Modelagem matemática e aplicações do problema de coloração em grafos

Pós-graduação em Matemática - IBILCE

Indicador multivariado policórico: proposta de indicador para o diagnóstico da aprendizagem organizacional

Pós-graduação em Engenharia Mecânica - FEG

Comparação da razão carga/deflexão entre fios ortodônticos de Ni-Ti termoativados 0,014”x0,025” e 0,016”x0,022”

The knowledge of the mechanical properties of nickel-titanium (NiTi) termoactives of the more accessible of the domestic market is still limited. Given this, the objective of this study was to evaluate and compare through deflection tests in brackets NiTi wires 03 term rectangular gauge 0.014 '' enabled x 0.025 '' and 0.016 '' x 0.022 '' of different brands (MORELLI (R), ORMCO (R) ORTHOSOURCE (R), ORTHOMETRIC (R), EURODONTO (R) and ADITEK (R)). All tests were carried out on universal testing machine EMIC DL 2000 under identical conditions and controlled at a temperature of 36 degrees C +/- 0.5 degrees C. Five measurements (N= 5) were performed for each thickness/wire tag that was deflected up to a limit of 4.0mm at a speed of 1.0mm/min. Each 0.2mm (round trip) of corresponding strength measured deflection for the construction of the graph of force x deflection at Tesc program version 3.04. Each graphic was evaluated according to the following variables: beginning of the Martensitic transformation (cN and mm), maximum strength (cN), the beginning and end of the plateau of deactivation (cN and mm) and length (mm) plateau. The average and standard deviation were calculated for all variables and statistical analysis was made by ANOVA tests 2 criteria and Turkey or Kruskal-Wallis and Dunn, a 5% level of significance. The results showed that the tests of 0.014 '' x0.025 '' ORTHOMETRIC (R) brands and ORMCO (R) showed the best results, as well as the wires of the MORELLI (R) and ORTHOSOURCE (R) to wires 0.016 '' x0.022 ''. In General, the gauge wires 0.014 '' x0.025 '' showed strength levels on the plateau of deactivation to 6 x smaller than 0.016 '' x0.022 '' caliber.

Determinação de comunidades em redes biológicas integradas

To understand how biological phenomena emerge, the nonlinear interactions among the components envolved in these and the correspondent connected elements, like genes, proteins, etc., can be represented by a mathematical object called graph or network, where interacting elements are represented by edges connecting pairs of nodes. The analysis of various graph-related properties of biological networks has revealed many clues about biological processes. Among these properties, the community structure, i.e. groups of nodes densely connected among themselves, but sparsely connected to other groups, are important for identifying separable functional modules within biological systems for the comprehension of the high-level organization of the cell. Communities' detection can be performed by many algorithms, but most of them are based on the density of interactions among nodes of the same community. So far, the detection and analysis of network communities in biological networks have only been pursued for networks composed by one type of interaction (e.g. protein-protein interactions or metabolic interactions). Since a real biological network is simultaneously composed by protein-protein, metabolic and transcriptional regulatory interactions, it would be interesting to investigate how communities are organized in this type of network. For this purpose, we detected the communities in an integrated biological network of the Escherichia coli and Saccharomyces cerevisiae by using the Clique Percolation Method and we veri ed, by calculating the frequency of each type of interaction and its related entropy, if components of communities... (Complete abstract click electronic access below)

A nature-inspired approach to speed up optimum-path forest clustering and its application to intrusion detection in computer networks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um estudo sobre a função exponencial

Pós-graduação em Matemática em Rede Nacional - IBILCE

Weak quasi-randomness for uniform hypergraphs

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs. Moreover, let K(k) be the complete graph on k vertices and M(k) the line graph of the graph of the k-dimensional hypercube. We will show that the pair of graphs (K(k),M(k)) has the property that if the number of copies of both K(k) and M(k) in another graph G are as expected in the random graph of density d, then G is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to d. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 1-38, 2012

Volumenpackungen nach SAE J1100

We present new algorithms to approximate the discrete volume of a polyhedral geometry using boxes defined by the US standard SAE J1100. This problem is NP-hard and has its main application in the car design process. The algorithms produce maximum weighted independent sets on a so-called conflict graph for a discretisation of the geometry. We present a framework to eliminate a large portion of the vertices of a graph without affecting the quality of the optimal solution. Using this framework we are also able to define the conflict graph without the use of a discretisation. For the solution of the maximum weighted independent set problem we designed an enumeration scheme which uses the restrictions of the SAE J1100 standard for an efficient upper bound computation. We evaluate the packing algorithms according to the solution quality compared to manually derived results. Finally, we compare our enumeration scheme to several other exact algorithms in terms of their runtime. Grid-based packings either tend to be not tight or have intersections between boxes. We therefore present an algorithm which can compute box packings with arbitrary placements and fixed orientations. In this algorithm we make use of approximate Minkowski Sums, computed by uniting many axis-oriented equal boxes. We developed an algorithm which computes the union of equal axis-oriented boxes efficiently. This algorithm also maintains the Minkowski Sums throughout the packing process. We also extend these algorithms for packing arbitrary objects in fixed orientations.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Twitter data analysis for financial markets

Over the time, Twitter has become a fundamental source of information for news. As a one step forward, researchers have tried to analyse if the tweets contain predictive power. In the past, in financial field, a lot of research has been done to propose a function which takes as input all the tweets for a particular stock or index s, analyse them and predict the stock or index price of s. In this work, we take an alternative approach: using the stock price and tweet information, we investigate following questions. 1. Is there any relation between the amount of tweets being generated and the stocks being exchanged? 2. Is there any relation between the sentiment of the tweets and stock prices? 3. What is the structure of the graph that describes the relationships between users?

