Related papers: On Quadratization of Pseudo-Boolean Functions
Methods of solving big Boolean equations can be broadly classified as algebraic, tabular, numerical and map methods. The most prominent among these classes are the algebraic and map methods. This paper surveys and compares these two types…
In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with…
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…
This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap…
Recently, there has been a lot of effort to represent words in continuous vector spaces. Those representations have been shown to capture both semantic and syntactic information about words. However, distributed representations of phrases…
The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is…
The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results…
We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions, theta functions, mock theta functions, partitions with…
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
Vector space models have become popular in distributional semantics, despite the challenges they face in capturing various semantic phenomena. We propose a novel probabilistic framework which draws on both formal semantics and recent…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
Current pseudo-Boolean solvers implement different variants of the cutting planes proof system to infer new constraints during conflict analysis. One of these variants is generalized resolution, which allows to infer strong constraints, but…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…