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Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a…
We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with…
Ciliated tissues such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal…
We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical…
Dynamical coherent structure (pattern) formation in the Klein-Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that besides spatial patterns discovered recently (V.M.Burlakov,…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
We investigate experimentally the connection between short time dynamics and long time dynamical heterogeneities within a dense granular media under cyclic shear. We show that dynamical heterogeneities result from a two timescales process.…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to…
In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of…
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
The important phenomenon of "stickiness" of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as classical and statistical mechanics,…
We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP…
Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative…
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
Dynamic facilitation theory assumes short-ranged dynamic constraints to be the essential feature of supercooled liquids and draws much of its conclusions from the study of kinetically constrained models. While deceptively simple, these…