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## Estudo do fenômeno da auto-intersecção em um anel anisotrópico; Study of the self-intersection anomaly in an anisotropic ring

García Sánchez, Jesús Antonio
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## Differential geometry of intersection curves in R(4) of three implicit surfaces

Alessio, Osmar
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica Formato: 455-471
ENG
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We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

## Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

Faustini,Mário Carneiro; Tsuzuki,Marcos Sales Guerra
Fonte: The Brazilian Society of Mechanical Sciences Publicador: The Brazilian Society of Mechanical Sciences
Tipo: Artigo de Revista Científica Formato: text/html
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The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

## Local intersection volume (LIV) descriptors: 3D-QSAR models for PGI2 receptor ligands

Martins,Rita C. A.; Albuquerque,Magaly G.; Alencastro,Ricardo B.
Tipo: Artigo de Revista Científica Formato: text/html
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Prostacyclin I2 inhibits platelet aggregation through specific binding to its membrane receptor. In this work, we developed 3D-QSAR models for a series of aromatic heterocyclic compounds from literature using the local intersection volume descriptor. The models obtained can be applied to design new PGI2 receptor ligands with potential platelet anti-aggregating activity.

## The Intersection Complex as a Weight Truncation and an Application to Shimura Varieties

Morel, Sophie Marguerite
Fonte: World Scientific Publishing Company Publicador: World Scientific Publishing Company
Tipo: Monograph or Book
EN_US
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The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an application of this to the cohomology of noncompact Shimura varieties.; Mathematics

## Algorithms and Data Structures for an Expanded Family of Matroid Intersection Problems

Frederickson, Greg N. ; Srinivas, Mandayam A.
Fonte: University of Rochester. Computer Science Department. Publicador: University of Rochester. Computer Science Department.
Tipo: Relatório
ENG
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Consider a matroid of rank n in which each element has a real-valued cost and one of d > 1 colors. A class of matroid intersection problems is studied in which one of the matroids is a partition matroid that specifies that a base have qj elements of color j, for j = 1, 2, ... , d. Relationships are characterized among the solutions to the family of problems generated when the vector (q1, q2, ... , qd) is allowed to range over all values that sum to n. A fast algorithm is given for solving such matroid intersection problems when d is small. A characterization is presented for how the solution changes when one element changes in cost. Data structures are given for updating the solution on-line each time the cost of an arbitrary matroid element is modified. Efficient update algorithms are given for maintaining a color-constrained minimum spanning tree in either a general or a planar graph. An application of the techniques to finding a minimum spanning tree with several degree-constrained vertices is described.

## Privacy preserving set intersection based on bilinear groups

Sang, Y.; Shen, H.
Fonte: Australian Computer Society; Sydney Publicador: Australian Computer Society; Sydney
Tipo: Conference paper
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We propose a more efficient privacy preserving set intersection protocol which improves the previously known result by a factor of O(N) in both the computation and communication complexities (N is the number of parties in the protocol). Our protocol is obtained in the malicious model, in which we assume a probabilistic polynomial-time bounded adversary actively controls a fixed set of t (t < N/2) parties. We use a (t + 1,N)-threshold version of the Boneh-Goh-Nissim (BGN) cryptosystem whose underlying group supports bilinear maps. The BGN cryptosystem is generally used in applications where the plaintext space should be small, because there is still a Discrete Logarithm (DL) problem after the decryption. In our protocol the plaintext space can be as large as bounded by the security parameter τ, and the intractability of DL problem is utilized to protect the private datasets. Based on the bilinear map, we also construct some efficient non-interactive proofs. The security of our protocol can be reduced to the common intractable problems including the random oracle, subgroup decision and discrete logarithm problems. The computation complexity of our protocol is O(NS2τ3) (S is the cardinality of each party's dataset), and the communication complexity is O(NS2τ) bits. A similar work by Kissner et al. (2006) needs O(N2S2τ3) computation complexity and O(N2S2τ) communication complexity for the same level of correctness as ours.; Yingpeng Sang...

