Asymptotic Exit Location Distributions in the Stochastic Exit Problem

Consider a two-dimensional continuous-time dynamical system, with an attracting fixed point $S$. If the deterministic dynamics are perturbed by white noise (random perturbations) of strength $\epsilon$, the system state will eventually leave the domain of attraction $\Omega$ of $S$. We analyse the case when, as $\epsilon\to0$, the exit location on the boundary $\partial\Omega$ is increasingly concentrated near a saddle point $H$ of the deterministic dynamics. We show that the asymptotic form of the exit location distribution on $\partial\Omega$ is generically non-Gaussian and asymmetric, and classify the possible limiting distributions. A key role is played by a parameter $\mu$, equal to the ratio $|\lambda_s(H)|/\lambda_u(H)$ of the stable and unstable eigenvalues of the linearized deterministic flow at $H$. If $\mu<1$ then the exit location distribution is generically asymptotic as $\epsilon\to0$ to a Weibull distribution with shape parameter $2/\mu$, on the $O(\epsilon^{\mu/2})$ length scale near $H$. If $\mu>1$ it is generically asymptotic to a distribution on the $O(\epsilon^{1/2})$ length scale, whose moments we compute. The asymmetry of the asymptotic exit location distribution is attributable to the generic presence of a `classically forbidden' region: a wedge-shaped subset of $\Omega$ with $H$ as vertex, which is reached from $S$, in the $\epsilon\to0$ limit, only via `bent' (non-smooth) fluctuational paths that first pass through the vicinity of $H$. We deduce from the presence of this forbidden region that the classical Eyring formula for the small-$\epsilon$ exponential asymptotics of the mean first exit time is generically inapplicable.Comment: This is a 72-page Postscript file, about 600K in length. Hardcopy requests to [email protected] or [email protected]

Insulated Neighborhoods: Structural and Functional Units of Mammalian Gene Control

Understanding how transcriptional enhancers control over 20,000 protein-coding genes to maintain cell-type-specific gene expression programs in all human cells is a fundamental challenge in regulatory biology. Recent studies suggest that gene regulatory elements and their target genes generally occur within insulated neighborhoods, which are chromosomal loop structures formed by the interaction of two DNA sites bound by the CTCF protein and occupied by the cohesin complex. Here, we review evidence that insulated neighborhoods provide for specific enhancer-gene interactions, are essential for both normal gene activation and repression, form a chromosome scaffold that is largely preserved throughout development, and are perturbed by genetic and epigenetic factors in disease. Insulated neighborhoods are a powerful paradigm for gene control that provides new insights into development and disease.National Institutes of Health (U.S.) (Grant HG002668

Information Technologies and Education for the Poor in Africa: Recommendations for a Pro-Poor ICT4D Non-Formal Education Policy

More than half of Africa\u27s youth and adults do not have basic literacy skills and/or have not completed primary or secondary school. It is deeply concerning how little serious attention has been paid to the potential ways in which ICT can enhance such skills, as part of a pro-poor model of ICT for Development (ICT4D). Such work is crucial if the goals of Education for All (EFA) and the Millennium Development Goals (MDG) are to be achieved. The present effort, Information Technologies and Education for the Poor in Africa (ITEPA), is designed to focus attention on what is being and has been attempted in this domain in some of the poorest communities in Africa

Comparative analysis of metazoan chromatin organization

Genome function is dynamically regulated in part by chromatin, which consists of the histones, non-histone proteins and RNA molecules that package DNA. Studies in Caenorhabditis elegans and Drosophila melanogaster have contributed substantially to our understanding of molecular mechanisms of genome function in humans, and have revealed conservation of chromatin components and mechanisms. Nevertheless, the three organisms have markedly different genome sizes, chromosome architecture and gene organization. On human and fly chromosomes, for example, pericentric heterochromatin flanks single centromeres, whereas worm chromosomes have dispersed heterochromatin-like regions enriched in the distal chromosomal ‘arms’, and centromeres distributed along their lengths. To systematically investigate chromatin organization and associated gene regulation across species, we generated and analysed a large collection of genome-wide chromatin data sets from cell lines and developmental stages in worm, fly and human. Here we present over 800 new data sets from our ENCODE and modENCODE consortia, bringing the total to over 1,400. Comparison of combinatorial patterns of histone modifications, nuclear lamina-associated domains, organization of large-scale topological domains, chromatin environment at promoters and enhancers, nucleosome positioning, and DNA replication patterns reveals many conserved features of chromatin organization among the three organisms. We also find notable differences in the composition and locations of repressive chromatin. These data sets and analyses provide a rich resource for comparative and species-specific investigations of chromatin composition, organization and function.National Science Foundation (U.S.) (1122374

Flat Plate Solar Collector Materials (and Designs with an Economic Methodology for Optimizing Collector Design)

The desirability of specific materials and designs for conventional flat-plate solar collector components is considered. Then a methodology for choosing the most economic component is presented, consisting of a computer simulation and a rate-of-return analysis. The effect of rising conventional fuel costs is examined. Examples of using the methodology are given, based on Southern California climatic and user-demand conditions. Selective absorber-plate coatings and film inner glazing are shown to be economic, yielding a rate-of-return of 23 percent and 29 percent, respectively

A High Energy X-Ray and Neutron Scattering Study of Iron Phosphate Glasses Containing Uranium

The atomic structure of iron phosphate glasses containing uranium has been studied by complementary neutron and x-ray scattering techniques. by combining x-ray and neutron structure factors, detailed information about different pair interactions has been obtained. Most of the basic structural features such as coordination numbers and O-O and P-O distances in uranium containing glasses are the same as those in the base glass of batch composition 40Fe2O3-60P2O5 (mol %). However, the Fe-O distances change slightly with the addition of uranium. The observed structural parameters support a structural model in which the waste elements occupy voids in the Fe-O-P network, hence, not altering the basic structure of the parent iron phosphate glass

MKID development for SuperSpec: an on-chip, mm-wave, filter-bank spectrometer

SuperSpec is an ultra-compact spectrometer-on-a-chip for millimeter and submillimeter wavelength astronomy. Its very small size, wide spectral bandwidth, and highly multiplexed readout will enable construction of powerful multibeam spectrometers for high-redshift observations. The spectrometer consists of a horn-coupled microstrip feedline, a bank of narrow-band superconducting resonator filters that provide spectral selectivity, and Kinetic Inductance Detectors (KIDs) that detect the power admitted by each filter resonator. The design is realized using thin-film lithographic structures on a silicon wafer. The mm-wave microstrip feedline and spectral filters of the first prototype are designed to operate in the band from 195-310 GHz and are fabricated from niobium with at Tc of 9.2K. The KIDs are designed to operate at hundreds of MHz and are fabricated from titanium nitride with a Tc of 2K. Radiation incident on the horn travels along the mm-wave microstrip, passes through the frequency-selective filter, and is finally absorbed by the corresponding KID where it causes a measurable shift in the resonant frequency. In this proceedings, we present the design of the KIDs employed in SuperSpec and the results of initial laboratory testing of a prototype device. We will also briefly describe the ongoing development of a demonstration instrument that will consist of two 500-channel, R=700 spectrometers, one operating in the 1-mm atmospheric window and the other covering the 650 and 850 micron bands.Comment: As submitted, except that "in prep" references have been update