On the combinatorics of suffix arrays

We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of Burrows-Wheeler arrays given in [1], that we apply by reducing suffix sorting to cyclic shift sorting through the use of an additional sentinel symbol. We show that the characterization of suffix arrays for a special case of binary alphabet given in [2] easily follows from our characterization. Based on our results, we also provide simple proofs for the enumeration results for suffix arrays, obtained in [3]. Our approach to characterizing suffix arrays is the first that exploits their relationship with Burrows-Wheeler permutations

Longest Common Separable Pattern between Permutations

In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for an arbitrary number of input permutations even if these permutations are separable. On the other hand, we show that the NP-hard problem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of $sqrt{Opt}$ (where $Opt$ is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.Comment: 15 page

Intellectual Philanthropy: The Seduction of the Masses

Intellectual Philanthropy: The Seduction of the Masses by Aurélie Vialette examines the practice of philanthropy in modern Spain. Through detailed studies of popular music, collective readings, dramas, working-class manuals, and fiction, Vialette reveals how depictions of urban philanthropic activities can inform our understanding of interactions in the economic, cultural, religious, and educational spheres, class power dynamics, and gender roles in urban Spanish society.https://docs.lib.purdue.edu/purduepress_previews/1013/thumbnail.jp

On recognizing words that are squares for the shuffle product

International audienceun résumé

Flexible RNA design under structure and sequence constraints using formal languages

The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical applications in biology, additional constraints must be taken into account, such as the presence/absence of regulatory motifs, either at a specific location or anywhere in the sequence. In this study, we investigate the design of RNA sequences from their targeted secondary structure, given these additional sequence constraints. To this purpose, we develop a general framework based on concepts of language theory, namely context-free grammars and finite automata. We efficiently combine a comprehensive set of constraints into a unifying context-free grammar of moderate size. From there, we use generic generic algorithms to perform a (weighted) random generation, or an exhaustive enumeration, of candidate sequences. The resulting method, whose complexity scales linearly with the length of the RNA, was implemented as a standalone program. The resulting software was embedded into a publicly available dedicated web server. The applicability demonstrated of the method on a concrete case study dedicated to Exon Splicing Enhancers, in which our approach was successfully used in the design of \emph{in vitro} experiments.Comment: ACM BCB 2013 - ACM Conference on Bioinformatics, Computational Biology and Biomedical Informatics (2013

Finding Occurrences of Protein Complexes in Protein-Protein Interaction Graphs

International audienceIn the context of comparative analysis of protein-protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex G in the protein-protein interaction graph H of another species with respect to (w.r.t.) orthologous proteins. Two problems are considered: the Exact-($\mu$G; $\mu$H)-Matching problem and the Max-($\mu$G; $\mu$H)-Matching problems, where $\mu$G (resp. $\mu$H) denotes in both problems the maximum number of orthologous proteins in H (resp. G) of a protein in G (resp. H). Following [10], the Exact-($\mu$G; $\mu$H)-Matching problem asks for an injective homomorphism of G to H w.r.t. orthologous proteins. The optimization version is called the Max-($\mu$G; $\mu$H)-Matching problem and is concerned with finding an injective mapping of a graph G to a graph H w.r.t. orthologous proteins that matches as many edges of G as possible. For both problems, we essentially focus on bounded degree graphs and extremal small values of parameters $\mu$G and $\mu$H

Comparing RNA structures using a full set of biologically relevant edit operations is intractable

7 pagesArc-annotated sequences are useful for representing structural information of RNAs and have been extensively used for comparing RNA structures in both terms of sequence and structural similarities. Among the many paradigms referring to arc-annotated sequences and RNA structures comparison (see \cite{IGMA_BliDenDul08} for more details), the most important one is the general edit distance. The problem of computing an edit distance between two non-crossing arc-annotated sequences was introduced in \cite{Evans99}. The introduced model uses edit operations that involve either single letters or pairs of letters (never considered separately) and is solvable in polynomial-time \cite{ZhangShasha:1989}. To account for other possible RNA structural evolutionary events, new edit operations, allowing to consider either silmutaneously or separately letters of a pair were introduced in \cite{jiangli}; unfortunately at the cost of computational tractability. It has been proved that comparing two RNA secondary structures using a full set of biologically relevant edit operations is {\sf\bf NP}-complete. Nevertheless, in \cite{DBLP:conf/spire/GuignonCH05}, the authors have used a strong combinatorial restriction in order to compare two RNA stem-loops with a full set of biologically relevant edit operations; which have allowed them to design a polynomial-time and space algorithm for comparing general secondary RNA structures. In this paper we will prove theoretically that comparing two RNA structures using a full set of biologically relevant edit operations cannot be done without strong combinatorial restrictions

Obtaining a Triangular Matrix by Independent Row-Column Permutations

International audienceGiven a square (0, 1)-matrix A, we consider the problem of deciding whether there exists a permutation of the rows and a permutation of the columns of A such that after carrying out these permutations , the resulting matrix is triangular. The complexity of the problem was posed as an open question by Wilf [7] in 1997. In 1998, DasGupta et al. [3] seemingly answered the question, proving it is NP-complete. However , we show here that their result is flawed, which leaves the question still open. Therefore, we give a definite answer to this question by proving that the problem is NP-complete. We finally present an exponential-time algorithm for solving the problem