Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

A conformationally constrained fused tricyclic nisin AB-ring system mimic toward an improved pyrophosphate binder of lipid II

The bacteria-specific membrane component lipid II is essential for bacterial cell wall synthesis. A tricyclic nisin mimic was designed and synthesized in which both thioether moieties were mimicked by an alkane-bridge, as well as the introduction of a third conformational constraint consisting of a macrocyclic lactam-bridge between the N-terminus and the B-ring. The newly designed tricyclic AB-ring mimic was found to bind lipid II since it was able to inhibit nisin-induced membrane leakage in a dose-dependent manner. These results imply that the tricyclic AB-ring mimic may form a novel class of lead structures for the development of nisin-based peptide antibiotics.     

Multivariate Normal Approximation on the Wiener Space: New Bounds in the Convex Distance

Journal of Theoretical Probability - We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field and that of a normal vector...     

Cumulants on the Wiener space

We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual “graph/diagram computations” adopted in most of the probabilistic literature.     

Central Limit Theorems for Multiple Skorokhod Integrals

In this paper, we prove a central limit theorem for a sequence of multiple Skorokhod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted Hermite variations of the fractional Brownian motion are discussed.     

Pre-organization induced synthesis of a crossed alkene-bridged nisin Z DE-ring mimic by ring-closing metathesis

An alkene-bridged mimic of the complex DE-bisthioether-ring system of the antibiotic nisin was prepared in one step from the linear precursor.     

Ring-closing alkyne metathesis approach toward the synthesis of alkyne mimics of thioether A-, B-, C-, and DE-ring systems of the lantibiotic nisin Z

[reaction: see text] Ring-closing alkyne metathesis toward the synthesis of the alkyne-brigded A-, B-, C-, and (D)E-ring mimics of the peptide antibiotic nisin Z is described. We have successfully synthesized alkyne-bridged cyclic peptides containing 4-7 amino acid residues in yields ranging from 18 to 82%.     

Entropy and the fourth moment phenomenon

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de Bruijn?s formula of information theory. When applied to sequences of functionals of a general Gaussian field, our results can be combined with the Carbery–Wright inequality in order to yield multidimensional entropic rates of convergence that coincide, up to a logarithmic factor, with those achievable in smooth distances (such as the 1-Wasserstein distance). In particular, our findings settle the open problem of proving a quantitative version of the multidimensional fourth moment theorem for random vectors having chaotic components, with explicit rates of convergence in total variation that are independent of the order of the associated Wiener chaoses. The results proved in the present paper are outside the scope of other existing techniques, such as for instance the multidimensional Stein?s method for normal approximations.     

Step-wise and pre-organization induced synthesis of a crossed alkene-bridged nisin Z DE-ring mimic by ring-closing metathesis

This paper describes two approaches for the synthesis of a crossed alkene-bridged mimic of the thioether ring system of the nisin Z DE-fragment. The first approach comprised the stepwise total synthesis featuring a cross metathesis and a macrolactamization on a solid support followed by a ring-closing metathesis in solution. Via this route the title compound was obtained in an overall yield of 7% (85% on average for 16 reaction steps). In the second approach, the linear precursor peptide was subjected to ring-closing metathesis and the bicyclic peptide with the correct side chain connectivity pattern was obtained in yields up to 95%. The preferred formation of the bicyclic crossed alkene-bridged mimic of the DE-ring suggests a favorable pre-organization of the linear precursor peptide.