Related papers: Right Buchberger algorithm over bijective skew PBW…
We demonstrate a method to parallelize the computation of a Gr\"obner basis for a homogenous ideal in a multigraded polynomial ring. Our method uses anti-chains in the lattice $\mathbb N^k$ to separate mutually independent S-polynomials for…
The dynamic algorithm to compute a Gr\"obner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no published followups. One reason for this may be that, at first…
Many rings and algebras arising in quantum mechanics can be interpreted as skew PBW (Poincar\'e-Birkhoff-Witt) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov…
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…
In the computation of a Gr"obner basis using Buchberger's algorithm, a key issue for improving the efficiency is to produce techniques for avoiding as many unnecessary critical pairs as possible. A good solution would be to avoid _all_…
In this paper, we study ideals spanned by polynomials or overconvergent series in a Tate algebra. With state-of-the-art algorithms for computing Tate Gr{\"o}bner bases, even if the input is polynomials, the size of the output grows with the…
We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high…
The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…
In this short paper we study for the skew PBW (Poincar\'e-Birkhoff-Witt) extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly…
Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present…
We sample some Poincare-Birkhoff-Witt theorems appearing in mathematics. Along the way, we compare modern techniques used to establish such results, for example, the Composition-Diamond Lemma, Groebner basis theory, and the homological…
We present an algorithm for computing Groebner bases of vanishing ideals of points that is optimized for the case when the number of points in the associated variety is less than the number of indeterminates. The algorithm first identifies…
We propose a new model for learning bilingual word representations from non-parallel document-aligned data. Following the recent advances in word representation learning, our model learns dense real-valued word vectors, that is, bilingual…
The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The…
We prove a sharp lower bound on the number of terms in an element of the reduced Gr\"obner basis of a Schubert determinantal ideal $I_w$ under the term order of [Knutson-Miller '05]. We give three applications. First, we give a…
We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Gr\"obner bases for the ideal of the data points.…