The Tandem Duplication Distance Is NP-Hard

In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this can be represented as the string operation AXB ? AXXB. Tandem exon duplications have been found in many species such as human, fly or worm, and have been largely studied in computational biology. The Tandem Duplication (TD) distance problem we investigate in this paper is defined as follows: given two strings S and T over the same alphabet, compute the smallest sequence of tandem duplications required to convert S to T. The natural question of whether the TD distance can be computed in polynomial time was posed in 2004 by Leupold et al. and had remained open, despite the fact that tandem duplications have received much attention ever since. In this paper, we prove that this problem is NP-hard, settling the 16-year old open problem. We further show that this hardness holds even if all characters of S are distinct. This is known as the exemplar TD distance, which is of special relevance in bioinformatics. One of the tools we develop for the reduction is a new problem called the Cost-Effective Subgraph, for which we obtain W[1]-hardness results that might be of independent interest. We finally show that computing the exemplar TD distance between S and T is fixed-parameter tractable. Our results open the door to many other questions, and we conclude with several open problems

Urethral duplication.

Urethral duplication is a rare congenital anomaly. Although a number of theories have been proposed to describe the embryology of the condition, the actual mechanism of the disorder is still unclear. We report here a case of urethral duplication in a 11-year-old boy complaining of a double stream, and review the current literature on this rare entity.</p

On Compensation Loops in Genomic Duplications

Electronic version of an article published as International Journal of Foundations of Computer Science 2020 31:01, 133-142, DOI: 10.1142/S0129054120400092 © World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijfcs[EN] In this paper, we investigate the compensation loops, a DNA rearrangement in chromosomes due to unequal crossing over. We study the e fect of compensation loops over the gene duplication, and we formalize it as a restricted case of gene duplication in general. We study this biological process under the point of view of formal languages, and we provide some results about the languages de fined in this way.Sempere Luna, JM. (2020). On Compensation Loops in Genomic Duplications. International Journal of Foundations of Computer Science. 31(1):133-142. https://doi.org/10.1142/S0129054120400092S133142311Bovet, D. P., & Varricchio, S. (1992). On the regularity of languages on a binary alphabet generated by copying systems. Information Processing Letters, 44(3), 119-123. doi:10.1016/0020-0190(92)90050-6Dassow, J., Mitrana, V., & Salomaa, A. (1997). Context-free evolutionary grammars and the structural language of nucleic acids. Biosystems, 43(3), 169-177. doi:10.1016/s0303-2647(97)00036-1Ehrenfeucht, A., & Rozenberg, G. (1984). On regularity of languages generated by copying systems. Discrete Applied Mathematics, 8(3), 313-317. doi:10.1016/0166-218x(84)90129-xLeupold, P., Martín-Vide, C., & Mitrana, V. (2005). Uniformly bounded duplication languages. Discrete Applied Mathematics, 146(3), 301-310. doi:10.1016/j.dam.2004.10.003Leupold, P., & Mitrana, V. (2007). Uniformly bounded duplication codes. RAIRO - Theoretical Informatics and Applications, 41(4), 411-424. doi:10.1051/ita:2007021Leupold, P., Mitrana, V., & Sempere, J. M. (2003). Formal Languages Arising from Gene Repeated Duplication. Lecture Notes in Computer Science, 297-308. doi:10.1007/978-3-540-24635-0_22Rozenberg, G., & Salomaa, A. (Eds.). (1997). Handbook of Formal Languages. doi:10.1007/978-3-642-59126-

06061 Abstracts Collection -- Theory of Evolutionary Algorithms

From 05.02.06 to 10.02.06, the Dagstuhl Seminar 06061 ``Theory of Evolutionary Algorithms\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Bounded prefix-suffix duplication

We consider a restricted variant of the prefix-suffix duplication operation, called bounded prefix-suffix duplication. It consists in the iterative duplication of a prefix or suffix, whose length is bounded by a constant, of a given word. We give a sufficient condition for the closure under bounded prefix-suffix duplication of a class of languages. Consequently, the class of regular languages is closed under bounded prefix-suffix duplication; furthermore, we propose an algorithm deciding whether a regular language is a finite k-prefix-suffix duplication language. An efficient algorithm solving the membership problem for the k-prefix-suffix duplication of a language is also presented. Finally, we define the k-prefix-suffix duplication distance between two words, extend it to languages and show how it can be computed for regular languages

Thirty Years On: Reflections on Haydn’s “Farewell” Symphony by James Webster

It has been just over thirty years since James Webster published his influential monograph Haydn’s “Farewell” Symphony and the Idea of Classical Style: Through-Composition and Cyclic Integration in His Instrumental Music (Cambridge University Press, 1991). To honor the anniversary of Webster’s groundbreaking book, the Encounters with Eighteenth-Century Music: A Virtual Forum steering committee asked L. Poundie Burstein, Elaine Sisman, and W. Dean Sutcliffe to offer perspectives on the book, and James Webster to respond to their perspectives. The interesting online session occurred on Tuesday, October 18, 2022, and included a lively open discussion following the presentations and Webster’s response. The three presenters and Webster graciously consented to publish their perspectives and response in this article to inaugurate the 2023 “Farewell” volume of HAYDN: Online Journal of the Haydn Society of North America

Prefix-suffix duplication

We consider a bio-inspired formal operation on words called prefix-suffix duplication which consists in the duplication of a prefix or suffix of a given word. The class of languages defined by the iterated application of the prefix-suffix duplication to a word is considered. We show that such a language is context-free if and only if the initial word contains just one letter. Moreover, every language in this class is semilinear and belongs to NL. We propose a 0(n2 logn) time and 0(n2 ) space recognition algorithm. Two algorithms are further proposed for computing the prefix-suffix duplication distance between two words, defined as the minimal number of prefix-suffix duplications applied to one of them in order to get the other one. The first algorithm runs in cubic time and uses quadratic space while the second one is more efficient, having 0(n2 logn) time complexity, but needs 0(n2 logn) space