Related papers: A Monomial-Oriented GVW for Computing Gr\"obner Ba…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
Let T(x) in k[x] be a monic non-constant polynomial and write R=k[x] / (T) the quotient ring. Consider two bivariate polynomials a(x, y), b(x, y) in R[y]. In a first part, T = p^e is assumed to be the power of an irreducible polynomial p. A…
Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models…
We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree…
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them…
We propose a family of quantum algorithms for estimating Gowers uniformity norms $ U^k $ over finite abelian groups and demonstrate their applications to testing polynomial structure and counting arithmetic progressions. Building on recent…
In April 2025 GMV announced a competition for finding the best method to solve a particular polynomial system over a finite field. In this paper we provide a method for solving the given equation system significantly faster than what is…
Semantic reasoning aims to infer new knowledge from existing knowledge, with OWL ontologies serving as a standardized framework for organizing information. A key challenge in semantic reasoning is verifying ontology consistency. However,…
This paper presents a novel approach to Grover adaptive search (GAS) for a combinatorial optimization problem whose objective function involves spin variables. While the GAS algorithm with a conventional design of a quantum dictionary…
Global Value Numbering(GVN) is a method for detecting redundant computations in programs. Here, we introduce the problem of Global Value Numbering in its original form, as conceived by Kildall(1973), and present an algorithm which is a…
In his Ph.D. thesis, Sean Griffin introduced a family of ideals and found monomial bases for their quotient rings. These rings simultaneously generalize the Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono and the cohomology…
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse…
Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it…
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the…
In light of the recent success of Graph Neural Networks (GNNs) and their ability to perform inference on complex data structures, many studies apply GNNs to the task of text classification. In most previous methods, a heterogeneous graph,…
Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM).…
The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate…
The Quantum Approximate Optimization Algorithm (QAOA) is among leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant…
This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…