Evolution of Directed Triangle Motifs in the Google+ OSN

Motifs are a fundamental building block and distinguishing feature of networks. While characteristic motif distribution have been found in many networks, very little is known today about the evolution of network motifs. This paper studies the most important motifs in social networks, triangles, and how directed triangle motifs change over time. Our chosen subject is one of the largest Online Social Networks, Google+. Google+ has two distinguishing features that make it particularly interesting: (1) it is a directed network, which yields a rich set of triangle motifs, and (2) it is a young and fast evolving network, whose role in the OSN space is still not fully understood. For the purpose of this study, we crawled the network over a time period of six weeks, collecting several snapshots. We find that some triangle types display significant dynamics, e.g., for some specific initial types, up to 20% of the instances evolve to other types. Due to the fast growth of the OSN in the observed time period, many new triangles emerge. We also observe that many triangles evolve into less-connected motifs (with less edges), suggesting that growth also comes with pruning. We complement the topological study by also considering publicly available user profile data (mostly geographic locations). The corresponding results shed some light on the semantics of the triangle motifs. Indeed, we find that users in more symmetric triangle motifs live closer together, indicating more personal relationships. In contrast, asymmetric links in motifs often point to faraway users with a high in-degree (celebrities)

A comprehensive study of rate capability in Multi-Wire Proportional Chambers

Systematic measurements on the rate capability of thin MWPCs operated in Xenon, Argon and Neon mixtures using CO2 as UV-quencher are presented. A good agreement between data and existing models has been found, allowing us to present the rate capability of MWPCs in a comprehensive way and ultimately connect it with the mobilities of the drifting ions.Comment: 29 pages, 18 figure

On the chemical equilibration of strangeness-exchange reaction in heavy-ion collisions

The strangeness-exchange reaction pi + Y -> K- + N is shown to be the dynamical origin of chemical equilibration for K- production in heavy-ion collisions up to beam energies of 10 A GeV. The hyperons occurring in this process are produced associately with K+ in baryon-baryon and meson-baryon interactions. This connection is demonstrated by the ratio K-/K+ which does not vary with centrality and shows a linear correlation with the yield of pions per participant. At incident energies above AGS this correlation no longer holds due to the change in the production mechanism of kaons.Comment: 9 pages, 4 figure

Numerical ranges of an operator on an indefinite inner product space

For n x n complex matrices A and an n x n Hermitian matrix S, we consider the S-numerical range of A and the positive S-numerical range of A defined by WS(A) = {〈Av, v〉S/〈v, v〉S : v ∈ ℂn, 〈v, v〉S ≠ 0} and W S + (A) = {〈Av, v〉S : v ∈ ℂn, 〈v, v〉S = 1}, respectively, where 〈u, v〉S = v*Su. These sets generalize the classical numerical range, and they are closely related to the joint numerical range of three Hermitian forms and the cone generated by it. Using some theory of the joint numerical range we can give a detailed description of WS(A) and WS + (A) for arbitrary Hermitian matrices S. In particular, it is shown that WS + (A) is always convex and WS(A) is always p-convex for all S. Similar results are obtained for the sets VS(A) = {〈Av, v〉/〈Sv, v〉: v ∈ ℂn, 〈Sv, v〉 ≠ 0}, VS + (A) = {〈Av, v〉: v ∈ ℂn, 〈Sv, v〉 = 1}, where 〈u, v〉 = v* u. Furthermore, we characterize those linear operators preserving WS(A), WS + (A), V S(A), or VS + (A). Possible generalizations of our results, including their extensions to bounded linear operators on an infinite dimensional Hilbert or Krein space, are discussed.published_or_final_versio