Product autoregressive models for non-negative variables

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt = Xα t−1Vt , 0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.

A simple randomized algorithm for consistent sequential prediction of ergodic time series

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if thesequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor.

Ergodic properties of triangle partitions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymptotic properties of stationary sequences.

Bibliography: p. 146.

Phylogenetic analyses of Cladophora vagabunda (L.) C. Hoek (Cladophorales, Chlorophyta) from Brazil based on SSU rDNA sequences

The complete SSU rDNA was sequenced for 10 individuals of Cladophora vagabunda collected along the coast of Brazil. For C. rupestris (L.) Kütz. a partial SSU rDNA sequence (1634 bp) was obtained. Phylogenetic trees indicate that Cladophora is paraphyletic, but the section Glomeratae sensu lato including C. vagabunda from Brazil, Japan and France, C. albida (Nees) Kütz., C. sericea (Hudson) Kütz., and C. glomerata (L.) Kütz. is monophyletic. Within this group C. vagabunda is paraphyletic. The sequence identity for the SSU rDNA varied from 98.9% to 100% for the Brazilian C. vagabunda, and from 98.3% to 99.7% comparing the Brazilian individuals to the ones from France and Japan. Sequence identity of the Brazilian C. vagabunda to C. albida and C. sericea vary from 98.0% to 98.6%. The SSU rDNA phylogeny support partially the morphological characteristics presented by Brazilian populations of C. vagabunda. On the other hand, C. rupestris from Brazil does not group with C. rupestris from France, both sequences presenting only 96.9% of identity. The inclusion of sequences of individuals from Brazil reinforces the need of taxonomical revision for the genus Cladophora and for the complex C. vagabunda.

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters. (c) 2008 American Institute of Physics.

Novel insights into the genomic basis of citrus canker based on the genome sequences of two strains of Xanthomonas fuscans subsp aurantifolii

Background: Citrus canker is a disease that has severe economic impact on the citrus industry worldwide. There are three types of canker, called A, B, and C. The three types have different phenotypes and affect different citrus species. The causative agent for type A is Xanthomonas citri subsp. citri, whose genome sequence was made available in 2002. Xanthomonas fuscans subsp. aurantifolii strain B causes canker B and Xanthomonas fuscans subsp. aurantifolii strain C causes canker C. Results: We have sequenced the genomes of strains B and C to draft status. We have compared their genomic content to X. citri subsp. citri and to other Xanthomonas genomes, with special emphasis on type III secreted effector repertoires. In addition to pthA, already known to be present in all three citrus canker strains, two additional effector genes, xopE3 and xopAI, are also present in all three strains and are both located on the same putative genomic island. These two effector genes, along with one other effector-like gene in the same region, are thus good candidates for being pathogenicity factors on citrus. Numerous gene content differences also exist between the three cankers strains, which can be correlated with their different virulence and host range. Particular attention was placed on the analysis of genes involved in biofilm formation and quorum sensing, type IV secretion, flagellum synthesis and motility, lipopolysacharide synthesis, and on the gene xacPNP, which codes for a natriuretic protein. Conclusion: We have uncovered numerous commonalities and differences in gene content between the genomes of the pathogenic agents causing citrus canker A, B, and C and other Xanthomonas genomes. Molecular genetics can now be employed to determine the role of these genes in plant-microbe interactions. The gained knowledge will be instrumental for improving citrus canker control.

Registration of temporal sequences of coronal and sagittal MR images through respiratory patterns

