A Tissue P System and a DNA Microfluidic Device for Solving the Shortest Common Superstring Problem

This paper describes a tissue P system for solving the Shortest Common Superstring Problem in linear time. This tissue P system is well suited for parallel and distributed implementation using a micro°uidic device working with DNA strands. The tP system is not based on the usual brute force generate/test technique applied in DNA computing, but builds the space solution gradually. The possible solutions/superstrings are build step by step through the parallel distributed combination of strings using the overlapping concatenation operation. Moreover, the DNA micro°uidic device solves the problem autonomously, without the need of external control or manipulation

On improving the approximation ratio of the r-shortest common superstring problem

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently been published, the general objective is now to break the conceptual lower bound barrier of 2. This paper is a step ahead in this direction. Here we focus on a particular instance of the SCS problem, meaning the r-SCS problem, which requires all input strings to be of the same length, r. Golonev et al. proved an approximation ratio which is better than the general one for r<= 6. Here we extend their approach and improve their approximation ratio, which is now better than the general one for r<= 7, and less than or equal to 2 up to r = 6

Computational Molecular Biology

Computational Biology is a fairly new subject that arose in response to the computational problems posed by the analysis and the processing of biomolecular sequence and structure data. The field was initiated in the late 60's and early 70's largely by pioneers working in the life sciences. Physicists and mathematicians entered the field in the 70's and 80's, while Computer Science became involved with the new biological problems in the late 1980's. Computational problems have gained further importance in molecular biology through the various genome projects which produce enormous amounts of data. For this bibliography we focus on those areas of computational molecular biology that involve discrete algorithms or discrete optimization. We thus neglect several other areas of computational molecular biology, like most of the literature on the protein folding problem, as well as databases for molecular and genetic data, and genetic mapping algorithms. Due to the availability of review papers and a bibliography this bibliography

A 2-2/3 Approximation for the Shortest Superstring Problem

Given a collection of strings S={s_1, ..., s_n} over an alphabet \Sigma, a superstring \alpha of S is a string containing each s_i as a substring; that is, for each i, 1\u3c=i\u3c=n, \alpha contains a block of |s_i| consecutive characters that match s_i exactly. The shortest superstring problem is the problem of finding a superstring \alpha of minimum length. The shortest superstring problem has applications in both data compression and computational biology. In data compression, the problem is a part of a general model of string compression proposed by Gallant, Maier and Storer (JCSS \u2780). Much of the recent interest in the problem is due to its application to DNA sequence assembly. The problem has been shown to be NP-hard; in fact, it was shown by Blum et al.(JACM \u2794) to be MAX SNP-hard. The first O(1)-approximation was also due to Blum et al., who gave an algorithm that always returns a superstring no more than 3 times the length of an optimal solution. Several researchers have published results that improve on the approximation ratio; of these, the best previous result is our algorithm ShortString, which achieves a 2 3/4-approximation (WADS \u2795). We present our new algorithm, G-ShortString, which achieves a ratio of 2 2/3. It generalizes the ShortString algorithm, but the analysis differs substantially from that of ShortString. Our previous work identified classes of strings that have a nested periodic structure, and which must be present in the worst case for our algorithms. We introduced machinery to descibe these strings and proved strong structural properties about them. In this paper we extend this study to strings that exhibit a more relaxed form of the same structure, and we use this understanding to obtain our improved result

Quantitative analyses in basic, translational and clinical biomedical research: metabolism, vaccine design and preterm delivery prediction

2 t.There is nothing more important than preserving life, and the thesis here presented is framed in the field of quantitative biomedicine (or systems biomedicine), which has as objective the application of physico-mathematical techniques in biomedical research in order to enhance the understanding of life's basis and its pathologies, and, ultimately, to defend human health. In this thesis, we have applied physico-mathematical methods in the three fundamental levels of Biomedical Research: basic, translational and clinical. At a basic level, since all pathologies have their basis in the cell, we have performed two studies to deepen in the understanding of the cellular metabolic functionality. In the first work, we have quantitatively analyzed for the first time calcium-dependent chloride currents inside the cell, which has revealed the existence of a dynamical structure characterized by highly organized data sequences, non-trivial long-term correlation that last in average 7.66 seconds, and "crossover" effect with transitions between persistent and anti-persistent behaviors. In the second investigation, by the use of delay differential equations, we have modeled the adenylate energy system, which is the principal source of cellular energy. This study has shown that the cellular energy charge is determined by an oscillatory non-stationary invariant function, bounded from 0.7 to 0.95. At a translational level, we have developed a new method for vaccine design that, besides obtaining high coverages, is capable of giving protection against viruses with high mutability rates such as HIV, HCV or Influenza. Finally, at a clinical level, first we have proven that the classic quantitative measure of uterine contractions (Montevideo Units) is incapable of predicting preterm labor immediacy. Then, by applying autoregressive techniques, we have designed a novel tool for premature delivery forecasting, based only in 30 minutes of uterine dynamics. Altogether, these investigations have originated four scientific publications, and as far as we know, our work is the first European thesis which integrates in the same framework the application of mathematical knowledge to biomedical fields in the three main stages of Biomedical Research: basic, translational and clinical