Percolation and epidemic thresholds in clustered networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks, thus extending this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.     

Bioactive eremophilanolides from Senecio poepigii

A new bioactive eremophilanolide, 1alpha-tigloyloxy-8betaH,10betaH-eremophil-7(11)-en-8alpha,12-olide, was isolated from Senecio poepigii and its structure was elucidated by spectral analysis. 1alpha-Angeloyloxy-8beta-methoxy-10betaH-eremophil-7(11)-en-8alpha,12-olide was also isolated. Antifungal and insect antifeedant properties were evaluated.     

Tetrapyrrole singlet excited state quenching by carotenoids in an artificial photosynthetic antenna

Two artificial photosynthetic antenna models consisting of a Si phthalocyanine (Pc) bearing two axially attached carotenoid moieties having either 9 or 10 conjugated double bonds are used to illustrate some of the function of carotenoids in photosynthetic membranes. Both models studied in toluene, methyltetrahydrofuran, and benzonitrile exhibited charge separated states of the type C*+-Pc*- confirming that the quenching of the Pc S1 state is due to photoinduced electron transfer. In hexane, the Pc S1 state of the 10 double bond carotenoid-Pc model was slightly quenched but the C*+-Pc*- transient was not spectroscopically detected. A semiclassical analysis of the data in hexane at temperatures ranging from 180 to 320 K was used to demonstrate that photoinduced electron transfer could occur. The model bearing the 10 double bond carotenoids exhibits biexponential fluorescence decay in toluene and in hexane, which is interpreted in terms of an equilibrium mixture of two isomers comprising s-cis and s-trans conformers of the carotenoid. The shorter fluorescence lifetime is associated with an s-cis carotenoid conformer where the close approach between the donor and acceptor moieties provides through-space electronic coupling in addition to the through-bond component.     

Asymptotic quadratic convergence of the parallel block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices

The proof of the asymptotic quadratic convergence is provided for the parallel two-sided block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices. The discussion covers the case of well-separated eigenvalues as well as clusters of eigenvalues. Having p processors, each parallel iteration step consists of zeroing 2p off-diagonal blocks chosen by dynamic ordering with the aim to maximize the decrease of the off-diagonal Frobenius norm. Numerical experiments illustrate and confirm the developed theory.     

Groups satisfying weak chain conditions on non-modular subgroups

In this paper (generalized) soluble groups for which the set of all non-modular subgroups satisfies some weak chain condition are described. Groups satisfying weak chain conditions on non-permutable subgroups are also considered.     

Large-scale supramolecular structure in solutions of low molar mass compounds and mixtures of liquids: II. Kinetics of the formation and long-time stability

Kinetics of the formation of large-scale supramolecular structure and its long-time stability were investigated in detail in solutions of electrolytes, nonelectrolytes, and mixtures of liquids. This structure comprises submicron-sized domains (large clusters) with higher solute concentration than in the rest of solution. In the case of mixtures of liquids, a complete real-time monitoring of the structure formation was possible in all cases. In the case of solutions of solid samples, the observation was possible in cases when the structure formation was significantly slower than the dissolution process. The time scale on which the supramolecular structure develops varies from minutes to weeks, depending on the concrete system. The long-time stability of the developed structure was investigated in time intervals ranging up to 15 months. In some systems the resulting domain structure appears stable, in others a very slow ceasing of domains is observed over very long time intervals. In all cases, however, slow kinetic effects are present in the systems investigated. Among others, data on some common substances of great chemical and biological importance such as sodium chloride, acetic acid, glucose, and ethanol, are presented.     

Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions

The aim of this paper is to introduce a new ant colony optimization procedure for the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions (CLARPIF), a variant of the Capacitated Arc Routing Problem (CARP) and of the Capacitated Arc Routing Problem with Intermediate Facilities (CARPIF). Computational results show that this algorithm is capable of providing substantial improvements over other known heuristics.     

Strong stabilization of models incorporating the thermoelastic Reissner–Mindlin plate equations with second sound

In this article we are concerned with the strong stabilization of models for the Reissner–Mindlin plate equations with second sound, that is, models that include thermal effects described according to Cattaneo's law of heat conduction instead of Fourier's law in classical thermoelasticity. Two models will be considered which are distinct with respect to the property of compactness or non-compactness of the resolvent of the generator of the underlying semigroup. In accordance with the compactness or non-compactness of the resolvent operator, a different criterion for strong stability is implemented to achieve the strong stabilization of each model. In the compact resolvent case we avail ourselves of a result given by Benchimol [C.D. Benchimol, A note on weak stabilizability of contraction semigroups, SIAM J. Control Optim. 16 (1978), pp. 373–379] and in the non-compact case we resort to a stability criterion Tomilov [Y. Tomilov, A resolvent approach to stability of operator semigroups, J. Operator Theory 46 (2001), pp. 63–98].     

A note on determinants,minors and a boundary map

We give an explicit formula for the first non-trivial boundary map of the Akin–Buchsbaum–Weyman resolution (Schur functors and Schur complexes, Adv. Math 1982;44:207-278). The role of the Laplace expansion formula is emphasized.     

Counting BPS States on the Enriques Calabi-Yau

We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them gives the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus three. This model turns out to be much simpler than the generic B-model and might be exactly solvable.