The Kohlrausch function: properties and applications

In a wide variety of applications, including the modelling of the glassy state of dense matter, non-exponential correlation functions in nuclear magnetic resonance, polymer dynamics, and bone and muscle rheology, Kohlrausch functions have proved to be more appropriate in modelling the associated relaxation and decay processes than the standard exponential function. However, mathematical results about this function, important for both computational and modelling endeavours, are spread over publications in several quite different areas of mathematics and science. The purpose of this paper is to review the key properties of Kohlrausch functions in a unified manner, which motivates its use in the modelling of molecular processes. Some representative applications and related computational issues are discussed

Exact and explicit probability densities for one-sided Levy stable distributions

We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy stable probability distributions of index \alpha, 0< \alpha <1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty, satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}), p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all the known results given by k\leq 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a 'fine-tuning' of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space

Measured magnetic moments and shape coexistence in the neutron-deficient nuclei Pt-184,Pt-186,Pt-188

A novel implantation-decay technique has been employed to measure the magnetic moments of the 2(1)(+) states in the neutron-deficient nuclei Pt-184, Pt-186, and Pt-188. The magnetic moment systematics for the even Pt isotopes now extend from Pt-184(78)106 to Pt-198(78)120, spanning the upper half of the valence neutron shell. Despite the prolate-to-oblate shape transition near A = 190, they remain remarkably constant. The g(2(1)(+)) values for Pt-184,Pt-186,Pt-188 are consistent with shape-coexistence models in which the deformed configuration has a larger effective number of valence protons than the less-deformed configuration

Sedentary Time and Physical Activity Surveillance Through Accelerometer Pooling in Four European Countries.

OBJECTIVE: The objective of this study was to pool, harmonise and re-analyse national accelerometer data from adults in four European countries in order to describe population levels of sedentary time and physical inactivity. METHODS: Five cross-sectional studies were included from England, Portugal, Norway and Sweden. ActiGraph accelerometer count data were centrally processed using the same algorithms. Multivariable logistic regression analyses were conducted to study the associations of sedentary time and physical inactivity with sex, age, weight status and educational level, in both the pooled sample and the separate study samples. RESULTS: Data from 9509 participants were used. On average, participants were sedentary for 530 min/day, and accumulated 36 min/day of moderate to vigorous intensity physical activity. Twenty-three percent accumulated more than 10 h of sedentary time/day, and 72% did not meet the physical activity recommendations. Nine percent of all participants were classified as high sedentary and low active. Participants from Norway showed the highest levels of sedentary time, while participants from England were the least physically active. Age and weight status were positively associated with sedentary time and not meeting the physical activity recommendations. Men and higher-educated people were more likely to be highly sedentary, while women and lower-educated people were more likely to be inactive. CONCLUSIONS: We found high levels of sedentary time and physical inactivity in four European countries. Older people and obese people were most likely to display these behaviours and thus deserve special attention in interventions and policy planning. In order to monitor these behaviours, accelerometer-based cross-European surveillance is recommended.The original studies were funded by the Norwegian Directorate of Health and the Norwegian School of Sport Sciences; the Portuguese Institute of Sport; a grant from the Stockholm County Council; and grants from the Swedish Council for Working Life and Social Research, and The Swedish Research Council for Environment, Agricultural Sciences, and Spatial Planning. AL, JL, JB and HvdP were supported by the Netherlands Organisation for Health Research and Development (Grant no. 200.600.001). KS was supported by the National Heart, Lung, And Blood Institute of the National Institutes of Health (award no. R01HL116381). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. KW was supported by the British Heart Foundation (Grant FS/12/58/29709). KW and SB were supported by the UK Medical Research Council (Grant MC_UU_12015/3)

Resolution of two-dimensional Currents in Superconductors from a two-dimensional magnetic field measurement by the method of regularization

The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization. Regularization directly addresses the inherent instability of this inversion problem for non-exact (noisy) data. Performance of the technique is evaluated for different current distributions and for data with varying amounts of added noise. Comparisons are made to other methods, and the present method is demonstrated to achieve a better regularizing (noise filtering) effect while also employing the generalized-cross validation (GCV) method to choose the optimal regularization parameter from the data, without detailed knowledge of the true (and generally unknown) solution. It is also shown that clean, noiseless data is an ineffective test of an inversion algorithm.Comment: To appear in the Physical Review B. Some text/figure additions and modification

Physical Activity Among Adolescent Cancer Survivors: The PACCS Study

OBJECTIVES Physical activity (PA) may modify risks of late effects after cancer. We aimed to examine levels of PA and sedentary time (ST) in a large, international sample of adolescent childhood cancer survivors in relation to sociodemographic and cancer-related factors and compare levels of PA and ST to reference cohorts. METHODS Survivors from any cancer diagnosis who had completed cancer treatment ≥1 year ago, aged 9 to 16 years, were eligible for the multicenter Physical Activity in Childhood Cancer Survivors study. PA and ST were measured by ActiGraph GT3X+ accelerometers. We performed linear regression analyses to assess factors associated with moderate-to-vigorous PA (MVPA) and ST, and compared marginal means of total PA, MVPA, and ST in 432 survivors to sex- and age-stratified references (2-year intervals) using immediate t-tests for aggregated data. RESULTS Among survivors, 34% fulfilled the World Health Organization's PA recommendation of ≥60 min of daily MVPA on average and their ST was 8.7 hours per day. Being female, older, overweight, a survivor of central nervous system tumor, or having experienced relapse were associated with lower MVPA and/or higher ST. Generally, male survivors spent less time in MVPA compared with references, whereas female survivors had similar levels. Both male and female survivors had higher ST than references in nearly all age groups. CONCLUSIONS The low PA and high ST in this large sample of adolescent childhood cancer survivors is worrisome. Combined, our results call for targeted interventions addressing both PA and ST in follow-up care after childhood cancer