Multicomponent periodic nanoparticle superlattices

In this article, we review the state-of-the-art in the preparation and characterization of multicomponent self-assembled superlattices of colloidal nanoparticles with core sizes in the range of 2–20 nm and interparticle spacing less than 2 nm down to intimate contact stemming from sintering. Several aspects of the field are discussed, including: structural organization, the role of particle size distribution, key interparticle forces at play, and methods of investigation of the structures. Contrary to the extensively studied colloidal crystals composed of microscale particles, the nanoparticles possess unique size-dependent properties, such as electronic, optical, or magnetic, which when combined into periodic structures can potentially lead to new collective states stemming from precise positioning of the nanocolloids. As such, we examine a number of emerging applications of this new class of metamaterials. Finally, we speculate on the potential impact of these materials, the new directions, and the challenges for the researchers.     

Le cation méthylènecyclopropyle: Etude théorique. Solvolyse des halogénocyclopropènes et des halogénométhylenecyclopropanes

The solvolysis in acid solution of allylic halides and acetates of methylenecyclopropanes and cyclopropylmethanes does not lead to ring opening when there is an ethoxycarbonyl substituent on the ring methylene. Only the cyclopropenyl derivative is obtained. A study of the electronic structure and the geometry of the possible allylic cation intermediate has been carried out using the MNDO method. In addition, the influence of the substituents on the ring opening of this cation has beeen examined. It appears that the ring opening is disfavoured upon substitution of an alkyl group by alkoxymethyl on the ring methylene group.     

An adaptive enrichment algorithm for advection‐dominated problems

We are interested in developing a numerical framework well suited for advection–diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. To resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular, we show that the method is not very sensitive to the choice of the enrichment and develop an adaptive algorithm to automatically choose the enrichment functions.Copyright © 2012 John Wiley & Sons, Ltd.     

Simulated likelihood inference for stochastic volatility models using continuous particle filtering

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models: it has the attractive feature of inheriting unconditional properties similar to the standard GARCH model but being conditionally heavier tailed. Second, we propose a likelihood-based inference technique for a large class of SV models relying on the recently introduced continuous particle filter. The approach is robust and simple to implement. The technique is applied to daily returns data for S&P 500 and Dow Jones stock price indices for various spans.     

A Note on Convergence of the Equi-Energy Sampler

This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed.     

Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices

We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials.     

Harmonic analysis in infinite dimension

We study the Hermite transform onL ²() where is a Gaussian measure on a Lusin locally convex spaceE. We are then lead to a Hilbert space () of analytic functions onE which is also a natural range for the Laplace transform. LetB be a convenient Hilbert-Schmidt operator on the Cameron-Martin spaceH of . There exists a natural sequence Cap _n of capacities onE associated toB. This implies the Kondratev-Yokoi theorem about positive linear forms on the Hida test-functions space.     

Some stable vector bundles with reducible theta divisor

 Let C be a curve of genus g and L a line bundle of degree 2g on C. Let M_L be the kernel of the evaluation map . We show that when L is general enough, the rank g bundle M_L and its exterior powers are stable, but admit a reducible theta divisor. Received: 16 September 2002 / Revised version: 29 October 2002 Published online: 14 February 2003 Mathematics Subject Classification (2000): 14H60     

Dispersion of tubular modes

I show that a theoretical expression for the dispersion (d²β/dω₂) of tubular modes in dispersive multimode square-law fibers coincides with the wave-optics result.