Dual random fragmentation and coagulation and an application to the genealogy of Yule processes

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.Comment: 14 page

Goethite on Mars - A laboratory study of physically and chemically bound water in ferric oxides

Thermogravimetric study of physically and chemically bound water in ferric oxides of limonite with application to goethite on Mar

Establishing bundleflowers in bermuda and switchgrass

Last updated: 10/22/201

Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese Restaurant Process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.Comment: 10 Figures, 2 Table

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Perceptions of the Use of Alcohol and Drugs after Sudden Bereavement by Unnatural Causes: Analysis of Online Qualitative Data

Bereavement is associated with an increased risk of psychiatric morbidity and all-cause mortality, particularly in younger people and after unnatural deaths. Substance misuse is implicated but little research has investigated patterns of drug or alcohol use after bereavement. We used a national online survey to collect qualitative data describing whether and how substance use changes after sudden bereavement. We conducted thematic analysis of free-text responses to a question probing use of alcohol and drugs after the sudden unnatural (non-suicide) death of a family member or a close friend. We analysed data from 243 adults in British Higher Education Institutions aged 18-40, identifying two main themes describing post-bereavement alcohol or drug use: (1) sense of control over use of drugs or alcohol (loss of control versus self-discipline), (2) harnessing the specific effects of drugs or alcohol. Across themes we identified age patterning in relation to substance misuse as a form of rebellion among those bereaved in childhood, and gender patterning in relation to men using alcohol to help express their emotions. The limitations of our sampling mean that these findings may not be generalizable from highly-educated settings to young people in the general population. Our findings describe how some young bereaved adults use drugs and alcohol to help them cope with traumatic loss, and suggest how clinicians might respond to any difficulties controlling substance use

Use of Alcohol and Unprescribed Drugs after Suicide Bereavement: Qualitative Study

Studies describing the impact of suicide bereavement report an excess risk of suicide, suicide attempt, psychiatric illness, and drug and alcohol use disorders compared with the general population. However, the nature of patterns of drug and alcohol use after suicide bereavement is unclear. We used an online survey to collect qualitative data to understand whether and how drug and alcohol use changes after suicide bereavement. We conducted thematic analysis of free-text responses to a question capturing their use of alcohol and drugs after the suicide of a family member or a close friend. Analysing data from 346 adults in Britain aged 18–40, we identified three main themes describing the relationship of suicide bereavement to alcohol or drug use: (1) control over drug or alcohol use, (2) the perceived purpose of using drugs or alcohol, and (3) the attribution of drug or alcohol misuse to external factors. Overlying these themes were dimensions of control and of awareness of potential harms. This study highlights that increased use of drugs and alcohol after suicide bereavement may form part of a bereaved person’s coping strategies, and that sensitive approaches are needed when judging whether and when to intervene

Bessel bridges decomposition with varying dimension. Applications to finance

We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger context where a time-varying drift term can be added. Then in the non-drifted case we extend many results already proven in the case of classical Bessel processes to our context. Our deepest result is a decomposition of the Bridge process associated to this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. On a more practical point of view, we give a methodology to compute the Laplace transform of additive functionals of our process and the associated bridge. This permits in particular to get directly access to the joint distribution of the value at t of the process and its integral. We finally give some financial applications to illustrate the panel of applications of our results

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page