The Singular Values of the GOE

As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are distributed as the positive eigenvalues of a Gaussian ensemble with chiral unitary symmetry (anti-GUE), while the odd-location singular values, conditioned on the even-location ones, can be algebraically transformed into a set of independent $\chi$-distributed random variables. We discuss three applications of this structure: first, there is a pair of bidiagonal square matrices, whose singular values are jointly distributed as the even- and odd-location ones of the GOE; second, the magnitude of the determinant of the GOE is distributed as a product of simple independent random variables; third, on symmetric intervals, the gap probabilities of the GOE can be expressed in terms of the Laguerre unitary ensemble (LUE). We work specifically with matrices of finite order, but by passing to a large matrix limit, we also obtain new insight into asymptotic properties such as the central limit theorem of the determinant or the gap probabilities in the bulk-scaling limit. The analysis in this paper avoids much of the technical machinery (e.g. Pfaffians, skew-orthogonal polynomials, martingales, Meijer $G$-function, etc.) that was previously used to analyze some of the applications.Comment: Introduction extended, typos corrected, reference added. 31 pages, 1 figur

Strategic Announcements of Reference Points in Disputes and Litigations

This note shows how the frequent occurrence of seeing exceedingly high claims in disputes and litigations can be rationalized by a model in which claimants display reference dependent preferences, expect the judge to use a generalized social welfare function, and strategically announce their reference points.reference points, claims, litigations

Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlev\'e II Transcendents

The stability and convergence rate of Olver's collocation method for the numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very sensitively on the particular choice of contours used as data of the RHP. By manually performing contour deformations that proved to be successful in the asymptotic analysis of RHPs, such as the method of nonlinear steepest descent, the numerical method can basically be preconditioned, making it asymptotically stable. In this paper, however, we will show that most of these preconditioning deformations, including lensing, can be addressed in an automatic, completely algorithmic fashion that would turn the numerical method into a black-box solver. To this end, the preconditioning of RHPs is recast as a discrete, graph-based optimization problem: the deformed contours are obtained as a system of shortest paths within a planar graph weighted by the relative strength of the jump matrices. The algorithm is illustrated for the RHP representing the Painlev\'e II transcendents.Comment: 20 pages, 16 figure

Distinct agonist regulation of muscarinic acetylcholine M2-M3 heteromers and their corresponding homomers

Each subtype of the muscarinic receptor family of G protein-coupled receptors is activated by similar concentrations of the neurotransmitter acetylcholine or closely related synthetic analogs such as carbachol. However, pharmacological selectivity can be generated by the introduction of a pair of mutations to produce Receptor Activated Solely by Synthetic Ligand (RASSL) forms of muscarinic receptors. These display loss of potency for acetylcholine/carbachol alongside a concurrent gain in potency for the ligand clozapine N-oxide. Co-expression of a form of wild type human M2 and a RASSL variant of the human M3 receptor resulted in concurrent detection of each of M2-M2 and M3-M3 homomers alongside M2-M3 heteromers at the surface of stably transfected Flp-InTM T-RExTM 293 cells. In this setting occupancy of the receptors with a muscarinic antagonist was without detectable effect on any of the muscarinic oligomers. However, selective agonist occupancy of the M2 receptor resulted in enhanced M2-M2 homomer interactions but decreased M2-M3 heteromer interactions. By contrast, selective activation of the M3 RASSL receptor did not significantly alter either M3-M3 homomer or M2-M3 heteromer interactions. Selectively targeting closely related receptor oligomers may provide novel therapeutic opportunities

Different Characteristics of the Bright Branches of the Globular Clusters M3 and M13

We carried out wide-field BVI CCD photometric observations of the GCs M3 and M13 using the BOAO 1.8 m telescope equipped with a 2K CCD. We present CMDs of M3 and M13. We have found AGB bumps at V = 14.85 for M3 at V = 14.25 for M13. It is found that AGB stars in M3 are more concentrated near the bump, while those in M13 are scattered along the AGB sequence. We identified the RGB bump of M3 at V = 15.50 and that of M13 at V = 14.80. We have estimated the ratios R and R2 for M3 and M13 and found that of R for M3 is larger than that for M13 while R2's for M3 and M13 are similar when only normal HB stars are used in R and R2 for M13. However, we found that R's for M3 and M13 are similar while R2 for M3 is larger than that for M13 when all the HB stars are included in R and R2 for M13. We have compared the observed RGB LFs of M3 and M13 with the theoretical RGB LF of Bergbusch & VandenBerg at the same radial distances from the cluster centers as used in R and R2 for M3 and M13. We found "extra stars" belonging to M13 in the comparison of the observed RGB LF of M13 and the theoretical RGB LF of Bergbusch & VandenBerg. In the original definition of R of Buzzoni et al., N(HB) corresponds to the lifetime of HB stars in the RR Lyrae instability strip at log T_eff = 3.85. So, the smaller R value resulting for M13 compared with that for M3 in the case where only normal HB stars are included in R and R2 for M13 may be partially caused by "extra stars", and the similar R's for M3 and M13 in the case where the all HB stars are included in R and R2 for M13 may be caused by "extra stars" in the upper RGB of M13. If "extra stars" in the upper RGB of M13 are caused by an effective "deep mixing" these facts support the contention that an effective "deep mixing" could lead to different HB morphologies between M3 and M13 and subsequent sequences.Comment: 24 pages, 7 figures, to be published in the A

