Related papers: On Quadratization of Pseudo-Boolean Functions
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as…
We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
We study two important operations on polynomials defined over complete discrete valuation fields: Euclidean division and factorization. In particular, we design a simple and efficient algorithm for computing slope factorizations, based on…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
In the present paper we describe new heuristic technique, which can be applied to the optimization of pseudo-Boolean functions including Black-Box functions. This technique is based on a simple procedure which consists in transition from…
Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this…
Unsupervised word segmentation in audio utterances is challenging as, in speech, there is typically no gap between words. In a preliminary experiment, we show that recent deep self-supervised features are very effective for word…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x \neq y\setminus z$, and $z =\{x\}$, where $x,y,z$ stand for variables ranging over the von…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach.…
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
In pseudo-boolean solving the currently most successful unit propagation strategy is a hybrid mode combining the watched literal scheme with the counting method. This short paper introduces new heuristics for this hybrid decision, which are…