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The constraint satisfaction problem (CSP) can be formulated as a homomorphism problem between relational structures: given a structure $\mathcal{A}$, for any structure $\mathcal{X}$, whether there exists a homomorphism from $\mathcal{X}$ to…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers…
Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…
The challenge of imbalanced learning lies not only in class imbalance problem, but also in the class overlapping problem which is complex. However, most of the existing algorithms mainly focus on the former. The limitation prevents the…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
Discrete facility layout design involves placing physical entities to minimize handling costs while adhering to strict safety and spatial constraints. This combinatorial problem is typically addressed using Mixed Integer Linear Programming…
We construct a CFT dual to string theory on AdS$_3$ with pure NS-NS flux. It is given by a symmetric orbifold of a linear dilaton theory deformed by a marginal operator from the twist-2 sector. We compute two- and three-point functions on…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
Contrast-Consistent Search (CCS) is an unsupervised probing method able to test whether large language models represent binary features, such as sentence truth, in their internal activations. While CCS has shown promise, its two-term…
Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear…
We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. For this…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled…