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This book studies complex systems with elements represented by
random variables. Its main goal is to study and compare uncertainty
of algorithms of network structure identification with applications
to market network analysis. For this, a mathematical model of
random variable network is introduced, uncertainty of
identification procedure is defined through a risk function, random
variables networks with different measures of similarity
(dependence) are discussed, and general statistical properties of
identification algorithms are studied. The volume also introduces a
new class of identification algorithms based on a new measure of
similarity and prove its robustness in a large class of
distributions, and presents applications to social networks, power
transmission grids, telecommunication networks, stock market
networks, and brain networks through a theoretical analysis that
identifies network structures. Both researchers and graduate
students in computer science, mathematics, and optimization will
find the applications and techniques presented useful.
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