General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it includes Appendi

Allelic variants of the amylose extender mutation of maize demonstrate phenotypic variation in starch structure resulting from modified protein–protein interactions

amylose extender (ae−) starches characteristically have modified starch granule morphology resulting from amylopectin with reduced branch frequency and longer glucan chains in clusters, caused by the loss of activity of the major starch branching enzyme (SBE), which in maize endosperm is SBEIIb. A recent study with ae− maize lacking the SBEIIb protein (termed ae1.1 herein) showed that novel protein–protein interactions between enzymes of starch biosynthesis in the amyloplast could explain the starch phenotype of the ae1.1 mutant. The present study examined an allelic variant of the ae− mutation, ae1.2, which expresses a catalytically inactive form of SBEIIb. The catalytically inactive SBEIIb in ae1.2 lacks a 28 amino acid peptide (Val272–Pro299) and is unable to bind to amylopectin. Analysis of starch from ae1.2 revealed altered granule morphology and physicochemical characteristics distinct from those of the ae1.1 mutant as well as the wild-type, including altered apparent amylose content and gelatinization properties. Starch from ae1.2 had fewer intermediate length glucan chains (degree of polymerization 16–20) than ae1.1. Biochemical analysis of ae1.2 showed that there were differences in the organization and assembly of protein complexes of starch biosynthetic enzymes in comparison with ae1.1 (and wild-type) amyloplasts, which were also reflected in the composition of starch granule-bound proteins. The formation of stromal protein complexes in the wild-type and ae1.2 was strongly enhanced by ATP, and broken by phosphatase treatment, indicating a role for protein phosphorylation in their assembly. Labelling experiments with [γ-32P]ATP showed that the inactive form of SBEIIb in ae1.2 was phosphorylated, both in the monomeric form and in association with starch synthase isoforms. Although the inactive SBEIIb was unable to bind starch directly, it was strongly associated with the starch granule, reinforcing the conclusion that its presence in the granules is a result of physical association with other enzymes of starch synthesis. In addition, an Mn2+-based affinity ligand, specific for phosphoproteins, was used to show that the granule-bound forms of SBEIIb in the wild-type and ae1.2 were phosphorylated, as was the granule-bound form of SBEI found in ae1.2 starch. The data strongly support the hypothesis that the complement of heteromeric complexes of proteins involved in amylopectin synthesis contributes to the fine structure and architecture of the starch granule

Further Evidence for the Decay K+ to pi+ neutrino-antineutrino

Additional evidence for the rare kaon decay K+ to pi+ neutrino-antineutrino has been found in a new data set with comparable sensitivity to the previously reported result. One new event was observed in the pion momentum region examined, 211<P<229 MeV/c, bringing the total for the combined data set to two. Including all data taken, the backgrounds were estimated to contribute 0.15 pm 0.05 events. The branching ratio is B=1.57^{+1.75}_{-0.82} 10^{-10}.Comment: 10 pages, 2 figure

Search for the decay K+→π+ννˉK^+\to \pi^+ \nu \bar\nu in the momentum region Pπ<195 MeV/cP_\pi < 195 {\rm ~MeV/c}

We have searched for the decay $K^+ \to \pi^+ \nu \bar\nu$ in the kinematic region with pion momentum below the $K^+ \to \pi^+ \pi^0$ peak. One event was observed, consistent with the background estimate of $0.73\pm 0.18$. This implies an upper limit on $B(K^+ \to \pi^+ \nu \bar\nu)< 4.2\times 10^{-9}$ (90% C.L.), consistent with the recently measured branching ratio of $(1.57^{+1.75}_{-0.82}) \times 10^{-10}$, obtained using the standard model spectrum and the kinematic region above the $K^+ \to \pi^+ \pi^0$ peak. The same data were used to search for $K^+ \to \pi^+ X^0$, where $X^0$ is a weakly interacting neutral particle or system of particles with $150 < M_{X^0} < 250 {\rm ~MeV/c^2}$.Comment: 4 pages, 2 figure

Measurement of Direct Photon Emission in K^+ -> pi^+ pi^0 gamma Decay

We have performed a measurement of the K^+ -> pi^+ pi^0 gamma decay and have observed 2 X 10^4 events. The best fit to the decay spectrum gives a branching ratio for direct photon emission of (4.7\pm0.8\pm0.3) X 10^{-6} in the pi^+ kinetic energy region of 55 to 90 MeV and requires no component due to interference with inner bremsstrahlung.Comment: 9 pages, 3 figures. To be submitted to PR

