Selection principle for the Fleming-Viot process with drift −1-1

We consider the Fleming-Viot particle system consisting of $N$ identical particles evolving in $\mathbb{R}_{>0}$ as Brownian motions with constant drift $-1$. Whenever a particle hits $0$, it jumps onto another particle in the interior. It is known that this particle system has a hydrodynamic limit as $N\rightarrow\infty$ given by Brownian motion with drift $-1$ conditioned not to hit $0$. This killed Brownian motion has an infinite family of quasi-stationary distributions (QSDs), with a Yaglom limit given by the unique QSD minimising the survival probability. On the other hand, for fixed $N<\infty$, this particle system converges to a unique stationary distribution as time $t\rightarrow\infty$. We prove the following selection principle: the empirical measure of the $N$-particle stationary distribution converges to the aforedescribed Yaglom limit as $N\rightarrow\infty$. The selection problem for this particular Fleming-Viot process is closely connected to the microscopic selection problem in front propagation, in particular for the $N$-branching Brownian motion. The proof requires neither fine estimates on the particle system nor the use of Lyapunov functions.Comment: 25 page

On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching

We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows

Quasi-stationary behavior of the stochastic FKPP equation on the circle

We consider the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation on the circle $\mathbb{S}$, \begin{equation} \partial_t u(t,x) = \frac{\alpha}{2}\Delta u +\beta\,u(1-u) + \sqrt{\gamma\,u(1-u)}\,\dot{\mathbb{W}}, \qquad (t,x)\in(0,\infty)\times \mathbb{S}, \end{equation} where $\dot{\mathbb{W}}$ is space-time white noise. While any solution will eventually be absorbed at one of two states, the constant 1 and the constant 0 on the circle, very little is known about the absorption time (also called fixation time in population genetics) or about the long-time behavior before absorption. We establish the existence and uniqueness of the quasi-stationary distribution (QSD) for the solution of the stochastic FKPP. We also show that the solution conditioned on not being absorbed at time $t$ converges to this unique QSD as $t\to\infty$, for any initial distribution. Furthermore, we characterize the leading-order asymptotics for the tail distribution of the absorption time and obtain some explicit calculations in the neutral case. Our proof relies on the observation that the absorbed (or killed) stochastic FKPP is dual to a system of $2$-type branching-coalescing Brownian motions killed when one type dies off, and on leveraging the relationship between these two killed processes.Comment: 41 pages, 3 figure

Clinical psychologists’ perceptions of barriers and facilitators to engaging service users in index offence assessment and formulation within a medium secure unit

Index offence assessment and formulation (IOAF) helps service users (SU) in secure units to make sense of their index offence, provides detailed understanding of risk and contributes to treatment planning and discharge decisions. Clinical psychologists’ perceptions of barriers and facilitators to engaging SUs in IOAF within the men’s and women’s services of one medium secure unit were explored through focus groups. Thematic analysis identified two relevant domains: person-specific factors and the organisational context. Person-specific barriers included challenges in working with fragmented narratives, conflicting motivations to engage, SU defences and distorted perceptions of clinical psychologists’ roles. Giving clarity and choice to SUs facilitated engagement with the work. Regarding the organisational context, clinical psychologists within both services identified the importance of having adequate resources and care-team support to complete this work. Findings highlight the importance of developing an evidence-based framework for IOAF to be embedded within clear ‘risk’ care pathways through secure services.</p

Relevance to Psychology of Beliefs About Socialism: Some New Research Questions

This article aims to stimulate discussion about the potential relevance of the concept of socialism for what we study and the questions we ask. The economic systems of capitalism and socialism are seldom considered subjects of interest in psychology. At this particular time, however, especially in the United States, the relevance of these systems for our theories and research on human behavior, health, and human welfare seem particularly relevant and potentially significant. I argue that discussions of socialism should be helpful in expanding the context of our concerns in psychology and the identification of important new variables. The growing crisis of inequality in the United States is the major impetus for this argument

Scaling Limit of the Fleming-Viot Multi-Colour Process

The Fleming-Viot process associated to a killed normally reflected diffusion $X_t$ is known to provide a particle representation for the quasi-stationary distribution of $X_t$. In this paper we establish three results for this particle system. We firstly establish that it also provides a particle representation for the principal right eigenfunction of the submarkovian infinitesimal generator of $X_t$. Secondly we establish that the Fleming-Viot process provides a representation for the $Q$-process. Thirdly we prove a conjecture due to Bieniek and Burdzy on the asymptotic distribution of the spine of the Fleming-Viot process and its side branches. We obtain these as corollaries of the following result. The Fleming-Viot multi-colour process is obtained by attaching genetic information to the particles in the Fleming-Viot process. We establish that under a suitable rescaling it converges to the Fleming-Viot superprocess from population genetics, with spatial inhomogeneity having the effect of speeding up the rate of genetic drift according to a simple formula.Comment: 58 pages, 5 figure

Assessing the Physiological Cost of Active Videogames (Xbox Kinect) Versus Sedentary Videogames in Young Healthy Males

Objectives: The aims of this study were twofold: (1) to compare the physiological costs of active videogames (AVGs) and sedentary videogames (SVGs) and (2) to compare the exercise intensities attained during AVGs with the exercise intensity criteria for moderate and vigorous physical activity, as stated in current physical activity recommendations for improving public health. Materials and Methods: Nineteen young males participated in the study (age, 23 ± 3 years; height, 178 ± 6 cm; weight, 78 ± 15 kg). Participants completed a maximum oxygen uptake (VO2max) test and a gaming session, including AVGs (“Reflex Ridge,” “River Rush,” and “Boxing” for the Microsoft [Redmond, WA] Kinect™) and SVGs (“FIFA 14” [Electronic Arts, Burnaby, BC, Canada] and “Call of Duty” [Activision, Santa Monica, CA]). Heart rate (HR) and oxygen uptake (VO2max) were recorded continuously during all videogames. Rating of perceived exertion (RPE) was taken every 3 minutes during AVGs and SVGs. Energy expenditure (EE), expressed as metabolic equivalents (METs), was calculated. One MET was defined as the volume of oxygen consumed at rest in a seated position and is equal to 3.5 mL of O2/kg of body mass/minute. The exercise intensity for each game was expressed as a percentage of VO2max and percentage of age-predicted maximum HR (HRmax). Results: Exercise intensity (percentage HRmax, percentage VO2max, and RPE) and EE (METs) were significantly higher during active gaming compared with sedentary gameplay (P < 0.01). AVGs elicited moderate levels of exercise intensity (64–72 percent HRmax) in line with current recommended physical activity guidelines. Conclusions: Our results indicate AVGs provoke physiological responses equivalent to a moderate-intensity physical activity