Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.

A Representation of Binary Matrices

Христина Костадинова, Красимир Йорджев - В статията се обсъжда представянето на произволна бинарна матрица с помощта на последователност от цели неотрицателни числа. Разгледани са някои предимства и недостатъци на това представяне като алтернатива на стандартното, общоприето представяне чрез двумерен масив. Показано е, че представянето на бинарните матрици с помощта на наредени n-торки от естествени числа води до по-бързи алгоритми и до съществена икономия на оперативна памет. Използуван е апарата на обектно-ориентираното програмиране със синтаксиса и семантиката на езика C++.

A contribution to the phytogeography of Brazilian campos: an analysis based on Poaceae

Twenty areas from eight Brazilian states were compared according to a list of 224 species of Poaceae. In order to determinate affinity patterns between the areas, a binary matrix was submitted to cluster and ordination analysis. The patterns found were then faced to climate and geographic position. The scores corresponding to the areas obtained from the cluster analysis showed a strong correlation to temperature. The scores corresponding to the species suggest a gradient that associates distribution patterns to the photosynthetic pathway (C3 or C4). The current results suggest that the traditional classification of the Southern American grasslands might require some modification in order to be broadly applicable in the Brazilian context.

RAPD analysis of genetic variability in a multiprovenance base population of Eucalyptus grandis hill ex maiden

This study aimed to evaluate the genetic variability among individuals of a base population of Eucalyptus grandis and to build a molecular marker database for the analyzed populations. The Eucalyptus grandis base population comprised 327 individuals from Coff's Harbour, Atherton and Rio Claro. A few plants came from other sites (Belthorpe MT. Pandanus, Kenilworth, Yabbra, etc.). Since this base population had a heterogeneous composition, the groups were divided according to geographic localization (latitude and longitude), and genetic breeding level. Thus, the influence of those two factors (geographic localization and genetic breeding level) on the genetic variability detected was discussed. The RAPD technique allowed the evaluation of 70 loci. The binary matrix was used to estimate the genetic similarity among individuals using Jaccard's Coefficient. Parametric statistical tests were used to compare within-group similarity of the means. The obtained results showed that the base population had wide genetic variability and a mean genetic similarity of 0.328. Sub-group 3 (wild materials from the Atherton region) showed mean genetic similarity of 0.318. S.P.A. (from Coff's Harbour region) had a mean genetic similarity of 0.322 and was found to be very important for maintenance of variation in the base population. This can be explained since the individuals from those groups accounted for most of the base population (48.3% for it). The base population plants with genetic similarity higher than 0.60 should be phenotypically analyzed again in order to clarify the tendency of genetic variability during breeding programs.

A contribution to the phytogeography of Brazilian campos: an analysis based on Poaceae

Twenty areas from eight Brazilian states were compared according to a list of 224 species of Poaceae. In order to determinate affinity patterns between the areas, a binary matrix was submitted to cluster and ordination analysis. The patterns found were then faced to climate and geographic position. The scores corresponding to the areas obtained from the cluster analysis showed a strong correlation to temperature. The scores corresponding to the species suggest a gradient that associates distribution patterns to the photosynthetic pathway (C3 or C4). The current results suggest that the traditional classification of the Southern American grasslands might require some modification in order to be broadly applicable in the Brazilian context.

Floristic composition and similarity analysis of an Atlantic rain forest fragment in Cananéia, São Paulo State, Brazil

The aim of this study is to investigate the floristic composition of an Atlantic rain forest fragment located in Cananéia, São Paulo, Brazil, and to contribute to the knowledge on Atlantic forest through the comparative analysis of this and other floristic surveys both on the southern and southeastern Brazil, in different soil and relief types. We surveyed 215 species in 132 genera and 51 families. Classification and ordination analysis were applied to a binary matrix in order to analyze the similarity among 24 surveys, including the present one, of Atlantic forest from the south and southeast coast of Brazil. Higher floristic similarity was observed among this area and the ones where there was marine influence and more rugged relief. The surveys in areas with greater marine influence (sandy soil) were separated from those in other conditions, possibly indicating a species replacement gradient from the steep slopes towards the lowland and were probably related to different edaphic conditions. A latitudinal gradient was found among the surveys apparently confirming a continuous species replacement along the Atlantic forest, related to a restricted distribution of the species. This suggests that it is essential to preserve areas from the whole Atlantic coast. Atlantic forest distribution is quite complex and its composition cannot be adequately represented by small localized areas.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.

