11,721 research outputs found
Phase transitions in Pareto optimal complex networks
The organization of interactions in complex systems can be described by
networks connecting different units. These graphs are useful representations of
the local and global complexity of the underlying systems. The origin of their
topological structure can be diverse, resulting from different mechanisms
including multiplicative processes and optimization. In spatial networks or in
graphs where cost constraints are at work, as it occurs in a plethora of
situations from power grids to the wiring of neurons in the brain, optimization
plays an important part in shaping their organization. In this paper we study
network designs resulting from a Pareto optimization process, where different
simultaneous constraints are the targets of selection. We analyze three
variations on a problem finding phase transitions of different kinds. Distinct
phases are associated to different arrangements of the connections; but the
need of drastic topological changes does not determine the presence, nor the
nature of the phase transitions encountered. Instead, the functions under
optimization do play a determinant role. This reinforces the view that phase
transitions do not arise from intrinsic properties of a system alone, but from
the interplay of that system with its external constraints.Comment: 14 pages, 7 figure
Robustness of the European power grids under intentional attack
The power grid defines one of the most important technological networks of
our times and sustains our complex society. It has evolved for more than a
century into an extremely huge and seemingly robust and well understood system.
But it becomes extremely fragile as well, when unexpected, usually minimal,
failures turn into unknown dynamical behaviours leading, for example, to sudden
and massive blackouts. Here we explore the fragility of the European power grid
under the effect of selective node removal. A mean field analysis of fragility
against attacks is presented together with the observed patterns. Deviations
from the theoretical conditions for network percolation (and fragmentation)
under attacks are analysed and correlated with non topological reliability
measures.Comment: 7 pages, 4 figure
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