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  • 2001  (6)
  • 1890
  • PACS. 03.75.Be Atom and neutron optics – 42.25.Fx Diffraction and scattering  (2)
  • PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes  (2)
  • snakes  (2)
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  • Electronic Resource  (6)
  • AV-Medium
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  • 2020-2024
  • 2000-2004  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 20 (2001), S. 511-515 
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We present a framework that allows for a systematic assessment of risk given a specific model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which allows for a (time-)local understanding of its level, together with a short term forecast. On the other hand, via a diffusion approximation, the time evolution of the probability density of risk is modeled by a Fokker-Planck equation. Then, as a final step, using Bayes theorem, beliefs are conditioned on the stationary probability density function as obtained from the Fokker-Planck equation. We believe this to be a highly rigorous framework to integrate subjective judgments of future market behavior and underlying models. In order to demonstrate the approach, we apply it to risk assessment of empirical interest rate scenario methodologies, i.e. the application of Principal Component Analysis to the the dynamics of bonds.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 20 (2001), S. 517-522 
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Factor based interest rate models are widely used for risk managing purposes, for option pricing and for identifying and capturing yield curve anomalies. The movements of a term structure of interest rates are commonly assumed to be driven by a small number of orthogonal factors such as SHIFT, TWIST and BUTTERFLY (BOW). These factors are usually obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). Although PCA diagonalizes the covariance matrix of either the interest rates or the interest rate changes, it does not use both covariance matrices simultaneously. Furthermore higher linear and nonlinear correlations are neglected. These correlations as well as the mean reverting properties of the interest rates become crucial, if one is interested in a longer time horizon (infrequent hedging or trading). We will show that Independent Component Analysis (ICA) is a more appropriate tool than PCA, since ICA uses the covariance matrix of the interest rates as well as the covariance matrix of the interest rate changes simultaneously. Additionally higher linear and nonlinear correlations may be easily incorporated. The resulting factors are uncorrelated for various time delays, approximately independent but nonorthogonal. This is in contrast to the factors obtained from the PCA, which are orthogonal and uncorrelated for identical times only. Although factors from the ICA are nonorthogonal, it is sufficient to consider only a few factors in order to explain most of the variation in the original data. Finally we will present examples that ICA based hedges outperforms PCA based hedges specifically if the portfolio is sensitive to structural changes of the yield curve.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 14 (2001), S. 289-297 
    ISSN: 1434-6079
    Keywords: PACS. 03.75.Be Atom and neutron optics – 42.25.Fx Diffraction and scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: The problem of atom diffraction from a reflecting magnetic diffraction grating is solved in the thin phase-grating approximation. The general problem for scalar diffraction is modelled using a semi-classical method in which the grating potential is separated into a reflecting term and a diffracting term. The trajectory of the atom in the reflecting potential is solved classically and the atom wave function in the diffracting potential found by integrating the phase change along the classical trajectory. The diffraction orders are obtained after Fourier transforming the result. This can be done independently of the grating potential resulting in a general formula for the diffraction efficiencies. The general result is applied to the problem of atom diffraction from a magnetic grating. Several approximations are required to reduce the problem to a form amenable to analytic solution. The results are compared with an accurate numerical method.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 14 (2001), S. 111-118 
    ISSN: 1434-6079
    Keywords: PACS. 03.75.Be Atom and neutron optics – 42.25.Fx Diffraction and scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    International journal of computer vision 44 (2001), S. 137-155 
    ISSN: 1573-1405
    Keywords: snakes ; pedal curves and surfaces ; curve and surface evolution ; level-set method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, we propose significant extensions to the “snake pedal” model, a powerful geometric shape modeling scheme introduced in (Vemuri and Guo, 1998). The extension allows the model to automatically cope with topological changes and for the first time, introduces the concept of a compact global shape into geometric active models. The ability to characterize global shape of an object using very few parameters facilitates shape learning and recognition. In this new modeling scheme, object shapes are represented using a parameterized function—called the generator—which accounts for the global shape of an object and the pedal curve (surface) of this global shape with respect to a geometric snake to represent any local detail. Traditionally, pedal curves (surfaces) are defined as the loci of the feet of perpendiculars to the tangents of the generator from a fixed point called the pedal point. Local shape control is achieved by introducing a set of pedal points—lying on a snake—for each point on the generator. The model dubbed as a “snake pedal” allows for interactive manipulation via forces applied to the snake. In this work, we replace the snake by a geometric snake and derive all the necessary mathematics for evolving the geometric snake when the snake pedal is assumed to evolve as a function of its curvature. Automatic topological changes of the model may be achieved by implementing the geometric snake in a level-set framework. We demonstrate the applicability of this modeling scheme via examples of shape recovery from a variety of 2D and 3D image data.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    International journal of computer vision 44 (2001), S. 87-109 
    ISSN: 1573-1405
    Keywords: colour ; statistics ; statistical modeling ; segmentation ; tracking ; active region models ; snakes ; image processing ; computer vision ; physics-based vision
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we investigate how best to model naturally arising distributions of colour camera data. It has become standard to model single mode distributions of colour data by ignoring the intensity component and constructing a Gaussian model of the chromaticity. This approach is appealing, because the intensity of data can change arbitrarily due to shadowing and shading, whereas the chromaticity is more robust to these effects. However, it is unclear how best to construct such a model, since there are many domains in which the chromaticity can be represented. Furthermore, the applicability of this kind of model is questionable in all but the most basic lighting environments. We begin with a review of the reflection processes that give rise to distributions of colour data. Several candidate models are then presented; some are from the existing literature and some are novel. Properties of the different models are compared analytically and the models are empirically compared within a region tracking application over two separate sets of data. Results show that chromaticity based models perform well in constrained environments where the physical model upon which they are based applies. It is further found that models based on spherical representations of the chromaticity data provide better performance than those based on more common planar representations, such as the chromaticity plane or the normalised colour space. In less constrained environments, however, such as daylight, chromaticity based models do not perform well, because of the effects of additional illumination components, which violate the physical model upon which they are based.
    Type of Medium: Electronic Resource
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