Ionic liquids and other liquid matrices for sensitive MALDI MS analysis

Although liquid matrix-assisted laser desorption/ionization (MALDI) has been used in mass spectrometry (MS) since the early introduction of MALDI, its substantial lack of sensitivity compared to solid (crystalline) MALDI was for a long time a major hurdle to its analytical competitiveness. In the last decade, this situation has changed with the development of new sensitive liquid matrices, which are often based on a binary matrix acid/base system. Some of these matrices were inspired by the recent progress in ionic liquid research, while others were developed from revisiting previous liquid MALDI work as well as from a combination of these two approaches. As a result, two high-performing liquid matrix classes have been developed, the ionic liquid matrices (ILMs) and the liquid support matrices (LSMs), now allowing MS measurements at a sensitivity level that is very close to the level of solid MALDI and in some cases even surpasses it. This chapter provides some basic information on a selection of highly successful representatives of these new liquid matrices and describes in detail how they are made and applied in MALDI MS analysis.

Análise da variabilidade genética de acessos dePsidium spp. (Myrtaceae) avaliados quanto à reação a Meloidogyne enterolobii

This study aimed to characterize molecular of 13 accessions of Psidium spp. (Myrtaceae) that was been identified for the reaction to rootknot guava nematode. The DNA extraction of the samples was carried according to the protocol of Shillito & Saul (1988). The molecular markers type fAFLP, were obtained from fAFLP Regular Plant Genomes Fingerprinting Kit' (Applied Biosystems from Brasil Ltda.) and were tested 24 selectives combinations of primers, of which 18 showed amplification that produced 272 polymorphic markers. To the analysis of the markers were employed the softwares GeneScan (ABI Prism versao 1.0) and Genotyper (ABI Prism version 1.03), and the data collected were transformed into a binary matrix that was analyzed in the software PAUP (Phylogenetic Analysis Using Parcimony - version 3.01). Were calculated genetic distance index intra and interespecific between the genotipes. It was found that the AFLP markers were efficient in the discrimination between accessions, as well as in showing genetic similarity among accessions identified as resistant to the nematode Meloidogyne enterolobii, which could be discussed in the future.

RAPD analysis of genetic variability in a multiprovenance base population of Eucalyptus grandis hill ex maiden

Este estudo visou avaliar a variabilidade e distância genética dentro de uma população-base de melhoramento genético de Eucalyptus grandis. A avaliação da variabilidade genética tem como objetivos principais analisar a base genética da população-base e montar um banco de dados marcadores moleculares da população em análise. Essa população é formada por 327 indivíduos, principalmente das procedências de Coff's Harbour, Atherton e Rio Claro. Devido à heterozigosidade natural dessa população, ela pode ser dividida em diversas subpopulações, de acordo com a latitude e longitude de origem; e dentro de subpopulações, em função do grau de melhoramento genético já realizado do material analisado no Brasil. Isso permitiu avaliar quanto da variabilidade detectada dentro da população-base foi devido a esses fatores: procedência e grau de melhoramento. A aplicação da técnica RAPD permitiu avaliar 70 locos polimórficos, que foram analisados utilizando-se o coeficiente de Jaccard, o que resultou em matrizes de similaridade genética entre os indivíduos. Os dados de similaridade genética posteriormente foram submetidos à análise estatística. Osdados indicaram que a população-base apresenta ampla base genética, com média de similaridade genética de 0,328. O subgrupo denominado Região 3, composto por material selvagem da macrorregião de Atherton, juntamente com material de APS da macrorregião de Coff's Harbour, foi um dos que mais contribuíram para a ampla base genética da população-base. Foi possível detectar diferença estatística entre as populações selvagens das procedências de Atherton e Coff's Harbour, assim como entre essas procedências e a de Rio Claro.

