Existence and approximation of probability measure solutions to models of collective behaviors

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown, expressed in terms of a probability measure evolving in time. We develop an existence and approximation theory of the solutions to such models and we show that some recently proposed models of crowd and swarm dynamics fit our theoretic paradigm.Comment: 31 pages, 1 figur

Eating Like a Rainbow: The Development of a Visual Aid for Nutritional Treatment of CKD Patients. A South African Project.

Providing nutritional education for chronic kidney disease (CKD) patients in South Africa is complicated by several conditions: the population is composed of diverse ethnic groups, each with its own culture and food preferences; eleven languages are spoken and illiteracy is common in the lower socio-economic groups. Food preparation and storage are affected by the lack of electricity and refrigeration, and this contributes to a monotonous diet. In traditional African culture, two meals per day are often shared “from the pot”, making portion control difficult. There is both under- and over-nutrition; late referral of CKD is common. Good quality protein intake is often insufficient and there are several misconceptions about protein sources. There is a low intake of vegetables and fruit, while daily sodium intake is high, averaging 10 g/day, mostly from discretionary sources. On this background, we would like to describe the development of a simplified, visual approach to the “renal diet”, principally addressed to illiterate/non-English speaking CKD patients in Southern Africa, using illustrations to replace writing. This tool “Five steps to improve renal diet compliance”, also called “Eating like a Rainbow”, was developed to try to increase patients’ understanding, and has so far only been informally validated by feedback from users. The interest of this study is based on underlining the feasibility of dietary education even in difficult populations, focusing attention on this fundamental issue of CKD care in particular in countries with limited access to chronic dialysis