Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows.

In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior-random walks, ballistic transport, and trapping-depending upon the filament's relative length and effective flexibility. Moreover, we find that filaments execute Lévy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of "conveyor belts." Evidence for these various transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and transporting a flexible ribbon.

[Models for risk assessment and prediction in breast cancer].

In the areas of prevention and life skills counseling for breast cancer, risk assessment and prediction can assist clinicians to decide if chemoprevention or prophylactic surgery is needed or suggestions on improving the quality of life for their clients. Several mathematical models, namely Gail Model, Claus Model, BRCAPRO Model and Cuzick-Tyrer Model etc. have been developed to make predictions, clinically. This paper has reviewed the development, operation, advantage versus disadvantage and areas of application for the four models. Having family history of breast cancer, one subject was calculated on the risks by the four models and different results were found. Up to 45 years old, the accumulative risks from the four models and population risk were 1.9%, 11.8%, 2.5%, 5.0% and 1.6%, respectively. To 75 years old, they were 20.2%, 32.5%, 13.1%, 25.0% and 8.5%, respectively. The subject had a relatively high breast cancer risk during her lifetime. A new model is supposed to include a variety of important risk factors and to be validated by large scale of case-control samples. Incidence of breast cancer in China had significantly increased during the last ten years, but the research on developing assessment methods of breast cancer risk had never been reported, suggesting that the development of models for Chinese population is necessary.