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 $n$ vertices, each composed of $n/2+O(1)$ 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 $n/2+O(\log n)$ bound of Moon. As a consequence, we obtain an induced-universal graph for $n$-vertex graphs containing only $O(2^{n/2})$ 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 $\Lambda_4$. However, at the minimum of the potential $\Lambda_4$ 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

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