The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

Sensory innervation of the guinea pig colon and rectum compared using retrograde tracing and immunohistochemistry.

Embargoed until 2 April 2017 as per publisher's policy

Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Molecular architecture of Gαo and the structural basis for RGS16-mediated deactivation

Heterotrimeric G proteins relay extracellular cues from heptahelical transmembrane receptors to downstream effector molecules. Composed of an α subunit with intrinsic GTPase activity and a βγ heterodimer, the trimeric complex dissociates upon receptor-mediated nucleotide exchange on the α subunit, enabling each component to engage downstream effector targets for either activation or inhibition as dictated in a particular pathway. To mitigate excessive effector engagement and concomitant signal transmission, the Gα subunit's intrinsic activation timer (the rate of GTP hydrolysis) is regulated spatially and temporally by a class of GTPase accelerating proteins (GAPs) known as the regulator of G protein signaling (RGS) family. The array of G protein-coupled receptors, Gα subunits, RGS proteins and downstream effectors in mammalian systems is vast. Understanding the molecular determinants of specificity is critical for a comprehensive mapping of the G protein system. Here, we present the 2.9 Å crystal structure of the enigmatic, neuronal G protein Gαo in the GTP hydrolytic transition state, complexed with RGS16. Comparison with the 1.89 Å structure of apo-RGS16, also presented here, reveals plasticity upon Gαo binding, the determinants for GAP activity, and the structurally unique features of Gαo that likely distinguish it physiologically from other members of the larger Gαi family, affording insight to receptor, GAP and effector specificity

Overcoming Calibration Problems in Pattern Labeling with Pairwise Ratings: Application to Personality Traits

We address the problem of calibration of workers whose task is to label patterns with continuous variables, which arises for instance in labeling images of videos of humans with continuous traits. Worker bias is particularly difficult to evaluate and correct when many workers contribute just a few labels, a situation arising typically when labeling is crowd-sourced. In the scenario of labeling short videos of people facing a camera with personality traits, we evaluate the feasibility of the pairwise ranking method to alleviate bias problems. Workers are exposed to pairs of videos at a time and must order by preference. The variable levels are reconstructed by fitting a Bradley-Terry-Luce model with maximum likelihood. This method may at first sight, seem prohibitively expensive because for N videos, p=N(N−1)/2 pairs must be potentially processed by workers rather that N videos. However, by performing extensive simulations, we determine an empirical law for the scaling of the number of pairs needed as a function of the number of videos in order to achieve a given accuracy of score reconstruction and show that the pairwise method is affordable. We apply the method to the labeling of a large scale dataset of 10,000 videos used in the ChaLearn Apparent Personality Trait challenge

Hamiltonian analysis of Poincar\'e gauge theory scalar modes

The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The explicit form of the Hamiltonian is presented. All constraints are obtained and classified. The Lagrange multipliers are derived. It is shown that a massive spin-$0^-$ mode has normal dynamical propagation but the associated massless $0^-$ is pure gauge. The spin-$0^+$ mode investigated here is also viable in general. Both modes exhibit a simple type of ``constraint bifurcation'' for certain special field/parameter values.Comment: 28 pages, LaTex, submitted to International Journal of Modern Physics

Chemistry in Infrared Dark Cloud Clumps: a Molecular Line Survey at 3 mm

We have observed 37 Infrared Dark Clouds (IRDCs), containing a total of 159 clumps, in high-density molecular tracers at 3 mm using the 22-meter ATNF Mopra Telescope located in Australia. After determining kinematic distances, we eliminated clumps that are not located in IRDCs and clumps with a separation between them of less than one Mopra beam. Our final sample consists of 92 IRDC clumps. The most commonly detected molecular lines are (detection rates higher than 8%): N2H+, HNC, HN13C, HCO+, H13CO+, HCN, C2H, HC3N, HNCO, and SiO. We investigate the behavior of the different molecular tracers and look for chemical variations as a function of an evolutionary sequence based on Spitzer IRAC and MIPS emission. We find that the molecular tracers behave differently through the evolutionary sequence and some of them can be used to yield useful relative age information. The presence of HNC and N2H+ lines do not depend on the star formation activity. On the other hand, HC3N, HNCO, and SiO are predominantly detected in later stages of evolution. Optical depth calculations show that in IRDC clumps the N2H+ line is optically thin, the C2H line is moderately optically thick, and HNC and HCO+ are optically thick. The HCN hyperfine transitions are blended, and, in addition, show self-absorbed line profiles and extended wing emission. These factors combined prevent the use of HCN hyperfine transitions for the calculation of physical parameters. Total column densities of the different molecules, except C2H, increase with the evolutionary stage of the clumps. Molecular abundances increase with the evolutionary stage for N2H+ and HCO+. The N2H+/HCO+ and N2H+/HNC abudance ratios act as chemical clocks, increasing with the evolution of the clumps.Comment: Accepted to ApJ. 29 page

Experimental demonstration of a BDCZ quantum repeater node

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, D\"{u}r, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.Comment: 5 pages, 4 figure

Influence of gauge-field fluctuations on composite fermions near the half-filled state

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial \mu} \propto e^{- \Delta \omega_c / 2 T} \left ( 1 + {A (\eta) \over \eta - 1} {(\Delta \omega_c)^{2 \over 1 + \eta} \over T} \right )$ for $T \ll \Delta \omega_c$, where $\Delta \omega_c = {e \Delta B \over mc}$. Here we assume that the interaction between the fermions is given by $v ({\bf q}) = V_0 / q^{2 - \eta} \ (1 \le \eta \le 2)$, where $A (\eta)$ is a $\eta$ dependent constant. This result can be interpreted as a divergent correction to the activation energy gap and is consistent with the divergent renormalization of the effective mass of the composite fermions.Comment: Plain Tex, 24 pages, 5 figures available upon reques