Related papers: On simplified models for dynamics of pointlike obj…

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…

Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…

Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Generic coarse-grained models are designed such that they are (i) simple and (ii) computationally efficient. They do not aim at representing particular materials, but classes of materials, hence they can offer insight into universal…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…

Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of…

We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…

A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of…

In this paper we provide theoretical results that relate steady states of continuous and discrete models arising from biology.

Physical systems obey strict symmetry principles. We expect that machine learning methods that intrinsically respect these symmetries should have higher prediction accuracy and better generalization in prediction of physical dynamics. In…

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…

Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…

In this article, we are interested in studying locomotion strategies for a class of shape-changing bodies swimming in a fluid. This class consists of swimmers subject to a particular linear dynamics, which includes the two most investigated…

We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…

Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…

Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…