Stability and Optimization in Structured Population Models on Graphs

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.Comment: 22 pages, 7 figure

Polynomial Profits in Renewable Resources Management

A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the target cost function is polynomial in the control. In specific situations, further information about the form of this dependence is obtained. As a consequence, in some cases the optimal control is proved to be necessarily bang--bang, in other cases the computations necessary to find the optimal control are significantly reduced

Differential Equations Modeling Crowd Interactions

Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting non locally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians, and also with other "agents".Comment: 26 pages, 5 figure

Adherence to the Mediterranean diet and nasopharyngeal cancer risk in Italy

Purpose: Few studies investigated the role of diet on nasopharyngeal cancer (NPC) risk in non-endemic areas. The aim of this study was to assess the association between adherence to the traditional Mediterranean diet and NPC risk in a southern European low-risk population. Methods: We conducted a hospital-based case-control study in Italy, including 198 histologically confirmed NPC cases and 594 matched controls. Dietary habits were collected by means of a validated food-frequency questionnaire, including 83 foods, food groups, or beverages. Adherence to the traditional Mediterranean diet was assessed through a Mediterranean Diet Score (MDS), based on nine dietary components characterizing this dietary profile, i.e., high intake of vegetables, fruits and nuts, cereals, legumes, and fish; low intake of dairy products and meat; high monounsaturated to saturated fatty acid ratio; and moderate alcohol intake. We estimated odds ratios (ORs) of NPC, and the corresponding 95% confidence intervals (CIs), for increasing MDS (i.e., increasing adherence) using multiple logistic regression models, adjusted for major confounding factors. Results: As compared to MDS 64 4, the ORs of NPC were 0.83 (95% CI: 0.54\u20131.25) for MDS of 5 and 0.66 (95% CI: 0.44\u20130.99) for MDS 65 6, with a significant trend of decreasing risk (p 0.043). The corresponding population attributable fraction was 22%, indicating that 22% of NPC cases in this population would be avoided by shifting all subjects to a score 656. Conclusions: Our study supports a favorable role of the Mediterranean diet on NPC risk