[1] We present a physical model to explain the behavior of longterm, time series measurements of chloride, a natural passive tracer, in rainfall and runoff in catchments [Kirchner et al., Nature, 403(524), 2000]. A spectral analysis of the data shows the chloride concentrations in rainfall to have a white noise spectrum, while in streamflow, the spectrum exhibits a fractal 1/f scaling. The empirically derived distribution of tracer travel times h(t) follows a power-law, indicating low-level contaminant delivery to streams for a very long time. Our transport model is based on a continuous time random walk (CTRW) with an event time distribution governed by y(t) $ A b t À1Àb . The CTRW using this power-law y(t) (with 0 < b < 1) is interchangeable with the time-fractional advection-dispersion equation (FADE) and has accounted for the universal phenomenon of anomalous transport in a broad range of disordered and complex systems. In the current application, the events can be realized as transit times on portions of the catchment network. The travel time distribution is the first passage time distribution F(t;l) at a distance l from a pulse input (at t = 0) at the origin. We show that the empirical h(t) is the catchment areal composite of F(t;l) and that the fractal 1/f spectral response found in many catchments is an example of the larger class of transport phenomena cited above. The physical basis of y(t), which determines F(t;l), is the origin of the extremely long chemical retention times in catchments.

We investigate the nonergodic properties of blinking nanocrystals modeled by a Lévy-walk stochastic process. Using a nonergodic mean field approach we calculate the distribution functions of the time averaged intensity correlation function. We show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nanocrystals our results describe ergodicity breaking in systems modeled by Lévy walks , for example, certain types of chaotic maps and spin dynamics to name a few.

ETOC: The behavior of a dimer-scale computational model predicts that short interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks govern both catastrophe and rescue.

BackgroundDifferentiation of primordial germ cells into mature spermatozoa proceeds through multiple stages, one of the most important of which is meiosis. Meiotic recombination is in turn a key part of meiosis. To achieve the highly specialized and diverse functions necessary for the successful completion of meiosis and the generation of spermatozoa thousands of genes are coordinately regulated through spermatogenesis. A complete and unbiased characterization of the transcriptome dynamics of spermatogenesis is, however, still lacking.ResultsIn order to characterize gene expression during spermatogenesis we sequenced eight mRNA samples from testes of juvenile mice from 6 to 38 days post partum. Using gene expression clustering we defined over 1,000 novel meiotically-expressed genes. We also developed a computational de-convolution approach and used it to estimate cell type-specific gene expression in pre-meiotic, meiotic and post-meiotic cells. In addition, we detected 13,000 novel alternative splicing events around 40% of which preserve an open reading frame, and found experimental support for 159 computational gene predictions. A comparison of RNA polymerase II (Pol II) ChIP-Seq signals with RNA-Seq coverage shows that gene expression correlates well with Pol II signals, both at promoters and along the gene body. However, we observe numerous instances of non-canonical promoter usage, as well as intergenic Pol II peaks that potentially delineate unannotated promoters, enhancers or small RNA clusters.ConclusionsHere we provide a comprehensive analysis of gene expression throughout mouse meiosis and spermatogenesis. Importantly, we find over a thousand of novel meiotic genes and over 5,000 novel potentially coding isoforms. These data should be a valuable resource for future studies of meiosis and spermatogenesis in mammals.