A comparative floristic analysis of a cerrado area in Botucatu, State of São Paulo (Brazil)

Based on the results of a phytosociological survey in a ''cerrado'' area located within the municipality of Botucatu, state of São Paulo Brazil, a comparative analysis of the 58 sampled tree species' is here presented using the data of other available floristics works for the ''cerrados in the same state. With a binary matrix of presence/absence of shared common species with the studied plot, a clustering analysis was performed thus obtaining a dendrogram which groups northern and southern areas with the same vegetation in the state of São Paulo previously treated as floristicaly differentiated. These results are discussed under the assumption that Isolated areas of ''cerrados'' are to be taken as targets for immediate conservation.

Optimal single-embryo mass spectrometry fingerprinting

In pre-implantation embryos, lipids play key roles in determining viability, cryopreservation and implantation properties, but often their analysis is analytically challenging because of the few picograms of analytes present in each of them. Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) allows obtaining individual phospholipid profiles of these microscopic organisms. This technique is sensitive enough to enable analysis of individual intact embryos and monitoring the changes in membrane lipid composition in the early stages of development serving as screening method for studies of biology and biotechnologies of reproduction. This article introduces an improved, more comprehensive MALDI-MS lipid fingerprinting approach that considerably increases the lipid information obtained from a single embryo. Using bovine embryos as a biological model, we have also tested optimal sample storage and handling conditions before the MALDI-MS analysis. Improved information at the molecular level is provided by the use of a binary matrix that enables phosphatidylcholines, sphingomyelins, phosphatidylserines, phosphatidylinositols and phosphoethanolamines to be detected via MALDI(±)-MS in both the positive and negative ion modes. An optimal MALDI-MS protocol for lipidomic monitoring of a single intact embryo is therefore reported with potential applications in human and animal reproduction, cell development and stem cell research. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

Caracterização genética de avestruzes (Struthio camelus) usando marcadores RAPD

O objetivo deste trabalho foi avaliar a variabilidade genética de populações de avestruzes (Struthio camelus) por meio de marcadores RAPD (Polimorfismos de DNA amplificado ao acaso). Foram coletadas 121 amostras de indivíduos procedentes dos estados do Pará, Maranhão, Tocantins e Minas Gerais. O DNA genômico foi extraído a partir de sangue total. A triagem de iniciadores permitiu a seleção de 15 entre os 60 analisados que foram amplificados pelo método PCR. Os produtos da PCR foram visualizados em gel de agarose 1,5% e foi gerada uma matriz binária para os fragmentos amplificados com presença (1) e ausência (0) de banda. Para a verificação do número ótimo de bandas polimórficas foi realizada a análise de bootstrap por meio do software GQMOL. Para a análise dos dados foi utilizado o programa NTSYS-pc (Numerical Taxonomy and Multivariate Analysis Sistem), versão 2.02. A similaridade entre as amostras foi analisada através do coeficiente de Jaccard. Foi gerada uma matriz de distância cofenética, usando o módulo Sahncof, do programa NTSYS 2.2. Para realização da estruturação gênica o procedimento empregado foi a análise de variância molecular (AMOVA), processada no software Arlequin 2.0 (Schneider et al., 2000). Os 15 iniciadores geraram um total de 109 bandas polimórficas. A análise de bootstrap mostrou que a partir de 100 bandas o trabalho já se torna mais confiável, uma vez que a magnitude da correlação foi bem próxima do valor máximo (r=0,99), como também a soma de quadrados dos desvios (SQd) atingiu valor baixo 1,25 e o valor do estresse (E) foi de 0,05. Na análise entre pares de grupos, foi verificado que a maior e menor similaridade estão em torno, respectivamente, de 0,86 e 0,00. No que diz respeito à distribuição de freqüência das similaridades obtidas entre os 5.644 pares formados na matriz genética, pode-se verificar que 32,69 % dos pares ficaram incluídos nas classes com similaridades variando de 0,01 a 0,10. Nota-se que a maior porcentagem (85,59%) dos pares ficou distribuídos nas três primeiras classes das extremidades e que a minoria deles (14,41%) apresentou similaridades variando de 0,21 a 1,00. O teste de Mantel mostrou correlação de 0,81 e o dendrograma gerou 67 grupos delimitados pela Sm que foi de 0,49. A maior similaridade foi de 0,86 e a menor de 0,06. Os dados relativos à análise de variância molecular mostraram que a porcentagem de variação genética entre procedências foi baixa e significativa (24,03%, p < 0,0001), evidenciando que grande parte da variação encontra-se dentro das populações (75,97 %). Os marcadores RAPD foram eficientes na caracterização da similaridade genética.

