By Hamed Amini, Andreea Minca (auth.), Evangelos Kranakis (eds.)
As good as highlighting probably precious functions for community research, this quantity identifies new objectives for mathematical examine that promise to supply insights into community platforms concept in addition to facilitating the cross-fertilization of rules among sectors. targeting monetary, safeguard and social facets of networking, the amount provides to the becoming physique of proof displaying that community research has functions to transportation, conversation, wellbeing and fitness, finance, and social coverage extra generally. It offers robust versions for figuring out the habit of complicated structures that, in flip, will impression quite a few state of the art sectors in technological know-how and engineering, resembling instant conversation, community safeguard, disbursed computing and social networking, monetary research, and cyber warfare.
The quantity bargains an insider’s view of state-of-the-art study in community structures, together with methodologies with giant strength for interdisciplinary program. The individuals have all awarded fabric at a sequence of workshops prepared on behalf of Canada’s MITACS initiative, which cash initiatives and learn provides in ‘mathematics for info know-how and intricate systems’. those complaints contain papers from workshops on monetary networks, community protection and cryptography, and social networks. MITACS has proven that the in part ghettoized nature of community platforms learn has ended in duplicated paintings in discrete fields, and therefore this initiative has the aptitude to save lots of time and speed up the speed of analysis in a few components of community structures research.
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Extra info for Advances in Network Analysis and its Applications
Deciphering the liquidity and credit crunch 2007–2008. Journal of Economic Perspectives, 23(1):77–100, 2009. 12. J. A. Chan-Lau, M. Espinosa, K. Giesecke, and J. A. Sole. Assessing the systemic implications of financial linkages. In Global Financial Stability Report. International Monetary Fund, 2009. 13. R. Cifuentes, G. Ferrucci, and H. Shin. Liquidity risk and contagion. Journal of the European Economic Association, 3:556–566, 2005. 14. R. Cont and A. Minca. Credit default swaps and systemic risk.
41. M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64:026118, 2001. 26 H. Amini and A. Minca 42. P. Sch¨onbucher. Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives. Working paper, 2005. 43. K. Soramaki, M. L. Bech, J. Arnold, R. J. Glass, and W. E. Beyeler. The topology of interbank payment flows. Physica A: Statistical Mechanics and its Applications, 379(1):317–333, 2007.
More precisely, µ+ (k), defined as the probability that a node chosen uniformly at random has a number k of incident links, is such that for a parameter γ > 0, µ+(k) ∼ k−γ for k larger than a given constant. A similar empirical result holds for the out-degree. p. if and only if ∑k µ(k)k(k − 2) > 0. Now consider the case of a simple epidemics on the random graph ER(n, c/n). Assume that each infected node with probability p infects its neighbours. The question of whether it is possible for a single node to infect a positive fraction of all nodes, is in fact equivalent to the existence of a giant component in the random graph ER(n, pc/n).
Advances in Network Analysis and its Applications by Hamed Amini, Andreea Minca (auth.), Evangelos Kranakis (eds.)