Large Sample Asymptotic Theory of Tests for Uniformity on the Grassmann Manifold

AbstractThe Grassmann manifold Gk,m − k consists of k-dimensional linear subspaces V in Rm. To each V in Gk,m − k, corresponds a unique m × m orthogonal projection matrix P idempotent of rank k. Let Pk,m − k denote the set of all such orthogonal projection matrices. We discuss distribution theory on Pk,m − k, presenting the differential form for the invariant measure and properties of the uniform distribution, and suggest a general family F(P) of non-uniform distributions. We are mainly concerned with large sample asymptotic theory of tests for uniformity on Pk,m − k. We investigate the asymptotic distribution of the standardized sample mean matrix U taken from the family F(P) under a sequence of local alternatives for large sample size n. For tests of uniformity versus the matrix Langevin distribution which belongs to the family F(P), we consider three optimal tests-the Rayleigh-style, the likelihood ratio, and the locally best invariant tests. They are discussed in relation to the statistic U, and are shown to be approximately, near uniformity, equivalent to one another. Zonal and invariant polynomials in matrix arguments are utilized in derivations

GDP, share prices and share returns: Australian and New Zealand evidence

With the aim of predicting share market returns, many empirical studies have delved into how financial and macroeconomic variables can be used to forecast return variability. The aim of this paper is to examine whether the ratio of aggregate share price to GDP can capture the variation of future returns on the aggregate share market within Australia and New Zealand. Using quarterly and semi-annual data for the period 1991-2003 for New Zealand and 1982-2006 for Australia, this study finds that the ratio of share price to GDP indeed captures a significant amount of the variation of returns on the New Zealand share market as well as the Australian share market; however results for Australian data do vary, depending on the sample period. Results in this paper generally provide support for the theory behind previous papers, specifically that of Rangvid (2006)

Comparison of quantum mechanical and classical trajectory calculations of cross sections for ion-atom impact ionization of negative - and positive -ions for heavy ion fusion applications

Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I$^{-}$ and Cs$^{+}$ ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential.Comment: submitted to Phys. Rev.

Simultaneous interval regression for K-nearest neighbor

International audienceIn some regression problems, it may be more reasonable to predict intervals rather than precise values. We are interested in finding intervals which simultaneously for all input instances x ∈X contain a β proportion of the response values. We name this problem simultaneous interval regression. This is similar to simultaneous tolerance intervals for regression with a high confidence level γ ≈ 1 and several authors have already treated this problem for linear regression. Such intervals could be seen as a form of confidence envelop for the prediction variable given any value of predictor variables in their domain. Tolerance intervals and simultaneous tolerance intervals have not yet been treated for the K-nearest neighbor (KNN) regression method. The goal of this paper is to consider the simultaneous interval regression problem for KNN and this is done without the homoscedasticity assumption. In this scope, we propose a new interval regression method based on KNN which takes advantage of tolerance intervals in order to choose, for each instance, the value of the hyper-parameter K which will be a good trade-off between the precision and the uncertainty due to the limited sample size of the neighborhood around each instance. In the experiment part, our proposed interval construction method is compared with a more conventional interval approximation method on six benchmark regression data sets

Structure and Magnetization of Two-Dimensional Vortex Arrays in the Presence of Periodic Pinning

Ground-state properties of a two-dimensional system of superconducting vortices in the presence of a periodic array of strong pinning centers are studied analytically and numerically. The ground states of the vortex system at different filling ratios are found using a simple geometric argument under the assumption that the penetration depth is much smaller than the spacing of the pin lattice. The results of this calculation are confirmed by numerical studies in which simulated annealing is used to locate the ground states of the vortex system. The zero-temperature equilibrium magnetization as a function of the applied field is obtained by numerically calculating the energy of the ground state for a large number of closely spaced filling ratios. The results show interesting commensurability effects such as plateaus in the B-H diagram at simple fractional filling ratios.Comment: 12 pages, 19 figures, submitted for publicatio

Cosmology from Moduli Dynamics

We investigate moduli field dynamics in supergravity/M-theory like set ups where we turn on fluxes along some or all of the extra dimensions. As has been argued in the context of string theory, we observe that the fluxes tend to stabilize the squashing (or shape) modes. Generically we find that at late times the shape is frozen while the radion evolves as a quintessence field. At earlier times we have a phase of radiation domination where both the volume and the shape moduli are slowly evolving. However, depending on the initial conditions and the parameters of the theory, like the value of the fluxes, curvature of the internal manifold and so on, the dynamics of the internal manifold can be richer with interesting cosmological consequences, including inflation.Comment: 38 pages, 6 figures; references adde

A neutron scattering study of two-magnon states in the quantum magnet copper nitrate

We report measurements of the two-magnon states in a dimerized antiferromagnetic chain material, copper nitrate (Cu(NO3)2*2.5D2O). Using inelastic neutron scattering we have measured the one and two magnon excitation spectra in a large single crystal. The data are in excellent agreement with a perturbative expansion of the alternating Heisenberg Hamiltonian from the strongly dimerized limit. The expansion predicts a two-magnon bound state for q ~ (2n+1)pi*d which is consistent with the neutron scattering data.Comment: 11 pages of revtex style with 6 figures include

Effective Field Theory for Layered Quantum Antiferromagnets with Non-Magnetic Impurities

We propose an effective two-dimensional quantum non-linear sigma model combined with classical percolation theory to study the magnetic properties of site diluted layered quantum antiferromagnets like La$_{2}$Cu$_{1-x}$M$_x$O$_{4}$ (M$=$Zn, Mg). We calculate the staggered magnetization at zero temperature, $M_s(x)$, the magnetic correlation length, $\xi(x,T)$, the NMR relaxation rate, $1/T_1(x,T)$, and the N\'eel temperature, $T_N(x)$, in the renormalized classical regime. Due to quantum fluctuations we find a quantum critical point (QCP) at $x_c \approx 0.305$ at lower doping than the two-dimensional percolation threshold $x_p \approx 0.41$. We compare our results with the available experimental data.Comment: Final version accepted for publication as a Rapid Communication on Physical Review B. A new discussion on the effect of disorder in layered quantum antiferromagnets is include

Spontaneous chiral symmetry breaking in the linked cluster expansion

We investigate dynamical chiral symmetry breaking in the Coulomb gauge Hamiltonian QCD. Within the framework of the linked cluster expansion we extend the BCS ansatz for the vacuum and include correlation beyond the quark-antiquark paring. In particular we study the effects of the three-body correlations involving quark-antiquark and transverse gluons. The high momentum behavior of the resulting gap equation is discussed and numerical computation of the chiral symmetry breaking is presented.Comment: 13 pages, 9 figure