23 papers · ranked by Valyu relevance
Wenwei Li
The incidence matrix of a projective plane of order n is a 0-1 matrix of order n 2 + n + 1. Two projective planes will be isomorphic if the incidence matrix of one projective plane could be transformed by permuting the rows and/or columns to the incidence matrix of the other one. After sorting the rows and columns, the…
Leonid Chindelevitch, João Paulo Pereira Zanetti, João Meidanis
Background Recently, Pereira Zanetti, Biller and Meidanis have proposed a new definition of a rearrangement distance between genomes. In this formulation, each genome is represented as a matrix, and the distance d is the rank distance between these matrices. Although defined in terms of matrices, the rank distance is…
Krasimir Yordzhev
This work examines the concept of S-permutation matrices, namely n 2 × n 2 permutation matrices containing a single 1 in each canonical n × n subsquare (block). The article suggests a formula for counting mutually disjoint pairs of n 2 × n 2 S-permutation matrices in the general case by restricting this task to the…
Krasimir Yordzhev
The concept of S-permutation matrix is considered. A general formula for counting all disjoint pairs of n 2 × n 2 S-permutation matrices as a function of the positive integer n is formulated and proven in this paper. To do that, the graph theory techniques have been used. It has been shown that to count the number of…
Krasimir Yordzhev
This work examines the problem to describe an efficient algorithm for obtaining n 2 × n 2 Sudoku matrices. For this purpose, we define the concepts of n× n Πn-matrix and disjoint Πn-matrices. The article, using the set-theoretical approach, describes an algorithm for obtaining n 2 -tuples of n × n mutually disjoint Πn…
Krasimir Yordzhev
The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to avoid checking whether each of the objects received possesses the necessary…
Steven R. Lippold
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on d elements as a square d×d matrix. Motivated by [4], we define a similar class of matrices which are a generalization of Permutation Matrices. We give explicit formulas for the multiplication of these matrices.…
Ştefan Tohăneanu, J. Francisco Vargas
Given two k ×n matrices A and B, we describe a couple of methods to solve the matrix equation XA = BY , where X is an invertible k × k matrix, and Y is an n × n permutation matrix, both of which we want to determine. We are interested in pursuing those techniques that have algebraic geometric flavour. An application to…
Maura John, Arthur Korte, Dominik G. Grimm
Permutation-based significance thresholds have been shown to be a robust alternative to Bonferroni-based significance thresholds in genome-wide association studies (GWAS). However, the implementation of permutation-based thresholds is computationally demanding. The recently published method permGWAS introduced a…
Mareike Fischer, Steffen Klaere, Minh Anh Thi Nguyen, Arndt von Haeseler
'Arndt von Haeseler'] Recently one step mutation matrices were introduced to model the impact of substitutions on arbitrary branches of a phylogenetic tree on an alignment site. This concept works nicely for the four-state nucleotide alphabet and provides an efficient procedure conjectured to compute the minimal number…
Vitaly Kocharovsky, Vladimir Kocharovsky, Vladimir Martyanov, Sergey Tarasov + 1 more
'Sergey Tarasov' 'Hung T. Diep'] We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for $k=1,2$ and 3) and the method for deriving such recurrence relations, which is based on the permanents of the…
Dhruvil Badani
A string is traditionally a sequence of characters. A permutation of a string is a rearrangement of the characters S into a one-one correspondence with S itself. A Matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The determinant is a value associated with a square matrix.
Yao-Tang Li, Zheng-Bo Li, Qi-Long Liu, Qiong Liu
The permutation transformation of tensors is introduced and its basic properties are discussed. The invariance under permutation transformations is studied for some important structure tensors such as symmetric tensors, positive definite (positive semidefinite) tensors, Z-tensors, M-tensors, Hankel tensors, P-tensors…
Cheng-yi Zhang, Weiwei Wang, Shuanghua Luo, Jianxing Zhao
The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, [1]) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions…
Robert John O’Shea
Graph canonisation and isomorphism testing representation are fundamental computational problems, whose complexity has remained unsolved to date. This study examines graph eigenprojections, demonstrating that linear-ordering transformations induce canonical properties therein to yield polynomial-time canonisation and…
Bartosz Tyrcha, Filip Brzęk, Piotr Zuchowski
This paper presents a general second-quantized form of a permutation operator interchanging $n$ pairs of electrons between interacting subsystems in the framework of the symmetry-adapted perturbation theory (SAPT). We detail the procedure for constructing this operator through the consecutive multiplication of…
Ulrich Lautenschlager
To analyze population structure based on multilocus geno-type data, a variety of popular tools perform model-based clustering, as-signing individuals to a prespecified number of ancestral populations. Since such methods often involve stochastic components, it is a common practice to perform multiple replicate analyses…
Mehmet Aziz Yirik, Maria Sorokina, Christoph Steinbeck
The generation of constitutional isomer chemical spaces has been a subject of cheminformatics since the early 1960s, with applications in structure elucidation and elsewhere. In order to perform such a generation efficiently, exhaustively and isomorphism-free, the structure generator needs to ensure the building of…
Mehmet Aziz Yirik, Maria Sorokina, Christoph Steinbeck
The generation of constitutional isomer chemical spaces has been a subject of cheminformatics since the early 1960s, with applications in structure elucidation and elsewhere. In order to perform such a generation efficiently, exhaustively and isomorphism-free, the structure generator needs to ensure the building of…
Evan D. Gorman, Manuel E. Lladser
Ultrametric matrices have a rich structure that is not apparent from their definition. Notably, the subclass of strictly ultrametric matrices are covariance matrices of certain weighted rooted binary trees. In applications, these matrices can be large and dense, making them difficult to store and handle. In this…
Cristina Jordán, Juan R. Torregrosa
An n × n matrix is called an N0-matrix if all its specified principal minors are nonpositive. In the context of partial matrices, a partial matrix is called a partial N0-matrix if all its specified principal minors are nonpositive. In this paper we characterize the existence of an N0-matrix completion of a partial…
Mark Abney
This article discusses problems with and solutions to performing valid permutation tests for quantitative trait loci in the presence of polygenic effects. Although permutation testing is a popular approach for determining statistical significance of a test statistic with an unknown distribution–for instance, the…
Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali + 15 more
Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven…