On support points of univalent functions and a disproof of a conjecture of Bombieri

We consider the linear functional for on the set of normalized univalent functions in the unit disk and use the result to disprove a conjecture of Bombieri.

     

Remarks on Estimation Problem for Stationary Processes in Continuous Time

The problem of estimating of the law (in the space of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure

Boundary Bias Correction for Nonparametric Deconvolution

In this paper we consider the deconvolution problem in nonparametric density estimation. That is, one wishes to estimate the unknown density of a random variable X, say f _X , based on the observed variables Y's, where Y = X + with being the error. Previous results on this problem have considered the estimation of f _X at interior points. Here we study the deconvolution problem for boundary points. A kernel-type estimator is proposed, and its mean squared error properties, including the rates of convergence, are investigated for supersmooth and ordinary smooth error distributions. Results of a simulation study are also presented.     

Simultaneous analysis of multiple PCR amplicons enhances capillary SSCP discrimination of MHC alleles

Major histocompatibility complex (MHC) genotyping still remains one of the most challenging issues for evolutionary ecologists. To date, none of the proposed methods have proven to be perfect, and all provide both important pros and cons. Although denaturing capillary electrophoresis has become a popular alternative, allele identification commonly relies upon conformational polymorphisms of two single‐stranded DNA molecules at the most. Using the MHC class II (β chain, exon 2) of the black kite (Aves: Accipitridae) as our model system, we show that the simultaneous analysis of overlapping PCR amplicons from the same target region substantially enhances allele discrimination. To cover this aim, we designed a multiplex PCR capable to generate four differentially sized and labeled amplicons from the same allele. Informative peaks to assist allele calling then fourfold those generated by the analysis of single PCR amplicons. Our approach proved successful to differentiate all the alleles (N=13) isolated from eight unrelated birds at a single optimal run temperature and electrophoretic conditions. In particular, we emphasize that this approach may constitute a straightforward and cost‐effective alternative for the genotyping of single or duplicated MHC genes displaying low to moderate sets of divergent alleles.     

Change of variable formulas for non-anticipative functionals on path space

We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Itô formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations.     

A Robust Algorithm for Blind Total Variation Restoration

Image restoration is a fundamental problem in image processing. Blind image restoration has a great value in its practical application. However, it is not an easy problem to solve due to its complexity and difficulty. In this paper, we combine our robust algorithm for known blur operator with an alternating minimization implicit iterative scheme to deal with blind deconvolution problem, recover the image and identify the point spread function（PSF）. The only assumption needed is satisfy the practical physical sense. Numerical experiments demonstrate that this minimization algorithm is efficient and robust over a wide range of PSF and have almost the same results compared with known PSF algorithm.     

Rayleigh–Ritz variation method and connected‐moments polynomial approach

We show that the connected‐moments polynomial approach proposed recently is equivalent to the well known Rayleigh–Ritz variation method in the Krylov space. We compare the latter with one of the original connected‐moments methods by means of a numerical test on an anharmonic oscillator. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Bipower-type estimation in a noisy diffusion setting

We consider a new class of estimators for volatility functionals in the setting of frequently observed Itō diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Itō semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale.     

A note on the central limit theorem for bipower variation of general functions

In this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006], where the central limit theorem was shown for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.