Convergence of Gradient Descent for Low-Rank Matrix Approximation

This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny-Study distance on this space

Observation of a cyclotron harmonic spike in microwave-induced resistances in ultraclean GaAs/AlGaAs quantum wells

We report the observation of a colossal, narrow resistance peak that arises in ultraclean (mobility 3X10^7cm^2/Vs) GaAs/AlGaAs quantum wells (QWs) under millimeterwave irradiation and a weak magnetic field. Such a spike is superposed on the 2nd harmonic microwave-induced resistance oscillations (MIRO) but having an amplitude > 300% of the MIRO, and a typical FWHM ~50 mK, comparable with the Landau level width. Systematic studies show a correlation between the spike and a pronounced negative magnetoresistance in these QWs, suggesting a mechanism based on the interplay of strong scatterers and smooth disorder. Alternatively, the spike may be interpreted as a manifestation of quantum interference between the quadrupole resonance and the higher-order cyclotron transition in well-separated Landau levels.Comment: 4pages, 4figure

The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries

The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core (excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin $j$, and compare it with the results obtained by other methods. By this approach the equation of state for a two-dimensional hard-sphere gas can be calculated directly.Comment: 9 pages, 1 figur

An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the thermodynamic quantity which can simultaneously describe both gas phase and condensed phase is solved with the help of the homogeneous Riemann-Hilbert problem, so one can judge whether there exists a phase transition and determine the phase transition point mathematically rigorously. A generalized statistics in which the maximum occupation numbers of different quantum states can take on different values is introduced, as a generalization of Bose-Einstein and Fermi-Dirac statistics.Comment: 17 pages, 2 figure

Spin Susceptibility of the Topological Superconductor UPt3 from Polarized Neutron Diffraction

Experiment and theory indicate that UPt3 is a topological superconductor in an odd-parity state, based in part from temperature independence of the NMR Knight shift. However, quasiparticle spin-flip scattering near a surface, where the Knight shift is measured, might be responsible. We use polarized neutron scattering to measure the bulk susceptibility with H||c, finding consistency with the Knight shift but inconsistent with theory for this field orientation. We infer that neither spin susceptibility nor Knight shift are a reliable indication of odd-parity

Effect of long range forces on the interfacial profiles in thin binary polymer films

We study the effect of surface fields on the interfacial properties of a binary polymer melt confined between two parallel walls. Each wall attracts a different component of the blend by a non-retarded van der Waals potential. An interface which runs parallel to the surfaces is stabilized in the center of the film. Using extensive Monte Carlo simulations we study the interfacial properties as a function of the film thickness, the strength of the surface forces and the lateral size over which the profiles across the film are averaged. We find evidence for capillary wave broadening of the apparent interfacial profiles. However, the apparent interfacial width cannot be described quantitatively by a simple logarithmic dependence on the film thickness. The Monte Carlo simulations reveal that the surface fields give rise to an additional reduction of the intrinsic interfacial width and an increase of the effective interfacial tension upon decreasing the film thickness. These modifications of the intrinsic interfacial properties are confirmed by self-consistent field calculations. Taking account of the thickness dependence of the intrinsic interfacial properties and the capillary wave broadening, we can describe our simulation results quantitatively.Comment: to appear in J.Chem.Phy

Detecting Pulsars with Interstellar Scintillation in Variance Images

Pulsars are the only cosmic radio sources known to be sufficiently compact to show diffractive interstellar scintillations. Images of the variance of radio signals in both time and frequency can be used to detect pulsars in large-scale continuum surveys using the next generation of synthesis radio telescopes. This technique allows a search over the full field of view while avoiding the need for expensive pixel-by-pixel high time resolution searches. We investigate the sensitivity of detecting pulsars in variance images. We show that variance images are most sensitive to pulsars whose scintillation time-scales and bandwidths are close to the subintegration time and channel bandwidth. Therefore, in order to maximise the detection of pulsars for a given radio continuum survey, it is essential to retain a high time and frequency resolution, allowing us to make variance images sensitive to pulsars with different scintillation properties. We demonstrate the technique with Murchision Widefield Array data and show that variance images can indeed lead to the detection of pulsars by distinguishing them from other radio sources.Comment: 8 papes, 9 figures, accepted for publication in MNRA