相关论文: Fixation for Distributed Clustering Processes

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…

A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…

The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…

A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…

We prove that, for every $k=1,2,...,$ every shortest-path metric on a graph of pathwidth $k$ embeds into a distribution over random trees with distortion at most $c$ for some $c=c(k)$. A well-known conjecture of Gupta, Newman, Rabinovich,…

We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…

The $d$-process generates a graph at random by starting with an empty graph with $n$ vertices, then adding edges one at a time uniformly at random among all pairs of vertices which have degrees at most $d-1$ and are not mutually joined. We…

We consider a general stable flow problem in a directed and capacitated network, where each vertex has a strict preference list over the incoming and outgoing edges. A flow is stable if no group of vertices forming a path can mutually…

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…

We give a deterministic algorithm for computing a global minimum vertex cut in a vertex-weighted graph $n$ vertices and $m$ edges in $\widehat O(mn)$ time. This breaks the long-standing $\widehat \Omega(n^{4})$-time barrier in dense graphs,…

The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…

Equip the edges of the lattice $\mathbb{Z}^2$ with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in $\mathbb{R}^2$ when the side lengths of the rectangle go to infinity. We prove that…

We consider the standard first passage percolation on $\mathbb{Z}^{d}$: with each edge of the lattice we associate a random capacity. We are interested in the maximal flow through a cylinder in this graph. Under some assumptions Kesten…

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…

In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…

We study a branching random walk with independent and identically distributed, heavy tailed displacements. The offspring law is supercritical and satisfies the Kesten-Stigum condition. We treat the case when the law of the displacements…

We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

We investigate a class of aggregation-diffusion equations with strongly singular kernels and weak (fractional) dissipation in the presence of an incompressible flow. Without the flow the equations are supercritical in the sense that the…

We consider the problem of clustering data that reside on discrete, low dimensional lattices. Canonical examples for this setting are found in image segmentation and key point extraction. Our solution is based on a recent approach to…