Related papers: Algorithmic local monomialization of a binomial: a…
We consider computational and implementation issues for the completion of monomial sets to involution using different involutive divisions. Every of these divisions produces its own completion procedure. For the polynomial case it yields an…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
We obtain the specialization of monomial symmetric functions on the alphabet (a-b)/(1-q). This gives a remarkable algebraic identity, and four new developments for the Macdonald polynomial associated with a row. The proofs are given in the…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
We review a family of local algorithms that permit the simulation of charged particles with purely local dynamics. Molecular dynamics formulations lead to discretizations similar to those of ``particle in cell'' methods in plasma physics.…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and $(\Delta+1)$-coloring algorithms by Barenboim and Elkin [6], by Kuhn [22], and by Panconesi and…
Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an…
We introduce several notions of `random fewnomials', i.e. random polynomials with a fixed number f of monomials of degree N. The f exponents are chosen at random and then the coefficients are chosen to be Gaussian random, mainly from the…
Binary polynomial optimization is equivalent to the problem of minimizing a linear function over the intersection of the multilinear set with a polyhedron. Many families of valid inequalities for the multilinear set are available in the…
We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary…
Can an ideal I in a polynomial ring k[x] over a field be moved by a change of coordinates into a position where it is generated by binomials $x^a - cx^b$ with c in k, or by unital binomials (i.e., with c = 0 or 1)? Can a variety be moved…
In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…
We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…
Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Following the paradigm of numerical algebraic geometry, an algebraic subvariety at a point…
Unitals can be obtained as closures of affine unitals via parallelisms. The isomorphism type of the closure depends on the chosen parallelism, which need not be unique. For affine $\operatorname{SL}(2,q)$-unitals, we introduce a class of…
A differential category is an additive symmetric monoidal category, that is, a symmetric monoidal category enriched over commutative monoids, with an algebra modality, axiomatizing smooth functions, and a deriving transformation on this…
Emerging hybrid accelerator architectures for high performance computing are often suited for the use of a data-parallel programming model. Unfortunately, programmers of these architectures face a steep learning curve that frequently…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
We propose two approaches for selecting variables in latent class analysis (i.e.,mixture model assuming within component independence), which is the common model-based clustering method for mixed data. The first approach consists in…