'I like money, I like many things'. The relationship between drugs and crime from the perspective of young people in contact with criminal justice systems

Based on research undertaken as part of the EU funded EPPIC project, this paper aims to update and elaborate on the relationship between drug use and offending behaviours by exploring variations within a cross-national sample of drug-experienced young people in touch with criminal justice systems. Adopting a trajectory-based approach, interviews were undertaken with 198 young people aged 15–25 in six European countries (Austria, Denmark, Germany, Italy, Poland, and UK). Data were analysed by applying the Bennett and Holloway categorization of the drugs-crime link, with a focus on the concept of social exclusion as developed by Seddon. Three main types of mechanisms (economic, pharmaceutical, and lifestyles) are used to interpret the data, showing how the relationship between drugs and offending can vary according to type of substances and over time. Furthermore, it can be associated with very different degrees of social exclusion and needs. The results suggest that while economic inequalities still play key roles in explaining drug use and offending, both behaviours can originate from a state of relative deprivation, resulting from the contradictions inherent in ‘bulimic societies’ that raise aspirations and desires while providing young people scarce opportunities for self-realisation and social recognition

A Lindley-type equation arising from a carousel problem

Abstract: In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phasetype distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley’s equation for the waiting time in the P H/U/1 queue. Although the latter equation has no simple solution, it appears that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the P H/U/1 queue depends on to the complete inter-arrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution

Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting

International audienceThe Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the authors prove that some associated estimators are unbiased, for each value of the size n of the systems of replicas and of resampling number k. Here we go beyond and prove these estimator's asymptotic normality when h goes to infinity, for any fixed value of k. The main ingredient is the asymptotic analysis of a functional equation on an appropriate characteristic function. Some numerical simulations illustrate the convergence to rely on Gaussian confidence intervals

A L\'evy input fluid queue with input and workload regulation

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the L\'evy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment $i$ of the L\'evy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of L\'evy processes, to workload and queuing models

Universal Order Statistics of Random Walks

We study analytically the order statistics of a time series generated by the successive positions of a symmetric random walk of n steps with step lengths of finite variance \sigma^2. We show that the statistics of the gap d_{k,n}=M_{k,n} -M_{k+1,n} between the k-th and the (k+1)-th maximum of the time series becomes stationary, i.e, independent of n as n\to \infty and exhibits a rich, universal behavior. The mean stationary gap (in units of \sigma) exhibits a universal algebraic decay for large k, /\sigma\sim 1/\sqrt{2\pi k}, independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, Proba.(d_{k,\infty}=\delta)\simeq (\sqrt{k}/\sigma) P(\delta \sqrt{k}/\sigma), in the scaling regime when \delta\sim \simeq \sigma/\sqrt{2\pi k}. The scaling function P(x) is universal and has an unexpected power law tail, P(x) \sim x^{-4} for large x. For \delta \gg the scaling breaks down and the pdf gets cut-off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multi-scaling behavior.Comment: 5 pages, 3 figures. Revised version, typos corrected. Accepted for publication in Physical Review Letter

Queues with Lévy input and hysteretic control

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009

A mathematical model for fibro-proliferative wound healing disorders

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders

Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure

Stakeholder ownership: a theoretical framework for cross national understanding and analyses of stakeholder involvement in issues of substance use, problem use and addiction

This project contributes to understanding of the role of different stakeholder groups in the formulation and implementation of policy in the addictions field in Austria, Denmark, Finland, Italy, Poland and the UK. It comprises a number of case studies which draw on a range of theoretical frameworks to examine stakeholder dynamics at international, national and local levels. Mainly qualitative methods were used: interviews, policy and documentation analyses, webcrawler network analysis, and simple surveys; one case study was based on a survey only. The case studies fall into four main categories: three focus on controversial issues in drug treatment policy and practice – opioid substitution treatment, drug consumption rooms, and heroin assisted treatment; three look at stakeholder activity in alcohol control and public health; one pilot case study considers the potential role of researchers in the development of a scientific network around gambling; and one looks at the role of nurses in implementing brief interventions. In addition, themes explored across case studies included the role of evidence and stakeholder activity, drug users as stakeholders, and the role of external stakeholders on national policy. Professional stakeholders at implementation level and families and drug users as stakeholders are also considered. The case studies revealed that, in many instances, the addictions field is characterised by tensions between groups, by entrenched relationships between some addiction-specific stakeholder groups and powerful political stakeholders, and by the dominance of some forms of evidence over other forms of knowledge. Science and scientists are only influential in policy terms if their scientific findings ‘fit’ with the wider political context. Nevertheless, at least within the European context, there are opportunities for new stakeholder groups to emerge and gain policy salience and there are opportunities for stakeholders to challenge prevailing frames of understanding the addictions and prevailing modes of responding to problems of substance misuse and addiction