Metodi molecolari nello studio della variabilità genetica di Tuber borchii

Tuber borchii (Ascomycota, order Pezizales) is highly valued truffle sold in local markets in Italy. Despite its economic importance, knowledge on its distribution and population variation is scarce. The objective of this work was to investigate the evolutionary forces shaping the genetic structure of this fungus using coalescent and phylogenetic methods to reconstruct the evolutionary history of populations in Italy. To assess population structure, 61 specimens were collected from 11 different Provinces of Italy. Sampling was stratified across hosts and habitats to maximize coverage in native oak and pine stands and both mychorrizae and fruiting bodies were collected. Samples were identified considering anatomo-morphological characters. DNA was extracted and both multilocus (AFLP) and single-locus (18 loci from rDNA, nDNA, and mtDNA) approaches were used to look for polymorphisms. Screening AFLP profiles, both Jaccard and Dice coefficients of similarity were utilized to transform binary matrix into a distance matrix and then to desume Neighbour-Joining trees. Though these are only preliminary examinations, phylogenetic trees were totally concordant with those deriving from single locus analyses. Phylogenetic analyses of the nuclear loci were performed using maximum likelihood with PAUP and a combined phylogenetic inference, using Bayesian estimation with all nuclear gene regions, was carried out. To reconstruct the evolutionary history, we estimated recurrent migration, migration across the history of the sample, and estimated the mutation and approximate age of mutations in each tree using SNAP Workbench. The combined phylogenetic tree using Bayesian estimation suggests that there are two main haplotypes that are difficult to be differentiated on the basis of morphology, of ecological parameters and symbiontic tree. Between these two lineages, that occur in sympatry within T. borchii populations, there is no evidence of recurrent migration. However, migration over the history of the sample was asymmetrical suggesting that isolation was a result of interrupted gene flow followed by range expansion. Low levels of divergence between the haplotypes indicate that there are likely to be two cryptic species within the T. borchii population sampled. Our results suggest that isolation between populations of T. borchii could have led to reproductive isolation between two lineages. This isolation is likely due to sympatric speciation caused by a multiple colonization from different refugia or a recent isolation. In attempting to determinate whether these haplotypes represent separate species or a partition of the same species we applied Biological and Mechanistic species Concepts. Notwithstanding, further analyses are necessary to evaluate if selection favoured premating or post-mating isolation.

Mathematical Modeling of the Weaving Structure Design

Красимир Йорджев, Христина Костадинова - В работата се разглежда една релация на еквивалентност в множеството от всички квадратни бинарни матрици. Обсъдена е комбинаторната задача за намиране мощността и елементите на фактормножеството относно тази релация. Разгледана е и възможността за получаване на някои специални елементи на това фактормножество. Предложен е алгоритъм за решаване на поставените задачи. Получените в статията резултати намират приложение при описанието топологията на различните тъкачни структури.