Related papers: Successive Difference Substitution Based on Column…

Goal-directed evaluation of Answer Set Programs is gaining traction thanks to its amenability to create AI systems that can, due to the evaluation mechanism used, generate explanations and justifications. s(CASP) is one of these systems and…

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…

Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…

We consider partial symmetric Toeplitz matrices where a positive definite completion exists. We characterize those patterns where the maximum determinant completion is itself Toeplitz. We then extend these results with positive definite…

The real radical ideal of a system of polynomials with finitely many complex roots is generated by a system of real polynomials having only real roots and free of multiplicities. It is a central object in computational real algebraic…

In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of…

We outline a procedure for jointly sampling substitution matrices and multiple sequence alignments, according to an approximate posterior distribution, using an MCMC-based algorithm. This procedure provides an efficient and simple method by…

Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular…

For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach that combines differential and difference algebra to analyze s(trong)-consistency of finite difference approximations.…

Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…

We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…

Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining…

We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a…

Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…

Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…