相关论文: On local equilibrium equations for clustering stat…

Recently, a new local optimality concept for minimax problems, termed calm local minimax points, has been introduced. In this paper, we extend this concept to a general class of nonsmooth, nonconvex nonconcave minimax problems with coupled…

A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates…

We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the…

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient…

The equilibrium states associated with the local majority-rule are divided into three classes, the states of system-wide coordination, the trapped states, and the states of period-2. The effect of clustering coefficient on the occurrence…

We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these…

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…

Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings…

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply…

We present a novel upper bound for the optimal index coding rate. Our bound uses a graph theoretic quantity called the local chromatic number. We show how a good local coloring can be used to create a good index code. The local coloring is…

Understanding the role of randomness when solving locally checkable labeling (LCL) problems in the LOCAL model has been one of the top priorities in the research on distributed graph algorithms in recent years. For LCL problems in…

In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and…

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…

A widely-used operation on graphs is local clustering, i.e., extracting a well-characterized community around a seed node without the need to process the whole graph. Recently local motif clustering has been proposed: it looks for a local…

We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…

Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…

This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…

In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…

An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…

We study the infinite-energy solutions of the Cahn-Hilliard equation in the whole 3D space in uniformly local phase spaces. In particular, we establish the global existence of solutions for the case of regular potentials of arbitrary…