16 research outputs found
On the Origin and Characteristics of Noise-Induced LĂ©vy Walks of E. Coli
LĂ©vy walks as a random search strategy have recently attracted a lot of attention, and have been described in many animal species. However, very little is known about one of the most important issues, namely how LĂ©vy walks are generated by biological organisms. We study a model of the chemotaxis signaling pathway of E. coli, and demonstrate that stochastic fluctuations and the specific design of the signaling pathway in concert enable the generation of LĂ©vy walks. We show that LĂ©vy walks result from the superposition of an ensemble of exponential distributions, which occurs due to the shifts in the internal enzyme concentrations following the stochastic fluctuations. With our approach we derive the power-law analytically from a model of the chemotaxis signaling pathway, and obtain a power-law exponent , which coincides with experimental results. This work provides a means to confirm LĂ©vy walks as natural phenomenon by providing understanding on the process through which they emerge. Furthermore, our results give novel insights into the design aspects of biological systems that are capable of translating additive noise on the microscopic scale into beneficial macroscopic behavior
Wavelet boundary element methods â Adaptivity and goal-oriented error estimation
This article is dedicated to the adaptive wavelet boundary element method. It computes an approximation to the unknown solution of the boundary integral equation under consideration with a rate , whenever the solution can be approximated with this rate in the setting determined by the underlying wavelet basis. The computational cost scale linearly in the number of degrees of freedom. Goal-oriented error estimation for evaluating linear output functionals of the solution is also considered. An algorithm is proposed that approximately evaluates a linear output functional with a rate , whenever the primal solution can be approximated with a rate and the dual solution can be approximated with a rate , while the cost still scale linearly in . Numerical results for an acoustic scattering problem and for the point evaluation of the potential in case of the Laplace equation are reported to validate and quantify the approach
Scaling up phenotypic plasticity with hierarchical population models
Contains fulltext :
84105.pdf (postprint version ) (Open Access)15 p