Density classification on infinite lattices and trees

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p1/2. We present solutions to that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations

Chronic effect of aerobic exercise on anthropometric, biochemical and hemodynamic variables in individuals with type 2 diabetes mellitus: A systematic review

Objective: The aim of this study was to analyze the effects of aerobic exercise on biochemical, anthropometric and hemodynamic profiles of patients with type 2 diabetes mellitus, in randomized clinical trials and case–control studies. Method: The databases used in the study were: MEDLINE, BVS (LiLacs), IBECS (Spain), MED Caribbean and Central Controlled Clinical Trial Registry. We included studies published from 2004 to 2014. Were analyzed anthropometric (body mass index, waist circumference and percentage of body fat), hemodynamic (blood pressure and heart rate) and biochemical parameters (glycemia, glycated hemoglobin, insulin, cholesterol-HDL, cholesterol-LDL and triglycerides). Results: The results showed that, aerobic exercise of moderate intensity and often three or more times a week, promoted a significant reduction in waist circumference, blood glucose and diastolic blood pressure. Conclusion: It is concluded that there are benefits of aerobic exercise of moderate intensity practiced regularly often more than three times a week on waist circumference, glycemia and diastolic blood pressure in diabetes mellitus type 2