Holderian Weak Invariance Principle for Stationary Mixing Sequences

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in Hölder spaces. Strong mixing and \(\rho \)-mixing conditions are investigated as well as \(\tau \)-dependent sequences. The main tools are deviation inequalities for mixing sequences.     

Percolation,morphogenesis, and burgers dynamics in blood vessels formation

Experiments of in vitro formation of blood vessels show that cells randomly spread on a gel matrix autonomously organize to form a connected vascular network. We propose a simple model which reproduces many features of the biological system. We show that both the model and the real system exhibit a fractal behavior at small scales, due to the process of migration and dynamical aggregation, followed at large scale by a random percolation behavior due to the coalescence of aggregates. The results are in good agreement with the analysis performed on the experimental data.     

A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes

A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.     

Colored operads,series on colored operads,and combinatorial generating systems

We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous grammars, allowing us to work with all these generating systems in a unified way. The theory of bud generating systems uses colored operads. Indeed, an object is generated by a bud generating system if it satisfies a certain equation in a colored operad. To compute the generating series of the languages of bud generating systems, we introduce formal power series on colored operads and several operations on these. Series on colored operads are crucial to express the languages specified by bud generating systems and allow us to enumerate combinatorial objects with respect to some statistics. Some examples of bud generating systems are constructed; in particular to specify some sorts of balanced trees and to obtain recursive formulas enumerating these.     

Construction dʼopérades ensemblistes à partir de monoïdes

We study a functorial construction from the category of monoids to the category of set-operads and we give some combinatorial examples of applications.     

Regioselective N‐Alkylation of Ethyl 4‐Benzyloxy‐1,2,3‐triazolecarboxylate: A Useful Tool for the Synthesis of Carboxylic Acid Bioisosteres

Acidic 4‐hydroxy‐1,2,3‐triazole is a proven bioisostere of acidic functions that has recently been used to replace the acidic moieties of biologically active leads. Straightforward chemical strategies for the synthesis of the three possible N‐alkylated 4‐hydroxy‐1,2,3‐triazole regioisomers have been designed and reported herein, by identifying the optimal conditions under which the alkylation of ethyl 4‐benzyloxy‐1,2,3‐triazolecarboxylate (compound 19 ) can be regiodirected to the triazole N(b) position and thus produce the only isomer that cannot be obtained via the cycloaddition reaction. Furthermore, an innovative platform for parallel synthesis, called Arachno and which has been patented by the authors' group, has been used to speed up the process, and an NMR study has been carried out to better understand the reactivity of compound 19 towards the N(b) position. A library of benzyloxy protected 4‐hydroxy‐1,2,3‐triazoles has been prepared using the two strategies: regiodirection for the N(b) and N(c) isomers and cycloaddition for the N(a) isomers; the processes are described herein. The three N‐alkylated regioisomer series have been characterized spectroscopically (NMR and MS). The subsequent catalytic hydrogenation of the 4‐benzyloxy protective group on the N‐alkylated‐4‐benzyloxy‐5‐ethoxycarbonyl‐1,2,3‐triazoles provided the corresponding substituted 4‐hydroxy‐1,2,3‐triazoles.     

On the asymptotic behavior of the parameter estimators for some diffusion processes: application to neuronal models

We consider a sample of i.i.d. times and we interpret each item as the first-passage time (FPT) of a diffusion process through a constant boundary. The problem is to estimate the parameters characterizing the underlying diffusion process through the experimentally observable FPT’s. Recently in Ditlevsen and Lánsky (Phys Rev E 71, 2005) and Ditlevsen and Lánsky (Phys Rev E 73, 2006) closed form estimators have been proposed for neurobiological applications. Here we study the asymptotic properties (consistency and asymptotic normality) of the class of moment type estimators for parameters of diffusion processes like those in Ditlevsen and Lánsky (Phys Rev E 71, 2005) and Ditlevsen and Lánsky (Phys Rev E 73, 2006). Furthermore, to make our results useful for application instances we establish upper bounds for the rate of convergence of the empirical distribution of each estimator to the normal density. Applications are also considered by means of simulated experiments in a neurobiological context.      

Weak invariance principle in some Besov spaces for stationary martingale differences

We extend the classical Donsker weak invariance principle to some Besov space framework. We consider polygonal line processes built from partial sums of stationary martingale differences and of independent and identically distributed random variables. The results obtained are shown to be optimal.