A geometric Newton method for Oja's vector field

Newton's method for solving the matrix equation $F(X)\equiv AX-XX^TAX=0$ runs up against the fact that its zeros are not isolated. This is due to a symmetry of $F$ by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a ``geometric'' Newton algorithm that finds the zeros of $F$. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Principal components; Scatter; Shape matrix; Sign; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate; Variance;

d0 Ferromagnetic Interface Between Non-magnetic Perovskites

We use computational and experimental methods to study d0 ferromagnetism at a charge- imbalanced interface between two perovskites. In SrTiO3/KTaO3 superlattice calculations, the charge imbalance introduces holes in the SrTiO3 layer, inducing a d0 ferromagnetic half-metallic 2D electron gas at the interface oxygen 2p orbitals. The charge imbalance overrides doping by vacancies at realistic concentrations. Varying the constituent materials shows ferromagnetism to be a gen- eral property of hole-type d0 perovskite interfaces. Atomically sharp epitaxial d0 SrTiO3/KTaO3, SrTiO3 /KNbO3 and SrTiO3 /NaNbO3 interfaces are found to exhibit ferromagnetic hysteresis at room temperature. We suggest the behavior is due to high density of states and exchange coupling at the oxygen t1g band in comparison with the more studied d band t2g symmetry electron gas.Comment: 5 pages, 5 figure

Searches for violation of fundamental time reversal and space reflection symmetries in solid state experiments

The electric dipole moment (EDM) of a particle violates both time reversal (T) and space reflection (P) symmetries. There have been recent suggestions for searches of the electron EDM using solid state experiments [1,2]. These experiments could improve the sensitivity compared to present atomic and molecular experiments by several orders of magnitude. In the present paper we calculate the expected effect. We also suggest that this kind of experiment is sensitive to T,P-violation in nuclear forces and calculate effects caused by the nuclear Schiff moment. The compounds under consideration contain magnetic Gd$^{3+}$ ions and oxygen O$^{2-}$ ions. We demonstrate that the main mechanism for the T,P-odd effects is related to the penetration of the Oxygen 2p-electrons to the Gd core. All the effects are related to the deformation of the crystal lattice.Comment: 13 pages, 6 figure

Radial Velocity Studies of Close Binary Stars. IX

Radial-velocity measurements and sine-curve fits to the orbital velocity variations are presented for the eighth set of ten close binary systems: AB And, V402 Aur, V445 Cep, V2082 Cyg, BX Dra, V918 Her, V502 Oph, V1363 Ori, KP Peg, V335 Peg. Half of the systems (V445 Cep, V2082 Cyg, V918 Her, V1363 Ori, V335 Peg) were discovered photometrically by the Hipparcos mission and all systems are double-lined (SB2) contact binaries. The broadening function method permitted improvement of the orbital elements for AB And and V502 Oph. The other systems have been observed for radial velocity variations for the first time; in this group are five bright (V<7.5) binaries: V445 Cep, V2082 Cyg, V918 Her, KP Peg and V335 Peg. Several of the studied systems are prime candidates for combined light and radial-velocity synthesis solutions.Comment: 17+ pages, 2 tables, 4 figure

Damagnetization cooling of a gas

We demonstrate demagnetization cooling of a gas of ultracold $^{52}$Cr atoms. Demagnetization is driven by inelastic dipolar collisions which couple the motional degrees of freedom to the spin degree. By that kinetic energy is converted into magnetic work with a consequent temperature reduction of the gas. Optical pumping is used to magnetize the system and drive continuous demagnetization cooling. Applying this technique, we can increase the phase space density of our sample by one order of magnitude, with nearly no atom loss. This method can be in principle extended to every dipolar system and could be used to achieve quantum degeneracy via optical means.Comment: 10 pages, 5 figure

Theory of Interplay of Nuclear Magnetism and Superconductivity in AuIn2

The recently reported coexistence of a magnetic order, with the critical temperature T_M=35 \mu*K, and superconductivity, with the critical temperature T_S=207 m*K, in AuIn_2 is studied theoretically. It is shown that superconducting (S) electrons and localized nuclear magnetic moments (LM's) interact dominantly via the contact hyperfine (EX) interaction, giving rise to a spiral (or domain-like) magnetic order in superconducting phase. The electromagnetic interaction between LM's and S electrons is small compared to the EX one giving minor contribution to the formation of the oscillatory magnetic order. In clean samples (l>\xi_0) of AuIn$_2$ the oscillatory magnetic order should produce a line of nodes in the quasiparticle spectrum of S electrons giving rise to the power law behavior. The critical field H_c(T=0) in the coexistence phase is reduced by factor two with respect to its bare value.Comment: 4 pages with 2 PS figures, RevTeX, submitted to Physical Review B - Rapid Communication

Extraction of Coherent Information from Non-Overlapping Receptive Fields

It has been suggested that long-range lateral connections in the cortex play a contextual role in that they modulate the gain of the response to primary receptive field input. In the first part of this paper I show that a network with a set of such pre-wired connections has a short-term dynamics that enhances and stabilizes coherent information defined across multiple, non-overlapping receptive fields. In the second part, I suggest a simple Hebbian rule that can develop the required pattern of synaptic strengths and describe two simulations where the networks discover information that is defined only by its coherence across receptive fields

The Palomar Testbed Interferometer Calibrator Catalog

The Palomar Testbed Interferometer (PTI) archive of observations between 1998 and 2005 is examined for objects appropriate for calibration of optical long-baseline interferometer observations - stars that are predictably point-like and single. Approximately 1,400 nights of data on 1,800 objects were examined for this investigation. We compare those observations to an intensively studied object that is a suitable calibrator, HD217014, and statistically compare each candidate calibrator to that object by computing both a Mahalanobis distance and a Principal Component Analysis. Our hypothesis is that the frequency distribution of visibility data associated with calibrator stars differs from non-calibrator stars such as binary stars. Spectroscopic binaries resolved by PTI, objects known to be unsuitable for calibrator use, are similarly tested to establish detection limits of this approach. From this investigation, we find more than 350 observed stars suitable for use as calibrators (with an additional $\approx 140$ being rejected), corresponding to $\gtrsim 95$ sky coverage for PTI. This approach is noteworthy in that it rigorously establishes calibration sources through a traceable, empirical methodology, leveraging the predictions of spectral energy distribution modeling but also verifying it with the rich body of PTI's on-sky observations.Comment: 100 pages, 7 figures, 7 tables; to appear in the May 2008ApJS, v176n