相关论文: RSK and Quantum Symmetric Functions: A Combinatori…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
We introduce the quadratic balanced optimization problem (QBOP) which can be used to model equitable distribution of resources with pairwise interaction. QBOP is strongly NP-hard even if the family of feasible solutions has a very simple…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…
In this work, we develop a new quantum algorithm to solve a combinatorial problem with significant practical relevance occurring in clutch manufacturing. It is demonstrated how quantum optimization can play a role in real industrial…
Quantum networks are gaining momentum in finding applications in a wide range of domains. However, little research has investigated the potential of a quantum network framework to enable highly reliable communications. The goal of this work…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on the Clifford analysis. Applications to the quantum field theory are described. Keywords: Functional calculus, Weyl calculus, Riesz…
We formulate binary optimization functions for single-vehicle routing, travelling salesperson and collision-free multi-vehicle routing with significant improvements in the number of variables over existing formulations. The provided…
We study a multi-symmetric generalization of the classical Schur functions called the multi-symmetric Schur functions. These functions form an integral basis for the ring of multi-symmetric functions indexed by tuples of partitions and are…
Our main result here is that the specialization at $t=1/q$ of the $Q_{km,kn}$ operators studied in [4] may be given a very simple plethystic form. This discovery yields elementary and direct derivations of several identities relating these…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…