In ultra-deep submicron VLSI designs, clock network layout plays an increasingly important role in determining circuit performance including timing, power consumption, cost, power supply noise and tolerance to process variations. It is required that a clock layout algorithm can achieve any prescribed skews with the minimum wire length and acceptable slew rate. Traditional zero-skew clock routing methods are not adequate to address this demand, since they tend to yield excessive wire length for prescribed skew targets. The interactions among skew targets, sink location proximities and capacitive load balance are analyzed. Based on this analysis, a maximum delay-target ordering merging scheme is suggested to minimize wire and buffer area, which results in lesser cost, power consumption and vulnerability to process variations. During the clock routing, buffers are inserted simultaneously to facilitate a proper slew rate level and reduce wire snaking. The proposed algorithm is simple and fast for practical applications. Experimental results on benchmark circuits show that the algorithm can reduce the total wire and buffer capacitance by 60% over an extension of the existing zero-skew routing method.

Mixture models are useful in describing a wide variety of random phenomena because of their flexibility in modeling. They have continued to receive increasing attention over the years from both a practical and theoretical point of view. In their applications, estimating the number of mixture components is often the main research objective or the first step toward it. Estimation of the number of mixture components heavily depends on the underlying distribution. As an extension of normal mixture models, we introduce a skew-normal mixture model and adapt the reversible jump Markov chain Monte Carlo algorithm to estimate the number of components with some applications to biological data. The reversible jump algorithm is also applied to the Cox proportional hazard model with frailty. We consider a regression model for the variance components in the proportional hazards frailty model. We propose a Bayesian model averaging procedure with a reversible jump Markov chain Monte Carlo step which selects the model automatically. The resulting regression coefficient estimates ignore the model uncertainty from the frailty distribution. Finally, the proposed model and the estimation procedure are illustrated with simulated example and real data.

The family of univariate skew-normal probability distributions, an extension of symmetric normal distribution to a general case of asymmetry, was originally proposed by Azzalani [1]. Since its introduction, very limited research has been conducted in this area. An extension of the univariate skew-normal distribution to the multivariate case was considered by Azzalani and Dalla Valle [4]. Its application in statistics was recently considered by Azzalani and Capitanio [3]. As a general result, Azzalani (1985) [See [1]] showed that, any symmetric distribution can be viewed as a member of a more general class of skewed distributions.In this study we establish some properties of general family of skewed distributions. Examples of general family of asymmetric distributions is presented in a way to show their differences from the corresponding symmetric distributions. The skew-logistic distribution and its properties are considered in great details. / Department of Mathematical Sciences

PERICINI, Matheus Henrique Machado. Utilização de metaheurísticas para balanceamento de carga em ambientes MapReduce. 2017. 71 f. Dissertação (Mestrado em Ciência da Computação)-Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Jonatas Martins (jonatasmartins@lia.ufc.br) on 2017-10-19T17:17:01Z No. of bitstreams: 1 2017_dis_mhmpericini.pdf: 2342022 bytes, checksum: 8bfd2d1fee199d87109de3ba41cb73df (MD5) / Approved for entry into archive by Jairo Viana (jairo@ufc.br) on 2017-10-30T17:13:30Z (GMT) No. of bitstreams: 1 2017_dis_mhmpericini.pdf: 2342022 bytes, checksum: 8bfd2d1fee199d87109de3ba41cb73df (MD5) / Made available in DSpace on 2017-10-30T17:13:30Z (GMT). No. of bitstreams: 1 2017_dis_mhmpericini.pdf: 2342022 bytes, checksum: 8bfd2d1fee199d87109de3ba41cb73df (MD5) Previous issue date: 2017 / With the increase in the number of data obtained by large companies, it was necessary to elaborate new strategies for the processing of this data in order to maintain the relevance of the information that they contain. One of the strategies that has been widely used is based on a programming model, called MapReduce, which uses division and conquest to process the data in a cluster of machines. Hadoop is one of the most consolidated implementations of the MapReduce model. But even such a strategy is subject to improvement. In it, the runtime depends on all the machines causing any overloaded machine to generate a delay in the delivery of the result. This overhead is caused by a problem commonly called Data Skew which consists of an unequal division of data, either by the size of the data or by the way it is divided. In order to solve this problem, we have proposed the MALiBU, an improvement of the execution strategy of Hadoop, which partitions the data between the machines using a meta-heuristic among them Simulated Annealing, Local Beam Search or Stochastic Beam Search. Experimental results showed improvements in the performance of Hadoop when using metaheuristics to distribute the data among the processing elements of the model, as well as among the three meta-heuristics evaluated, which has the best results. / Com o aumento do número de dados obtidos por grandes empresas, foi necessário elaborar novas estratégias para o processamento desses dados de modo a manter sua relevância e aproveitar suas informações. Uma das estratégias que tem sido amplamente utilizada tem como base um modelo de programação, chamado MapReduce, que utiliza divisão e conquista para processar os dados em um cluster de máquinas. O Hadoop é uma das implementações mais consolidadas do modelo de MapReduce. Mas mesmo tal estratégia é passível de melhorias. Nela o tempo de execução é dependente de todas as máquinas fazendo com que qualquer máquina sobrecarregada gere um atraso na entrega do resultado. Essa sobrecarga é causada por um problema chamado comumente de Data Skew que consiste em uma divisão desigual dos dados causado pelo tamanho dos dados, o modo como eles são divididos, ou o processamento desigual dos dados. Visando resolver esse problema, propusemos o MALiBU, uma melhoria da estratégia de execução do MapReduce que particiona os dados entre as máquinas usando uma meta-heurística dentre elas Simulated Annealing, Local Beam Search ou Stochastic Beam Search. Resultados experimentais mostraram melhorias no desempenho do MapReduce quando se faz uso de meta-heurística para distribuir os dados entre as máquinas, bem como mostraram, dentre as três meta-heurísticas avaliadas, qual delas melhor balanceia a carga.

