Signature features with the visibility transformation

The signature in rough path theory provides a graduated summary of a path through an examination of the effects of its increments. Inspired by recent developments of signature features in the context of machine learning, we explore a transformation that is able to embed the effect of the absolute position of the data stream into signature features. This unified feature is particularly effective for its simplifying role in allowing the signature feature set to accommodate nonlinear functions of absolute and relative values

Signatures of Bose-Einstein condensation in an optical lattice

We discuss typical experimental signatures for the Bose-Einstein condensation (BEC) of an ultracold Bose gas in an inhomogeneous optical lattice at finite temperature. Applying the Hartree-Fock-Bogoliubov-Popov formalism, we calculate quantities such as the momentum-space density distribution, visibility and peak width as the system is tuned through the superfluid to normal phase transition. Different from previous studies, we consider systems with fixed total particle number, which is of direct experimental relevance. We show that the onset of BEC is accompanied by sharp features in all these signatures, which can be probed via typical time-of-flight imaging techniques. In particular, we find a two-platform structure in the peak width across the phase transition. We show that the onset of condensation is related to the emergence of the higher platform, which can be used as an effective experimental signature.Comment: 5 pages, 3 figure

Phase coherence, visibility, and the superfluid--Mott-insulator transition on one-dimensional optical lattices

We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte-Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et.al.[Phy. Rev. Lett. 95, 050404 (2005); Phys. Rev. A 72, 053606 (2005)]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that as the interaction strength, U, is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than one.Comment: 4 pages, 5 figure

Use of ERTS-1 data: Summary report of work on ten tasks

The author has identified the following significant results. Depth mapping's for a portion of Lake Michigan and at the Little Bahama Bank test site have been verified by use of navigation charts and on-site visits. A thirteen category recognition map of Yellowstone Park has been prepared. Model calculation of atmospheric effects for various altitudes have been prepared. Radar, SLAR, and ERTS-1 data for flooded areas of Monroe County, Michigan are being studied. Water bodies can be reliably recognized and mapped using maximum likelihood processing of ERTS-1 digital data. Wetland mapping has been accomplished by slicing of single band and/or ratio processing of two bands for a single observation date. Both analog and digital processing have been used to map the Lake Ontario basin using ERTS-1 data. Operating characteristic curves were developed for the proportion estimation algorithm to determine its performance in the measurement of surface water area. The signal in band MSS-5 was related to sediment content of waters by modelling approach and by relating surface measurements of water to processed ERTS data. Radiance anomalies in ERTS-1 data could be associated with the presence of oil on water in San Francisco Bay, but the anomalies were of the same order as those caused by variations in sediment concentration and tidal flushing

Nonclassical effects in two-photon interference experiments: event-by-event simulations

It is shown that both the visibility ${\cal V} = 1/2$ predicted for two-photon interference experiments with two independent sources\textcolor{black}{, like the Hanbury Brown-Twiss experiment,} and the visibility ${\cal V} = 1$ predicted for two-photon interference experiments with a parametric down-conversion source\textcolor{black}{, like the Ghosh-Mandel experiment,} can be explained \textcolor{black}{by a discrete event simulation. This simulation approach reproduces the statistical distributions of wave theory not by requiring the knowledge of the solution of the wave equation of the whole system but by generating detection events one-by-one according to an unknown distribution.} There is thus no need to invoke quantum theory to explain the so-called nonclassical effects in the interference of signal and idler photons in parametric down conversion. Hence, a revision of the commonly accepted criterion of the nonclassical nature of light\textcolor{black}{, ${\cal V} > 1/2$,} is called for.Comment: arXiv admin note: substantial text overlap with arXiv:1208.2368, arXiv:1006.172

Controlling induced coherence for quantum imaging

Induced coherence in parametric down-conversion between two coherently pumped nonlinear crystals that share a common idler mode can be used as an imaging technique. Based on the interference between the two signal modes of the crystals, an image can be reconstructed. By obtaining an expression for the interference pattern that is valid in both the low- and the high-gain regimes of parametric down-conversion, we show how the coherence of the light emitted by the two crystals can be controlled. With our comprehensive analysis we provide deeper insight into recent discussions about the application of induced coherence to imaging in different regimes. Moreover, we propose a scheme for optimizing the visibility of the interference pattern so that it directly corresponds to the degree of coherence of the light generated in the two crystals. We find that this scheme leads in the high-gain regime to a visibility arbitrarily close to unity.Comment: 9 pages, 4 figure

Wheat signature modeling and analysis for improved training statistics

The author has identified the following significant results. The spectral, spatial, and temporal characteristics of wheat and other signatures in LANDSAT multispectral scanner data were examined through empirical analysis and simulation. Irrigation patterns varied widely within Kansas; 88 percent of wheat acreage in Finney was irrigated and 24 percent in Morton, as opposed to less than 3 percent for western 2/3's of the State. The irrigation practice was definitely correlated with the observed spectral response; wheat variety differences produced observable spectral differences due to leaf coloration and different dates of maturation. Between-field differences were generally greater than within-field differences, and boundary pixels produced spectral features distinct from those within field centers. Multiclass boundary pixels contributed much of the observed bias in proportion estimates. The variability between signatures obtained by different draws of training data decreased as the sample size became larger; also, the resulting signatures became more robust and the particular decision threshold value became less important