By Hamed Amini, Andreea Minca (auth.), Evangelos Kranakis (eds.)
As good as highlighting very likely priceless functions for community research, this quantity identifies new pursuits for mathematical study that promise to supply insights into community structures concept in addition to facilitating the cross-fertilization of principles among sectors. targeting monetary, safeguard and social points of networking, the quantity provides to the becoming physique of proof exhibiting that community research has functions to transportation, conversation, wellbeing and fitness, finance, and social coverage extra generally. It offers robust types for realizing the habit of complicated platforms that, in flip, will influence quite a few state-of-the-art sectors in technology and engineering, corresponding to instant communique, community safety, disbursed computing and social networking, monetary research, and cyber warfare.
The quantity bargains an insider’s view of state-of-the-art learn in community structures, together with methodologies with sizeable power for interdisciplinary software. The members have all offered fabric at a sequence of workshops prepared on behalf of Canada’s MITACS initiative, which money tasks and research offers in ‘mathematics for info know-how and complicated systems’. those lawsuits comprise papers from workshops on monetary networks, community safeguard and cryptography, and social networks. MITACS has proven that the in part ghettoized nature of community structures examine has resulted in duplicated paintings in discrete fields, and hence this initiative has the capability to save lots of time and speed up the speed of analysis in a few components of community platforms research.
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2 Shock Transmission in the NYYA Model The NYYA model allows for the possibility of non-zero recovery on defaulted loans. , σ > c jk . 1). Thus the shock transmitted to each creditor of the defaulted bank is min σ − c jk ,w . P. Gleeson et al. As in the GK model, shocks transmitted from banks which default at timestep n will affect the creditor banks at timestep n + 1, and a cascade of banks failures may ensue. This cascade mechanism bears some resemblance to the “fictitious default” cascade used by Eisenberg and Noe  (“EN” for short) to determine the clearing payment vector in a system with defaults, see Appendix A.
1. This convention ensures that shocks due to defaults on loans travel in the direction of the arrows on the edges. Thus p jk is the probability that a randomly-chosen bank in the system has j debtors (or, more strictly, that it has j asset loans, since multiple links are possible) and k creditors (strictly speaking, k liability loans). In the second step, each node (bank) of the skeleton structure is endowed with a balance sheet and the edges between banks are weighted with loan magnitudes. P.
2 Models of Contagion in Banking Networks We consider simplified models of banking networks, as introduced by GK and NYYA. As noted in May and Arinaminpathy , such “deliberately oversimplified” mathematical models are caricatures of real banking networks, but may nevertheless lead to useful insights. These model networks can be considered as generated in two steps. First, a “skeleton” structure of N nodes (representing banks) and directed edges (to represent the interbank positions) is created.