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We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums…

alg-geom · Mathematics 2008-02-03 T. Graber , R. Pandharipande

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

Classical Analysis and ODEs · Mathematics 2023-05-31 Marcel de Jeu

We design a new algorithm for solving parametric systems having finitely many complex solutions for generic values of the parameters. More precisely, let $f = (f_1, \ldots, f_m)\subset \mathbb{Q}[y][x]$ with $y = (y_1, \ldots, y_t)$ and $x…

Symbolic Computation · Computer Science 2021-12-22 Huu Phuoc Le , Mohab Safey El Din

We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic…

Logic in Computer Science · Computer Science 2017-09-05 Jochen Burghardt

In this paper we develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the…

Algebraic Topology · Mathematics 2022-04-04 Askold Khovanskii , Ivan Limonchenko , Leonid Monin

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

Computational Complexity · Computer Science 2010-02-03 Ryan Williams

Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…

Programming Languages · Computer Science 2023-11-07 Azadeh Farzan , Dominik Klumpp , Andreas Podelski

We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to $p=10$). Besides, we discuss possible reasons for which the…

Numerical Analysis · Mathematics 2017-09-14 Lorenzo Mascotto , Franco Dassi

General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding…

Commutative Algebra · Mathematics 2016-04-01 Chiara Marcolla , Emmanuela Orsini , Massimiliano Sala

In this paper we present a quantifier elimination method for conjunctions of linear real arithmetic constraints. Our algorithm is based on the Fourier-Motzkin variable elimination procedure, but by case splitting we are able to reduce the…

Symbolic Computation · Computer Science 2025-04-23 Valentin Promies , Jasper Nalbach , Erika Ábrahám , Paul Kobialka

In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…

Optimization and Control · Mathematics 2015-06-12 Paul Shearer , Anna C. Gilbert

In this paper, we focus on computing local minimizers of a multivariate polynomial optimization problem under certain genericity conditions. By using a technique in computer algebra and the second-order optimality condition, we provide a…

Optimization and Control · Mathematics 2024-05-10 Vu Trung Hieu , Akiko Takeda

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic…

Machine Learning · Statistics 2023-09-19 Paul Viallard , Pascal Germain , Amaury Habrard , Emilie Morvant

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…

Programming Languages · Computer Science 2015-07-01 Delia Kesner

We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…

Logic in Computer Science · Computer Science 2025-05-01 Alexander Baumgartner , Temur Kutsia , Jordi Levy , Mateu Villaret

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

Machine Learning · Computer Science 2020-02-26 Lukáš Adam , Václav Mácha , Václav Šmídl , Tomáš Pevný

We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of…

Molecular Networks · Quantitative Biology 2021-07-06 Dima Grigoriev , Alexandru Iosif , Hamid Rahkooy , Thomas Sturm , Andreas Weber

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite…

Symbolic Computation · Computer Science 2018-05-01 Sicun Gao , André Platzer , Edmund M. Clarke

Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…

Combinatorics · Mathematics 2016-07-19 Bart Sevenster , Jacob Turner

The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…

Computational Complexity · Computer Science 2011-04-13 Edith Hemaspaandra , Henning Schnoor