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Planar functions are mappings from a finite field $\mathbb{F}_q$ to itself with an extremal differential property. Such functions give rise to finite projective planes and other combinatorial objects. There is a subtle difference between…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
We introduce a deterministic approach to edge detection and image segmentation by formulating pseudo-Boolean polynomials on image patches. The approach works by applying a binary classification of blob and edge regions in an image based on…
We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and…
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps >…
Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…