Related papers: Equational Bit-Vector Solving via Strong Gr\"obner…
In this paper, we develop new theory connected with resonant vector bundles that will allow for the use of validated numerics to rigorously determine the stability of pulse solutions in the context of the Swift-Hohenberg equation. For many…
Gr\"{o}bner bases are nowadays central tools for solving various problems in commutative algebra and algebraic geometry. A typical use of Gr\"{o}bner bases is the multivariate polynomial system solving, which enables us to construct…
Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in $n \times m$ variables, we develop theory \& algorithms for Gr\"obner bases in not only algebras with straightening law (ASLs or Hodge…
The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require…
Computations over the rational numbers often encounter the problem of intermediate coefficient growth. A solution to this is provided by modular methods, which apply the algorithm under consideration modulo a number of primes and then lift…
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with…
This survey intends to present the basic notions of Geometric Invariant Theory (GIT) through its paradigmatic application in the construction of the moduli space of holomorphic vector bundles. Special attention is paid to the notion of…
The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the…
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a…
This paper is concerned with the study of properties of the exact solution of the fundamental integrable $G_2$ vertex model. The model $R$-matrix and respective spin chain are presented in terms of the basis generators of the $G_2$ Lie…
This paper presents two modular grad-div algorithms for calculating solutions to the Navier-Stokes equations (NSE). These algorithms add to an NSE code a minimally intrusive module that implements grad-div stabilization. The algorithms do…
While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a…
We propose a simple string bit formalism for interacting strings in a plane wave background, in terms of supersymmetric quantum mechanics with a symmetric product target-space. We construct the light-cone supersymmetry generators and…
We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…
We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
In this paper we bring together the areas of combinatorics and propositional satisfiability. Many combinatorial theorems establish, often constructively, the existence of positive integer functions, without actually providing their closed…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging numerically for large-scale sparse/dense system, especially when it has zero eigenvalues. Based on a direct sum…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…