Related papers: Dynamical Cavity Method for Hypergraphs and its Ap…
The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used…
Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically…
We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random graph. Although the case of random…
Dense subgraph mining is a fundamental technique in graph mining, commonly applied in fraud detection, community detection, product recommendation, and document summarization. In such applications, we are often interested in identifying…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
Force-directed approach is one of the most widely used methods in graph drawing research. There are two main problems with the traditional force-directed algorithms. First, there is no mature theory to ensure the convergence of iteration…
We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form, the moments of the total number of solutions as a function of d and K, where the average is over…
We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…
Initial value problems for the integrable discrete equations on quad-graphs are investigated. A geometric criterion of the well-posedness of such a problem is found. The effects of the interaction of the solutions with the localized defects…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
We consider the power of local algorithms for approximately solving Max $k$XOR, a generalization of two constraint satisfaction problems previously studied with classical and quantum algorithms (MaxCut and Max E3LIN2). In Max $k$XOR each…
Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum…
In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\mathbb{R}^d$, a kernel function $k: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$, and a query point $\mathbf{q} \in \mathbb{R}^d$, and…
The Conway-99 problem questions the existence of a strongly regular graph with 99 vertices and specific parameters. A \textit{strongly} regular graph is a regular graph that exhibits two additional properties: vertices must share a fixed…
Multi-hop reasoning has been widely studied in recent years to seek an effective and interpretable method for knowledge graph (KG) completion. Most previous reasoning methods are designed for dense KGs with enough paths between entities,…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate…
Strongly coupled dissipative optical cavities with nonlinear interactions give new opportunities to explore symmetry breaking phenomena and phase transitions, Josephson dynamics and quantum criticality. Among the different experimental…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their…
We study the performance of stochastic local search algorithms for random instances of the $K$-satisfiability ($K$-SAT) problem. We introduce a new stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a…