Related papers: Signature-Based Gr\"obner Basis Algorithms --- Ext…

In this paper we give an insight into the behaviour of signature-based Gr\"obner basis algorithms, like F5, G2V or SB, for inhomogeneous input. On the one hand, it seems that the restriction to sig-safe reductions puts a penalty on the…

Signature-based algorithms are a popular kind of algorithms for computing Groebner basis, including the famous F5 algorithm, F5C, extended F5, G2V and the GVW algorithm. In this paper, an efficient method is proposed to solve the…

An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…

Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field…

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…

Border bases, a generalization of Groebner bases, have actively been researched during recent years due to their applicability to industrial problems. A. Kehrein and M. Kreuzer formulated the so called Border Basis Algorithm, an algorithm…

This paper introduces a strategy for signature-based algorithms to compute Groebner basis. The signature-based algorithms generate S-pairs instead of S-polynomials, and use s-reduction instead of the usual reduction used in the Buchberger…

The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be…

A designated verifier signature scheme allows a signer to generate a signature that only the designated verifier can verify. This paper proposes multi-signer strong designated multi-verifier signature schemes based on multiple cryptographic…

The signatures of polynomials were originally introduced by Faug\`{e}re for the efficient computation of Gr\"obner bases [Fau02], and redefined by Arri-Perry [AP11] as the standard monomials modulo the module of syzygies. Since it is…

We show herein that a pattern based on FGLM techniques can be used for computing Gr\"obner bases, or related structures, associated to linear codes. This Gr\"obner bases setting turns out to be strongly related to the combinatorics of the…

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based…

The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in…

In this contribution, a Bayes Ying Yang(BYY) harmony based approach for on-line signature verification is presented. In the proposed method, a simple but effective Gaussian Mixture Models(GMMs) is used to represent for each user's signature…

The general principle for a quantum signature scheme is proposed and investigated based on ideas from classical signature schemes and quantum cryptography. The suggested algorithm is implemented by a symmetrical quantum key cryptosystem and…

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…

This paper considers parallel Gr\"obner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We summarize three different Gr\"obner bases implementations: shared memory parallel, pure distributed memory…

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the…

In this paper we present a new methodology for solving multiobjective integer linear programs using tools from algebraic geometry. We introduce the concept of partial Gr\"obner basis for a family of multiobjective programs where the…

Motivation: ``Molecular signatures'' or ``gene-expression signatures'' are used to predict patients' characteristics using data from coexpressed genes. Signatures can enhance understanding about biological mechanisms and have diagnostic…