Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics

Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the generalized central limit theorem leading to scale-free forms of the jump length or waiting time distributions. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Levy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful to describe recent experimental single particle tracking data, that feature a combination of CTRW and FBM properties.Comment: 25 pages, IOP style, 5 figure

Septation of Infectious Hyphae Is Critical for Appressoria Formation and Virulence in the Smut Fungus Ustilago Maydis

Differentiation of hyphae into specialized infection structures, known as appressoria, is a common feature of plant pathogenic fungi that penetrate the plant cuticle. Appressorium formation in U. maydis is triggered by environmental signals but the molecular mechanism of this hyphal differentiation is largely unknown. Infectious hyphae grow on the leaf surface by inserting regularly spaced retraction septa at the distal end of the tip cell leaving empty sections of collapsed hyphae behind. Here we show that formation of retraction septa is critical for appressorium formation and virulence in U. maydis. We demonstrate that the diaphanous-related formin Drf1 is necessary for actomyosin ring formation during septation of infectious hyphae. Drf1 acts as an effector of a Cdc42 GTPase signaling module, which also consists of the Cdc42-specific guanine nucleotide exchange factor Don1 and the Ste20-like kinase Don3. Deletion of drf1, don1 or don3 abolished formation of retraction septa resulting in reduced virulence. Appressorium formation in these mutants was not completely blocked but infection structures were found only at the tip of short filaments indicating that retraction septa are necessary for appressorium formation in extended infectious hyphae. In addition, appressoria of drf1 mutants penetrated the plant tissue less frequently

Assessing written work by determining competence to achieve the module-specific learning outcomes.

This chapter describes lasers and other sources of coherent light that operate in a wide wavelength range. First, the general principles for the generation of coherent continuous-wave and pulsed radiation are treated including the interaction of radiation with matter, the properties of optical resonators and their modes as well as such processes as Q-switching and mode-locking. The general introduction is followed by sections on numerous types of lasers, the emphasis being on todayʼs most important sources of coherent light, in particular on solid-state lasers and several types of gas lasers. An important part of the chapter is devoted to the generation of coherent radiation by nonlinear processes with optical parametric oscillators, difference- and sum-frequency generation, and high-order harmonics. Radiation in the extended ultraviolet (EUV) and x-ray ranges can be generated by free electron lasers (FEL) and advanced x-ray sources. Ultrahigh light intensities up to 1021 W/cm2 open the door to studies of relativistic laser–matter interaction and laser particle acceleration. The chapter closes with a section on laser stabilization