相关论文: Adjacency Criterion For Gradient Flow With Multipl…

We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…

In this paper we consider a control system of the form $\dot x = F(x)u$, linear in the control variable $u$. Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an…

In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…

We study a class of dynamical multi-commodity flow networks in transportation networks. These are modeled as dynamical systems describing the evolution of the densities of a number of different commodities across the cells of a…

A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…

This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…

In this paper we study the stable set of the gradient flow associated with a critical point of an analytic function. In particular we present simple topological conditions which imply that this set contains an infinite family of…

We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…

We consider the initial value problem for a scalar conservation law in one space dimension with a single spatial flux discontinuity, the so-called two-flux problem. We prove that a well-known front tracking algorithm has a convergence rate…

Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this…

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced in [M.E.J. Newman, Phys.…

We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no…

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…

The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence…

We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…

We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…

We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global…

This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…

For a class of coalescing stochastic flows on the real line the existence of dual flows is proved. A stochastic flow and its dual are constructed as a forward and backward perfect cocycles over the same metric dynamical system. The metric…