Multidimensional cluster stability analysis from a Brazilian Bradyrhizobium sp RFLP/PCR data set

The taxonomy of the N(2)-fixing bacteria belonging to the genus Bradyrhizobium is still poorly refined, mainly due to conflicting results obtained by the analysis of the phenotypic and genotypic properties. This paper presents an application of a method aiming at the identification of possible new clusters within a Brazilian collection of 119 Bradryrhizobium strains showing phenotypic characteristics of B. japonicum and B. elkanii. The stability was studied as a function of the number of restriction enzymes used in the RFLP-PCR analysis of three ribosomal regions with three restriction enzymes per region. The method proposed here uses Clustering algorithms with distances calculated by average-linkage clustering. Introducing perturbations using sub-sampling techniques makes the stability analysis. The method showed efficacy in the grouping of the species B. japonicum and B. elkanii. Furthermore, two new clusters were clearly defined, indicating possible new species, and sub-clusters within each detected cluster. (C) 2008 Elsevier B.V. All rights reserved.

A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

Wavelet-based dynamic time warping

Dynamic Time Warping (DTW), a pattern matching technique traditionally used for restricted vocabulary speech recognition, is based on a temporal alignment of the input signal with the template models. The principal drawback of DTW is its high computational cost as the lengths of the signals increase. This paper shows extended results over our previously published conference paper, which introduces an optimized version of the DTW I hat is based on the Discrete Wavelet Transform (DWT). (C) 2008 Elsevier B.V. All rights reserved.

Wavelet-based cepstrum calculation

In this paper we present a new wavelet-based algorithm for low-cost computation of the cepstrum. It can be used for real time precise pitch determination in automatic speech and speaker recognition systems. Many wavelet families are examined to determine the one that works best. The results confirm the efficacy and accuracy of the proposed technique for pitch extraction. (C) 2008 Elsevier B.V. All rights reserved.

Repetition-free longest common subsequence

We study the following problem. Given two sequences x and y over a finite alphabet, find a repetition-free longest common subsequence of x and y. We show several algorithmic results, a computational complexity result, and we describe a preliminary experimental study based on the proposed algorithms. We also show that this problem is APX-hard. (C) 2009 Elsevier B.V. All rights reserved.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

An all-substrings common subsequence algorithm

Given two strings A and B of lengths n(a) and n(b), n(a) <= n(b), respectively, the all-substrings longest common subsequence (ALCS) problem obtains, for every substring B` of B, the length of the longest string that is a subsequence of both A and B. The ALCS problem has many applications, such as finding approximate tandem repeats in strings, solving the circular alignment of two strings and finding the alignment of one string with several others that have a common substring. We present an algorithm to prepare the basic data structure for ALCS queries that takes O(n(a)n(b)) time and O(n(a) + n(b)) space. After this preparation, it is possible to build that allows any LCS length to be retrieved in constant time. Some trade-offs between the space required and a matrix of size O(n(b)(2)) the querying time are discussed. To our knowledge, this is the first algorithm in the literature for the ALCS problem. (C) 2007 Elsevier B.V. All rights reserved.

Perspectivas históricas da pesquisa operacional

Pós-graduação em Educação Matemática - IGCE

A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Computer Mathematics for Motivated Students

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

A modified epidemiological model for computer viruses

Since the computer viruses pose a serious problem to individual and corporative computer systems, a lot of effort has been dedicated to study how to avoid their deleterious actions, trying to create anti-virus programs acting as vaccines in personal computers or in strategic network nodes. Another way to combat viruses propagation is to establish preventive policies based on the whole operation of a system that can be modeled with population models, similar to those that are used in epidemiological studies. Here, a modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained. Then, disease-free and endemic equilibrium points are calculated, stability and bifurcation conditions are derived and some numerical simulations are shown. The relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks. (C) 2009 Elsevier Inc. All rights reserved.