Stochastic epidemics and rumours on finite random networks

In this paper, we investigate the stochastic spread of epidemics and rumours on networks. We focus on the general stochastic (SIR) epidemic model and a recently proposed rumour model on networks in Nekovee et al. (2007) [3], and on networks with different random structures, taking into account the structure of the underlying network at the level of the degree–degree correlation function. Using embedded Markov chain techniques and ignoring density correlations between neighbouring nodes, we derive a set of equations for the final size of the epidemic/rumour on a homogeneous network that can be solved numerically, and compare the resulting distribution with the solution of the corresponding mean-field deterministic model. The final size distribution is found to switch from unimodal to bimodal form (indicating the possibility of substantial spread of the epidemic/rumour) at a threshold value that is higher than that for the deterministic model. However, the difference between the two thresholds decreases with the network size, n, following a n^−1/3 behaviour. We then compare results (obtained by Monte Carlo simulation) for the full stochastic model on a homogeneous network, including density correlations at neighbouring nodes, with those for the approximating stochastic model and show that the latter reproduces the exact simulation results with great accuracy. Finally, further Monte Carlo simulations of the full stochastic model are used to explore the effects on the final size distribution of network size and structure (using homogeneous networks, simple random graphs and the Barabasi–Albert scale-free networks).     

Synthesis of new fluorinated allyl ethers for the surface modification of thiol–ene ultraviolet‐curable formulations

Thiol–ene photocurable systems based on a trifunctional thiol [trimethylolpropane tris‐(3‐mercaptopropanoate)] and two different multifunctional allyl ethers (trimethylolpropane triallyl ether and Boltorn U2, an allyl functional dendritic polyester) were examined. To these systems, small amounts (<1 wt %) of fluorinated allyl ethers were added for the modification of their surface properties. Two new fluorinated allyl ethers, 1H,1H‐perfluoro‐1‐heptylallyl ether and 1H,1H‐perfluoro‐1‐decylallyl ether, were synthesized for this purpose by allylation of the corresponding 1H,1H‐perfluoro alcohols. The fluorinated monomers, despite their very low concentrations, caused sharp changes in the surface properties of the films and in the solvent resistance without any changes in the curing conditions and bulk properties. Completely hydrophobic surfaces were obtained (as a result of the selective enrichment of the fluorinated monomers on the film surfaces) that depended on the monomer structure and its concentration. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2583–2590, 2002     

Iron(III) porphyrin catalyzed aziridination of alkenes with bromamine-T as nitrene source

[reaction: see text] Iron(III) porphyrin complexes Fe(Por)Cl are effective catalysts for aziridination of alkenes using bromamine-T as the nitrene source. The catalytic system can operate under mild conditions with alkenes as limiting reagents. The aziridination reaction is general and suitable for a wide variety of alkenes, including aromatic, aliphatic, cyclic, and acyclic olefins, as well as alpha,beta-unsaturated esters. For 1,2-disubstituted olefins, the reactions proceeded with moderate to low stereospecificity.     

Asymmetric barrier model for heavy ion fusion and its relation to channel coupling

A new asymmetric parabolic effective fusion barrier model for heavy ion fusion is developed.     

Dual standard addition for quantitative NMR analysis

A technique is described for quantitative NMR measurement which involves the use of a pair of internal standards. This procedure overcomes several of the problems encountered with only one standard material. A computer programme is described for statistical treatment of the results.     

Microdetermination of molecular weight in high molecular weight polymers soluble in benzene at 37° C

Summary A simplified method has been developed to determine molecular weight by using a constant volume of solvent and using polystyrene as a standard, molecular weights up to 51000 can be obtained with less than 2% error from a graph. If calculated by computer, 5% error is the maximum.

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Zusammenfassung Ein vereinfachtes Verfahren unter Verwendung eines konstanten Lösungsmittelvolumens sowie von Polystrol als Standardsubstanz ermöglicht die Bestimmung von Molekulargewichten bis zu 51 000 mit einer Fehlerbreite von 2% an Hand einer Eichkurve. Bei Berechnung mit einem Computer ist die maximale Fehlerbreite 5%.

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This work was supported by the U. S. Air Force under Contract #F33615-73-C-5013.