Fractional Operators, Dirichlet Averages, and Splines

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

Modern BLAST Programs

widely used program in bioinformatics. By sacrificing sensitivity for speed, it makes sequence comparison practical on huge sequence databases currently available. The original version of BLAST was developed in 1990. Since then it has spawned a variant of specialized programs. This chapter surveys the development of BLAST and BLAST-like programs for homology search, alignment statistics that are used in assessment of reported matches in BLAST, and provides the reader with guidance to select appropriate programs and set proper parameters to match research requirements.

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The Maximum Resource Bin Packing Problem

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems. For the off-line variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing. For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms. We study the general versions of the problems as well as the parameterized versions where on the item sizes, for some integer k. there is an upper bound of 1/

Identification of sugarcane genes involved in the purine synthesis pathway

Nucleotide synthesis is of central importance to all cells. In most organisms, the purine nucleotides are synthesized de novo from non-nucleotide precursors such as amino acids, ammonia and carbon dioxide. An understanding of the enzymes involved in sugarcane purine synthesis opens the possibility of using these enzymes as targets for chemicals which may be effective in combating phytopathogen. Such an approach has already been applied to several parasites and types of cancer. The strategy described in this paper was applied to identify sugarcane clusters for each step of the de novo purine synthesis pathway. Representative sequences of this pathway were chosen from the National Center for Biotechnology Information (NCBI) database and used to search the translated sugarcane expressed sequence tag (SUCEST) database using the available basic local alignment search tool (BLAST) facility. Retrieved clusters were further tested for the statistical significance of the alignment by an implementation (PRSS3) of the Monte Carlo shuffling algorithm calibrated using known protein sequences of divergent taxa along the phylogenetic tree. The sequences were compared to each other and to the sugarcane clusters selected using BLAST analysis, with the resulting table of p-values indicating the degree of divergence of each enzyme within different taxa and in relation to the sugarcane clusters. The results obtained by this strategy allowed us to identify the sugarcane proteins participating in the purine synthesis pathway.<br>A via de síntese de purino nucleotídeos é considerada uma via de central importância para todas as células. Na maioria dos organismos, os purino nucleotídeos são sintetizados ''de novo'' a partir de precursores não-nucleotídicos como amino ácidos, amônia e dióxido de carbono. O conhecimento das enzimas envolvidas na via de síntese de purinas da cana-de-açúcar vai abrir a possibilidade do uso dessas enzimas como alvos no desenho racional de inibidores no combate a agentes fitopatogênicos, como esta sendo feita com diversos parasitos e células cancerosas. A seguinte estratégia esta sendo utilizada na identificação de genes de cana-de-açúcar para cada membro da via de síntese de purinas: Seqüências representativas dos genes que compões a via foram escolhidas do banco de dados NCBI. Essas seqüências de peptídeos estão sendo utilizadas em buscas ao banco de dados gerado pelo SUCEST pelo programa BLAST (implementação tBLASTn). Alinhamentos com os clusters de cana-de-a��úcar são posteriormente analisados para sua significância estatística pela implementação PRSS3 do algoritmo conhecido como Monte Carlo shuffling. Para calibrar a análise dos resultados de PRSS3, foram empregadas seqüências conhecidas de diferentes taxas ao longo da arvore filogenética. Essas seqüências são comparadas duas a duas e com o cluster da cana-de-açúcar. A tabela de valores-p resultante indica o grau estatístico de similaridade e divergência entre as seqüências já descritas e entre essas e os clusters de cana-de-açúcar. Os resultados obtidos dessas análises estão descritos neste artigo