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The continuous quadratic knapsack (CQK) problem involves minimizing a diagonal convex quadratic function subject to box constraints and a single linear equality constraint. It has numerous applications in resource allocation, multicommodity…
Based on the combinatory theory of rooted colored trees, we investigate the conditions for the explicit stochastic Runge-Kutta (SRK) methods to preserve quadratic invariants (QI) up to certain orders of accuracy. These conditions can supply…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon's product formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of…
Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
Newton's method for polynomial root finding is one of mathematics' most well-known algorithms. The method also has its shortcomings: it is undefined at critical points, it could exhibit chaotic behavior and is only guaranteed to converge…
We study an infinite version of the "jeu de taquin" sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank-$k$ (SR-$k$) methods. Each iteration of SR-$k$ incorporates the curvature information with~$k$ Hessian-vector products…
Recently we explained that the classical $Q$ Schur functions stand behind various well-known properties of the cubic Kontsevich model, and the next step is to ask what happens in this approach to the generalized Kontsevich model (GKM) with…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
We discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field $\mathbb{F}_q$. We solve this problem in the case…
We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…
We perform equilibrium computer simulations of a two-dimensional pinned flexible polymer exposed to a quenched disorder potential consisting of hard disks. We are especially interested in the high-density regime of the disorder, where…