Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Complete mitochondrial genomes confirm the distinctiveness of the horse-dog and sheep-dog strains of Echinococcus granulosus

Unlike other members of the genus, Echinococcus granulosus is known to exhibit considerable levels of variation in biology, physiology and molecular genetics. Indeed, some of the taxa regarded as 'genotypes' within E. granulosus might be sufficiently distinct as to merit specific status. Here, complete mitochondrial genomes are presented of 2 genotypes of E. granulosus (G1-sheep-dog strain: G4-horse-dog strain) and of another taeniid cestode, Taenia crassiceps. These genomes are characterized and compared with those of Echinococcus multilocularis and Hymenolepis diminuta. Genomes of all the species are very similar in structure, length and base-composition. Pairwise comparisons of concatenated protein-coding genes indicate that the G1 and G4 genotypes of E. granulosus are almost as distant from each other as each is from a distinct species, E. multilocularis. Sequences for the variable genes atp6 and nad3 were obtained from additional genotypes of E. granulosus, from E. vogeli and E. oligarthrus. Again, pairwise comparisons showed the distinctiveness of the G1 and G4 genotypes. Phylogenetic analyses of concatenated atp6, nad1 (partial) and cox1 (partial) genes from E. multilocularis, E. vogeli, E. oligarthrus, 5 genotypes of E. granulosus, and using T. crassiceps as an outgroup, yielded the same results. We conclude that the sheep-dog and horse-dog strains of E. granulosus should be regarded as distinct at the specific level.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

Complete genomic sequence of the Australian south-west genotype of Sindbis virus: Comparisons with other Sindbis strains and identification of a unique deletion in the 3 '-untranslated region

Our previous studies have shown that two distinct genotypes of Sindbis (SIN) virus occur in Australia. One of these, the Oriental/Australian type, circulates throughout most of the Australian continent, whereas the recently identified south-west (SW) genetic type appears to be restricted to a distinct geographic region located in the temperate south-west of Australia. We have now determined the complete nucleotide and translated amino acid sequences of a SW isolate of SIN virus (SW6562) and performed comparative analyses with other SIN viruses at the genomic level. The genome of SW6562 is 11,569 nucleotides in length, excluding the cap nucleotide and poly (A) tail. Overall this virus differs from the prototype SIN virus (strain AR339) by 23% in nucleotide sequence and 12.5% in amino acid sequence. Partial sequences of four regions of the genome of four SW isolates were determined and compared with the corresponding sequences from a number of SIN isolates from different regions of the World. These regions are the non-structural protein (nsP3), the E2 gene, the capsid gene, and the repeated sequence elements (RSE) of the 3'UTR. These comparisons revealed that the SW SIN viruses were more closely related to South African and European strains than to other Australian isolates of SIN virus. Thus the SW genotype of SIN virus may have been introduced into this region of Australia by viremic humans or migratory birds and subsequently evolved independently in the region. The sequence data also revealed that the SW genotype contains a unique deletion in the RSE of the 3'UTR region of the genome. Previous studies have shown that deletions in this region of the SIN genome can have significant effects on virus replication in mosquito and avian cells, which may explain the restricted distribution of this genotype of SIN virus.

Decompositions of complete graphs into theta graphs with fewer than ten edges

A theta graph is a graph consisting of three pairwise internally disjoint paths with common end points. Methods for decomposing the complete graph K-nu into theta graphs with fewer than ten edges are given.

The complete sequence of a 9000 bp fragment of the right arm of Saccharomyces cerevisiae chromosome VII contains four previously unknown open reading frames

We report the sequence of a 9000 bp fragment from the right arm of Saccharomyces cerevisiae chromosome VII. Analysis of the sequence revealed four complete previously unknown open reading frames, which were named G7587, G7589, G7591 and G7594 following standard rules for provisional nomenclature. Outstanding features of some of these proteins were the homology of the putative protein coded by G7589 with proteins involved in transcription regulation and the transmembrane domains predicted in the putative protein coded by G7591.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.

Erythema induratum of Bazin and renal tuberculosis: report of an association

Erythema induratum of Bazin is a disease that usually affects women, in whom erythematous subcutaneous nodules and plaques appear on the posterior part of the lower extremities, some of which ulcerate. In many countries, tuberculosis is still the main etiologic factor. We report a case of a 40-year-old woman who presented a course of protracted and recurrent episodes over five years of cutaneous lesions on her legs. These tend to involute, but new crops appear at irregular intervals. It was painful, erythematous-violaceous nodules, some of which drained a reddish secretion. The histopathologic features of the lesions demonstrated inflammatory infiltration, with predominance of neutrophils in dermis and hypodermis, necrotizing vasculitis in the arterioles and septal fibrosis. There was no granuloma. The Ziehl-Neelsen stain did not revealed acid-fast bacilli, and the culture of biopsy specimen was negative. The tuberculin skin test was strongly positive (17 mm). The chest X-ray was normal. Few months later she presented adynamia and urinary complaints, such as polacyuria and dysuria. It has been done an urynalysis, which demonstrated acid pH urine, sterile pyuria and microscopic hematuria. It was then raised the diagnostic hypothesis of renal tuberculosis. The urine culture for M. tuberculosis was positive in two out of ten samples. The treatment was instituted with rifampin, isoniazid and pyrazinamide, with complete regression. This case illustrates a clear association between erythema induratum and renal tuberculosis, demonstrated by the remission of the cutaneous lesions after the treatment of the renal tuberculosis.

Treatment of chronic hepatitis C in non-responsive patients with pegylated interferon associated with ribavirin and thalidomide: report of six cases of total remission

Hepatitis C virus (HCV) infection is an important public health issue worldwide. It is estimated that over 170 million people are infected with the virus. The present study reports six cases in which patients did not respond to combination therapy with pegylated interferon and ribavirin. However, after the addition of thalidomide to the therapy, the patients presented negative RNA PCR. The use of thalidomide combined with pegylated interferon and ribavirin for the treatment of hepatitis C is described here for the first time in the related literature.