Related papers: An age structured demographic theory of technologi…

Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…

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,…

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…

We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…

Diffusion models undergo a phase transition in a critical time window during generation dynamics, with two complementary diagnoses of criticality. The symmetry breaking picture views the critical window as when trajectories bifurcate into…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

Aging is a universal consequence of life, yet researchers have identified no universal theme. This manuscript considers aging from the perspective of entropy, wherein things fall apart. We first examine biological information change as a…

Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…

To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge…

We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of…

Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…

Diffusion models are the mainstream approach for time series generation tasks. However, existing diffusion models for time series generation require retraining the entire framework to introduce specific conditional guidance. There also…

Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point. This fixed-point becomes…

We study the equilibrium phases of a generalized Lotka-Volterra model characterized by a species interaction matrix which is random, sparse and symmetric. Dynamical fluctuations are modeled by a demographic noise with amplitude proportional…

Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…

This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…

Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…

When the output of an atomistic simulation (such as the Gillespie stochastic simulation algorithm, SSA) can be approximated as a diffusion process, we may be interested in the dynamic features of the deterministic (drift) component of this…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…