This work discusses the determination of the breathing patterns in time sequence of images obtained from magnetic resonance (MR) and their use in the temporal registration of coronal and sagittal images. The registration is made without the use of any triggering information and any special gas to enhance the contrast. The temporal sequences of images are acquired in free breathing. The real movement of the lung has never been seen directly, as it is totally dependent on its surrounding muscles and collapses without them. The visualization of the lung in motion is an actual topic of research in medicine. The lung movement is not periodic and it is susceptible to variations in the degree of respiration. Compared to computerized tomography (CT), MR imaging involves longer acquisition times and it is preferable because it does not involve radiation. As coronal and sagittal sequences of images are orthogonal to each other, their intersection corresponds to a segment in the three-dimensional space. The registration is based on the analysis of this intersection segment. A time sequence of this intersection segment can be stacked, defining a two-dimension spatio-temporal (2DST) image. The algorithm proposed in this work can detect asynchronous movements of the internal lung structures and lung surrounding organs. It is assumed that the diaphragmatic movement is the principal movement and all the lung structures move almost synchronously. The synchronization is performed through a pattern named respiratory function. This pattern is obtained by processing a 2DST image. An interval Hough transform algorithm searches for synchronized movements with the respiratory function. A greedy active contour algorithm adjusts small discrepancies originated by asynchronous movements in the respiratory patterns. The output is a set of respiratory patterns. Finally, the composition of coronal and sagittal image pairs that are in the same breathing phase is realized by comparing of respiratory patterns originated from diaphragmatic and upper boundary surfaces. When available, the respiratory patterns associated to lung internal structures are also used. The results of the proposed method are compared with the pixel-by-pixel comparison method. The proposed method increases the number of registered pairs representing composed images and allows an easy check of the breathing phase. (C) 2010 Elsevier Ltd. All rights reserved.

DNA sequences generated by BCH codes over GF(4)

The question raised by researchers in the field of mathematical biology regarding the existence of error-correcting codes in the structure of the DNA sequences is answered positively. It is shown, for the first time, that DNA sequences such as proteins, targeting sequences and internal sequences are identified as codewords of BCH codes over Galois fields.

A two-phase approach for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We recently evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach in delineating breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Molecular phylogeny of Wolbachia endosymbionts in southeast asian mosquitoes (Diptera: Culicidae) based on wsp gene sequences

Wolbachia are maternally inherited intracellular bacteria that infect a wide range of arthropods and nematodes and are associated with various reproductive abnormalities in their hosts. Insect-associated Wolbachia form a monophyletic clade in the α-Proteobacteria and recently have been separated into two supergroups (A and B) and 19 groups. Our recent polymerase chain reaction (PCR) survey using wsp specific primers indicated that various strains of Wolbachia were present in mosquitoes collected from Southeast Asia. Here, we report the phylogenetic relationship of the Wolbachia strains found in these mosquitoes using wsp gene sequences. Our phylogenetic analysis revealed eight new Wolbachia strains, five in the A supergroup and three in the B supergroup. Most of the Wolbachia strains present in Southeast Asian mosquitoes belong to the established Mors, Con, and Pip groups.

wsp Gene sequences from the Wolbachia of filarial nematodes

Wolbachia endosymbiotic bacteria are widespread in arthropods and are also present in filarial nematodes. Almost all filarial species so far examined have been found to harbor these endosymbionts. The sequences of only three genes have been published for nematode Wolbachia (i.e., the genes coding for the proteins FtsZ and catalase and for 16S rRNA). Here we present the sequences of the genes coding for the Wolbachia surface protein (WSP) from the endosymbionts of eight species of filaria. Complete gene sequences were obtained from the endosymbionts of two different species, Dirofilaria immitis and Brugia malayi. These sequences allowed us to design general primers for amplification of the wsp gene from the Wolbachia of all filarial species examined. For these species, partial WSP sequences (about 600 base pairs) were obtained with these primers. Phylogenetic analysis groups these nematode wsp sequences into a coherent cluster. Within the nematode cluster, wsp-based Wolbachia phylogeny matches a previous phylogeny obtained with ftsZ gene sequences, with a good consistency of the phylogeny of hosts (nematodes) and symbionts (Wolbachia). In addition, different individuals of the same host species (Dirofilaria immitis and Wuchereria bancrofti) show identical wsp gene sequences.

A two-phase strategy for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We previously evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach to delineate breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Bellerophon: a program to detect chimeric sequences in multiple sequence alignments

Bellerophon is a program for detecting chimeric sequences in multiple sequence datasets by an adaption of partial treeing analysis. Bellerophon was specifically developed to detect 16S rRNA gene chimeras in PCR-clone libraries of environmental samples but can be applied to other nucleotide sequence alignments.