相关论文: Improved method for finding optimal formulae for b…
A new non-Hermitian E2-quasi-exactly solvable model is constructed containing two previously known models of this type as limits in one of its three parameters. We identify the optimal finite approximation to the double scaling limit to the…
This study investigates a new hybrid method for solving the combinatorial problem of optimizing fractional functions with 0-1 binary variables. The method combines density matrix minimization (DMM), tabu search (TS), and the Dinkelbach…
We show that the recent breakthrough result of [Buchbinder and Feldman, FOCS'24] could further lead to a deterministic $(1-\kappa_{f}/e-\varepsilon)$-approximate algorithm for maximizing a submodular function with curvature $\kappa_{f}$…
Compositional data and multivariate count data with known totals are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. It is often the case that many of the compositional components are highly…
We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by…
Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when…
This paper is intended to give closed formulae for binomial determinants with consecutive or almost consecutive rows or columns, as well as calculating the generator of left nullspaces defined by some binomial matrices. In the meantime, we…
We introduce a basis for a bi-dimensional finite matrix calculus and a bi-dimensional finite matrix action principle. As an application, we analyze scalar and spinorial fields in $D=4n+2$ in this approach. We verify that to establish a…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
In this paper, we present a new formula for the determinant of a $4 \times 4$ matrix. We approach via the sparse optimization problem and derive the formula through the Least Absolute Shrinkage and Selection Operator (LASSO). Our formula…
We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earlier work by the author on exact formulas for bivariate…
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Models coming from different physical applications are very large in size. Simulation with such systems is expensive so one usually obtains a reduced model (by model reduction) that replicates the input-output behaviour of the original full…
We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C^4 x C^4 -> C^4. This…
In this paper, we study deformations of Brieskorn polynomials of two variables obtained by adding linear terms consisting of the conjugates of complex variables and prove that the deformed polynomial maps have only indefinite fold and cusp…
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix…
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming…
We introduce a new class of irreducible pentanomials over $\mathbb{F}_2$ of the form $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ and use $f$ to define the finite field extension of degree $m$. We give the exact number of…
A bilinear quadrature numerically evaluates a continuous bilinear map, such as the $L^2$ inner product, on continuous $f$ and $g$ belonging to known finite-dimensional function spaces. Such maps arise in Galerkin methods for differential…