1,720,998 research outputs found
Axelrod's Model in Two Dimensions
Full text linkIn 1997 R. Axelrod introduced a model in which individuals have one of possible opinions about each of issues and neighbors interact at a rate proportional to the fraction of opinions they share. Thanks to work by Lanchier and collaborators there are now a number of results for the one dimensional model. Here, we consider Axelrod's model on a square subset of the two-dimensional lattice start from a randomly chosen initial state and simplify things by supposing that and large. If is large then most neighbors have all opinions different and do not interact, so by a result of Lanchier the system soon reaches a highly disordered absorbing state. In contrast if is small, then there is a giant component of individuals who share at least one opinion. In this case we show that consensus develops on this percolating cluster.</p
Dynamics on and of Complex Networks
Full text linkNetworks -- abstract objects composed of \emph{vertices} connected by \emph{edges}, are ubiquitous in the real world. Examples such as social networks, the world wide web, and neural networks in the brainare constantly evolving in their topology, the state of their vertices, or a combination of the two.This dissertation presents a computational and theoretical study of three models of network dynamics, one corresponding to each of these modes of evolution.The first study models the disintegration of a social network of voters with binary opinions, who prefer to be connected to others with the same opinion. We study two versions of the model: the network evolves by voters in discordant ties choosing to either adopt the opinion of their neighbors, or to rewire their ties to some randomly chosen voter of (i) the same, or (ii) any, opinion. We examine how the probability of rewiring, and the initial fraction in the minority, determine the final minority fraction , when the network has bifurcated. In case (i), there is a critical probability, that is independent of , above which is unchanged from , and below which there is full concensus. In case (ii), the behavior above the critical probability, that now depends on , is similar; but below it, matches the result of starting with . Using simulations and approximate calculations, we explain why these two nearly identical models have such dramatically different behaviors.The second model, called the \emph{quadratic contact process} (QCP) involves ``birth'' and ``death'' events on a static network. Vertices take on the binary states occupied(1) or vacant(0). We consider two versions of the model -- Vertex QCP, and Edge QCP, corresponding to birth events and respectively, where `' represents an edge. We study the fraction of occupied vertices at steady state as a function of the birth rate, keeping the death rate constant. To investigate the effects of network topology, we study the QCP on homogeneous networks with a bounded or rapidly decaying degree distribution, and those with a heavy tailed degree distribution. From our simulation results and mean field calculations, we conclude that on the homogeneous networks, there is a discontinuous phase transition with aregion of bistability, whereas on the heavy tailed networks, thetransition is continuous. Furthermore, the critical birth rate is positive in the former but zero in the latter.In the third study, we propose a general scheme for spatial networks evolving in order to reduce their total edge lengths. We study the properties of the equilbria of two networks from this class, one of which interpolate between two well studied objects: the Erd\H{o}s-R\'{e}nyi random graph, and the random geometric graph. The first of our two evolutions can be used as a model for a social network where individuals have fixed opinions about a number of issues and adjust their ties to be connected to people with similar views. The second evolution which preserves the connectivity of the network has potential applications in the design of transportation networks and other distribution systems.</p
Voter Models On Graphs
No full textThe voter model which describes the flow of information through interactions between neighbors has been widely studied in the field of probability. In this paper we study two variations of the voter model, one is called the Latent Voter Model and the other is called the Zealot Voter Model. Both models are implemented in a space that is a random graph.In the latent voter model, which models the spread of a technology through a social network, individuals who have just changedtheir choice have a latent period, which is exponential with rate ,during which they will not buy a new device. We study site and edge versions of this model on random graphs generated by a configuration model in which the degrees have . We show that if the number ofvertices and then the fraction of 1's at time converges tothe solution of . Using this we showthe latent voter model has a quasi-stationary state in which each opinion has probability and persists in this state for a time that is for any O(n)xd(x)d(x)p_kxk\ge 1p_0$individuals with opinion 1 change to 0. As in the contact process on trees, we are interested in determining when the zealotssurvive and when they will survive locally, i.e., the root of the tree is in state 1 infinitely often.</p
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
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
Contact processes with quenched disorder on and on Erdos-Renyi graphs
Full text linkIn real systems impurities and defects play an important role in determining
their properties. Here we will consider what probabilists have called the
contact process in a random environment and what physicists have more precisely
named the contact process with quenched disorder. We will concentrate our
efforts on the special case called the random dilution model, in which sites
independently and with probability are active and particles on them give
birth at rate , while the other sites are inert and particles on them
do not give birth. We show that the resulting inhomogeniety can make dramatic
changes in the behavior in the supercritical, subcritical, and critical
behavior. In particular, the usual exponential decay of the desnity of
particles in the subcritical phase becomes a power law (the Griffiths phase),
and polynomial decay at the critical value becomes a power of .Comment: 26 pages, 7 figure
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