We call for a shift in the social sciences towards more precise, daring predictions and greater intellectual humility.

What is life? Active particles tools towards behavioral dynamics in social-biology and economics

This review paper is devoted to study the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on the challenging perspective of developing a mathematical theory for living systems including mutations and selection. The quest starts with the identification of a number of common complexity features of living systems. Then, mathematical structures are derived to include these features, while mathematical models are derived by inserting in the structures models of individual based interactions. Three applications are examined by active particles methods, i.e., models of SARS2-CoV-2 pandemics, models of idiosyncratic learning in open markets and of the dynamics of prices accounting for human behaviors. A critical study, which pervades the whole paper, shows that also economics can be viewed as a behavioral science thus accounting for specific aspects typical of living systems.