Gravitational waves from BH-NS binaries: Effective Fisher matrices and parameter estimation using higher harmonics

Inspiralling black hole-neutron star (BH-NS) binaries emit a complicated gravitational wave signature, produced by multiple harmonics sourced by their strong local gravitational field and further modulated by the orbital plane's precession. Some features of this complex signal are easily accessible to ground-based interferometers (e.g., the rate of change of frequency); others less so (e.g., the polarization content); and others unavailable (e.g., features of the signal out of band). For this reason, an ambiguity function (a diagnostic of dissimilarity) between two such signals varies on many parameter scales and ranges. In this paper, we present a method for computing an approximate, effective Fisher matrix from variations in the ambiguity function on physically pertinent scales which depend on the relevant signal to noise ratio. As a concrete example, we explore how higher harmonics improve parameter measurement accuracy. As previous studies suggest, for our fiducial BH-NS binaries and for plausible signal amplitudes, we see that higher harmonics at best marginally improve our ability to measure parameters. For non-precessing binaries, these Fisher matrices separate into intrinsic (mass, spin) and extrinsic (geometrical) parameters; higher harmonics principally improve our knowledge about the line of sight. For the precessing binaries, the extra information provided by higher harmonics is distributed across several parameters. We provide concrete estimates for measurement accuracy, using coordinates adapted to the precession cone in the detector's sensitive band.Comment: 19 pages, 11 figure

Role of G{alpha}12 and G{alpha}13 as Novel Switches for the Activity of Nrf2, a Key Antioxidative Transcription Factor

G{alpha}12 and G{alpha}13 function as molecular regulators responding to extracellular stimuli. NF-E2-related factor 2 (Nrf2) is involved in a protective adaptive response to oxidative stress. This study investigated the regulation of Nrf2 by G{alpha}12 and G{alpha}13. A deficiency of G{alpha}12, but not of G{alpha}13, enhanced Nrf2 activity and target gene transactivation in embryo fibroblasts. In mice, G{alpha}12 knockout activated Nrf2 and thereby facilitated heme catabolism to bilirubin and its glucuronosyl conjugations. An oligonucleotide microarray demonstrated the transactivation of Nrf2 target genes by G{alpha}12 gene knockout. G{alpha}12 deficiency reduced Jun N-terminal protein kinase (JNK)-dependent Nrf2 ubiquitination required for proteasomal degradation, and so did G{alpha}13 deficiency. The absence of G{alpha}12, but not of G{alpha}13, increased protein kinase C {delta} (PKC {delta}) activation and the PKC {delta}-mediated serine phosphorylation of Nrf2. G{alpha}13 gene knockout or knockdown abrogated the Nrf2 phosphorylation induced by G{alpha}12 deficiency, suggesting that relief from G{alpha}12 repression leads to the G{alpha}13-mediated activation of Nrf2. Constitutive activation of G{alpha}13 promoted Nrf2 activity and target gene induction via Rho-mediated PKC {delta} activation, corroborating positive regulation by G{alpha}13. In summary, G{alpha}12 and G{alpha}13 transmit a JNK-dependent signal for Nrf2 ubiquitination, whereas G{alpha}13 regulates Rho-PKC {delta}-mediated Nrf2 phosphorylation, which is negatively balanced by G{alpha}12

Tau functions as Widom constants

We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed as the Fredholm determinant of an integral operator with block integrable kernel constructed in terms of elementary parametrices. Its logarithmic derivatives with respect to parameters are given by contour integrals involving these parametrices and the solution of the Riemann-Hilbert problem. In the case of one circle, the tau function coincides with Widom's determinant arising in the asymptotics of block Toeplitz matrices. Our construction gives the Jimbo-Miwa-Ueno tau function for Riemann-Hilbert problems of isomonodromic origin (Painlev\'e VI, V, III, Garnier system, etc) and the Sato-Segal-Wilson tau function for integrable hierarchies such as Gelfand-Dickey and Drinfeld-Sokolov.Comment: 26 pages, 6 figure

Effect of Calcinated Oyster Shell Powder on Growth, Yield, Spawn Run, and Primordial Formation of King Oyster Mushroom (Pleurotus Eryngii)

This study was conducted to evaluate the calcium (Ca) absorption efficacy of king oyster mushroom (Pleurotus eryngii) grown on sawdust medium supplemented with Ca-sources, including oyster shell powder, and to determine the efficacy of oyster shell powder as a calcium supplement on growth, yield, spawn run and primordial formation of P. eryngii. Optimum calcination of oyster shell powder was achieved at the temperature of 620.56 degrees C. A 1% supplementation of oyster shell powder in sawdust medium did not suppress the mycelial growth of P. eryngii. Also the supplementation of 2% calcinated oyster shell powder to sawdust medium potentially increased the calcium content up to a level of 315.7 +/- 15.7 mg/100 g in the fruiting body of P. eryngii, without extension of duration of spawn run and the retardation of the days to primordial formation. These results suggest that the shellfish by-products, including oyster shell powder, can be utilized to develop calcium enriched king oyster mushrooms.open2