Search results for "FACTORIZATION"
showing 10 items of 221 documents
DYTurbo: fast predictions for Drell–Yan processes
2019
The European physical journal / C 80(5), 251 (2020). doi:10.1140/epjc/s10052-020-7757-5
A Push Forward Construction and the Comprehensive Factorization for Internal Crossed Modules
2014
In a semi-abelian category, we give a categorical construction of the push forward of an internal pre-crossed module, generalizing the pushout of a short exact sequence in abelian categories. The main properties of the push forward are discussed. A simplified version is given for action accessible categories, providing examples in the categories of rings and Lie algebras. We show that push forwards can be used to obtain the crossed module version of the comprehensive factorization for internal groupoids.
Sorting suffixes of a text via its Lyndon Factorization
2013
The process of sorting the suffixes of a text plays a fundamental role in Text Algorithms. They are used for instance in the constructions of the Burrows-Wheeler transform and the suffix array, widely used in several fields of Computer Science. For this reason, several recent researches have been devoted to finding new strategies to obtain effective methods for such a sorting. In this paper we introduce a new methodology in which an important role is played by the Lyndon factorization, so that the local suffixes inside factors detected by this factorization keep their mutual order when extended to the suffixes of the whole word. This property suggests a versatile technique that easily can b…
Factorizations of the Fibonacci Infinite Word
2015
The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from elementary properties of the Fibonacci numbers.
A subquadratic algorithm for minimum palindromic factorization
2014
We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns the minimum number of palindromes $S_1,\ldots, S_\ell$ such that $S = S_1 \cdots S_\ell$. We also show that the time complexity is $\mathcal{O}(n)$ on average and $\Omega(n\log n)$ in the worst case. The last result is based on a characterization of the palindromic structure of Zimin words.
On generalized Lyndon words
2018
Abstract A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as a nonincreasing factorization of generalized Lyndon words. We give new characterizations of the first and the last factor in this factorization as well as new characterization of generalized Lyndon words. We also give more specific results on two special cases: the classical one and the one arising from the alternating lexicographical order.
Extending the Unmixing methods to Multispectral Images
2021
In the past few decades, there has been intensive research concerning the Unmixing of hyperspectral images. Some methods such as NMF, VCA, and N-FINDR have become standards since they show robustness in dealing with the unmixing of hyperspectral images. However, the research concerning the unmixing of multispectral images is relatively scarce. Thus, we extend some unmixing methods to the multispectral images. In this paper, we have created two simulated multispectral datasets from two hyperspectral datasets whose ground truths are given. Then we apply the unmixing methods (VCA, NMF, N-FINDR) to these two datasets. By comparing and analyzing the results, we have been able to demonstrate some…
Universal aspects in the behavior of the entanglement spectrum in one dimension: Scaling transition at the factorization point and ordered entangled …
2013
We investigate the scaling of the entanglement spectrum and of the R\'enyi block entropies and determine its universal aspects in the ground state of critical and noncritical one-dimensional quantum spin models. In all cases, the scaling exhibits an oscillatory behavior that terminates at the factorization point and whose frequency is universal. Parity effects in the scaling of the R\'enyi entropies for gapless models at zero field are thus shown to be a particular case of such universal behavior. Likewise, the absence of oscillations for the Ising chain in transverse field is due to the vanishing value of the factorizing field for this particular model. In general, the transition occurring…
An efficient algorithm for stopping on a sink in a directed graph
2013
Abstract Vertices of an unknown directed graph of order n are revealed one by one in some random permutation. At each point, we know the subgraph induced by the revealed vertices. Our goal is to stop on a sink, a vertex with no out-neighbors. We show that if a sink exists this can be achieved with probability Θ ( 1 / n ) , which is best possible.
A second-order sparse factorization method for Poisson's equation with mixed boundary conditions
1992
Abstract We propose an algorithm for solving Poisson's equation on general two-dimensional regions with an arbitrary distribution of Dirichlet and Neumann boundary conditions. The algebraic system, generated by the five-point star discretization of the Laplacian, is solved iteratively by repeated direct sparse inversion of an approximating system whose coefficient matrix — the preconditioner — is second-order both in the interior and on the boundary. The present algorithm for mixed boundary value problems generalizes a solver for pure Dirichlet problems (proposed earlier by one of the authors in this journal (1989)) which was found to converge very fast for problems with smooth solutions. T…