Related papers: Non-Orthodox Combinatorial Models Based on Discord…
Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
Modern CDCL SAT solvers easily solve industrial instances containing tens of millions of variables and clauses, despite the theoretical intractability of the SAT problem. This gap between practice and theory is a central problem in solver…
This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to…
This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis, non-negative matrix factorisation and latent Dirichlet allocation. The main…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…
Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…
We use testing to check if a combinational circuit $N$ always evaluates to 0 (written as $N \equiv 0$). We call a set of tests proving $N \equiv 0$ a complete test set (CTS). The conventional point of view is that to prove $N \equiv 0$ one…
Tripartite graph-based recommender systems markedly diverge from traditional models by recommending unique combinations such as user groups and item bundles. Despite their effectiveness, these systems exacerbate the longstanding cold-start…
We introduce an approach that aims to combine the usage of satisfiability modulo theories (SMT) solvers with the Combinatory Logic Synthesizer (CL)S framework. (CL)S is a tool for the automatic composition of software components from a…
Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…
Short text clustering is a challenging problem due to its sparseness of text representation. Here we propose a flexible Self-Taught Convolutional neural network framework for Short Text Clustering (dubbed STC^2), which can flexibly and…
Clustering is the task of gathering similar data samples into clusters without using any predefined labels. It has been widely studied in machine learning literature, and recent advancements in deep learning have revived interest in this…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…
Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are…
We introduce the notion of a \emph{braided dihedral set} (BDS) to describe set-theoretical solutions of the Yang-Baxter equation (YBE) that furnish representations of the infinite dihedral group on the Cartesian square of the underlying…
Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be…
Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear…
Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints.…