The Semantic View and the Alpha-model

In what follows, I discuss the semantic view of theories, specifically in the ‘state space’ formulation that has been developed by Bas van Fraassen, Frederick Suppe, and others and applied by Elisabeth Lloyd. I consider the claims that the state space view makes about how scientific theories are best understood. I then discuss a particular model from network theory, the alpha-model developed by Duncan Watts, and try to apply the state space view to the alpha-model theory. I argue that the way Watts uses the alpha-model is not described very easily under the state space approach, because its parameters are idealized in a way that the state space approach does not account for, and because the relation between the alpha-model and the world is not one of statistical fit between its models and data

Small-World File-Sharing Communities

Web caches, content distribution networks, peer-to-peer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can first identify and then exploit interesting structure within a community's access patterns. To this end, we propose a novel perspective on file sharing based on the study of the relationships that form among users based on the files in which they are interested. We propose a new structure that captures common user interests in data--the data-sharing graph-- and justify its utility with studies on three data-distribution systems: a high-energy physics collaboration, the Web, and the Kazaa peer-to-peer network. We find small-world patterns in the data-sharing graphs of all three communities. We analyze these graphs and propose some probable causes for these emergent small-world patterns. The significance of small-world patterns is twofold: it provides a rigorous support to intuition and, perhaps most importantly, it suggests ways to design mechanisms that exploit these naturally emerging patterns

Threshold model of cascades in temporal networks

Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. There is a consensus that bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work, we propose an extension of Watts' classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to thresholds as the fraction of contacts, we also investigate the number of contacts within the time window as a basis for influence. To elucidate the model's behavior, we run the model on real and randomized empirical contact datasets.Comment: 7 pages, 5 figures, 2 table

"Die Invasion der Physiker": Naturwissenschaft und Soziologie in der Netzwerkanalyse

"Im Jahre 2002 erscheint das Buch 'Linked' von Albert-László Barabasi. Es trägt den Untertitel 'The New Science of Networks'. Das Buch wird sofort ein wissenschaftlicher Bestseller. Fast noch bekannter wird ein ähnliches Buch 'Six Degrees. The Science of a Connected Age' von Duncan Watts. Die Berichte und Rezensionen über beide Bücher erscheinen, unter anderem in der New York Times, im Economist, Science Magazine und in Nature und sorgen für die Wahrnehmung der Bücher in einer breiten Öffentlichkeit. Barabasi ist Physiker an der Universität von Notre Dame in Indiana, USA; Duncan Watts ist promovierter Physiker, lehrt aber auch Soziologe an der Columbia University in New York. Obgleich die soziale Netzwerkanalyse zu diesem Zeitpunkt, je nach dem, wann man ihren Beginn verortet, bereits 50 oder 70 Jahre als ist, offenbart die 'Neuerfindung', dass die Physiker kaum an die vorhandene Tradition anschließen. Diese Ignoranz der Physiker gegenüber den Entwicklungen in der Ethnologie, Sozialpsychologie und Soziologie führte innerhalb der Fachwelt der Netzwerkforscher zu heftigen Diskussionen. Dabei ist die Geschichte der Netzwerkanalyse durch die Zusammenarbeit von Wissenschaftlern verschiedener Disziplinen geprägt. Neben den Sozialwissenschaften waren schon immer auch Mathematiker und an wesentlicher Stelle auch Physiker beteiligt. Die neuere Dominanz von Physikern führt dazu, dass naturwissenschaftliche Weltsichten zur Erklärung von sozialen Sachverhalten herangezogen werden. Das bedeutet, dass Physiker neben Soziobiologen und Hirnforschern sich nun vermehrt auf einem Terrain tummeln, welches ureigenes sozialwissenschaftliches Gebiet ist. Im Vortrag werden einerseits die Kontroversen um die erfolgreichen Bücher nachgezeichnet, andererseits wird gefragt, warum eigentlich die Bücher von Naturwissenschaftlern eine offensichtlich größere Aufmerksamkeit erfahren, als die Werke der Sozialwissenschaftler." (Autorenreferat

What\u27s in a Name? The Matrix as an Introduction to Mathematics

In lieu of an abstract, here is the article\u27s first paragraph: In my classes on the nature of scientific thought, I have often used the movie The Matrix to illustrate the nature of evidence and how it shapes the reality we perceive (or think we perceive). As a mathematician, I usually field questions related to the movie whenever the subject of linear algebra arises, since this field is the study of matrices and their properties. So it is natural to ask, why does the movie title reference a mathematical object

Cascade Dynamics of Multiplex Propagation

Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However we show that when the propagation requires simultaneous exposure to multiple sources of activation, called multiplex propagation, the effect of random links is just the opposite: it makes the propagation more difficult to achieve. We calculate analytical and numerically critical points for a threshold model in several classes of complex networks, including an empirical social network.Comment: 4 pages, 5 figures, for similar work visit http://hsd.soc.cornell.edu and http://www.imedea.uib.es/physdep