Optimally ending an epidemic

A stochastic and controlled version of the classic three-dimensional Kermack–McKendrick model for the spread of epidemics is considered. The aim is to end the epidemic as soon as possible, taking the quadratic control costs into account. An exact and explicit solution is found in a particular case by making use of the method of similarity solutions to solve the partial differential equation satisfied by the value function, subject to the appropriate conditions.     

The enhanced Sanov theorem and propagation of chaos

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the ($k$-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean–Vlasov type limit, as shown in two corollaries.     

Static portfolio choice under Cumulative Prospect Theory

We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory (CPT). The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the risk-free asset. When it exists, the optimal holding is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. It conceptually resembles Merton’s optimal holding for a CRRA expected-utility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skew-normal distribution. In particular, we show how a CPT investor is highly sensitive to the skewness of the excess return on the risky asset. In the model we adopt, with a piecewise-power value function with different shape parameters, loss aversion might be violated for reasons that are now well-understood in the literature. Nevertheless, we argue that this violation is acceptable.     

Expedited analysis of DFT outputs: Introducing moanalyzer

MOAnalyzer, a Matlab‐based program, has been developed to facilitate the analysis of density functional theory output files from ORCA. The program allows the user to define fragments within a molecule and then provides information on the contribution of each fragment to the molecular orbitals based on the Loewdin population analysis. Correlations to spectroscopy (X‐ray absorption and X‐ray emission) are also obtained, and the resulting information can be visualized in tables or MO diagrams. © 2012 Wiley Periodicals, Inc.     

Arborescent polymers and other dendrigraft polymers: A journey into structural diversity

Arborescent polymers are characterized by a dendritic, multilevel branched architecture derived from successive grafting reactions. In spite of their much larger size, these materials display properties analogous to dendrimers and hyperbranched polymers, the two other dendritic polymer families. The distinguishing features of arborescent polymers are their assembly from polymeric building blocks of uniform size and their very high molecular weights attained in few synthetic steps. This article offers an overview of the historical aspects of the development of dendrigraft polymers, starting from our initial efforts on the synthesis of arborescent polystyrenes. Major subsequent developments in the synthetic techniques from our and other research groups allowing the synthesis of dendrigraft copolymers, tailoring of the structural characteristics of the molecules, and further simplifications to their synthesis are also reviewed, with emphasis over the broad range of architectures attainable in these systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3803–3810, 2007     

Manganese-quinizarin-pyrazinecarboxylic acid mixed-ligand complex in aprotic media. Formation of a manganese(III)- semiquinone binuclear species

The monoanion of pyrazincarboxylic acid (PcA^–), the dianion of quinizarine (Qz⁼) and manganese(II) yield a soluble deep-blue complex in dimethylsulphoxide whose Mn^II:Qz⁼:PcA^– stoichiometry has been established as 1:1:1. This mixed-ligand complex is oxidized in two steps, each involving one equivalent of charge per complex present, as indicated by controlled-potential electrolyses done at +0.30V versus s.c.e. and +0.50 V versus s.c.e.. The association between the metal ion and the ligands prevail and the oxidations finally produce a dark-red complex which possesses the same stoichiometry as the original deep-blue species. In the latter the metal ion is present in oxidation state +3 with the quinizarine dianion as the corresponding semiquinone of the oxidized quinizarine. The monoanion of pyrazincarboxylic acid remains unchanged. Controlled-potential electrolysis at –0.20 V versus s.c.e. of a solution of the mixed-ligand complex indicates that it is binuclear, generating a Mn^II-Mn^IIImixed-valence species. The latter is, in turn, reduced at –1.60 V versus s.c.e. producing probably a mononuclear of manganese(II) species. If manganese(II) is combined with the semiquinone of quinizarine the metal ion exhibits themagnetic characteristic of manganese(III) and thesemiquinone is reduced to the quinizarine dianion, indicating that the mixed-ligand formed exhibits intramolecular charge-transfer. This is a good example of a binuclear species accumulating four oxidation equivalents after oxidation of both metal centers and the quinizarine ligands.