23 papers · ranked by Valyu relevance
Zixiang Xu, Yiwei Zhang, Gennian Ge
Permutation codes under different metrics have been extensively studied due to their potentials in various applications. Generalized Cayley metric is introduced to correct generalized transposition errors, including previously studied metrics such as Kendall's τ-metric, Ulam metric and Cayley metric as special cases.…
Ting Wang, Xiaoyan Yang, Bin Ge, Chenxing Xia + 2 more
Existing chaos-based color image encryption algorithms still face several challenges, including insufficient dynamical complexity of low-dimensional chaotic maps, residual boundary regularity caused by fixed block partitioning, and limited diffusion among RGB channels. To address these issues, this paper proposes a…
Eli Bagno, Estrella Eisenberg, Shulamit Reches, Moriah Sigron
A permutation is called block-wise simple if it contains no interval of the form 𝑝1 ⊕𝑝2 or 𝑝1 ⊖𝑝2 . We present this new set of permutations and explore some of its combinatorial properties. We present a generating function for this set, as well as a recursive formula for counting block-wise simple permutations.…
Anderson M. Winkler, Matthew A. Webster, Diego Vidaurre, Thomas E. Nichols + 1 more
'Thomas E. Nichols' 'Stephen M. Smith'] Under weak and reasonable assumptions, mainly that data are exchangeable under the null hypothesis, permutation tests can provide exact control of false positives and allow the use of various non-standard statistics. There are, however, various common examples in which global…
Ron M. Adin, Eli Bagno, Yuval Roichman
The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that, for 321-avoiding permutations, the set of left-to-right maxima has the same distribution when the block number is assumed to be k as when the last descent of the inverse is assumed to be at position n…
Rosa Orellana, Franco Saliola, Anne Schilling, Mike Zabrocki
the symmetric group Authors: ['Rosa Orellana' 'Franco Saliola' 'Anne Schilling' 'Mike Zabrocki'] Abstract. We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by…
Zihan Zhang
Permutation codes have received a great attention due to various applications. For different applications, one needs permutation codes under different metrics. The generalized Cayley metric was introduced by Chee and Vu [4] and this metric includes several other metrics as special cases. However, the generalized Cayley…
Rutilo Moreno, Luis Manuel Rivera
We introduce and study k-commuting permutations. One of our main results is a characterization of permutations that k-commute with a given permutation. Using this characterization, we obtain formulas for the number of permutations that k-commute with a permutation $\beta$, for some cycle types of $\beta$. Our…
Chi-Long Li, Kun-Tze Chen, Chin Lung Lu
The techniques of next generation sequencing allow an increasing number of draft genomes to be produced rapidly in a decreasing cost. However, these draft genomes usually are just partially sequenced as collections of unassembled contigs, which cannot be used directly by currently existing algorithms for studying their…
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…
Maura John, Arthur Korte, Marco Todesco, Dominik G Grimm + 1 more
To make population-aware permutations more efficient, we introduce a block matrix decomposition in [mthst2] and show how we can use this to compute $β^_{(1:b)}$ for batch-wise LMMs and $(1:q)β^_{(1:b)}$ for permutations. The [mthst1] can be found in the [sup1].Lemma 2Let $Z\inRn\times(c-1)$be an arbitrary matrix…
Md. Khaledur Rahman, M. Sohel Rahman
The genome rearrangement problem computes the minimum number of operations that are required to sort all elements of a permutation. A block-interchange operation exchanges two blocks of a permutation which are not necessarily adjacent and in a prefix block-interchange, one block is always the prefix of that…
Megan Bennett, Lei Cao
A blocker of 123-avoiding permutation matrices refers to the set of zeros contained within an n × n 123-forcing matrix. Recently, Brualdi and Cao provided a characterization of all minimal blockers, which are blockers with a cardinality of n. Building upon their work, a new type of blocker, flag-shaped blockers, which…
Ying Chih Lin, Chun-Yuan Lin, Chunhung Richard Lin
Background A classical problem in studying genome rearrangements is understanding the series of rearrangement events involved in transforming one genome into another in accordance with the parsimonious principle when two genomes with the same set of genes differ in gene order. The most studied event is the reversal…
Jarno Alanko, Hideo Bannai, Bastien Cazaux, Pierre Peterlongo + 1 more
Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals’ haplotype data, however, require excessive computing times and therefore are not…
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…
Md. Shafiqul Islam, Md. Khaledur Rahman, M. Sohel Rahman
A transposition is an operation that exchanges two adjacent blocks in a permutation. A prefix transposition always moves a prefix of the permutation to another location. In this article, we use a data structure, called the permutation tree, to improve the running time of the best known approximation algorithm (with…
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…
Anastasia C. Diseth, Simon J. Puglisi
Given a sequence S of subsets of symbols drawn from an alphabet of size σ, a subset rank query srank(i, c) asks for the number of subsets before the ith subset that contain the symbol c. It was recently shown (Alanko et al., Proc. SIAM ACDA, 2023) that subset rank queries on the spectral Burrows-Wheeler lead to…
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…
Torsten Pook, Martin Schlather, Gustavo de los Campos, Chris Carolin Schoen + 1 more
The concept of haplotype blocks has been shown to be useful in genetics. Fields of application range from the detection of regions under positive selection to statistical methods that make use of dimension reduction. We propose a novel approach (“HaploBlocker”) for defining and inferring haplotype blocks that focuses…
Ardalan Naseri, Ahsan Sanaullah, Shaojie Zhang, Degui Zhi
With the increasing availability of high-quality phased haplotype data, researchers can more effectively identify detailed patterns of haplotype sharing and investigate the population genetic processes that shape them. In this work, we define block cores as genomic segments where multiple haplotype blocks overlap. We…
Chris Zhang, Mary Pitman, Anjali Dixit, Sumudu Leelananda + 7 more
DNA-encoded libraries (DELs) provide the means to make and screen millions of diverse compounds against a target of interest in a single experiment. However, despite producing large volumes of binding data at a relatively low cost, the DEL selection process is susceptible to noise, necessitating computational follow-up…