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We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with max-stable distribution. The fitness determines the node attractiveness w.r.t. incoming edges as well as the spatial range for outgoing edges. For max-stable fitness distributions, we thus obtain complex spatial network, which we coin extremal linkage network.
The Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. There are $n$ sites (or loci), a finite number of letters (or alleles) at every site, and w
The path W[0,t] of a Brownian motion on a d-dimensional torus T^d run for time t is a random compact subset of T^d. We study the geometric properties of the complement T^d W[0,t] for t large and d >= 3. In particular, we show that the largest region
We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of two generalized Wigner ensembles, provided that the first four moments
We introduce an algebra of data linkages. Data linkages are intended for modelling the states of computations in which dynamic data structures are involved. We present a simple model of computation in which states of computations are modelled as data
A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introdu