40,951 research outputs found
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
Deformation of Hypersurfaces Preserving the Moebius Metric and a Reduction Theorem
A hypersurface without umbilics in the n+1 dimensional Euclidean space is
known to be determined by the Moebius metric and the Moebius second fundamental
form up to a Moebius transformation when n>2. In this paper we consider Moebius
rigidity for hypersurfaces and deformations of a hypersurface preserving the
Moebius metric in the high dimensional case n>3. When the highest multiplicity
of principal curvatures is less than n-2, the hypersurface is Moebius rigid.
Deformable hypersurfaces and the possible deformations are also classified
completely. In addition, we establish a Reduction Theorem characterizing the
classical construction of cylinders, cones, and rotational hypersurfaces, which
helps to find all the non-trivial deformable examples in our classification
with wider application in the future.Comment: 51 pages. A mistake in the proof to Theorem 9.2 has been fixed.
Accepted by Adv. in Mat
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