From Classical to Quantum Mechanics: "How to translate physical ideas into mathematical language"

In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint operators and so on) - Quantum Mechanics properly that specifies the Hilbert space, the Heisenberg rule, the free Hamiltonian... We show that General Quantum Axiomatics (up to a supplementary "axiom of classicity") can be used as a non-standard mathematical ground to formulate all the ideas and equations of ordinary Classical Statistical Mechanics. So the question of a "true quantization" with "h" must be seen as an independent problem not directly related with quantum formalism. Moreover, this non-standard formulation of Classical Mechanics exhibits a new kind of operation with no classical counterpart: this operation is related to the "quantization process", and we show why quantization physically depends on group theory (Galileo group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows to map Classical Mechanics into Quantum Mechanics, giving all operators of Quantum Mechanics and Schrodinger equation. Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We find also that this approach gives a natural semi-classical formalism: some exact quantum results are obtained only using classical-like formula. So this procedure has the nice property of enlightening in a more comprehensible way both logical and analytical connection between classical and quantum pictures.Comment: 47 page

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

Investigation of spatial misregistration effects in multispectral scanner data

The author has identified the following significant results. A model for estimating the expected proportion of multiclass pixels in a scene was generalized and extended to include misregistration effects. Another substantial effort was the development of a simulation model to generate signatures to represent the distributions of signals from misregistered multiclass pixels, based on single class signatures. Spatial misregistration causes an increase in the proportion of multiclass pixels in a scene and a decorrelation between signals in misregistered data channels. The multiclass pixel proportion estimation model indicated that this proportion is strongly dependent on the pixel perimeter and on the ratio of the total perimeter of the fields in the scene to the area of the scene. Test results indicated that expected values computed with this model were similar to empirical measurements made of this proportion in four LACIE data segments

Bottle Fillers for the Natural Sciences Building

Proposed by Melissa Gast-Goodman, Administrative Coordinator, ICPS and Dr. Daniel Gleason, Director, ICPS. ($3,495.16

Derivation of the quantum probability law from minimal non-demolition measurement

One more derivation of the quantum probability rule is presented in order to shed more light on the versatile aspects of this fundamental law. It is shown that the change of state in minimal quantum non-demolition measurement, also known as ideal measurement, implies the probability law in a simple way. Namely, the very requirement of minimal change of state, put in proper mathematical form, gives the well known Lueders formula, which contains the probability rule.Comment: 8 page

Characterization and analysis of the Nimbus-7 SBUV data in the non-sync period (February 1987 - June 1990)

The SBUV instrument, on Nimbus-7, measures the backscatter ultraviolet radiance at 12 wavelengths. The radiance data from these wavelengths was used to deduce the ozone profile and the total column ozone. In February 1987, there was an instrument malfunction. The purpose of this paper is to describe the malfunction, to determine the effect of the malfunction on the data quality, and if possible, to correct for the effects of the malfunction on the data from the SBUV instrument

Non-Contextual Hidden Variables and Physical Measurements

For a hidden variable theory to be indistinguishable from quantum theory for finite precision measurements, it is enough that its predictions agree for some measurement within the range of precision. Meyer has recently pointed out that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can thus be effectively nullified if only finite precision measurements are considered. We generalise this result: it is possible to ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.Comment: Typo corrected. Final version: to appear in Phys. Rev. Let

Group I metabotropic glutamate receptors are expressed in the chicken retina and by cultured retinal amacrine cells

Glutamate is well established as an excitatory neurotransmitter in the vertebrate retina. Its role as a modulator of retinal function, however, is poorly understood. We used immunocytochemistry and calcium imaging techniques to investigate whether metabotropic glutamate receptors are expressed in the chicken retina and by identified GABAergic amacrine cells in culture. Antibody labeling for both metabotropic glutamate receptors 1 and 5 in the retina was consistent with their expression by amacrine cells as well as by other retinal cell types. In double-labeling experiments, most metabotropic glutamate receptor 1-positive cell bodies in the inner nuclear layer also label with anti-GABA antibodies. GABAergic amacrine cells in culture were also labeled by metabotropic glutamate receptor 1 and 5 antibodies. Metabotropic glutamate receptor agonists elicited Ca2+ elevations in cultured amacrine cells, indicating that these receptors were functionally expressed. Cytosolic Ca2+ elevations were enhanced by metabotropic glutamate receptor 1-selective antagonists, suggesting that metabotropic glutamate receptor 1 activity might normally inhibit the Ca2+ signaling activity of metabotropic glutamate receptor 5. These results demonstrate expression of group I metabotropic glutamate receptors in the avian retina and suggest that glutamate released from bipolar cells onto amacrine cells might act to modulate the function of these cells

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure