Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Association between dairy product intake and abdominal obesity in Azorean adolescents

BACKGROUND: Some studies have reported an inverse association between dairy product (DP) consumption and weight or fat mass loss. OBJECTIVES: The objective of our study was to assess the association between DP intake and abdominal obesity (AO) among Azorean adolescents. SUBJECTS/METHODS: This study was a cross-sectional analysis. A total of 903 adolescents (370 boys) aged 15--16 years was evaluated. Anthropometric measurements were collected (weight, height and waist circumference (WC)) and McCarthy’s cut-points were used to categorize WC. AO was defined when WC was X90th percentile. Adolescent food intake was assessed using a self-administered semiquantitative food frequency questionnaire and DP intake was categorized in o2 and X2 servings/day. Data were analyzed separately for girls and boys, and logistical regression was used to estimate the association between DPs and AO adjusting for potential confounders. RESULTS: The prevalence of AO was 54.9% (boys: 32.1% and girls: 70.7%, Po0.001). For boys and girls, DP consumption was 2.3±1.9 and 2.1±1.6 servings/day (P¼0.185), respectively. In both genders, the proportion of adolescents with WC o90th percentile was higher among individuals who reported a dairy intake of X2 servings/day compared with those with an intake o2 servings/day (boys: 71% vs 65% and girls: 36% vs 24%, Po0.05). After adjustments for confounders, two or more DP servings per day were a negative predictor of AO (odds ratio, 0.217; 95% confidence interval, 0.075 -- 0.633) only in boys. CONCLUSION: We found a protective association between DP intake and AO only in boys.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.