## Intersection : Exploration du concept à travers la composition de trois oeuvres musicales

Moore, Stephanie
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
FR
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Dans mon travail de recherche et de création musicale, je m’inspire du concept d’intersection pour sa capacité à donner naissance à quelque chose de nouveau. Ce mémoire de maîtrise documente une exploration de ce concept dans trois contextes différents : une pièce instrumentale, une pièce mixte et une pièce pour chœur. J’emploie le mot « intersection » dans le sens figuré de deux éléments abstraits ou concrets qui se rencontrent. La nature de leur rencontre ainsi que les résultats possibles m’intéressent également. Je vise l’intégration du concept à tous les niveaux d’une pièce : du global (la conception, la forme) jusqu’au local (la facture et l’emploi des techniques de composition). Le choix de procédés est très ouvert et dépend entièrement du contexte de la pièce et du résultat artistique envisagé. Ainsi, dans chacune de mes trois pièces de maîtrise, j’ai choisi une approche différente de l’idée de l’intersection. J’ai expérimenté une variété de moyens et de procédés, ainsi que la fonction de la composante extra-musicale (lorsqu’il y en a une). Au premier chapitre, je discute de mon quintette Finding Common Ground qui explore l’intersection de l’écriture pour percussion avec l’écriture pour les quatre autres instruments plutôt « mélodiques ». Ensuite...

## Intersection local times of independent Brownian motions as generalized white noise functionals

Albeverio, Sergio; Oliveira, Maria João; Streit, Ludwig
Fonte: Springer Verlag Publicador: Springer Verlag
Tipo: Artigo de Revista Científica
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The original publication is available at http://www.springerlink.com/content/14jtbl19nh37ggtx/fulltext.pdf; A "chaos expansion" of the intersection local time functional of two independent Brownian motions in Rd is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their Lp-properties are discussed. An important tool for deriving the chaos expansion is a computation of the "S-transform" of the corresponding regularized intersection local times and a control about their singular limit.; peerreviewed

## Metodos computacionais para determinação de pontos de intersecção de n esferas no 'R POT. N'; Computacional methods for determination of points of intersection of n sphere in 'R POT. N'

Marcos Roberto da Silva Gonçalves
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
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Neste trabalho, abordamos o problema da determinação de pontos de intersecção de n esferas no Rn. Este problema, além de ser importante matematicamente, é um problema com muitas aplicações, que vão desde a localização de pontos no globo, pelo sistema GPS, até a posicionamento de átomos em estruturas moleculares. O problema de encontrar a intersecção de n esferas no Rn é, em geral, formulado como um conjunto de n equações não-lineares, onde se deseja determinar a sua solução através de um método eficiente e confiável. Mostramos que, com exceção de alguns casos, o problema é geralmente resolvido de forma eficaz, empregando técnicas de álgebra linear. Reformulamos o problema de forma a convertê-lo em um problema linear e apresentamos dois métodos baseados na decomposição de matrizes. Testamos os métodos para casos particulares de baixa dimensão, analisando o custo computacional e possíveis dificuldades que podem surgir devido a erros de medição; We consider the problem of determining the points of intersection of n spheres in R n. This problem has many applications, such as the location of points on the globe by the GPS system and problems related to molecular geometry optimization. The problem of finding the intersection of n spheres in R n is generally expressed as a set of nonlinear equations...

## Intersection Cohomology. Simplicial Blow-up and Rational Homotopy

Chataur, David; Saralegi-Aranguren, Martintxo; Tanré, Daniel
Tipo: Artigo de Revista Científica
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Let X be a pseudomanifold. In this text, we use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. We do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C.P. Rourke and B.J. Sanderson. We define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, we get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, we use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology. For that, we construct a functor from the category of filtered face sets to a category of perverse commutative differential graded Q-algebras (cdga's) due to Hovey. We establish also the existence and unicity of a positively graded, minimal model of some perverse cdga's...

## Tropical Intersection Theory from Toric Varieties

Katz, Eric
Tipo: Artigo de Revista Científica
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We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on complete toric varieties. These objects fit into the framework of tropical intersection theory developed by Allermann and Rau. Standard facts about intersection theory on toric varieties are applied to show that the definitions of tropical intersection product on tropical cycles in $\R^n$ given by Allermann-Rau and Mikhalkin are equivalent. We introduce an induced tropical intersection theory on subvarieties on a toric variety. This gives a conceptional proof that the intersection of tropical $\psi$-classes on $\cmbar_{0,n}$ used by Kerber and Markwig computes classical intersection numbers.

