Spikes for the gierer-meinhardt system with many segments of different diffusivities

We rigorously prove results on spiky patterns for the Gierer-Meinhardt system with a large number of jump discontinuities in the diffusion coefficient of the inhibitor. Using numerical computations in combination with a Turing-type instability analysis, this system has been investigated by Benson, Maini and Sherratt

Optimal Haplotype Assembly from High-Throughput Mate-Pair Reads

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide polymorphisms (SNPs). A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes.Comment: 10 pages, 4 figures, Submitted to ISIT 201

Spatial period-multiplying instabilities of hexagonal Faraday waves

A recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales. These patterns both arise as secondary states once the primary hexagonal pattern becomes unstable. In one of these patterns (so-called `superlattice-II') the original hexagonal symmetry is broken in a subharmonic instability to form a striped pattern with a spatial scale increased by a factor of 2sqrt{3} from the original scale of the hexagons. In contrast, the time-averaged pattern is periodic on a hexagonal lattice with an intermediate spatial scale (sqrt{3} larger than the original scale) and apparently has 60 degree rotation symmetry. We present a symmetry-based approach to the analysis of this bifurcation. Taking as our starting point only the observed instantaneous symmetry of the superlattice-II pattern presented in and the subharmonic nature of the secondary instability, we show (a) that the superlattice-II pattern can bifurcate stably from standing hexagons; (b) that the pattern has a spatio-temporal symmetry not reported in [1]; and (c) that this spatio-temporal symmetry accounts for the intermediate spatial scale and hexagonal periodicity of the time-averaged pattern, but not for the apparent 60 degree rotation symmetry. The approach is based on general techniques that are readily applied to other secondary instabilities of symmetric patterns, and does not rely on the primary pattern having small amplitude

Energy Relaxation of Hot Dirac Fermions in Graphene

We develop a theory for the energy relaxation of hot Dirac fermions in graphene. We obtain a generic expression for the energy relaxation rate due to electron-phonon interaction and calculate the power loss due to both optical and acoustic phonon emission as a function of electron temperature $T_{\mathrm{e}}$ and density $n$. We find an intrinsic power loss weakly dependent on carrier density and non-vanishing at the Dirac point $n = 0$, originating from interband electron-optical phonon scattering by the intrinsic electrons in the graphene valence band. We obtain the total power loss per carrier $\sim 10^{-12} - 10^{-7} \mathrm{W}$ within the range of electron temperatures $\sim 20 - 1000 \mathrm{K}$. We find optical (acoustic) phonon emission to dominate the energy loss for $T_{\mathrm{e}} > (<) 200-300 \mathrm{K}$ in the density range $n = 10^{11}-10^{13} \mathrm{cm}^{-2}$.Comment: 5 page

An Unfinished Canvas: Local Partnerships in Support of Arts Education in California

In 2006, at the request of The William and Flora Hewlett Foundation, SRI International conducted a study aimed at assessing the status of arts education in California relative to state goals. The final report, An Unfinished Canvas. Arts Education in California: Taking Stock of Policy and Practice, revealed a substantial gap between policy and practice. The study found that elementary schools in particular are failing to meet state goals for arts education. In light of these findings, The Hewlett Foundation commissioned a series of follow-up studies to identify policy mechanisms or other means of increasing student access to arts education. This study, focusing on the ability of school districts to leverage support for arts education through partnerships with local arts organizations, is one of the follow-up studies.Partnerships may allow for the pooling of resources and lend support to schools in a variety of ways including artists-in-residency programs, professional development for teachers, exposing students to the arts through the provision of one-time performances at school sites, and organizing field trips to performances and exhibits. According to the California Visual and Performing Arts Framework for California Public Schools, partnerships among districts, schools, and arts organizations are most successful when they are embedded within a comprehensive, articulated program of arts education. Questions about the nature of partnerships that California districts and schools have been able to form with arts organizations, and the success of these partnerships to increase students' access to a sequential standards-based course of study in the four arts disciplines, served as the impetus for this study.A team of SRI researchers conducted case studies of partnerships between districts and arts organizations in six diverse California communities in spring 2008. The case study sites were selected for their particular arts education activities and diverse contexts and, as a result, do not offer generalizable data about partnerships between school districts and arts organizations in California. Instead, we highlight the ways that a sample of partnerships promotes arts education in California elementary schools to inform others who may be interested in building partnerships between school districts and arts organizations