Related papers: A Theoretical Review on Solving Algebra Problems

Logic programs, more specifically, Answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (eg probabilities) of an ASP to its standard…

In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed…

Computational sociology is growing in popularity, yet the analytic tools employed differ widely in power, transparency, and interpretability. In computer science, methods gain popularity after surpassing benchmarks of predictive accuracy,…

In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators.…

One influential approach to assessing the "goodness" of arguments is offered by the Pragma-Dialectical school (p-d) (Eemeren & Grootendorst 1992). This can be compared with Rhetorical Structure Theory (RST) (Mann & Thompson 1988), an…

The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…

Recent research has explored how Language Models (LMs) can be used for feature representation and prediction in tabular machine learning tasks. This involves employing text serialization and supervised fine-tuning (SFT) techniques. Despite…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

The ability of semantic reasoning over the sentence pair is essential for many natural language understanding tasks, e.g., natural language inference and machine reading comprehension. A recent significant improvement in these tasks comes…

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have…

As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…

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…

In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…

We generalize the notions of the St\"ackel transform and the coupling constant metamorphosis to quasi-exactly solvable systems. We discover that for a variety of one-dimensional and separable multidimensional quasi-exactly solvable systems,…

In this paper, we study the convergence of Alternating Projection (AP) algorithm for the matrix completion and compressed sensing problems. We also present computational evidence for the excellent performance of the algorithm. Also, in the…

In this paper, we explore the problem of automatic statute prediction where for a given case description, a subset of relevant statutes are to be predicted. Here, the term "statute" refers to a section, a sub-section, or an article of any…

Set Shaping Theory (SST) moves beyond the classical fixed-space model by constructing bijective mappings the original sequence set into structured regions of a larger sequence space. These shaped subsets are characterized by a reduced…

In this paper, we present ASPEN, an answer set programming (ASP) implementation of a recently proposed declarative framework for collective entity resolution (ER). While an ASP encoding had been previously suggested, several practical…

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical…

Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…