Convergent Sequences of Dense Graphs I: Subgraph Frequencies, Metric Properties and Testing

We consider sequences of graphs and define various notions of convergence related to these sequences: ``left convergence'' defined in terms of the densities of homomorphisms from small graphs into the graphs of the sequence, and ``right convergence'' defined in terms of the densities of homomorphisms from the graphs of the sequence into small graphs; and convergence in a suitably defined metric. In Part I of this series, we show that left convergence is equivalent to convergence in metric, both for simple graphs, and for graphs with nodeweights and edgeweights. One of the main steps here is the introduction of a cut-distance comparing graphs, not necessarily of the same size. We also show how these notions of convergence provide natural formulations of Szemeredi partitions, sampling and testing of large graphs.Comment: 57 pages. See also http://research.microsoft.com/~borgs/. This version differs from an earlier version from May 2006 in the organization of the sections, but is otherwise almost identica

A simulação do real organizacional: O método dos casos como ponte entre o conhecimento tácito e o académico

O desenvolvimento da ciência organizacional tem sido marcado pelo desdobramento de modas e modelos nas mais diversas áreas. O presente artigo reflecte sobre o seu papel, particularmente, por via dos estudos de caso. Sendo as escolas de negócios e de gestão um dos actores importantes na difusão destes modismos, o método dos casos, enquanto estratégia pedagógica, é entendido aqui como um importante veículo de coordenação entre a investigação científica organizacional e a sua realidade. Contribui para a aproximação entre os vários intervenientes neste processo (professores, alunos, gestores, líderes e empresários). Advoga-se a sua importância por estabelecer uma ponte entre a academia e a o mundo organizacional, entre o conhecimento teórico dos académicos e o conhecimento tácito dos agentes empresariais.The development of organizational science has been marked by the growth of models and fashions in different areas. The aim of this article is about it’s role, namely, by the hand of case studies. Business and management schools are one of important agents in models and fashions diffusion process. The case method, while pedagogic strategy, is an important vehicle of coordination between organizational scientific investigation and its reality. It contributes to different actors get close of each other (teachers, students, managers, leaders, business men). We address the relevance to build a bridge between the academic world and the organizational one, between the academic theoretical knowledge and tacit knowledge of organizational managers

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

Dirichlet fundamental domains and complex-projective varieties

We prove that for every finitely-presented group G there exists a 2-dimensional irreducible complex-projective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas.Comment: 1 figur

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph obtain by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determine probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product cayley graphs (complete cycle, complete $K_n$, charter and $n$-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as $t\longrightarrow \infty$ but for quantum state is not always satisfy.Comment: 21, page. Accepted for publication on CT

Nuclear dependence of the transverse single-spin asymmetry in the production of charged hadrons at forward rapidity in polarized p+pp+p, p+p+Al, and p+p+Au collisions at sNN=200\sqrt{s_{_{NN}}}=200 GeV

We report on the nuclear dependence of transverse single-spin asymmetries (TSSAs) in the production of positively-charged hadrons in polarized $p^{\uparrow}+p$, $p^{\uparrow}+$Al and $p^{\uparrow}+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The measurements have been performed at forward rapidity ($1.4<\eta<2.4$) over the range of $1.8<p_{T}<7.0$ GeV$/c$ and $0.1<x_{F}<0.2$. We observed a positive asymmetry $A_{N}$ for positively-charged hadrons in \polpp collisions, and a significantly reduced asymmetry in $p^{\uparrow}$+$A$ collisions. These results reveal a nuclear dependence of charged hadron $A_N$ in a regime where perturbative techniques are relevant. These results provide new opportunities to use \polpA collisions as a tool to investigate the rich phenomena behind TSSAs in hadronic collisions and to use TSSA as a new handle in studying small-system collisions.Comment: 303 authors from 66 institutions, 9 pages, 2 figures, 1 table. v1 is version accepted for publication in Physical Review Letters. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm