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A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number. In this limit, the concentration of tracers is shown to…

Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for…

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Network diffusion models are applicable to many socioeconomic interactions, yet network interaction is hard to observe or measure. Whenever the diffusion process is unobserved, the number of possible realizations of the latent matrix that…

Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals…

Machine learning models that operate on graph-structured data, such as molecular graphs or social networks, often make accurate predictions but offer little insight into why certain predictions are made. Counterfactual explanations address…

In this paper, we deal with distributed estimation problems in diffusion networks with heterogeneous nodes, i.e., nodes that either implement different adaptive rules or differ in some other aspect such as the filter structure or length, or…

This work studies the problem of learning under both large datasets and large-dimensional feature space scenarios. The feature information is assumed to be spread across agents in a network, where each agent observes some of the features.…

We study the properties of the ``Rigid Laplacian'' operator, that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the…

The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…

We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…

We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…

In this paper, we address the problem of how a network of agents can collaboratively fit a linear model when each agent only ever has an arbitrary summand of the regression data. This problem generalizes previously studied…

Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multi-player replicator dynamics in a constant environment. The two-player terms…

Multiagent systems aim to accomplish highly complex learning tasks through decentralised consensus seeking dynamics and their use has garnered a great deal of attention in the signal processing and computational intelligence societies. This…

We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…