## Regularity of Intersection Local Times of Fractional Brownian Motions

Wu, Dongsheng; Xiao, Yimin
Tipo: Artigo de Revista Científica
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Let $B^{\alpha_i}$ be an $(N_i,d)$-fractional Brownian motion with Hurst index ${\alpha_i}$ ($i=1,2$), and let $B^{\alpha_1}$ and $B^{\alpha_2}$ be independent. We prove that, if $\frac{N_1}{\alpha_1}+\frac{N_2}{\alpha_2}>d$, then the intersection local times of $B^{\alpha_1}$ and $B^{\alpha_2}$ exist, and have a continuous version. We also establish H\"{o}lder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and intersection points. One of the main motivations of this paper is from the results of Nualart and Ortiz-Latorre ({\it J. Theor. Probab.} {\bf 20} (2007)), where the existence of the intersection local times of two independent $(1,d)$-fractional Brownian motions with the same Hurst index was studied by using a different method. Our results show that anisotropy brings subtle differences into the analytic properties of the intersection local times as well as rich geometric structures into the sets of intersection times and intersection points.; Comment: 27 pages

## Combinatorial Intersection Cohomology for Fans

Barthel, Gottfried; Brasselet, Jean-Paul; Fieseler, Karl-Heinz; Kaup, Ludger
Tipo: Artigo de Revista Científica
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We continue the approach toward a purely combinatorial "virtual" intersection cohomology for possibly non-rational fans, based on our investigation of equivariant intersection cohomology for toric varieties (see math.AG/9904159). Fundamental objects of study are "minimal extension sheaves" on "fan spaces". These are flabby sheaves of graded modules over a sheaf of polynomial rings, satisfying three relatively simple axioms that characterize the properties of the equivariant intersection cohomology sheaf on a toric variety, endowed with the finite topology given by open invariant subsets. These sheaves are models for the "pure" objects of a "perverse category"; a "Decomposition Theorem" is shown to hold. -- Formalizing those fans that define "equivariantly formal" toric varieties (where equivariant and non-equivariant intersection cohomology determine each other by Kunneth type formulae), we study "quasi-convex" fans (including fans with convex or with "co-convex" support). For these, there is a meaningful "virtual intersection cohomology". We characterize quasi-convex fans by a topological condition on the support of their boundary fan and prove a generalization of Stanley's "Local-Global" formula realizing the intersection Poincare polynomial of a complete toric variety in terms of local data. Virtual intersection cohomology of quasi-convex fans is shown to satify Poincare duality. To describe the local data in terms of virtual intersection cohomology of lower-dimensional complete polytopal fans...

## On $k$-connectivity and minimum vertex degree in random $s$-intersection graphs

Zhao, Jun; Yağan, Osman; Gligor, Virgil
Tipo: Artigo de Revista Científica
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Random $s$-intersection graphs have recently received much interest in a wide range of application areas. Broadly speaking, a random $s$-intersection graph is constructed by first assigning each vertex a set of items in some random manner, and then putting an undirected edge between all pairs of vertices that share at least $s$ items (the graph is called a random intersection graph when $s=1$). A special case of particular interest is a uniform random $s$-intersection graph, where each vertex independently selects the same number of items uniformly at random from a common item pool. Another important case is a binomial random $s$-intersection graph, where each item from a pool is independently assigned to each vertex with the same probability. Both models have found numerous applications thus far including cryptanalysis, and the modeling of recommender systems, secure sensor networks, online social networks, trust networks and small-world networks (uniform random $s$-intersection graphs), as well as clustering analysis, classification, and the design of integrated circuits (binomial random $s$-intersection graphs). In this paper, for binomial/uniform random $s$-intersection graphs, we present results related to $k$-connectivity and minimum vertex degree. Specifically...

