Non-Asymptotic Analysis of Tangent Space Perturbation

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear subspace. To process noisy data samples from a nonlinear manifold, PCA must be applied locally, at a scale small enough such that the manifold is approximately linear, but at a scale large enough such that structure may be discerned from noise. Using eigenspace perturbation theory and non-asymptotic random matrix theory, we study the stability of the subspace estimated by PCA as a function of scale, and bound (with high probability) the angle it forms with the true tangent space. By adaptively selecting the scale that minimizes this bound, our analysis reveals an appropriate scale for local tangent plane recovery. We also introduce a geometric uncertainty principle quantifying the limits of noise-curvature perturbation for stable recovery. With the purpose of providing perturbation bounds that can be used in practice, we propose plug-in estimates that make it possible to directly apply the theoretical results to real data sets.Comment: 53 pages. Revised manuscript with new content addressing application of results to real data set

Gaston Memorial Hospital: Driving Quality Improvement With Data, Guidelines, and Real-Time Feedback

Describes efforts to reduce variance in provider practice patterns through data analysis and benchmarking of process-of-care measures. Discusses strategies such as sharing data, feedback, and best practices in ways physicians can utilize them immediately

Nanodust detection near 1 AU from spectral analysis of Cassini/RPWS radio data

Nanodust grains of a few nanometer in size are produced near the Sun by collisional break-up of larger grains and picked-up by the magnetized solar wind. They have so far been detected at 1 AU by only the two STEREO spacecraft. Here we analyze the spectra measured by the radio and plasma wave instrument onboard Cassini during the cruise phase close to Earth orbit; they exhibit bursty signatures similar to those observed by the same instrument in association to nanodust stream impacts on Cassini near Jupiter. The observed wave level and spectral shape reveal impacts of nanoparticles at about 300 km/s, with an average flux compatible with that observed by the radio and plasma wave instrument onboard STEREO and with the interplanetary flux models

Multiple sources or late injection of short-lived r-nuclides in the early solar system?

Comparisons between the predicted abundances of short-lived r-nuclides (107Pd, 129I, 182Hf, and 244Pu) in the interstellar medium (ISM) and the observed abundances in the early solar system (ESS) conclusively showed that these nuclides cannot simply be derived from galactic chemical evolution (GCE) if synthesized in a unique stellar environment. It was thus suggested that two di erent types of stars were responsible for the production of light and heavy r-nuclides. Here, new constraints on the 244Pu=238U production ratio are used in an open nonlinear GCE model. It is shown that the two r-process scenario cannot explain the low abundance of 244Pu in the ESS and that this requires either than actinides be produced at an additional site (A-events) or more likely, that 129I and 244Pu be inherited from GCE and 107Pd and 182Hf be injected in the ESS by the explosion of a nearby supernova.Comment: 4 pages, 1 figure, Nucl. Phys. A, in press (proceedings of NIC8

Interim report on the hydrologic features of the Green Swamp area in Central Florida

The Green Swamp area in central Florida is another area where man is developing agricultural land from marginal land. Though the area is by no means as extensive as that of the Everglades, the present efforts for its development are similar to the early efforts for developing the Everglades in that many miles of canals and ditches have been constructed to improve the drainage. Lest the early mistakes of the Everglades be repeated, the Florida Department of Water Resources considered that an appraisal of the physical and hydrologic features of the area was needed to determine the broad effects of draining and developing the swamp. This reconnaissance provides information required by the State of Florida for determining its responsibility and policy in regard to the Green Swamp area and for formulating future plans for water management of the area. Some of the features that have been determined are: the amount of rainfall on the area; the pattern of surfacewater drainage; the amount and direction of surface-water runoff; the direction of ground-water movement; the interrelationship of rainfall, surface water, and ground water; the effects of improved drainage facilities'; and the effects of the hydrologic environment on the chemical quality of water of the area.(PDF contains 106 pages.

Classical and Quantum Ensembles via Multiresolution. I. BBGKY Hierarchy

A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY hierarchy of kinetic equations. We construct the multiscale representation for hierarchy of reduced distribution functions in the variational approach and multiresolution decomposition in polynomial tensor algebras of high-localized states. Numerical modeling shows the creation of various internal structures from localized modes, which are related to localized or chaotic type of behaviour and the corresponding patterns (waveletons) formation. The localized pattern is a model for energy confinement state (fusion) in plasma.Comment: 5 pages, 3 figures, espcrc2.sty, Presented at IX International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Section III "Simulations and Computations in Theoretical Physics and Phenomenology", ACAT 2003, December, 2003, KEK, Tsukub

Photocurrent measurements in topological insulator Bi2Se3\text{Bi}_2\text{Se}_3 nanowires

Circular photogalvanic currents are a promising new approach for spin-optoelectronics. To date, such currents have only been induced in topological insulator flakes or extended films. It is not clear whether they can be generated in nanodevices. In this paper, we demonstrate the generation of circular photogalvanic currents in $\text{Bi}_2\text{Se}_3$ nanowires. Each nanowire shows topological surface states. Here, we generate and distinguish the different photocurrent contributions via the driving light wave. We separate the circular photogalvanic currents from those due to thermal Seebeck effects, through controlling the laser light polarization. The results reveal a spin-polarized surface-Dirac electron flow in the nanowires arising from spin-momentum locking and spin-orbit effects. The second photocurrent contribution described in this letter is caused by the thermal Seebeck effect. By scanning the photocurrent, it can be spatially resolved; upon reversing the gradient direction along the nanowire, the photocurrent changes its sign, and close to the gold contacts, the amplitudes of the different photocurrent contributions are affected by the proximity to the contacts. In the center of the nanowires, where the effects from the gold contact/ topological insulator stacks vanish, the spin-polarized current remains constant along the nanowires. This opens up a new method of all-optical spin current generation in topological insulator nanowires and hybrid structures for nanoscale spin-orbitronics.Comment: 5 pages, 4 figure

Quantum Chinos Game: winning strategies through quantum fluctuations

We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial quantization of the game (semiclassical) allows us to find a winning strategy for the second player, but it is unstable w.r.t. the classical strategy. However, in a fully quantum version of the game we find a winning strategy for the first player that is optimal: the symmetric classical situation is broken at the quantum level.Comment: REVTEX4.b4 file, 3 table

Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally H\"older continuous. We also argue a result on Littlewood-Paley functions which are obtained by the $\alpha$-harmonic extension of an $L^p(\mathbb{R}^d)$ function.Comment: 23 page