The CLIC positron source based on compton schemes

The CLIC polarized positron source is based on a positron production scheme in which polarized photons are produced by a Compton process. In one option, Compton backscattering takes place in a so-called “Compton ring”, where an electron beam of 1 GeV interacts with circularly-polarized photons in an optical resonator. The resulting circularly-polarized gamma photons are sent on to an amorphous target, producing pairs of longitudinally polarized electrons and positrons. The nominal CLIC bunch population is 4.2x109 particles per bunch at the exit of the Pre-Damping Ring (PDR). Since the photon flux coming out from a "Compton ring" is not sufficient to obtain the requested charge, a stacking process is required in the PDR. Another option is to use a Compton Energy Recovery Linac (ERL) where a quasicontinual stacking in the PDR could be achieved. A third option is to use a "Compton Linac" which would not require stacking. We describe the overall scheme as well as advantages and constraints of the three options

The CLIC Positron Sources Based on Compton Schemes

International audienceThe CLIC polarized positron source is based on a positron production scheme in which polarized photons are produced by Compton process. Compton backscattering happens in a so-called "Compton ring" where an electron beam of 1.06 GeV interacts with a powerful laser beam amplified in an optical resonator. The circularly-polarized gamma rays are sent on to a target, producing pairs of longitudinally polarized electrons and positrons. An Adiabatic Matching Device maximizes the capture of the positrons. A normal-conducting 2 GHz Linac accelerates the beam up to 2.424 GeV before injection into the Pre-Damping Ring (PDR). The nominal CLIC bunch population is 4.4x10**9 particles per bunch. Since the photon flux coming out from a "Compton ring" is not sufficient to obtain the requested charge, a stacking process is required in the PDR. Another option is to use a "Compton Energy Recovery Linac" where a quasi-continual stacking in the PDR could be achieved. A third option is to use a "Compton Linac" which would not require stacking. We describe the overall scheme as well as advantages and constraints of the three different options

Measurement of the Proton and Deuteron Spin Structure Function g_1 in the Resonance Region

We have measured the proton and deuteron spin structure functions g_1^p and g_1^d in the region of the nucleon resonances for W^2 < 5 GeV^2 and $Q^2\simeq 0.5$ and $Q^2\simeq 1.2$ GeV^2 by inelastically scattering 9.7 GeV polarized electrons off polarized $^{15}NH_3$ and $^{15}ND_3$ targets. We observe significant structure in g_1^p in the resonance region. We have used the present results, together with the deep-inelastic data at higher W^2, to extract $\Gamma(Q^2)\equiv\int_0^1 g_1(x,Q^2) dx$. This is the first information on the low-Q^2 evolution of Gamma toward the Gerasimov-Drell-Hearn limit at Q^2 = 0.Comment: 7 pages, 2 figure

Precision Determination of the Neutron Spin Structure Function g1n

We report on a precision measurement of the neutron spin structure function $g^n_1$ using deep inelastic scattering of polarized electrons by polarized ^3He. For the kinematic range 0.014<x<0.7 and 1 (GeV/c)^2< Q^2< 17 (GeV/c)^2, we obtain $\int^{0.7}_{0.014} g^n_1(x)dx = -0.036 \pm 0.004 (stat) \pm 0.005 (syst)$ at an average $Q^2=5 (GeV/c)^2$. We find relatively large negative values for $g^n_1$ at low $x$. The results call into question the usual Regge theory method for extrapolating to x=0 to find the full neutron integral $\int^1_0 g^n_1(x)dx$, needed for testing quark-parton model and QCD sum rules.Comment: 5 pages, 3 figures To be published in Phys. Rev. Let

Discrimination of Timbre in Early Auditory Responses of the Human Brain

The issue of how differences in timbre are represented in the neural response still has not been well addressed, particularly with regard to the relevant brain mechanisms. Here we employ phasing and clipping of tones to produce auditory stimuli differing to describe the multidimensional nature of timbre. We investigated the auditory response and sensory gating as well, using by magnetoencephalography (MEG).Thirty-five healthy subjects without hearing deficit participated in the experiments. Two different or same tones in timbre were presented through conditioning (S1) – testing (S2) paradigm as a pair with an interval of 500 ms. As a result, the magnitudes of auditory M50 and M100 responses were different with timbre in both hemispheres. This result might support that timbre, at least by phasing and clipping, is discriminated in the auditory early processing. The second response in a pair affected by S1 in the consecutive stimuli occurred in M100 of the left hemisphere, whereas both M50 and M100 responses to S2 only in the right hemisphere reflected whether two stimuli in a pair were the same or not. Both M50 and M100 magnitudes were different with the presenting order (S1 vs. S2) for both same and different conditions in the both hemispheres.Our results demonstrate that the auditory response depends on timbre characteristics. Moreover, it was revealed that the auditory sensory gating is determined not by the stimulus that directly evokes the response, but rather by whether or not the two stimuli are identical in timbre