## Toroidality and projective-planarity of intersection graphs of subgroups of finite groups

Rajkumar, R.; Devi, P.
Tipo: Artigo de Revista Científica
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Let $G$ be a group. The intersection graph of subgroups of $G$, denoted by $\mathscr{I}(G)$, is a graph with all the proper subgroups of $G$ as its vertices and two distinct vertices in $\mathscr{I}(G)$ are adjacent if and only if the corresponding subgroups having a non-trivial intersection in $G$. In this paper, we classify the finite groups whose intersection graph of subgroups are toroidal or projective-planar. In addition, we classify the finite groups whose intersection graph of subgroups are one of bipartite, complete bipartite, tree, star graph, unicyclic, acyclic, cycle, path or totally disconnected. Also we classify the finite groups whose intersection graph of subgroups does not contain one of $K_5$, $K_4$, $C_5$, $C_4$, $P_4$, $P_3$, $P_2$, $K_{1,3}$, $K_{2,3}$ or $K_{1,4}$ as a subgraph. We estimate the girth of the intersection graph of subgroups of finite groups. Moreover, we characterize some finite groups by using their intersection graphs. Finally, we obtain the clique cover number of the intersection graph of subgroups of groups and show that intersection graph of subgroups of groups are weakly $\alpha$-perfect.; Comment: 38 pages, 10 figures. arXiv admin note: text overlap with arXiv:1505.03462, some corrections made

## Analyzing Stratified Spaces Using Persistent Versions of Intersection and Local Homology

Bendich, Paul
Tipo: Dissertação Formato: 797394 bytes; application/pdf
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This dissertation places intersection homology and local homology within the framework of persistence, which was originally developed for ordinary homology by Edelsbrunner, Letscher, and Zomorodian. The eventual goal, begun but not completed here, is to provide analytical tools for the study of embedded stratified spaces, as well as for high-dimensional and possibly noisy datasets for which the number of degrees of freedom may vary across the parameter space. Specifically, we create a theory of persistent intersection homology for a filtered stratified space and prove several structural theorems about the pair groups asso- ciated to such a filtration. We prove the correctness of a cubic algorithm which computes these pair groups in a simplicial setting. We also define a series of intersec- tion homology elevation functions for an embedded stratified space and characterize their local maxima in dimension one. In addition, we develop a theory of persistence for a multi-scale analogue of the local homology groups of a stratified space at a point. This takes the form of a series of local homology vineyards which allow one to assess the homological structure within a one-parameter family of neighborhoods of the point. Under the assumption of dense sampling...

## Triangle-Triangle Intersection Determination and Classification to Support Qualitative Spatial Reasoning

Sabharwal,Chaman L.; Leopold,Jennifer L.; McGeehan,Douglas
Fonte: Instituto Politécnico Nacional, Centro de Innovación y Desarrollo Tecnológico en Cómputo Publicador: Instituto Politécnico Nacional, Centro de Innovación y Desarrollo Tecnológico en Cómputo
Tipo: Artigo de Revista Científica Formato: text/html
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In CAD/CAM modeling, objects are represented using the Boundary Representation (ANSI Brep) model Detection of possible intersection between objects can be based on the objects' boundaries (ie., triangulated surfaces), and computed using triangle-triangle intersection. Usually only a cross intersection algorithm is needed; however, it is beneficial to have a single robust and fast intersection detection algorithm for both cross and coplanar intersections. For qualitative spatial reasoning, a general-purpose algorithm is desirable for accurately differentiating the relations in a region connection calculus, a task that requires consideration of intersection between objects. Herein we present a complete uniform integrated algorithm for both cross and coplanar intersection. Additionally, we present parametric methods for classifying and computing intersection points. This work is applicable to most region connection calculi, particularly VRCC-3D+, which detects intersections between 3D objects as well as their projections in 2D that are essential for occlusion detection.

## Selection of MOSFET Sizes by Fuzzy Sets Intersection in the Feasible Solutions Space

Polanco-Martagón,S.; Reyes-Salgado,G.; Flores-Becerra,G.; Tlelo-Cuautle,E.; Fraga,L.G. de la; Guerra-Gómez,I.; Duarte-Villaseñor,M.A.
Fonte: UNAM, Centro de Ciencias Aplicadas y Desarrollo Tecnológico Publicador: UNAM, Centro de Ciencias Aplicadas y Desarrollo Tecnológico
Tipo: Artigo de Revista Científica Formato: text/html