Related papers: Convex Dynamics and Applications
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…
We consider the model of a point-vortex under a periodic perturbation and give sufficient conditions for the existence of generalized quasi-periodic solutions with rotation number. The proof uses Aubry-Mather theory to obtain the existence…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as…
General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
A mathematical modeling process for phenomena with a single state variable that attempts to be realistic must be given by a scalar nonautonomous differential equation $x'=f(t,x)$ that is concave with respect to the state variable $x$ in…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
Image feature matching is a fundamental part of many geometric computer vision applications, and using multiple images can improve performance. In this work, we formulate multi-image matching as a graph embedding problem then use a Graph…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
We explore the oscillatory behavior observed in inversion methods applied to large-scale text-to-image diffusion models, with a focus on the "Flux" model. By employing a fixed-point-inspired iterative approach to invert real-world images,…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…