Sigmoidal cosine series on the interval

We construct a set of functions, say, psi([r])(n) composed of a cosine function and a sigmoidal transformation gamma(r) of order r > 0. The present functions are orthonormal with respect to a proper weight function on the interval [-1, 1]. It is proven that if a function f is continuous and piecewise smooth on [-1, 1] then its series expansion based on psi([r])(n) converges uniformly to f so long as the order of the sigmoidal transformation employed is 0 < r

General bounds on Bayes errors for regression with Gaussian processes

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

Splines in Numerical Integration

AMS Subj. Classification: 65D07, 65D30.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Weight loss strategies, stress, and cognitive function:supervised versus unsupervised dieting

The early stages of dieting to lose weight have been associated with neuro-psychological impairments. Previous work has not elucidated whether these impairments are a function solely of unsupported or supported dieting. Raised cortico-steroid levels have been implicated as a possible causal mechanism. Healthy, overweight, pre-menopausal women were randomised to one of three conditions in which they dieted either as part of a commercially available weight loss group, dieted without any group support or acted as non-dieting controls for 8 weeks. Testing occurred at baseline and at 1, 4 and 8 weeks post baseline. During each session, participants completed measures of simple reaction time, motor speed, vigilance, immediate verbal recall, visuo-spatial processing and (at Week 1 only) executive function. Cortisol levels were gathered at the beginning and 30 min into each test session, via saliva samples. Also, food intake was self-recorded prior to each session and fasting body weight and percentage body fat were measured at each session. Participants in the unsupported diet condition displayed poorer vigilance performance (p=0.001) and impaired executive planning function (p=0.013) (along with a marginally significant trend for poorer visual recall (p=0.089)) after 1 week of dieting. No such impairments were observed in the other two groups. In addition, the unsupported dieters experienced a significant rise in salivary cortisol levels after 1 week of dieting (p<0.001). Both dieting groups lost roughly the same amount of body mass (p=0.011) over the course of the 8 weeks of dieting, although only the unsupported dieters experienced a significant drop in percentage body fat over the course of dieting (p=0.016). The precise causal nature of the relationship between stress, cortisol, unsupported dieting and cognitive function is, however, uncertain and should be the focus of further research. © 2005 Elsevier Ltd. All rights reserved.

Weight loss improves biomarkers endothelial function and systemic inflammation in obese postmenopausal Saudi women.

Background: Although postmenopausal associated disorders are important public health problems worldwide, to date limited studies evaluated the endothelial function and systemic inflammation response to weight loss in obese postmenopausal women. Objective: This study was done to evaluate the endothelial function and systemic inflammation response to weight loss in obese postmenopausal Saudi women. Material and methods: Eighty postmenopausal obese Saudi women (mean age 52.64±6.13 year) participated in two groups: Group (A) received aerobic exercise on treadmill and diet whereas, group (B) received no intervention. Markers of inflammation and endothelial function were measured before and after 3 months at the end of the study. Results: The values of body mass index(BMI), interleukin-6 (IL-6), tumor necrosis factor-alpha (TNF-α), C-reactive protein (CRP), inter-cellular adhesion molecule (ICAM-1), vascular cell adhesion molecule (VCAM-1) and plasminogen activator inhibitor- 1 activity (PAI-1:Ac) were significantly decreased in group (A), while changes were not significant in group (B). Also, there were significant differences between mean levels of the investigated parameters in group (A) and group (B) after treatment. Conclusion: Weight loss ameliorates inflammatory cytokines and markers of endothelial function in obese postmenopausal Saudi women.

Exercise, appetite, and energy balance: The interactions between energy expenditure and intake, and the implications for weight management

This book disseminates current information pertaining to the modulatory effects of foods and other food substances on behavior and neurological pathways and, importantly, vice versa. This ranges from the neuroendocrine control of eating to the effects of life-threatening disease on eating behavior. The importance of this contribution to the scientific literature lies in the fact that food and eating are an essential component of cultural heritage but the effects of perturbations in the food/cognitive axis can be profound. The complex interrelationship between neuropsychological processing, diet, and behavioral outcome is explored within the context of the most contemporary psychobiological research in the area. This comprehensive psychobiology- and pathology-themed text examines the broad spectrum of diet, behavioral, and neuropsychological interactions from normative function to occurrences of severe and enduring psychopathological processes