The Car Resequencing Problem with Pull-Off Tables

The car sequencing problem determines sequences of different car models launched down a mixed-model assembly line. To avoid work overloads of workforce, car sequencing restricts the maximum occurrence of labor-intensive options, e.g., a sunroof, by applying sequencing rules. We consider this problem in a resequencing context, where a given number of buffers (denoted as pull-off tables) is available for rearranging a stirred sequence. The problem is formalized and suited solution procedures are developed. A lower bound and a dominance rule are introduced which both reduce the running time of our graph approach. Finally, a real-world resequencing setting is investigated.

Rechnergestützte Planung von Distributionszentren durch Einsatz der Graphentheorie

Obwohl Distributionszentren (DZ) zentrale Kernelemente von Lieferketten darstellen, lässt sich gegenwärtig keine strukturierte Methodik finden, um diese objektiv, systematisch und insbesondere ganzheitlich über alle Funktionsbereiche hinweg – vom Wareneingang über die Kommissionierung bis zum Warenausgang – zu planen. Der vorliegende Artikel befasst sich mit dieser wissenschaftlichen Lücke und beschreibt wie mit Hilfe von analytisch modellierten Standardmodulen innerhalb der verschiedenen Funktionsbereiche eines DZ durch Anwendung eines graphentheoretischen Ansatzes funktionsbereichsübergreifende Varianten von DZ generiert werden können. Zur automatisierten Ermittlung der optimalen Standardmodulkombination bzw. der optimalen DZ-Variante werden modifizierte Algorithmen zur Findung der kürzesten Wege innerhalb eines Graphen angewendet.

A Dynamic Route Planning Prototype for Cognitive Cities

A software prototype for dynamic route planning in the travel industry for cognitive cities is presented in this paper. In contrast to existing tools, the prototype enhances the travel experience (i.e., sightseeing) by allowing additional flexibility to the user. The theoretical background of the paper strengthens the understanding of the introduced concepts (e.g., cognitive cities, fuzzy logic, graph databases) to comprehend the presented prototype. The prototype applies an instantiation and enhancement of the graph database Neo4j . For didactical reasons and to strengthen the understanding of this prototype a scenario, applied to route planning in the city of Bern (Switzerland) is shown in the paper.

