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The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
We propose a data-driven framework to simplify the description of spatiotemporal climate variability into few entities and their causal linkages. Given a high-dimensional climate field, the methodology first reduces its dimensionality into…
Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved…
Clustering is a fundamental collective phenomenon in agent-based models (ABMs) of opinion dynamics. To study clustering in systems with co-evolving social and opinion variables, we derive stochastic partial differential equation (SPDE)…
The recent pandemic emphasized the need to consider the role of human behavior in shaping epidemic dynamics. In particular, it is necessary to extend beyond the classical epidemiological structures to fully capture the interplay between the…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
Epidemic models study the spread of an undesired agent through a population, be it infectious diseases through a country, misinformation in online social media, or pests infesting a region. In combating these epidemics, we rely neither on…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
The exploration of epidemic dynamics on dynamically evolving ("adaptive") networks poses nontrivial challenges to the modeler, such as the determination of a small number of informative statistics of the detailed network state (that is, a…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
We develop a new structured compartmental model for the coevolutionary dynamics between susceptible and infectious individuals in heterogeneous SI epidemiological systems. In this model, the susceptible compartment is structured by a…
In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…
Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses,…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Empirical data on the dynamics of human face-to-face interactions across a variety of social venues have recently revealed a number of context-independent structural and temporal properties of human contact networks. This universality…