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The Web as a graph
, 2000
"... The pages and hyperlinks of the WorldWide Web maybe viewed as nodes and edges in a directed graph. This graph has about a billion nodes today,several billion links, and appears to grow exponentially with time. There are many reasonsmathematical, sociological, and commercialfor studying the e ..."
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Cited by 177 (2 self)
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The pages and hyperlinks of the WorldWide Web maybe viewed as nodes and edges in a directed graph. This graph has about a billion nodes today,several billion links, and appears to grow exponentially with time. There are many reasonsmathematical, sociological, and commercialfor studying the evolution of this graph. We first review a set of algorithms that operate on the Web graph, addressing problems from Web search, automatic community discovery, and classification. We then recall a number of measurements and properties of the Web graph. Noting that traditional random graph models do not explain these observations, we propose a new family of random graph models.
A Simulation of the Structure of Academic Science
, 1997
"... The contemporary structure of scientific activity, including the publication of papers in academic journals, citation behaviour, the clustering of research into specialties and so on has been intensively studied over the last fifty years. A number of quantitative relationships between aspects of t ..."
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Cited by 28 (2 self)
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The contemporary structure of scientific activity, including the publication of papers in academic journals, citation behaviour, the clustering of research into specialties and so on has been intensively studied over the last fifty years. A number of quantitative relationships between aspects of the system have been observed. This paper reports on a simulation designed to see whether it is possible to reproduce the form of these observed relationships using a small number of simple assumptions. The simulation succeeds in generating a specialty structure with 'areas' of science displaying growth and decline. It also reproduces Lotka's Law concerning the distribution of citations among authors. The simulation suggests that it is possible to generate many of the quantitative features of the present structure of science and that one way of looking at scientific activity is as a system in which scientific papers generate further papers, with authors (scientists) playing a necessary but incidental role. The theoretical implications of these suggestions are briefly explored.
Sir Gilbert Walker and a Connection between El Niño and Statistics
"... Abstract. The eponym “Walker Circulation ” refers to a concept used by atmospheric scientists and oceanographers in providing a physical explanation for the El Niño–Southern Oscillation phenomenon, whereas the eponym “Yule–Walker equations ” refers to properties satisfied by the autocorrelations of ..."
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Abstract. The eponym “Walker Circulation ” refers to a concept used by atmospheric scientists and oceanographers in providing a physical explanation for the El Niño–Southern Oscillation phenomenon, whereas the eponym “Yule–Walker equations ” refers to properties satisfied by the autocorrelations of an autoregressive process. But how many statisticians (or, for that matter, atmospheric scientists) are aware that the “Walker ” in both terms refers to the same individual, Sir Gilbert Thomas Walker, and that these two appellations arose in conjunction with the same research on the statistical prediction of climate? Like George Udny Yule (the “Yule ” in Yule– Walker), Walker’s motivation was to devise a statistical model that exhibited quasiperiodic behavior. The original assessments of Walker’s work, both in the meteorology and in statistics, were somewhat negative. With hindsight, it is argued that his research should be viewed as quite successful.
Contract no: 20851A2/1/020 Time Series: General
"... Time series: a stretch of values on the same scale indexed by a timelike parameter. The basic data and parameters are functions. Time series take on a dazzling variety of shapes and forms, indeed there are as many time series as there are functions of real numbers. Some common examples of time ser ..."
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Time series: a stretch of values on the same scale indexed by a timelike parameter. The basic data and parameters are functions. Time series take on a dazzling variety of shapes and forms, indeed there are as many time series as there are functions of real numbers. Some common examples of time series forms are provided in Figure 1. One notes periods, trends, wandering and integervalues. The time series such as those in the Figure may be contemporaneous and a goal may be to understand the interrelationships. Concepts and fields related to time series include: longitudinal data, growth curves, repeated measures, econometric models, multivariate analysis, signal processing and systems analysis. The field, time series analysis, consists of the techniques which when applied to time series lead to improved knowledge. The purposes include summary, decision, description, prediction.