Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Partitions selection strategy for set of clustering solutions

Clustering is a difficult task: there is no single cluster definition and the data can have more than one underlying structure. Pareto-based multi-objective genetic algorithms (e.g., MOCK Multi-Objective Clustering with automatic K-determination and MOCLE-Multi-Objective Clustering Ensemble) were proposed to tackle these problems. However, the output of such algorithms can often contains a high number of partitions, becoming difficult for an expert to manually analyze all of them. In order to deal with this problem, we present two selection strategies, which are based on the corrected Rand, to choose a subset of solutions. To test them, they are applied to the set of solutions produced by MOCK and MOCLE in the context of several datasets. The study was also extended to select a reduced set of partitions from the initial population of MOCLE. These analysis show that both versions of selection strategy proposed are very effective. They can significantly reduce the number of solutions and, at the same time, keep the quality and the diversity of the partitions in the original set of solutions. (C) 2010 Elsevier B.V. All rights reserved.

Generalized external indexes for comparing data partitions with overlapping categories

There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833-841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. (c) 2010 Elsevier B.V. All rights reserved.

Ergodic properties of triangle partitions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MODEL PARTITIONS AND COMPACT TEST CASE SUITES

We present a generalized test case generation method, called the G method. Although inspired by the W method, the G method, in contrast, allows for test case suite generation even in the absence of characterization sets for the specification models. Instead, the G method relies on knowledge about the index of certain equivalences induced at the implementation models. We show that the W method can be derived from the G method as a particular case. Moreover, we discuss some naturally occurring infinite classes of FSM models over which the G method generates test suites that are exponentially more compact than those produced by the W method.

Rare earth and other chemical element contents and partitions in bottom sediments, micronodules, and nodules from the bioproductive zone of the Pacific Ocean

Concentrations and compositions of rare earth elements (REE) in three micronodule fractions (50-250, 250-500, and >500 ?m), coexisting macronodules, and host sediments were studied. Samples were collected at three sites (Guatemala Basin, Peru Basin, and northern equatorial Pacific) located in elevated bioproductivity zones of surface waters. Influence of micronodule size is dominant for REE compositions and subordinate for REE concentrations. For example, Ce concentration inversely correlates with micronodule size and drops to the lowest value in macronodules and host sediments. Decrease of Ce concentration is generally accompanied by Mn/Fe increase in micro- and macronodules. Hence, the role of diagenetic source of material directly correlates with micronodule sizes. Contribution of the diagenetic source is maximal for macronodules. REE composition distinctions for micronodules and macronodules can be attributed to variations of hydrogenic iron oxyhydroxides and diagenetic (hydrothermal) iron hydroxophosphates that are the major REE carriers in ferromanganese ore deposits. Relationship and general trend in chemistry of coexisting macronodules suggest that they can represent products of the initial stage of nodule formation.

The anatomy of melancholy : what it is, with all the kinds, causes, symptomes, prognostics, and several cures of it : in three partitions. With yheir several sections, members, and subsections, philosophically, medicinally, historically opened and cut up. /

Added engraved t.-p.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

Pyrimidine-5'-nucleotidase Campinas, A New Mutation (p.r56g) In The Nt5c3 Gene Associated With Pyrimidine-5'-nucleotidase Type I Deficiency And Influence Of Gilbert's Syndrome On Clinical Expression.

Pyrimidine-5'-nucleotidase type I (P5'NI) deficiency is an autosomal recessive condition that causes nonspherocytic hemolytic anemia, characterized by marked basophilic stippling and pyrimidine nucleotide accumulation in erythrocytes. We herein present two African descendant patients, father and daughter, with P5'N deficiency, both born from first cousins. Investigation of the promoter polymorphism of the uridine diphospho glucuronosyl transferase 1A (UGT1A) gene revealed that the father was homozygous for the allele (TA7) and the daughter heterozygous (TA6/TA7). P5'NI gene (NT5C3) gene sequencing revealed a further change in homozygosity at amino acid position 56 (p.R56G), located in a highly conserved region. Both patients developed gallstones; however the father, who had undergone surgery for the removal of stones, had extremely severe intrahepatic cholestasis and, liver biopsy revealed fibrosis and siderosis grade III, leading us to believe that the homozygosity of the UGT1A polymorphism was responsible for the more severe clinical features in the father. Moreover, our results show how the clinical expression of hemolytic anemia is influenced by epistatic factors and we describe a new mutation in the P5'N gene associated with enzyme deficiency, iron overload, and severe gallstone formation. To our knowledge, this is the first description of P5'N deficiency in South Americans.

Preserved Fertility In A Patient With Gynecomastia Associated With The P.pro695ser Mutation In The Androgen Receptor.

The androgen insensitivity syndrome (AIS) is described as a dysfunction of the androgen receptor (AR) in 46,XY individuals, which can be associated with mutations in the AR gene or can be due to unknown mechanisms. Different mutations in AIS generally cause variable phenotypes that range from a complete hormone resistance to a mild form usually associated with male infertility. The purpose of this study was to search for mutations in the AR gene in a fertile man with gynecomastia and to evaluate the influence of the mutation on the AR transactivation ability. Sequencing of the AR gene revealed the p.Pro695Ser mutation. It is located within the AR ligand-binding domain. Bioinformatics analysis indicated a deleterious role, which was verified after testing transactivation activity and N-/C-terminal (N/C) interaction by in vitro expression of a reporter gene and 2-hybrid assays. p.Pro695Ser showed low levels of both transactivation activity and N/C interaction at low dihydrotestosterone (DHT) conditions. As the ligand concentration increased, both transactivation activity and N/C interaction also increased and reached normal levels. Therefore, this study provides functional insights for the p.Pro695Ser mutation described here for the first time in a patient with mild AIS. The expression profile of p.Pro695Ser not only correlates to the patient's phenotype, but also suggests that a high-dose DHT therapy may overcome the functional deficit of the mutant AR.