Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Implications of purinergic receptor-mediated intracellular calcium transients in neural differentiation

Purinergic receptors participate, in almost every cell type, in controlling metabolic activities and many physiological functions including signal transmission, proliferation and differentiation. While most of P2Y receptors induce transient elevations of intracellular calcium concentration by activation of intracellular calcium pools and forward these signals as waves which can also be transmitted into neighboring cells, P2X receptors produce calcium spikes which also include activation of voltage-operating calcium channels. P2Y and P2X receptors induce calcium transients that activate transcription factors responsible for the progress of differentiation through mediators including calmodulin and calcineurin. Expression of P2X2 as well as of P2X7 receptors increases in differentiating neurons and glial cells, respectively. Gene expression silencing assays indicate that these receptors are important for the progress of differentiation and neuronal or glial fate determination. Metabotropic receptors, mostly P2Y1 and P2Y2 subtypes, act on embryonic cells or cells at the neural progenitor stage by inducing proliferation as well as by regulation of neural differentiation through NFAT translocation. The scope of this review is to discuss the roles of purinergic receptor-induced calcium spike and wave activity and its codification in neurodevelopmental and neurodifferentiation processes.

The impact of asymptomatic vertebral fractures on quality of life in older community-dwelling women: the São Paulo Ageing & Health Study

OBJECTIVES: The aim of this study was to investigate the impact of asymptomatic vertebral fractures on the quality of life in older women as part of the Sao Paulo Ageing & Health Study. METHODS: This study was a cross-sectional study with a random sample of 180 women 65 years of age or older with or without vertebral fractures. The Quality of Life Questionnaire of the European Foundation for Osteoporosis was administered to all subjects. Anthropometric data were obtained by physical examination, and the body mass index was calculated. Lateral thoracic and lumbar spine X-ray scans were obtained to identify asymptomatic vertebral fractures using a semi-quantitative method. RESULTS: Women with asymptomatic vertebral fractures had lower total scores [61.4(15.3) vs. 67.1(14.2), p = 0.03] and worse physical function domain scores [69.5(20.1) vs. 77.3(17.1), p = 0.02] for the Quality of Life Questionnaire of the European Foundation for Osteoporosis compared with women without fractures. The total score of this questionnaire was also worse in women classified as obese than in women classified as overweight or normal. High physical activity was related to a better total score for this questionnaire (p = 0.01). Likewise, lower physical function scores were observed in women with higher body mass index values (p<0.05) and lower physical activity levels (p,0.05). Generalized linear models with gamma distributions and logarithmic link functions, adjusted for age, showed that lower total scores and physical function domain scores for the Quality of Life Questionnaire of the European Foundation for Osteoporosis were related to a high body mass index, lower physical activity, and the presence of vertebral fractures (p<0.05). CONCLUSION: Vertebral fractures are associated with decreased quality of life mainly physical functioning in older community-dwelling women regardless of age, body mass index, and physical activity. Therefore, the results highlight the importance of preventing and controlling asymptomatic vertebral fractures to reduce their impact on quality of life among older women.