Related papers: Finitary Process Evolution I: Information Geometry…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
We provide an asymptotic analysis of a nonlinear integro-differential equation describing the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is…
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…
We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a…
We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…
Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory,…
Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on…
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it…
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types, that elaborates this complexity, result from the activity of gene networks and…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…