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Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…

Cooperative transmission is an emerging communication technique that takes advantage of the broadcast nature of wireless channels. However, due to low spectral efficiency and the requirement of orthogonal channels, its potential for use in…

We present a computational protocol, based on density matrix perturbation theory, to obtain non-adiabatic, frequency-dependent electron-phonon self-energies for molecules and solids. Our approach enables the evaluation of electron-phonon…

Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…

Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…

A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.

This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…

We propose a flexible gradient tracking approach with adjustable computation and communication steps for solving distributed stochastic optimization problem over networks. The proposed method allows each node to perform multiple local…

This works aims at understanding further convergence properties of first order local search methods with complex geometries. We focus on the composite optimization model which unifies within a simple formalism many problems of this type. We…

This survey revisits classical combinatorial optimization algorithms and extends them to two-stage stochastic models, particularly focusing on client-element problems. We reformulate these problems to optimize element selection under…

A statistical estimation model with qualitative input provides a mechanism to fuse human intuition in the form of qualitative information into a statistical model. We investigate the statistical properties of this model and devise a…

Using multiple-choice questions (MCQs) has become a standard for assessing LLM capabilities efficiently. A variety of metrics can be employed for this task. However, previous research has not conducted a thorough assessment of them. At the…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

We develop a unified operator framework for scalar, multivariate, and functional regression based on integral operators defined with respect to general measures. Within this framework, classical regression models, including…

This paper studies the performance of some state-of-the-art cooperative full-duplex relaying protocols in the context of a large wireless network modelled using stochastic geometry tools. We investigate the outage behaviour for different…

In this paper, we propose a hybrid framework to solve large-scale permutation-based combinatorial problems effectively using a high-performance quadratic unconstrained binary optimization (QUBO) solver. To do so, transformations are…

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…