This research explores factor analysis applied to data from skewed distributions for the general skew model, the selection-elliptical model, the selection-normal model, the skew-elliptical model and the skew-normal model for finite sample sizes. In terms of asymptotics, or large sample sizes, quasi-maximum likelihood methods are broached numerically. The skewed models are formed using selection distribution theory, which is based on Rao’s weighted distribution theory. The models assume the observed variable of the factor model is from a skewed distribution by defining the distribution of the unobserved common factors skewed and the unobserved unique factors symmetric. Numerical examples are provided using maximum likelihood selection skew-normal factor analysis. The numerical examples, such as maximum likelihood parameter estimation with the resolution of the “sign switching” problem and model fitting using likelihood methods, illustrate that the selection skew-normal factor analysis model better fits skew-normal data than does the normal factor analysis model.

Matrix variate skew elliptically contoured distributions generalize several classes of important distributions. This paper defines and explores matrix variate skew elliptically contoured distributions. In particular, we discuss two stochastic representations of the matrix variate skew elliptically contoured distributions.

A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the semi-direct product of the group with a polynomial ring on the vector space. Each representation of a group defines a different skew group algebra, which may have its own interesting deformations. In this work, we explicitly describe all graded Hecke algebras arising as deformations of the skew group algebra of any finite group acting by the regular representation. We then focus on rank two exceptional complex reflection groups acting by any irreducible representation. We consider in-depth the reflection representation and a nonfaithful rotation representation. Alongside our study of cohomology for the rotation representation, we develop techniques valid for arbitrary finite groups acting by a representation with a central kernel. Additionally, we consider combinatorial questions about reflection length and codimension orderings on complex reflection groups. We give algorithms using character theory to compute reflection length, atoms, and poset relations. Using a mixture of theory, explicit examples, and calculations using the software GAP, we show that Coxeter groups and the infinite family G(m,1,n) are the only irreducible complex reflection groups for which the reflection length and codimension orders coincide. We describe the atoms in the codimension order for the groups G(m,p,n). For arbitrary finite groups, we show that the codimension atoms are contained in the support of every generating set for cohomology, thus yielding information about the degrees of generators for cohomology.

The concept of Hopf-Galois extensions was introduced by S. Chase and M. Sweedler in 1969 and provides a generalisation of classical Galois theory. Later, Hopf-Galois theory for separable extensions of fields was studied by C. Greither and B. Pareigis. They showed how to recast the problem of classifying all Hopf-Galois structures on a finite separable extension of fields as a problem in group theory. Many major advances relating to the classification of Hopf-Galois structures were made by N. Byott, S. Carnahan, L. Childs, and T. Kohl. On the other hand, and seemingly unrelated to Hopf-Galois theory, in 1992 V. Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested considering set-theoretic solutions of the Yang-Baxter equation. Later, W. Rump introduced braces as a tool to study non-degenerate involutive set-theoretic solutions, and through the efforts of D. Bachiller, F. Ced'o, E. Jespers, and J. Okni'nski the classification of these solutions was reduced to that of braces. Recently, skew braces were introduced by L. Guarnieri and L. Vendramin in order to study the non-degenerate (not necessarily involutive) set-theoretic solutions. Additionally, a fruitful discovery, initially noticed by D. Bachiller, revealed a connection between Hopf-Galois theory and skew braces, which linked the classification of Hopf-Galois structures to that of skew braces. Currently, the classification of Hopf-Galois structures and skew braces of a given order remains among important topics of research. In this thesis, as our main results, we determine all Hopf-Galois structures on Galois extensions of fields of degree p^3, and at the same time we provide a complete classification of all skew braces of order p^3, for a prime number p. These findings hence offer applications to Galois module theory in number theory on the one hand, and to the study of the solutions of the quantum Yang-Baxter equation in mathematical physics on the other hand.

<p>Skew in telecommunication normally means the difference in arrival time of bits transmitted at the same time in differential transmission. As an increasing of transmission data bit rate and more importantly, a data and clock signal rise time of become faster, digital system interconnects became behaving as transmission line. The high speed signals become microwave in nature. The problem is that modern digital designs and verifications require knowledge that has formerly not been needed for a data bit rate of below than 100Mbit but also at the higher frequency range as 5 to 15GHz, however, most references on the necessary subjects are too abstract to be immediately applicable to the skew. For this reason a new method to investigate the skew were introduced, and with which, test board were measured. Since the test boards are made in devise material, and lines on the boards are configured out in distinct structures. In this paper, several methods were applied to find out the skew, and by comparing the results, it could be found that how factors affect the skew, not only the material factor, but some manufactory reason.</p>

The computation of a piecewise smooth function that approximates a finite set of data points is decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function is then computed as the optimal estimator with respect to this measure field. Applications to image processing and time series prediction are presented as well.