Dirichlet spaces on H-convex sets in Wiener space

We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$. We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset if $U$ is $H$-convex and $H$-open. For the proof, the relations between $H$-notions and quasi-notions are also studied.Comment: 18 pages, 1 figure. Erratum has been added, which was accepted for publication in Bull. Sci. Mat

LD-Spline: Mapping SNPs on genotyping platforms to genomic regions using patterns of linkage disequilibrium

<p>Abstract</p> <p>Background</p> <p>Gene-centric analysis tools for genome-wide association study data are being developed both to annotate single locus statistics and to prioritize or group single nucleotide polymorphisms (SNPs) prior to analysis. These approaches require knowledge about the relationships between SNPs on a genotyping platform and genes in the human genome. SNPs in the genome can represent broader genomic regions via linkage disequilibrium (LD), and population-specific patterns of LD can be exploited to generate a data-driven map of SNPs to genes.</p> <p>Methods</p> <p>In this study, we implemented LD-Spline, a database routine that defines the genomic boundaries a particular SNP represents using linkage disequilibrium statistics from the International HapMap Project. We compared the LD-Spline haplotype block partitioning approach to that of the four gamete rule and the Gabriel et al. approach using simulated data; in addition, we processed two commonly used genome-wide association study platforms.</p> <p>Results</p> <p>We illustrate that LD-Spline performs comparably to the four-gamete rule and the Gabriel et al. approach; however as a SNP-centric approach LD-Spline has the added benefit of systematically identifying a genomic boundary for each SNP, where the global block partitioning approaches may falter due to sampling variation in LD statistics.</p> <p>Conclusion</p> <p>LD-Spline is an integrated database routine that quickly and effectively defines the genomic region marked by a SNP using linkage disequilibrium, with a SNP-centric block definition algorithm.</p

Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control

Optical phase estimation is a vital measurement primitive that is used to perform accurate measurements of various physical quantities like length, velocity and displacements. The precision of such measurements can be largely enhanced by the use of entangled or squeezed states of light as demonstrated in a variety of different optical systems. Most of these accounts however deal with the measurement of a very small shift of an already known phase, which is in stark contrast to ab-initio phase estimation where the initial phase is unknown. Here we report on the realization of a quantum enhanced and fully deterministic phase estimation protocol based on real-time feedback control. Using robust squeezed states of light combined with a real-time Bayesian estimation feedback algorithm, we demonstrate deterministic phase estimation with a precision beyond the quantum shot noise limit. The demonstrated protocol opens up new opportunities for quantum microscopy, quantum metrology and quantum information processing.Comment: 5 figure

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be published in one of the AIP Conference Proceedings serie

Methods for specifying the target difference in a randomised controlled trial : the Difference ELicitation in TriAls (DELTA) systematic review

Peer reviewedPublisher PD

Calibrating the Performance of SNP Arrays for Whole-Genome Association Studies

To facilitate whole-genome association studies (WGAS), several high-density SNP genotyping arrays have been developed. Genetic coverage and statistical power are the primary benchmark metrics in evaluating the performance of SNP arrays. Ideally, such evaluations would be done on a SNP set and a cohort of individuals that are both independently sampled from the original SNPs and individuals used in developing the arrays. Without utilization of an independent test set, previous estimates of genetic coverage and statistical power may be subject to an overfitting bias. Additionally, the SNP arrays' statistical power in WGAS has not been systematically assessed on real traits. One robust setting for doing so is to evaluate statistical power on thousands of traits measured from a single set of individuals. In this study, 359 newly sampled Americans of European descent were genotyped using both Affymetrix 500K (Affx500K) and Illumina 650Y (Ilmn650K) SNP arrays. From these data, we were able to obtain estimates of genetic coverage, which are robust to overfitting, by constructing an independent test set from among these genotypes and individuals. Furthermore, we collected liver tissue RNA from the participants and profiled these samples on a comprehensive gene expression microarray. The RNA levels were used as a large-scale set of quantitative traits to calibrate the relative statistical power of the commercial arrays. Our genetic coverage estimates are lower than previous reports, providing evidence that previous estimates may be inflated due to overfitting. The Ilmn650K platform showed reasonable power (50% or greater) to detect SNPs associated with quantitative traits when the signal-to-noise ratio (SNR) is greater than or equal to 0.5 and the causal SNP's minor allele frequency (MAF) is greater than or equal to 20% (N = 359). In testing each of the more than 40,000 gene expression traits for association to each of the SNPs on the Ilmn650K and Affx500K arrays, we found that the Ilmn650K yielded 15% times more discoveries than the Affx500K at the same false discovery rate (FDR) level

Strong vacuum squeezing from bichromatically driven Kerrlike cavities: from optomechanics to superconducting circuits

Squeezed light, displaying less fluctuation than vacuum in some observable, is key in the flourishing field of quantum technologies. Optical or microwave cavities containing a Kerr nonlinearity are known to potentially yield large levels of squeezing, which have been recently observed in optomechanics and nonlinear superconducting circuit platforms. Such Kerr-cavity squeezing however suffers from two fundamental drawbacks. First, optimal squeezing requires working close to turning points of a bistable cycle, which are highly unstable against noise thus rendering optimal squeezing inaccessible. Second, the light field has a macroscopic coherent component corresponding to the pump, making it less versatile than the so-called squeezed vacuum, characterised by a null mean field. Here we prove analytically and numerically that the bichromatic pumping of optomechanical and superconducting circuit cavities removes both limitations. This finding should boost the development of a new generation of robust vacuum squeezers in the microwave and optical domains with current technology

Becoming original: effects of strategy instruction

Visual arts education focuses on creating original visual art products. A means to improve originality is enhancement of divergent thinking, indicated by fluency, flexibility and originality of ideas. In regular arts lessons, divergent thinking is mostly promoted through brainstorming. In a previous study, we found positive effects of an explicit instruction of metacognition on fluency and flexibility in terms of the generation of ideas, but not on the originality of ideas. Therefore, we redesigned the instruction with a focus on building up knowledge about creative generation strategies by adding more complex types of association, and adding generation through combination and abstraction. In the present study, we examined the effects of this intervention by comparing it with regular brainstorming instruction. In a pretest-posttest control group design, secondary school students in the comparison condition received the brainstorm lesson and students in the experimental condition received the newly developed instruction lesson. To validate the effects, we replicated this study with a second cohort. The results showed that in both cohorts the strategy instruction of 50 min had positive effects on students' fluency, flexibility and originality. This study implies that instructional support in building up knowledge about creative generation strategies may improve students' creative processes in visual arts education