Bayesian inverse problems for recovering coefficients of two scale elliptic equations

We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information on the solution. We consider both the uniform and the Gaussian prior probability measures. We use the two scale homogenized equation whose solution contains the solution of the homogenized equation which describes the macroscopic behaviour, and the corrector which encodes the microscopic behaviour. We approximate the posterior probability by a probability measure determined by the solution of the two scale homogenized equation. We show that the Hellinger distance of these measures converges to zero when the microscale converges to zero, and establish an explicit convergence rate when the solution of the two scale homogenized equation is sufficiently regular. Sampling the posterior measure by Markov Chain Monte Carlo (MCMC) method, instead of solving the two scale equation using fine mesh for each proposal with extremely high cost, we can solve the macroscopic two scale homogenized equation. Although this equation is posed in a high dimensional tensorized domain, it can be solved with essentially optimal complexity by the sparse tensor product finite element method, which reduces the computational complexity of the MCMC sampling method substantially. We show numerically that observations on the macrosopic behaviour alone are not sufficient to infer the microstructure. We need also observations on the corrector. Solving the two scale homogenized equation, we get both the solution to the homogenized equation and the corrector. Thus our method is particularly suitable for sampling the posterior measure of two scale coefficients

Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens

We study the classical first-kind boundary integral equation reformulations of time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens. We prove continuity and coercivity of the relevant boundary integral operators (the acoustic single-layer and hypersingular operators respectively) in appropriate fractional Sobolev spaces, with wavenumber-explicit bounds on the continuity and coercivity constants. Our analysis is based on spectral representations for the boundary integral operators, and builds on results of Ha-Duong (Jpn J Ind Appl Math 7:489--513 (1990) and Integr Equat Oper Th 15:427--453 (1992)).Comment: v2 has minor corrections compared to v1. arXiv admin note: substantial text overlap with arXiv:1401.280

Fin-Tail Coordination during Escape and Predatory Behavior in Larval Zebrafish

Larval zebrafish innately perform a suite of behaviors that are tightly linked to their evolutionary past, notably escape from threatening stimuli and pursuit and capture of prey. These behaviors have been carefully examined in the past, but mostly with regard to the movements of the trunk and tail of the larvae. Here, we employ kinematics analyses to describe the movements of the pectoral fins during escape and predatory behavior. In accord with previous studies, we find roles for the pectoral fins in slow swimming and immediately after striking prey. We find novel roles for the pectoral fins in long-latency, but not in short-latency C-bends. We also observe fin movements that occur during orienting J-turns and S-starts that drive high-velocity predatory strikes. Finally, we find that the use of pectoral fins following a predatory strike is scaled to the velocity of the strike, supporting a role for the fins in braking. The implications of these results for central control of coordinated movements are discussed, and we hope that these results will provide baselines for future analyses of cross-body coordination using mutants, morphants, and transgenic approaches

SNP assay to detect the ‘Hyuuga’ red-brown lesion resistance gene for Asian soybean rust

Asian soybean rust (ASR), caused by Phakopsora pachyrhizi Syd., has the potential to become a serious threat to soybean, Glycine max L. Merr., production in the USA. A novel rust resistance gene, Rpp?(Hyuuga), from the Japanese soybean cultivar Hyuuga has been identified and mapped to soybean chromosome 6 (Gm06). Our objectives were to fine-map the Rpp?(Hyuuga) gene and develop a high-throughput single nucleotide polymorphism (SNP) assay to detect this ASR resistance gene. The integration of recombination events from two different soybean populations and the ASR reaction data indicates that the Rpp?(Hyuuga) locus is located in a region of approximately 371 kb between STS70887 and STS70923 on chromosome Gm06. A set of 32 ancestral genotypes which is predicted to contain 95% of the alleles present in current elite North American breeding populations and the sources of the previously reported ASR resistance genes (Rpp1, Rpp2, Rpp3, Rpp4, Rpp5, and rpp5) were genotyped with five SNP markers. We developed a SimpleProbe assay based on melting curve analysis for SNP06-44058 which is tighly linked to the Rpp?(Hyuuga) gene. This SNP assay can differentiate plants/lines that are homozygous/homogeneous or heterozygous/heterogeneous for the resistant and susceptible alleles at the Rpp?(Hyuuga) locus

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Formation of Toxic Oligomeric α-Synuclein Species in Living Cells

