Exact simulation of the Wright-Fisher diffusion

The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming-Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.Comment: 36 pages, 2 figure, 2 tables. This version corrects an error in the proof of Lemma 6.

Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. We also show that products of discrete net and Dirichlet mixture model priors satisfy our conditions, again under an identifiability assumption. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.Comment: 20 page

Wavelength conversion at 10 Gb/s by four-wave mixing over a 30-nm interval

We show that the use of a long semiconductor optical amplifier increases the error-free conversion interval of a four-wave mixing (FWM)-based wavelength converter. 30-nm wavelength down-conversion and 15-nm up-conversion have been obtained at 10 Gb/s. This result is a significant improvement over the previous best performance of a FWM-based wavelength converter and suggests that the full erbium-doped fiber amplifier bandwidth can be covered with FWM wavelength converters

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

A new super-Backlund transformation for the N=1 supersymmetric sinh-Gordon equation is constructed. Based on this construction we propose a type-II integrable defect for the supersymmetric sinh-Gordon model consistent with this new transformation through the Lagrangian formalism. Explicit expressions for the modified conserved energy, momentum and supercharges are also computed. In addition, we show for the model that the type-II defect can also been regarded as a pair of fused defects of a previously introduced type. The explicit derivation of the associated defect matrices is also presented as a necessary condition for the integrability of the model.Comment: Latex 31 pages. Version accepted for publicatio

Pseudo-Class III malocclusion treatment with Balters' Bionator.

The aim of this article is to show the use of the Balters' Bionator in pseudo-Class III treatment. The importance of differentiating between true Class III and pseudo-Class III is emphasized. The therapeutic results of a Balters' Bionator appliance are presented in three case reports of subjects in the mixed dentition. In this stage of development it is possible to correct an isolated problem. The use of the Bionator III in this kind of malocclusion enabled the correction of a dental malocclusion in a few months and therapeutic stability of a mesially-positioned mandible encouraging favourable skeletal growth

N=1 super sinh-Gordon model with defects revisited

The Lax pair formalism is considered to discuss the integrability of the N=1 supersymmetric sinh-Gordon model with a defect. We derive associated defect matrix for the model and construct the generating functions of the modified conserved quantities. The corresponding defect contributions for the modified energy and momentum of the model are explicitly computed.Comment: Latex 26 page

Searching for variable stars in Galactic Open Clusters

A long-term project, aiming at systematic search for variable stars in Galactic Open Clusters, was started at the Geneva Observatory in 2002. We have been observing regularly a sample of twenty-seven Galactic Open Clusters in the U, B, V Geneva filters. The goal is to identify and to study their variable stars, as well as the connection between the variable stars in a cluster and the cluster properties. We present the status of this work in progress, and show preliminary results for one of these clusters, IC 4651.Comment: To appear in the proceedings of Stellar Pulsation: Challenges for theory and observations Conference, Santa Fe, NM, US