Medidas autosemejantes en el plano, momentos y matrices de Hessenberg

La tesis MEDIDAS AUTOSEMEJANTES EN EL PLANO, MOMENTOS Y MATRICES DE HESSENBERG se enmarca entre las áreas de la teoría geométrica de la medida, la teoría de polinomios ortogonales y la teoría de operadores. La memoria aborda el estudio de medidas con soporte acotado en el plano complejo vistas con la óptica de las matrices infinitas de momentos y de Hessenberg asociadas a estas medidas que en la teoría de los polinomios ortogonales las representan. En particular se centra en el estudio de las medidas autosemejantes que son las medidas de equilibrio definidas por un sistema de funciones iteradas (SFI). Los conjuntos autosemejantes son conjuntos que tienen la propiedad geométrica de descomponerse en unión de piezas semejantes al conjunto total. Estas piezas pueden solaparse o no, cuando el solapamiento es pequeño la teoría de Hutchinson [Hut81] funciona bien, pero cuando no existen restricciones falla. El problema del solapamiento consiste en controlar la medida de este solapamiento. Un ejemplo de la complejidad de este problema se plantea con las convoluciones infinitas de distribuciones de Bernoulli, que han resultado ser un ejemplo de medidas autosemejantes en el caso real. En 1935 Jessen y A. Wintner [JW35] ya se planteaba este problema, lejos de ser sencillo ha sido estudiado durante más de setenta y cinco años y siguen sin resolverse las principales cuestiones planteadas ya por A. Garsia [Gar62] en 1962. El interés que ha despertado este problema así como la complejidad del mismo está demostrado por las numerosas publicaciones que abordan cuestiones relacionadas con este problema ver por ejemplo [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05],[JKS07] [JKS11]. En el primer capítulo comenzamos introduciendo con detalle las medidas autosemejante en el plano complejo y los sistemas de funciones iteradas, así como los conceptos de la teoría de la medida necesarios para describirlos. A continuación se introducen las herramientas necesarias de teoría de polinomios ortogonales, matrices infinitas y operadores que se van a usar. En el segundo y tercer capítulo trasladamos las propiedades geométricas de las medidas autosemejantes a las matrices de momentos y de Hessenberg, respectivamente. A partir de estos resultados se describen algoritmos para calcular estas matrices a partir del SFI correspondiente. Concretamente, se obtienen fórmulas explícitas y algoritmos de aproximación para los momentos y matrices de momentos de medidas fractales, a partir de un teorema del punto fijo para las matrices. Además utilizando técnicas de la teoría de operadores, se han extendido al plano complejo los resultados que G. Mantica [Ma00, Ma96] obtenía en el caso real. Este resultado es la base para definir un algoritmo estable de aproximación de la matriz de Hessenberg asociada a una medida fractal u obtener secciones finitas exactas de matrices Hessenberg asociadas a una suma de medidas. En el último capítulo, se consideran medidas, μ, más generales y se estudia el comportamiento asintótico de los autovalores de una matriz hermitiana de momentos y su impacto en las propiedades de la medida asociada. En el resultado central se demuestra que si los polinomios asociados son densos en L2(μ) entonces necesariamente el autovalor mínimo de las secciones finitas de la matriz de momentos de la medida tiende a cero. ABSTRACT The Thesis work “Self-similar Measures on the Plane, Moments and Hessenberg Matrices” is framed among the geometric measure theory, orthogonal polynomials and operator theory. The work studies measures with compact support on the complex plane from the point of view of the associated infinite moments and Hessenberg matrices representing them in the theory of orthogonal polynomials. More precisely, it concentrates on the study of the self-similar measures that are equilibrium measures in a iterated functions system. Self-similar sets have the geometric property of being decomposable in a union of similar pieces to the complete set. These pieces can overlap. If the overlapping is small, Hutchinson’s theory [Hut81] works well, however, when it has no restrictions, the theory does not hold. The overlapping problem consists in controlling the measure of the overlap. The complexity of this problem is exemplified in the infinite convolutions of Bernoulli’s distributions, that are an example of self-similar measures in the real case. As early as 1935 [JW35], Jessen and Wintner posed this problem, that far from being simple, has been studied during more than 75 years. The main cuestiones posed by Garsia in 1962 [Gar62] remain unsolved. The interest in this problem, together with its complexity, is demonstrated by the number of publications that over the years have dealt with it. See, for example, [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05], [JKS07] [JKS11]. In the first chapter, we will start with a detailed introduction to the self-similar measurements in the complex plane and to the iterated functions systems, also including the concepts of measure theory needed to describe them. Next, we introduce the necessary tools from orthogonal polynomials, infinite matrices and operators. In the second and third chapter we will translate the geometric properties of selfsimilar measures to the moments and Hessenberg matrices. From these results, we will describe algorithms to calculate these matrices from the corresponding iterated functions systems. To be precise, we obtain explicit formulas and approximation algorithms for the moments and moment matrices of fractal measures from a new fixed point theorem for matrices. Moreover, using techniques from operator theory, we extend to the complex plane the real case results obtained by Mantica [Ma00, Ma96]. This result is the base to define a stable algorithm that approximates the Hessenberg matrix associated to a fractal measure and obtains exact finite sections of Hessenberg matrices associated to a sum of measurements. In the last chapter, we consider more general measures, μ, and study the asymptotic behaviour of the eigenvalues of a hermitian matrix of moments, together with its impact on the properties of the associated measure. In the main result we demonstrate that, if the associated polynomials are dense in L2(μ), then necessarily follows that the minimum eigenvalue of the finite sections of the moments matrix goes to zero.

Constructs and evaluation strategies for intelligent speculative parallelism - armageddon revisited

This report addresses speculative parallelism (the assignment of spare processing resources to tasks which are not known to be strictly required for the successful completion of a computation) at the user and application level. At this level, the execution of a program is seen as a (dynamic) tree —a graph, in general. A solution for a problem is a traversal of this graph from the initial state to a node known to be the answer. Speculative parallelism then represents the assignment of resources to múltiple branches of this graph even if they are not positively known to be on the path to a solution. In highly non-deterministic programs the branching factor can be very high and a naive assignment will very soon use up all the resources. This report presents work assignment strategies other than the usual depth-first and breadth-first. Instead, best-first strategies are used. Since their definition is application-dependent, the application language contains primitives that allow the user (or application programmer) to a) indícate when intelligent OR-parallelism should be used; b) provide the functions that define "best," and c) indícate when to use them. An abstract architecture enables those primitives to perform the search in a "speculative" way, using several processors, synchronizing them, killing the siblings of the path leading to the answer, etc. The user is freed from worrying about these interactions. Several search strategies are proposed and their implementation issues are addressed. "Armageddon," a global pruning method, is introduced, together with both a software and a hardware implementation for it. The concepts exposed are applicable to áreas of Artificial Intelligence such as extensive expert systems, planning, game playing, and in general to large search problems. The proposed strategies, although showing promise, have not been evaluated by simulation or experimentation.