Background: Misfolding, oligomerization, and fibrillization of α-synuclein are thought to be central events in the onset and progression of Parkinson's disease (PD) and related disorders. Although fibrillar α-synuclein is a major component of Lewy bodies (LBs), recent data implicate prefibrillar, oligomeric intermediates as the toxic species. However, to date, oligomeric species have not been identified in living cells. Methodology/Principal Findings: Here we used bimolecular fluorescence complementation (BiFC) to directly visualize α-synuclein oligomerization in living cells, allowing us to study the initial events leading to α-synuclein oligomerization, the precursor to aggregate formation. This novel assay provides us with a tool with which to investigate how manipulations affecting α-synuclein aggregation affect the process over time. Stabilization of α-synuclein oligomers via BiFC results in increased cytotoxicity, which can be rescued by Hsp70 in a process that reduces the formation of α-synuclein oligomers. Introduction of PD-associated mutations in α-synuclein did not affect oligomer formation but the biochemical properties of the mutant α-synuclein oligomers differ from those of wild type α-synuclein. Conclusions/Significance: This novel application of the BiFC assay to the study of the molecular basis of neurodegenerative disorders enabled the direct visualization of α-synuclein oligomeric species in living cells and its modulation by Hsp70, constituting a novel important tool in the search for therapeutics for synucleinopathies

Torsional angle dependence and switching of inner sphere reorganisation energies for electron and hole charge transfer processes involving phenyl substituted diketopyrrolopyrroles; a density functional study

This document is the Accepted Manuscript version of the following article: Jesus Calvo-Castro, Callum J. McHugh, Andrew J. McLean, ‘Torsional angle dependence and switching of inner sphere reorganisation energies for electron and hole transfer processes involving phenyl substituted diketopyrrolopyrroles; a density functional study’, Dyes and Pigments, Vol. 113, pp. 609-617, February 2015. The Version of Record is available online at doi: https://doi.org/10.1016/j.dyepig.2014.09.031. Published by Elsevier.Determination of inner sphere reorganisation energies is important in the development of organic charge mediating materials and electron transfer reactions. In this study, hole and electron inner sphere reorganisation energies, lambda(h) and lambda(e) respectively, have been computed for the first time for a series of structurally related diketopyrrolopyrrole (DPP) molecular motifs. Inner sphere reorganisation energies for self-exchange electron transfer reactions are calculated as being lower than those associated hole transfer processes in model planar phenyl and thiophenyl substituted DPP systems. It is found that lambda(e) lambda(h).Peer reviewedFinal Accepted Versio

First Observation of τ→3πηντ\tau\to 3\pi\eta\nu_{\tau} and τ→f1πντ\tau\to f_{1}\pi\nu_{\tau} Decays

We have observed new channels for $\tau$ decays with an $\eta$ in the final state. We study 3-prong tau decays, using the $\eta\to\gamma\gamma$ and \eta\to 3\piz decay modes and 1-prong decays with two \piz's using the $\eta\to\gamma\gamma$ channel. The measured branching fractions are \B(\tau^{-}\to \pi^{-}\pi^{-}\pi^{+}\eta\nu_{\tau}) =(3.4^{+0.6}_{-0.5}\pm0.6)\times10^{-4} and \B(\tau^{-}\to \pi^{-}2\piz\eta\nu_{\tau} =(1.4\pm0.6\pm0.3)\times10^{-4}. We observe clear evidence for $f_1\to\eta\pi\pi$ substructure and measure \B(\tau^{-}\to f_1\pi^{-}\nu_{\tau})=(5.8^{+1.4}_{-1.3}\pm1.8)\times10^{-4}. We have also searched for $\eta'(958)$ production and obtain 90% CL upper limits \B(\tau^{-}\to \pi^{-}\eta'\nu_\tau)<7.4\times10^{-5} and \B(\tau^{-}\to \pi^{-}\piz\eta'\nu_\tau)<8.0\times10^{-5}.Comment: 11 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Search for the Decays B^0 -> D^{(*)+} D^{(*)-}

Using the CLEO-II data set we have searched for the Cabibbo-suppressed decays B^0 -> D^{(*)+} D^{(*)-}. For the decay B^0 -> D^{*+} D^{*-}, we observe one candidate signal event, with an expected background of 0.022 +/- 0.011 events. This yield corresponds to a branching fraction of Br(B^0 -> D^{*+} D^{*-}) = (5.3^{+7.1}_{-3.7}(stat) +/- 1.0(syst)) x 10^{-4} and an upper limit of Br(B^0 -> D^{*+} D^{*-}) D^{*\pm} D^\mp and B^0 -> D^+ D^-, no significant excess of signal above the expected background level is seen, and we calculate the 90% CL upper limits on the branching fractions to be Br(B^0 -> D^{*\pm} D^\mp) D^+ D^-) < 1.2 x 10^{-3}.Comment: 12 page postscript file also available through http://w4.lns.cornell.edu/public/CLNS, submitted to Physical Review Letter