1,721,092 research outputs found
A survey of some recent developments in measures of association
Full text linkThis paper surveys some recent developments in measures of association
related to a new coefficient of correlation introduced by the author. A
straightforward extension of this coefficient to standard Borel spaces (which
includes all Polish spaces), overlooked in the literature so far, is proposed
at the end of the survey.Comment: 22 pages. Minor changes in this revisio
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Two probabilistic models of competition
Full text linkIn this thesis we introduce and study two probabilistic models of competition and their applications. The first model is a particular contact process, and is intended to simulate propagation dynamics in real social networks. The second one stems from game theory and is of more theoretical value, as it is used to prove the existence of solutions to a certain non-linear partial differential equation.The first model consists of two competing first passage percolation processes started from uniformly chosen subsets of a random regular graph on N vertices. The processes are allowed to spread with different rates, start from vertex subsets of different sizes or at different times. We obtain tight results regarding the sizes of the vertex sets occupied by each process, showing that in the generic situation one process will occupy Theta(1)N^α vertices, for some 0 < α < 1. The value of α is calculated in terms of the relative rates of the processes, as well as the sizes of the initial vertex sets and the possible time advantage of one process.The second model is a version of the stochastic "Tug-of-War" game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function is shifted by an appropriate constant, the values of the game after n steps converge in the continuous case and the case of finite graphs with loops. Using this we prove the existence of solutions to the infinity Laplace equation with vanishing Neumann boundary condition
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Superconcentration and related topics
No full textA certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach. Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012. The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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Contributions to Stein's method and some limit theorems in probability
Full text linkIn this dissertation we investigate three different problems related to (1) concentration inequalities using Stein's method of exchangeable pair, (2) first-passage percolation along thin lattice cylinders and (3) limiting spectral distribution of random linear combinations of projection matrices.Stein's method is a semi-classical tool for establishing distributional convergence, particularly effective in problems involving dependent random variables. A version of Stein's method for concentration inequalities was introduced in the Ph.D.~thesis of Sourav Chatterjee to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures.In the first part of the dissertation we provide some extensions of the theory and three new applications: (1) We obtain a concentration inequality for the magnetization in the Curie-Weiss model at critical temperature (where it obeys a non-standard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymptotics for the number of triangles in the Erd\H os-R\' enyi random graph when . Similar results are derived also for general subgraph counts. (3) We obtain some interesting concentration inequalities for the Ising model on lattices that hold at all temperatures. In the second part, we consider first-passage percolation across thin cylinders of the form . We prove that the first-passage times obey Gaussian central limit theorems as long as grows slower than . We obtain appropriate moment bounds and use decomposition of the first-passage time into an approximate sum of independent random variables and a renormalization type argument to prove the result. It is an open question as to what is the fastest that can grow so that a Gaussian CLT still holds. We conjecture that is the right answer for~ and provide some numerical evidence for that.Finally, in the last part we consider limiting spectral distributions of random matrices of the form where 's are i.i.d.~mean zero and variance one random variables, 's are some given sequence of real numbers with norm one and 's are projection matrices with dimension growing to infinity. We provide sufficient conditions under which the limiting spectral distribution is Gaussian. We also provide examples from the theory of representations of symmetric group for which our results hold
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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