Quenched central limit theorem for the stochastic heat equation in weak disorder

We continue with the study of the mollified stochastic heat equation in $d\geq 3$ given by $d u_{\epsilon,t}=\frac 12\Delta u_{\epsilon,t}+ \beta \epsilon^{(d-2)/2} \,u_{\epsilon,t} \,d B_{\epsilon,t}$ with spatially smoothened cylindrical Wiener process $B$, whose (renormalized) Feynman-Kac solution describes the partition function of the continuous directed polymer. In an earlier work (\cite{MSZ16}), a phase transition was obtained, depending on the value of $\beta>0$ in the limiting object of the smoothened solution $u_\epsilon$ as the smoothing parameter $\epsilon\to 0$ This partition function naturally defines a quenched polymer path measure and we prove that as long as $\beta>0$ stays small enough while $u_\epsilon$ converges to a strictly positive non-degenerate random variable, the distribution of the diffusively rescaled Brownian path converges under the aforementioned polymer path measure to standard Gaussian distribution.Comment: Minor revisio

New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.Comment: 31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physic

Stretched Polymers in Random Environment

We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments.Comment: Dedicated to Erwin Bolthausen on the occasion of his 65th birthda

Developments in perfect simulation of Gibbs measures through a new result for the extinction of Galton-Watson-like processes

This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are like supermartingales when large values are taken. This result has deep consequences on perfect simulation, showing that local modifications on the interactions of a model do not affect simulability. We also pose the question to optimize over a class of sequences of sets that influence the sufficient condition for the perfect simulation of the Gibbs measure. We completely solve this question both for the long range Ising models and for the spin models with finite range interactions.Comment: 28 page

The Continuum Directed Random Polymer

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter beta, and for a given beta and realization of the noise the path evolves in a Markovian way. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all beta > 0 and for almost all realizations of the white noise the path measure has the same Holder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page

Possible Indication of Narrow Baryonic Resonances Produced in the 1720-1790 MeV Mass Region

Signals of two narrow structures at M=1747 MeV and 1772 MeV were observed in the invariant masses M_{pX} and M_{\pi^{+}X} of the pp->ppX and pp->p\pi^{+}X reactions respectively. Many tests were made to see if these structures could have been produced by experimental artefacts. Their small widths and the stability of the extracted masses lead us to conclude that these structures are genuine and may correspond to new exotic baryons. Several attempts to identify them, including the possible "missing baryons" approach, are discussed.Comment: 17 pages including 8 figures and 3 tables. ReVte

Pharmacokinetic analysis of diazepam liberation from avizafone in healthy volunteers : Non-compartmental approach and compartmental modeling

Date du colloque&nbsp;: 04/2009</p

dfpk : An R-package for Bayesian dose-finding designs using Pharmacokinetics (PK) for phase I clinical trials

Background and objective Dose-finding, aiming at finding the maximum tolerated dose, and pharmacokinetics studies are the first in human studies in the development process of a new pharmacological treatment. In the literature, to date only few attempts have been made to combine pharmacokinetics and dose-finding and to our knowledge no software implementation is generally available. In previous papers, we proposed several Bayesian adaptive pharmacokinetics-based dose-finding designs in small populations. The objective of this work is to implement these dose-finding methods in an R package, called dfpk. Methods All methods were developed in a sequential Bayesian setting and Bayesian parameter estimation is carried out using the rstan package. All available pharmacokinetics and toxicity data are used to suggest the dose of the next cohort with a constraint regarding the probability of toxicity. Stopping rules are also considered for each method. The ggplot2 package is used to create summary plots of toxicities or concentration curves. Results For all implemented methods, dfpk provides a function (nextDose) to estimate the probability of efficacy and to suggest the dose to give to the next cohort, and a function to run trial simulations to design a trial (nsim). The sim.data function generates at each dose the toxicity value related to a pharmacokinetic measure of exposure, the AUC, with an underlying pharmacokinetic one compartmental model with linear absorption. It is included as an example since similar data-frames can be generated directly by the user and passed to nsim. Conclusion The developed user-friendly R package dfpk, available on the CRAN repository, supports the design of innovative dose-finding studies using PK information

\pi N and \eta p deexcitation channels of the N^* and \Delta baryonic resonances between 1470 and 1680 MeV

Two reactions, pp->ppX and pp->p\pi^+X, are used to study the 1.47<M<1.68 GeV baryonic mass range. Three different final states are considered in the invariant masses: N^* or \Delta^+, p\pi^0, and p\eta. The last two channels are defined by software cuts applied to the missing mass of the first reaction. Several narrow structures are extracted with widths \sigma(\Gamma) varying between 3 and 9 MeV. Some structures are observed in one channel but not in others. Such nonobservation may be due either to the spectrometer momenta limits or to the physics (e.g. no such disintegration channel is allowed from the narrow state considered). We tentatively conclude that the broad Particle Data Group (PDG) baryonic resonances N(1520)D13, N(1535)S11, Delta(1600)P33, and N(1675)D15 are collective states built from several narrow and weakly excited resonances, each having a (much) smaller width than the one reported by PDG.Comment: 29 pages, plus 50 (.png) figures Will be published in a slightly reduced size in Phys. Rev.