Noncolliding Squared Bessel Processes

We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function $J_{\nu}$ is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.Comment: v3: LaTeX2e, 26 pages, no figure, corrections made for publication in J. Stat. Phy

Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals

Yor's generalized meander is a temporally inhomogeneous modification of the $2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the non-colliding particle systems of the generalized meanders and prove that they are the Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the elements of matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann-Liouville differintegrals of functions comprising the Bessel functions $J_{\nu}$ used in the fractional calculus, where orders of differintegration are determined by $\nu-\kappa$. As special cases of the two parameters $(\nu, \kappa)$, the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random matrix theory.Comment: LaTeX, 35 pages, v3: The argument given in Section 3.2 was simplified. Minor corrections were mad

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

The Intentional Use of Service Recovery Strategies to Influence Consumer Emotion, Cognition and Behaviour

Service recovery strategies have been identified as a critical factor in the success of. service organizations. This study develops a conceptual frame work to investigate how specific service recovery strategies influence the emotional, cognitive and negative behavioural responses of . consumers., as well as how emotion and cognition influence negative behavior. Understanding the impact of specific service recovery strategies will allow service providers' to more deliberately and intentionally engage in strategies that result in positive organizational outcomes. This study was conducted using a 2 x 2 between-subjects quasi-experimental design. The results suggest that service recovery has a significant impact on emotion, cognition and negative behavior. Similarly, satisfaction, negative emotion and positive emotion all influence negative behavior but distributive justice has no effect

Meta-analysis of 49 549 individuals imputed with the 1000 Genomes Project reveals an exonic damaging variant in ANGPTL4 determining fasting TG levels

Background So far, more than 170 loci have been associated with circulating lipid levels through genomewide association studies (GWAS). These associations are largely driven by common variants, their function is often not known, and many are likely to be markers for the causal variants. In this study we aimed to identify more new rare and low-frequency functional variants associated with circulating lipid levels. Methods We used the 1000 Genomes Project as a reference panel for the imputations of GWAS data from ~60 000 individuals in the discovery stage and ~90 000 samples in the replication stage. Results Our study resu

Effects of gait training with body weight support on a treadmill vs. overground for individuals with stroke

Made available in DSpace on 2018-11-26T17:24:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-04-01Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Objective: To investigate the effects of gait training with body weight support (BWS) on a treadmill versus overground in individuals with chronic stroke. Design: Randomized controlled trial. Setting: University research laboratory. Participants: Individuals (N=28) with chronic stroke (>6mo from the stroke event). Interventions: Participants were randomly assigned to receive gait training with BWS on a treadmill (n=14) or overground (n=14) 3 times a week for 6 weeks. Main Outcome Measures: Gait speed measured using the 10-meter walk test, endurance measured using the 6-minute walk test, functional independence measured using the motor domain of the FIM, lower limb recovery measured using the lower extremity domain of the Fugl-Meyer assessment, step length, step length symmetry ratio, and single-limb support duration. Measurements were obtained at baseline, immediately after the training session, and 6 weeks after the training session. Results: At 1 week after the last training session, both groups improved in all outcome measures except paretic step length and step length symmetry ratio, which were improved only in the overground group (P=.01 and P=.01, respectively). At 6 weeks after the last training session, all improvements remained and the treadmill group also improved paretic step length (P.05). Conclusions: Individuals with chronic stroke equally improve gait speed and other gait parameters after 18 sessions of BWS gait training on either a treadmill or overground. Only the overground group improved step length symmetry ratio, suggesting a role of integrating overground walking into BWS interventions poststroke. (C) 2016 by the American Congress of Rehabilitation MedicineCruzeiro do Sul Univ, Inst Phys Act & Sport Sci, Rua Galvao Bueno 868, BR-01506000 Sao Paulo, SP, BrazilSao Paulo State Univ, Dept Phys Educ, Rio Claro, SP, BrazilVet Adm Maryland Hlth Care Syst, Maryland Exercise & Robot Ctr Excellence, Baltimore, MD USAUniv Maryland, Sch Med, Dept Phys Therapy & Rehabil Sci, Baltimore, MD 21201 USAUniv Southampton, Fac Hlth Sci, Southampton, Hants, EnglandSao Paulo State Univ, Dept Phys Educ, Rio Claro, SP, Brazi