Vitamin D inadequacy in Belgian postmenopausal osteoporotic women

BACKGROUND: Inadequate serum vitamin D [25(OH)D] concentrations are associated with secondary hyperparathyroidism, increased bone turnover and bone loss, which increase fracture risk. The objective of this study is to assess the prevalence of inadequate serum 25(OH)D concentrations in postmenopausal Belgian women. Opinions with regard to the definition of vitamin D deficiency and adequate vitamin D status vary widely and there are no clear international agreements on what constitute adequate concentrations of vitamin D. METHODS: Assessment of 25-hydroxyvitamin D [25(OH)D] and parathyroid hormone was performed in 1195 Belgian postmenopausal women aged over 50 years. Main analysis has been performed in the whole study population and according to the previous use of vitamin D and calcium supplements. Four cut-offs of 25(OH)D inadequacy were fixed : < 80 nmol/L, <75 nmol/L, < 50 nmol/L and < 30 nmol/L. RESULTS: Mean (SD) age of the patients was 76.9 (7.5) years, body mass index was 25.7 (4.5) kg/m(2). Concentrations of 25(OH)D were 52.5 (21.4) nmol/L. In the whole study population, the prevalence of 25(OH)D inadequacy was 91.3 %, 87.5 %, 43.1 % and 15.9% when considering cut-offs of 80, 75, 50 and 30 nmol/L, respectively. Women who used vitamin D supplements, alone or combined with calcium supplements, had higher concentrations of 25(OH)D than non-users. Significant inverse correlations were found between age/serum PTH and serum 25(OH)D (r = -0.23/r = -0.31) and also between age/serum PTH and femoral neck BMD (r = -0.29/r = -0.15). There is a significant positive relation between age and PTH (r = 0.16), serum 25(OH)D and femoral neck BMD (r = 0.07). (P < 0.05) Vitamin D concentrations varied with the season of sampling but did not reach statistical significance (P = 0.09). CONCLUSION: This study points out a high prevalence of vitamin D inadequacy in Belgian postmenopausal osteoporotic women, even among subjects receiving vitamin D supplements

From combinatorial games to shape-symmetric morphisms

Siegel suggests in his book on combinatorial games that quite simple games provide us with challenging problems: ``No general formula is known for computing arbitrary Grundy values of Wythoff's game. In general, they appear chaotic, though they exhibit a striking fractal-like pattern.''. This observation is the first motivation behind this chapter. We present some of the existing connections between combinatorial game theory and combinatorics on words. In particular, multidimensional infinite words can be seen as tiling of $N^d$. They naturally arise from subtraction games on $d$ heaps of tokens. We review notions such as $k$-automatic, $k$-regular or shape-symmetric multidimensional words. The underlying general idea is to associate a finite automaton with a morphism