A uniform reconstruction formula in integral geometry

A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used

Twistor Theory and Differential Equations

This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic vector bundles over T\CP^1. A different framework is provided for the dispersionless analogues of soliton equations, like dispersionless KP or $SU(\infty)$ Toda system in 2+1 dimensions. Their solutions correspond to deformations of (parts of) T\CP^1, and ultimately to Einstein--Weyl curved geometries generalising the flat Minkowski space. A number of exercises is included and the necessary facts about vector bundles over the Riemann sphere are summarised in the Appendix.Comment: 23 Pages, 9 Figure

Kopyor Coconut Detection Using Sound-based Dynamic TIME Warping Method

Kopyor coconut is a coconut that has genetic abnormalities which cause the coconut meat to have a unique texture and is detached from the coconut shell. Its uniqueness attracts many enthusiasts resulting in a high economic value, 4-5 times that of the ordinary coconut. From its external appearance, kopyor coconut does not differ with ordinary coconut and this poses a challenge in the detection stage. To date, both farmers and sellers use a traditional approach by listening to the sound of whisk from kopyor coconut to detect them. Unfortunately, this approach relies heavily on experience and expertise of the person. Therefore, a new detection approach is proposed based on sound recognition using Mel Frequency Cepstrum Coefficient (MFCC) as the method for feature extraction and Dynamic Time Warping (DTW) as the method for feature matching. Objects that will be detected are kopyor coconuts and ordinary coconut which has grown mature. By implementing both methods, a program has been developed to detect kopyor coconut with an accuracy of 93.8%

Generalized quantum tomographic maps

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of "thick" quantum tomography. Applications for quantum state measurements of photons and matter waves are discussed.Comment: 8 page

Two-Dimensional Magnetic Resonance Tomographic Microscopy using Ferromagnetic Probes

We introduce the concept of computerized tomographic microscopy in magnetic resonance imaging using the magnetic fields and field gradients from a ferromagnetic probe. We investigate a configuration where a two-dimensional sample is under the influence of a large static polarizing field, a small perpendicular radio-frequency field, and a magnetic field from a ferromagnetic sphere. We demonstrate that, despite the non-uniform and non-linear nature of the fields from a microscopic magnetic sphere, the concepts of computerized tomography can be applied to obtain proper image reconstruction from the original spectral data by sequentially varying the relative sample-sphere angular orientation. The analysis shows that the recent proposal for atomic resolution magnetic resonance imaging of discrete periodic crystal lattice planes using ferromagnetic probes can also be extended to two-dimensional imaging of non-crystalline samples with resolution ranging from micrometer to Angstrom scales.Comment: 9 pages, 11 figure

An international prospective general population-based study of respiratory work disability

Background: Previous cross-sectional studies have shown that job change due to breathing problems at the workplace (respiratory work disability) is common among adults of working age. That research indicated that occupational exposure to gases, dust and fumes was associated with job change due to breathing problems, although causal inferences have been tempered by the cross-sectional nature of previously available data. There is a need for general population-based prospective studies to assess the incidence of respiratory work disability and to delineate better the roles of potential predictors of respiratory work disability.Methods: A prospective general population cohort study was performed in 25 centres in 11 European countries and one centre in the USA. A longitudinal analysis was undertaken of the European Community Respiratory Health Survey including all participants employed at any point since the baseline survey, 6659 subjects randomly sampled and 779 subjects comprising all subjects reporting physician-diagnosed asthma. The main outcome measure was new-onset respiratory work disability, defined as a reported job change during follow-up attributed to breathing problems. Exposure to dusts (biological or mineral), gases or fumes during follow-up was recorded using a job-exposure matrix. Cox proportional hazard regression modelling was used to analyse such exposure as a predictor of time until job change due to breathing problems.Results: The incidence rate of respiratory work disability was 1.2/1000 person-years of observation in the random sample (95% CI 1.0 to 1.5) and 5.7/1000 person-years in the asthma cohort (95% CI 4.1 to 7.8). In the random population sample, as well as in the asthma cohort, high occupational exposure to biological dust, mineral dust or gases or fumes predicted increased risk of respiratory work disability. In the random sample, sex was not associated with increased risk of work disability while, in the asthma cohort, female sex was associated with an increased disability risk (hazard ratio 2.8, 95% CI 1.3 to 5.9).Conclusions: Respiratory work disability is common overall. It is associated with workplace exposures that could be controlled through preventive measures

Tomographic approach to resolving the distribution of LISA Galactic binaries

The space based gravitational wave detector LISA is expected to observe a large population of Galactic white dwarf binaries whose collective signal is likely to dominate instrumental noise at observational frequencies in the range 10^{-4} to 10^{-3} Hz. The motion of LISA modulates the signal of each binary in both frequency and amplitude, the exact modulation depending on the source direction and frequency. Starting with the observed response of one LISA interferometer and assuming only doppler modulation due to the orbital motion of LISA, we show how the distribution of the entire binary population in frequency and sky position can be reconstructed using a tomographic approach. The method is linear and the reconstruction of a delta function distribution, corresponding to an isolated binary, yields a point spread function (psf). An arbitrary distribution and its reconstruction are related via smoothing with this psf. Exploratory results are reported demonstrating the recovery of binary sources, in the presence of white Gaussian noise.Comment: 13 Pages and 9 figures high resolution figures can be obtains from http://www.phys.utb.edu/~rajesh/lisa_tomography.pd

Entropic uncertainty relations for electromagnetic beams

The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed in terms of the Hermite polynomials squared. It is shown that measurements of optical-field intensities may be used to determine the tomograms of electromagnetic-radiation modes. Furthermore, entropic uncertainty relations associated with these tomograms are found and applied to establish the compatibility conditions of the the field profile properties with Hermite--Gauss beam description. Numerical evaluations for some Hermite--Gauss modes illustrating the corresponding entropic uncertainty relations are finally given.Comment: Invited talk at the XV Central European Workshop on Quantum Optics (Belgrade, Serbia, 30 May -- 3 June 2008), to appear in Physica Scripta

Isospin Dependence in the Odd-Even Staggering of Nuclear Binding Energies

The FRS-ESR facility at GSI provides unique conditions for precision measurements of large areas on the nuclear mass surface in a single experiment. Values for masses of 604 neutron-deficient nuclides (30<=Z<=92) were obtained with a typical uncertainty of 30 microunits. The masses of 114 nuclides were determined for the first time. The odd-even staggering (OES) of nuclear masses was systematically investigated for isotopic chains between the proton shell closures at Z=50 and Z=82. The results were compared with predictions of modern nuclear models. The comparison revealed that the measured trend of OES is not reproduced by the theories fitted to masses only. The spectral pairing gaps extracted from models adjusted to both masses, and density related observables of nuclei agree better with the experimental data.Comment: Physics Review Letters 95 (2005) 042501 http://link.aps.org/abstract/PRL/v95/e04250