Effects of plant growth promoting rhizobacteria (PGPR) on yield,growth and nutrient contents in organically growing raspberry

During 2003 and 2005, plant growth promoting effects of two Bacillus strains OSU-142 (N2-fixing) and M3 (N2-fixing and phosphate solubilizing) were tested alone or in combinations on organically grown primocane fruiting raspberry (cv. Heritage) plants in terms of yield, growth, nutrient composition of leaves and variation of soil nutrient element composition in the province of Erzurum, Turkey. The results showed that Bacillus M3 treatment stimulated plant growth and resulted in significant yield increase. Inoculation of raspberry plant roots and rhizosphere with M3 and/or OSU-142 + M3, significantly increased yield (33.9% and 74.9%), cane length (13.6% and 15.0%), number of cluster per cane (25.4% and 28.7%) and number of berries per cane (25.1% and 36.0%) compared with the control, respectively. In addition, N, P and Ca contents of raspberry leaves with OSU-142 + M3 treatment, and Fe and Mn contents of the leaves of raspberry with M3 and OSU-142 + M3 applications significantly improved under organic growing conditions. Bacterial applications also significantly effected soil total N, available P, K, Ca, Mg, Fe, Mn, Zn contents and pH. Available P contents in soil was determined to be increased from 1.55 kg P2O5/da at the beginning of the study to 2.83 kg P2O5/da by OSU-142, to 5.36 kg P2O5/da by M3 and to 4.71 kg P2O5/da by OSU-142 + M3 treatments. The results of this study suggest that Bacillus M3 alone or in combination with Bacillus OSU-142 have the potential to increase the yield, growth and nutrition of raspberry plant under organic growing conditions

Effects of plant growth promoting bacteria (PGPB) on yield, growth and nutrient contents of organically grown strawberry

The effects of plant growth promoting bacteria (PGPB) on the fruit yield, growth and nutrient element content of strawberry cv. Fern were investigated under organic growing conditions between 2006 and 2008. The experimental plot was a completely randomized design with 3 replicates. Three PGPB strains (Pseudomonas BA-8, Bacillus OSU-142 and Bacillus M-3) were used alone or in combination as biofertilizer agent in the experiment. Data through 3 years showed that the use of PGPB significantly increased fruit yield, plant growth and leaf P and Zn contents. Root inoculation of M3 and floral and foliar spraying of OSU-142 and BA-8 bacteria stimulated plant growth resulting in significant yield increases. M3 + BA-8, BA-8 + OSU-142, M3, M3 + OSU-142 and BA-8 applications increased cumulative yield by 33.2%, 18.4%, 18.2%, 15.3% and 10.5%, respectively. Number of fruits per plant significantly increased by the applications of M3 + BA-8 (91.73) and M3 (81.58) compared with the control (68.66). In addition, P and Zn contents of strawberry leaves with bacterial inoculation significantly increased under organic growing conditions. Available P contents in soil were increased from 0.35 kg P2O5/da at the beginning of the study to 2.00, 1.97 and 1.82 kg P2O5/da by M3 + OSU-142, M3 + BA-8 and M3 + BA-8 + OSU-142 applications, respectively. Overall, the results of this study suggest that root inoculation of Bacillus M3 alone or in combination with spraying Bacillus OSU-142 or Pseudomonas BA-8 have the potential to increase the yield, growth and nutrition content of strawberry plant under organic growing conditions

Spectroscopy of 50^{50}Sc and ab initio calculations of B(M3)B(M3) strengths

The GRIFFIN spectrometer at TRIUMF-ISAC has been used to study excited states and transitions in $^{50}$Sc following the $\beta$-decay of $^{50}$Ca. Branching ratios were determined from the measured $\gamma$-ray intensities, and angular correlations of $\gamma$ rays have been used to firmly assign the spins of excited states. The presence of an isomeric state that decays by an $M3$ transition with a $B(M3)$ strength of 13.6(7)\,W.u. has been confirmed. We compare with the first {\it ab initio} calculations of $B(M3$) strengths in light and medium-mass nuclei from the valence-space in-medium similarity renormalization group approach, using consistently derived effective Hamiltonians and $M3$ operator. The experimental data are well reproduced for isoscalar $M3$ transitions when using bare $g$-factors, but the strength of isovector $M3$ transitions are found to be underestimated by an order of magnitude