Related papers: Riemannian and Lorentzian flow-cut theorems

Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…

In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…

Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This…

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the…

Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how…

We establish the incompressible low--Mach/high--Reynolds limit for the Boltzmann equation for a broad class of initial data, without recourse to any asymptotic expansion. Exploiting the local Maxwellian manifold and the macro--micro…

We consider the standard first passage percolation model in the rescaled graph $\mathbb{Z}^d/n$ for $d\geq2$ and a domain $\Omega$ of boundary $\Gamma$ in $\mathbb{R}^d$. Let $\Gamma ^1$ and $\Gamma ^2$ be two disjoint open subsets of…

Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…

The multicast capacity of a directed network is closely related to the $s$-$t$ maximum flow, which is equal to the $s$-$t$ minimum cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is…

A popular class of algorithms to optimize the dual LP relaxation of the discrete energy minimization problem (a.k.a.\ MAP inference in graphical models or valued constraint satisfaction) are convergent message-passing algorithms, such as…

We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.

In his paper `Conjectures on Bridgeland Stability', Joyce asked if one can desingularise the transverse intersection point of an immersed Lagrangian using JLT expanders such that one gets a Lagrangian mean curvature flow via the…

In this paper, we first present a Gearhardt-Pr\"uss type theorem with a sharp bound for m-accretive operators. Then we give two applications: (1) give a simple proof of the result proved by Constantin et al. on relaxation enhancement…

In this paper we formulate some conjectures about algebraic flows on Shimura varieties. In the first part of the paper we prove the `logarithmic Ax-Lindemann theorem'. We then prove a result concerning the topological closure of the images…

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general…

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an…

In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set…

Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove…

We consider the efficiency of turbulence, a dimensionless parameter that characterises the fraction of the input energy stored into a turbulent flow field. We first show that the inverse of the efficiency provides an upper bound for the…

We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…