Neutrino oscillations in de Sitter space-time

We try to understand flavor oscillations and to develop the formulae for describing neutrino oscillations in de Sitter space-time. First, the covariant Dirac equation is investigated under the conformally flat coordinates of de Sitter geometry. Then, we obtain the exact solutions of the Dirac equation and indicate the explicit form of the phase of wave function. Next, the concise formulae for calculating the neutrino oscillation probabilities in de Sitter space-time are given. Finally, The difference between our formulae and the standard result in Minkowski space-time is pointed out.Comment: 13 pages, no figure

Analysis of the Movement of Chlamydomonas Flagella: The Function of the Radial-spoke System Is Revealed by Comparison of Wild-type and Mutant Flagella

The mutation uni-1 gives rise to uniflagellate Chlamydomonas cells which rotate around a fixed point in the microscope field, so that the flagellar bending pattern can be photographed easily . This has allowed us to make a detailed analysis of the wild-type flagellar bending pattern and the bending patterns of flagella on several mutant strains. Cells containing uni-1, and recombinants of uni-1 with the suppressor mutations, sup(_pf)-1 and sup(_pf)-3, show the typical asymmetric bending pattern associated with forward swimming in Chlamydomonas, although sup(_pf)-1 flagella have about one-half the normal beat frequency, apparently as the result of defective function of the outer dynein arms. The pf-17 mutation has been shown to produce nonmotile flagella in which radial spoke heads and five characteristic axonemal polypeptides are missing. Recombinants containing pf-17 and either sup(_pf)-1 or sup(_pf)-3 have motile flagella, but still lack radial-spoke heads and the associated polypeptides . The flagellar bending pattern of these recombinants lacking radial-spoke heads is a nearly symmetric, large amplitude pattern which is quite unlike the wild-type pattern . However, the presence of an intact radial-spoke system is not required to convert active sliding into bending and is not required for bend initiation and bend propagation, since all of these processes are active in the sup(_pf) pf-17 recombinants. The function of the radial-spoke system appears to be to convert the symmetric bending pattern displayed by these recombinants into the asymmetric bending pattern required for efficient swimming, by inhibiting the development of reverse bends during the recovery phase of the bending cycle

Measuring reproducibility of high-throughput experiments

Reproducibility is essential to reliable scientific discovery in high-throughput experiments. In this work we propose a unified approach to measure the reproducibility of findings identified from replicate experiments and identify putative discoveries using reproducibility. Unlike the usual scalar measures of reproducibility, our approach creates a curve, which quantitatively assesses when the findings are no longer consistent across replicates. Our curve is fitted by a copula mixture model, from which we derive a quantitative reproducibility score, which we call the "irreproducible discovery rate" (IDR) analogous to the FDR. This score can be computed at each set of paired replicate ranks and permits the principled setting of thresholds both for assessing reproducibility and combining replicates. Since our approach permits an arbitrary scale for each replicate, it provides useful descriptive measures in a wide variety of situations to be explored. We study the performance of the algorithm using simulations and give a heuristic analysis of its theoretical properties. We demonstrate the effectiveness of our method in a ChIP-seq experiment.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS466 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The breakage prediction for hydromechanical deep drawing based on local bifurcation theory

A criterion of sheet metal localized necking under plane stress was established based on the bifurcation theory and the characteristics theory of differential equation. In order to be capable to incorporate the directional dependence of the plastic strain rate on stress rate, Ito-Goya’s constitutive equation which gave a one to one relationship between stress rate component and plastic strain rate component was employed. The hydromechanical deep drawing process of a cylindrical cup part was simulated using the commercial software ABAQUS IMPLICIT. The onset of breakage of the part during the forming process was predicted by combining the simulation results with the local necking criterion. The proposed method is applied to the hydro-mechanical deep drawing process for A2219 aluminum alloy sheet metal to predict the breakage of the cylindrical cup part. The proposed method can be applied to the prediction of breakage in the forming of the automotive bodies

Open-closed field algebras

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a \C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few references are adde

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Effects of Line-tying on Resistive Tearing Instability in Slab Geometry

The effects of line-tying on resistive tearing instability in slab geometry is studied within the framework of reduced magnetohydrodynamics (RMHD).\citep{KadomtsevP1974,Strauss1976} It is found that line-tying has a stabilizing effect. The tearing mode is stabilized when the system length $L$ is shorter than a critical length $L_{c}$, which is independent of the resistivity $\eta$. When $L$ is not too much longer than $L_{c}$, the growthrate $\gamma$ is proportional to $\eta$ . When $L$ is sufficiently long, the tearing mode scaling $\gamma\sim\eta^{3/5}$ is recovered. The transition from $\gamma\sim\eta$ to $\gamma\sim\eta^{3/5}$ occurs at a transition length $L_{t}\sim\eta^{-2/5}$.Comment: Correct a typ