30,325 research outputs found
Impact of edge-removal on the centrality betweenness of the best spreaders
The control of epidemic spreading is essential to avoid potential fatal
consequences and also, to lessen unforeseen socio-economic impact. The need for
effective control is exemplified during the severe acute respiratory syndrome
(SARS) in 2003, which has inflicted near to a thousand deaths as well as
bankruptcies of airlines and related businesses. In this article, we examine
the efficacy of control strategies on the propagation of infectious diseases
based on removing connections within real world airline network with the
associated economic and social costs taken into account through defining
appropriate quantitative measures. We uncover the surprising results that
removing less busy connections can be far more effective in hindering the
spread of the disease than removing the more popular connections. Since
disconnecting the less popular routes tend to incur less socio-economic cost,
our finding suggests the possibility of trading minimal reduction in
connectivity of an important hub with efficiencies in epidemic control. In
particular, we demonstrate the performance of various local epidemic control
strategies, and show how our approach can predict their cost effectiveness
through the spreading control characteristics.Comment: 11 pages, 4 figure
Weak Parity
We study the query complexity of Weak Parity: the problem of computing the
parity of an n-bit input string, where one only has to succeed on a 1/2+eps
fraction of input strings, but must do so with high probability on those inputs
where one does succeed. It is well-known that n randomized queries and n/2
quantum queries are needed to compute parity on all inputs. But surprisingly,
we give a randomized algorithm for Weak Parity that makes only
O(n/log^0.246(1/eps)) queries, as well as a quantum algorithm that makes only
O(n/sqrt(log(1/eps))) queries. We also prove a lower bound of
Omega(n/log(1/eps)) in both cases; and using extremal combinatorics, prove
lower bounds of Omega(log n) in the randomized case and Omega(sqrt(log n)) in
the quantum case for any eps>0. We show that improving our lower bounds is
intimately related to two longstanding open problems about Boolean functions:
the Sensitivity Conjecture, and the relationships between query complexity and
polynomial degree.Comment: 18 page
Adjacency labeling schemes and induced-universal graphs
We describe a way of assigning labels to the vertices of any undirected graph
on up to vertices, each composed of bits, such that given the
labels of two vertices, and no other information regarding the graph, it is
possible to decide whether or not the vertices are adjacent in the graph. This
is optimal, up to an additive constant, and constitutes the first improvement
in almost 50 years of an bound of Moon. As a consequence, we
obtain an induced-universal graph for -vertex graphs containing only
vertices, which is optimal up to a multiplicative constant,
solving an open problem of Vizing from 1968. We obtain similar tight results
for directed graphs, tournaments and bipartite graphs
Strain-stress study of AlxGa1-xN/AlN heterostructures on c-plane sapphire and related optical properties
This work presents a systematic study of stress and strain of AlxGa1-xN/AlN
with composition ranging from GaN to AlN, grown on a c-plane sapphire by
metal-organic chemical vapor deposition, using synchrotron radiation
high-resolution X-ray diffraction and reciprocal space mapping. The c-plane of
the AlxGa1-xN epitaxial layers exhibits compressive strain, while the a-plane
exhibits tensile strain. The biaxial stress and strain are found to increase
with increasing Al composition, although the lattice mismatch between the
AlxGa1-xN and the buffer layer AlN gets smaller. A reduction in the lateral
coherence lengths and an increase in the edge and screw dislocations are seen
as the AlxGa1-xN composition is varied from GaN to AlN, exhibiting a clear
dependence of the crystal properties of AlxGa1-xN on the Al content. The
bandgap of the epitaxial layers is slightly lower than predicted value due to a
larger tensile strain effect on the a-axis compared to the compressive strain
on the c-axis. Raman characteristics of the AlxGa1-xN samples exhibit a shift
in the phonon peaks with the Al composition. The effect of strain is also
discussed on the optical phonon energies of the epitaxial layers. The
techniques discussed here can be used to study other similar materials.Comment: 14 pages, 5 figures, 2 table
Radion Potential and Brane Dynamics
We examine the cosmology of the Randall-Sundrum model in a dynamic setting
where scalar fields are present in the bulk as well as the branes. This
generates a mechanism similar to that of Goldberger-Wise for radion
stabilization and the recovery of late-cosmology features in the branes. Due to
the induced radion dynamics, the inflating branes roll towards the minimum of
the radion potential, thereby exiting inflation and reheating the Universe. In
the slow roll part of the potential, the 'TeV' branes have maximum inflation
rate and energy as their coupling to the radion and bulk modes have minimum
suppresion. Hence, when rolling down the steep end of the potential towards the
stable point, the radion field (which appears as the inflaton of the effective
4D theory in the branes) decays very fast, reheats the Universe .This process
results decayin a decrease of brane's canonical vacuum energy .
However, at the minimum of the potential is small but not
neccessarily zero and the fine-tuning issue remains .Density perturbation
constraints introduce an upper bound when the radion stabilizies. Due to the
large radion mass and strong suppression to the bulk modes, moduli problems and
bulk reheating do not occur. The reheat temperature and a sufficient number of
e-folding constraints for the brane-universe are also satisfied. The model
therefore recovers the radiation dominated FRW universe.Comment: 16 pages, 3 figures,extraneous sentences removed, 2 footnotes added,
some typos correcte
Molecular Clock on a Neutral Network
The number of fixed mutations accumulated in an evolving population often
displays a variance that is significantly larger than the mean (the
overdispersed molecular clock). By examining a generic evolutionary process on
a neutral network of high-fitness genotypes, we establish a formalism for
computing all cumulants of the full probability distribution of accumulated
mutations in terms of graph properties of the neutral network, and use the
formalism to prove overdispersion of the molecular clock. We further show that
significant overdispersion arises naturally in evolution when the neutral
network is highly sparse, exhibits large global fluctuations in neutrality, and
small local fluctuations in neutrality. The results are also relevant for
elucidating the topological structure of a neutral network from empirical
measurements of the substitution process.Comment: 10 page
Mutations of the Drosophila zinc finger-encoding gene vielfältig impair mitotic cell divisions and cause improper chromosome segretation.
High energy Scattering in 2+1 QCD: A Dipole Picture
A dipole picture of high energy scattering is developed in the 2+1
dimensional QCD, following Mueller. A generalized integral equation for the
dipole density with a given separation and center of mass position is derived,
and meson-meson non-forward scattering amplitude is therefore calculated. We
also calculate the amplitude due to two pomeron exchange, and the triple
pomeron coupling. We compare the result obtained by this method to our previous
result based on an effective action approach, and find the two results agree at
the one pomeron exchange level.Comment: minor typos corrected. Postscript files are available through
anonymous ftp quark.het.brown.edu, in the directory /pub/preprints, file name
is 9407299. Hard copy is available upon reques
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