268,891 research outputs found
Optimizing spread dynamics on graphs by message passing
Cascade processes are responsible for many important phenomena in natural and
social sciences. Simple models of irreversible dynamics on graphs, in which
nodes activate depending on the state of their neighbors, have been
successfully applied to describe cascades in a large variety of contexts. Over
the last decades, many efforts have been devoted to understand the typical
behaviour of the cascades arising from initial conditions extracted at random
from some given ensemble. However, the problem of optimizing the trajectory of
the system, i.e. of identifying appropriate initial conditions to maximize (or
minimize) the final number of active nodes, is still considered to be
practically intractable, with the only exception of models that satisfy a sort
of diminishing returns property called submodularity. Submodular models can be
approximately solved by means of greedy strategies, but by definition they lack
cooperative characteristics which are fundamental in many real systems. Here we
introduce an efficient algorithm based on statistical physics for the
optimization of trajectories in cascade processes on graphs. We show that for a
wide class of irreversible dynamics, even in the absence of submodularity, the
spread optimization problem can be solved efficiently on large networks.
Analytic and algorithmic results on random graphs are complemented by the
solution of the spread maximization problem on a real-world network (the
Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem
Contamination source inference in water distribution networks
We study the inference of the origin and the pattern of contamination in
water distribution networks. We assume a simplified model for the dyanmics of
the contamination spread inside a water distribution network, and assume that
at some random location a sensor detects the presence of contaminants. We
transform the source location problem into an optimization problem by
considering discrete times and a binary contaminated/not contaminated state for
the nodes of the network. The resulting problem is solved by Mixed Integer
Linear Programming. We test our results on random networks as well as in the
Modena city network
Identifying spatial invasion of pandemics on metapopulation networks via anatomizing arrival history
Spatial spread of infectious diseases among populations via the mobility of
humans is highly stochastic and heterogeneous. Accurate forecast/mining of the
spread process is often hard to be achieved by using statistical or mechanical
models. Here we propose a new reverse problem, which aims to identify the
stochastically spatial spread process itself from observable information
regarding the arrival history of infectious cases in each subpopulation. We
solved the problem by developing an efficient optimization algorithm based on
dynamical programming, which comprises three procedures: i, anatomizing the
whole spread process among all subpopulations into disjoint componential
patches; ii, inferring the most probable invasion pathways underlying each
patch via maximum likelihood estimation; iii, recovering the whole process by
assembling the invasion pathways in each patch iteratively, without burdens in
parameter calibrations and computer simulations. Based on the entropy theory,
we introduced an identifiability measure to assess the difficulty level that an
invasion pathway can be identified. Results on both artificial and empirical
metapopulation networks show the robust performance in identifying actual
invasion pathways driving pandemic spread.Comment: 14pages, 8 figures; Accepted by IEEE Transactions on Cybernetic
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