By Myriam P. Sassano, Araceli N. Proto (auth.), Araceli N. Proto, Massimo Squillante, Janusz Kacprzyk (eds.)

In this quantity contemporary advances within the use of recent quantitative versions for the research of assorted difficulties on the topic of the dynamics of social and monetary platforms are provided. the bulk chapters describe instruments and strategies of commonly perceived computational intelligence, particularly fuzzy good judgment, evolutionary computation, neural networks and a few non-standard probabilistic and statistical analyses. as a result of excessive complexity of the platforms and difficulties thought of, in lots of events it is crucial to contemplate while analytic, topological and statistical elements and practice applicable approaches and algorithms. This quantity is an instantaneous results of vibrant discussions held in the course of the 5th overseas Workshop on Dynamics of Social and budget friendly structures (DYSES) which used to be held at Benevento, Italy September 20-25, 2010, in addition to a number of post-workshop conferences and consultations.

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Eboli A cut in a ﬂow network is a partition of a network in two subnetworks such that all source nodes are in one part and all sink nodes are in the other part. In the present case, a cut in a FFN N is a partition U, U of {A ∪ Ω ∪ T ∪ H}, where U and U are two non-empty sets such that A ⊆ U and (T, H) ∈ U . For a cut U, U of a FFN N, let L+ (U ) be the set of forward links going from U into U , and et L− (U ) be the set of backward links, going in the opposite direction. , from nodes in U into nodes in U , and let f [L− (U )] = L− (U) f (l) be the ﬂow that crosses the cut in the backward direction.

Using a network structure involving four banks, they model financial contagion as an equilibrium phenomenon and demonstrate that the spread of contagion crucially depends on the nature of the interbank network. They show that the possibility of contagion depends on the number of direct connections between banks and moreover robustness to contagion reveals to be increasing in the number of direct connections. More precisely, Allen and Gale consider a market with different banks each of which is characterized by the liquidity demand of its depositors.

De Marco, and C. Donnini (1 − q)C = yR =⇒ y = (1 − q)C . R The value, at time t = 1, of the maximum amount of long asset that can be liquidated without causing a run on the bank i can be therefore interpreted as a contagion threshold: (1 − q)C b(q) = r y − . (10) R More precisely, suppose that Fi is the subset of failed banks in N \ {i} then the bank i is expected to fail if (11) ∑ λih > b(q). 2 The Contagion Network Given the network of deposits with adjacency matrix (ai j )i, j and building upon the sufficient contagion condition (11) which guarantees the contagion of a bank i given the default of the others, we can construct networks of financial contagion with adjacency matrix ( fi j )i, j where fi j = 1 means that bank i is expected to fail given that bank j has failed and fi j = 0 otherwise.