Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Photoelectrocatalysis: Principles, nanoemitter applications and routes to bio-inspired systems

An overview on processes that are relevant in light-induced fuel generation, such as water photoelectrolysis or carbon dioxide reduction, is given. Considered processes encompass the photophysics of light absorption, excitation energy transfer to catalytically active sites and interfacial reactions at the catalyst/solution phase boundary. The two major routes envisaged for realization of photoelectrocatalytic systems, e.g. bio-inspired single photon catalysis and multiple photon inorganic or hybrid tandem cells, are outlined. For development of efficient tandem cell structures that are based on non-oxidic semiconductors, stabilization strategies are presented. Physical surface passivation is described using the recently introduced nanoemitter concept which is also applicable in photovoltaic (solid state or electrochemical) solar cells and first results with p-Si and p-InP thin films are presented. Solar-to-hydrogen efficiencies reach 12.1% for homoepitaxial InP thin films covered with Rh nanoislands. In the pursuit to develop biologically inspired systems, enzyme adsorption onto electrochemically nanostructured silicon surfaces is presented and tapping mode atomic force microscopy images of heterodimeric enzymes are shown. An outlook towards future envisaged systems is given. © 2010 The Royal Society of Chemistry.

High-Q hybrid 3D-2D slab-3D photonic crystal microcavity.

The radiation loss in the escaping light cone with a two-dimensional (2D) photonic crystal slab microcavity can be suppressed by means of cladding the low-Q slab microcavity by three-dimensional woodpile photonic crystals with the complete bandgap when the resonance frequency is located inside the complete bandgap. It is confirmed that the hybrid microcavity based on a low-Q, single-defect photonic crystal slab microcavity shows improvement of the Q factor without affecting the mode volume and modal frequency. Whereas 2D slab microcavities exhibit Q saturation with an increase in the number of layers, for the analyzed hybrid microcavities with a small gap between the slab and woodpiles, the Q factor does not saturate.

Beam-target double-spin asymmetry A{LT} in charged pion production from deep inelastic scattering on a transversely polarized {3}He target at 1.4

We report the first measurement of the double-spin asymmetry A{LT} for charged pion electroproduction in semi-inclusive deep-inelastic electron scattering on a transversely polarized {3}He target. The kinematics focused on the valence quark region, 0.16