Search results for "Permutation"
showing 10 items of 132 documents
Las matemáticas del cubo de Rubik
2013
[ES] En este artículo mostramos cómo podemos utilizar el cubo de Rubik para presentar algunos conceptos básicos de la teoría de grupos y cómo podemos usar esta para resolver el cubo de Rubik.
Two Simple Constructive algorithms for the Distributed Assembly Permutation Flowshop Scheduling Problem
2014
Nowadays, it is necessary to improve the management of complex supply chains which are often composed of multi-plant facilities. This paper proposes a Distributed Assembly Permutation Flowshop Scheduling Problem (DAPFSP). This problem is a generalization of the Distributed Permutation Flowshop Scheduling Problem (DPFSP) presented by Naderi and Ruiz (Comput Oper Res, 37(4):754–768, 2010). The first stage of the DAPFSP is composed of f identical production factories. Each center is a flowshop that produces jobs that have to be assembled into final products in a second assembly stage. The objective is to minimize the makespan. Two simple constructive algorithms are proposed to solve the proble…
Transmission of Genetic Properties in Permutation Problems: Study of Lehmer Code and Inversion Table Encoding
2021
Solution encoding describes the way decision variables are represented. In the case of permutation problems, the classical encoding should ensure that there are no duplicates. During crossover operations, repairs may be carried out to correct or avoid repetitions. The use of indirect encoding aims to define bijections between the classical permutation and a different representation of the decision variables. These encodings are not sensitive to duplicates. However, they lead to a loss of genetic properties during crossbreeding. This paper proposes a study of the impact of this loss both in the space of decision variables and in that of fitness values. We consider two indirect encoding: the …
Scatter Search vs. Genetic Algorithms
2005
The purpose of this work is to compare the performance of a scatter search (SS) implementation and an implementation of a genetic algorithm (GA) in the context of searching for optimal solutions to permutation problems. Scatter search and genetic algorithms are members of the evolutionary computation family. That is, they are both based on maintaining a population of solutions for the purpose of generating new trial solutions. Our computational experiments with four well-known permutation problems reveal that in general a GA with local search outperforms one without it. Using the same problem instances, we observed that our specific scatter search implementation found solutions of a higher …
Complete next-to-leading order gluino contributions to and
2011
Abstract We present the first complete order α s corrections to the Wilson coefficients (at the high scale) of the various versions of magnetic and chromomagnetic operators which are induced by a squark–gluino exchange. For this matching calculation, we work out the on-shell amplitudes b → s γ and b → s g , both in the full and in the effective theory up to order α s 2 . The most difficult part of the calculation is the evaluation of the two-loop diagrams in the full theory; these can be split into two classes: a) diagrams with one gluino and a virtual gluon; b) diagrams with two gluinos or with one gluino and a four-squark vertex. Accordingly, the Wilson coefficients can be split into a pa…
The Pauli Principle and Systems Consisting of Composite Particles
1993
In nature we often deal with many-body systems that are described in terms of particles that are not elementary but themselves composite. Examples of such composite particles are hadrons, atoms, phonons, and Cooper pairs. For the description of systems consisting of such composite particles in terms of the underlying degrees of freedom group theory plays an important role, in particular the symmetric group to describe the permutational symmetry of the wave function of the system, and unitary groups to describe the symmetry forced on the system by the interaction between the particles.
Permutation Tests in Linear Regression
2015
Exact permutation tests are available only in rather simple linear models. The problem is that, although standard assumptions allow permuting the errors of the model, we cannot permute them in practice, because they are unobservable. Nevertheless, the residuals of the model can be permuted. A proof is given here which shows that it is possible to approximate the unobservable permutation distribution where the true errors are permuted by permuting the residuals. It is shown that approximation holds asymptotically and almost surely for certain quadratic statistics as well as for statistics which are expressible as the maximum of appropriate linear functions. The result is applied to testing t…
Predicting the Significance of Necessity
2019
With Necessary Condition Analysis (NCA), a necessity effect is estimated by calculating the amount of empty space in the upper-left corner in a plot with a predictor X and an outcome Y, and recently a method for testing the statistical significance of the necessity effect through permutation has been proposed. In the present simulation study, this method was found to give significant results already with a very weak true population necessity effect, i.e., exhibit high power, unless the sample size is very small. However, in some situations the significance of the necessity effect tends to increase with increased degree of sufficiency, which is paradoxical for a method whose objective is to …
Recent results on syntactic groups of prefix codes
2012
International audience; We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.
Commensurability in Artin groups of spherical type
2019
Let $A$ and $A'$ be two Artin groups of spherical type, and let $A_1,\dots,A_p$ (resp. $A'_1,\dots,A'_q$) be the irreducible components of $A$ (resp. $A'$). We show that $A$ and $A'$ are commensurable if and only if $p=q$ and, up to permutation of the indices, $A_i$ and $A'_i$ are commensurable for every $i$. We prove that, if two Artin groups of spherical type are commensurable, then they have the same rank. For a fixed $n$, we give a complete classification of the irreducible Artin groups of rank $n$ that are commensurable with the group of type $A_n$. Note that it will remain 6 pairs of groups to compare to get the complete classification of Artin groups of spherical type up to commensur…