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Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…
This paper develops two mathematical models to understand subjects' behavior in response to the urgency of a change and inputs from governments e.g., (subsides) in the context of the diffusion of the solar photovoltaic in Italy. The first…
This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features:…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and…
Administrative data allows us to count for the number of residents. The geo-localization of people by mobile phone, by quantifying the number of people at a given moment in time, enriches the amount of useful information for "smart"…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we…
This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty.…
This paper studies the evolution of economic activities using a continuous time-space aggregation-diffusion model, which encompasses competing effects of agglomeration and congestion. To bring the model to the real data, a novel…
A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
In several countries, including Italy, a prominent approach to population health surveillance involves conducting repeated cross-sectional surveys at short intervals of time. These surveys gather information on the health status of…
In this paper we analyze the rural-urban migration phenomena as it is usually observed in economies which are in the early stages of industrialization. The analysis is conducted by means of a statistical mechanics approach which builds a…
Repeated small dynamic networks are integral to studies in evolutionary game theory, where networked public goods games offer novel insights into human behaviors. Building on these findings, it is necessary to develop a statistical model…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent on dynamically changing population structures, appear in a…
The structure and evolution of Terrestrial Transportation Infrastructures (TTIs) are shaped by both socio-political and geographical factors, hence encoding crucial information about how resources and power are distributed through a…
We propose a stochastic map model of economic dynamics. In the last decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of…
In this paper we investigate the spatio-temporal dynamics of obesity rates across Italian regions from 2010 to 2022, aiming to identify spatial and temporal trends and assess potential heterogeneities. We implement a Bayesian hierarchical…