Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Biometric template security using higher order spectra

A method of improving the security of biometric templates which satisfies desirable properties such as (a) irreversibility of the template, (b) revocability and assignment of a new template to the same biometric input, (c) matching in the secure transformed domain is presented. It makes use of an iterative procedure based on the bispectrum that serves as an irreversible transformation for biometric features because signal phase is discarded each iteration. Unlike the usual hash function, this transformation preserves closeness in the transformed domain for similar biometric inputs. A number of such templates can be generated from the same input. These properties are illustrated using synthetic data and applied to images from the FRGC 3D database with Gabor features. Verification can be successfully performed using these secure templates with an EER of 5.85%

Cardiac state diagnosis using higher order spectra of heart rate variability

Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart, by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computer-based intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are nonlinear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of nonlinear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and seven classes of arrhythmia. We present some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. We also extracted features from the HOS and performed an analysis of variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test.

The applicability of biased estimation in model and model order selection

Biased estimation has the advantage of reducing the mean squared error (MSE) of an estimator. The question of interest is how biased estimation affects model selection. In this paper, we introduce biased estimation to a range of model selection criteria. Specifically, we analyze the performance of the minimum description length (MDL) criterion based on biased and unbiased estimation and compare it against modern model selection criteria such as Kay's conditional model order estimator (CME), the bootstrap and the more recently proposed hook-and-loop resampling based model selection. The advantages and limitations of the considered techniques are discussed. The results indicate that, in some cases, biased estimators can slightly improve the selection of the correct model. We also give an example for which the CME with an unbiased estimator fails, but could regain its power when a biased estimator is used.

Critical discourse analysis and political economy of communication : understanding the new corporate order

This article uses critical discourse analysis to analyse material shifts in the political economy of communications. It examines texts of major corporations to describe four key changes in political economy: (1) the separation of ownership from control; (2) the separation of business from industry; (3) the separation of accountability from responsibility; and (4) the subjugation of ‘going concerns’ by overriding concerns. The authors argue that this amounts to a political economic shift from traditional concepts of ‘capitalism’ to a new ‘corporatism’ in which the relationships between public and private, state and individual interests have become redefined and obscured through new discourse strategies. They conclude that the present financial and regulatory ‘crisis’ cannot be adequately resolved without a new analytic framework for examining the relationships between corporation, discourse and political economy.

Peripheral higher order aberrations in emmetropes and myopes

Purpose: Poor image quality in the peripheral field may lead to myopia. Most studies measuring the higher order aberrations in the periphery have been restricted to the horizontal visual field. The purpose of this study was to measure higher order monochromatic aberrations across the central 42º horizontal x 32º vertical visual fields in myopes and emmetropes. ---------- Methods: We recruited 5 young emmetropes with spherical equivalent refractions +0.17 ± 0.45D and 5 young myopes with spherical equivalent refractions -3.9 ± 2.09D. Measurements were taken with a modified COAS-HD Hartmann-Shack aberrometer (Wavefront Sciences Inc). Measurements were taken while the subjects looked at 38 points arranged in a 7 x 6 matrix (excluding four corner points) through a beam splitter held between the instrument and the eye. A combination of the instrument’s software and our own software was used to estimate OSA Zernike coefficients for 5mm pupil diameter at 555nm for each point. The software took into account the elliptical shape of the off-axis pupil. Nasal and superior fields were taken to have positive x and y signs, respectively. ---------- Results: The total higher order RMS (HORMS) was similar on-axis for emmetropes (0.16 ± 0.02 μm) and myopes (0.17 ± 0.02 μm). There was no common pattern for HORMS for emmetropes across the visual field where as 4 out of 5 myopes showed a linear increase in HORMS in all directions away from the minimum. For all subjects, vertical and horizontal comas showed linear changes across the visual field. The mean rate of change of vertical coma across the vertical meridian was significantly lower (p = 0.008) for emmetropes (-0.005 ± 0.002 μm/deg) than for myopes (-0.013 ± 0.004 μm/deg). The mean rate of change of horizontal coma across the horizontal meridian was lower (p = 0.07) for emmetropes (-0.006 ± 0.003 μm/deg) than myopes (-0.011 ± 0.004 μm/deg). ---------- Conclusion: We have found differences in patterns of higher order aberrations across the visual fields of emmetropes and myopes, with myopes showing the greater rates of change of horizontal and vertical coma.

The inherent equitable jurisdiction and the plenary power of the Supreme Court of New South Wales to order the winding up of companies

Not all companies in Australia are amenable to a winding up order pursuant to the Corporations Act 2001 (Cth). The Supreme Court of New South Wales has previously dealt with such winding up applications by apparently focusing on the inherent jurisdiction of the court to consider whether the court has jurisdiction to firstly consider the winding up application. This article proposes an original alternative paradigm: the plenary power provided to the court by s 23 of the Supreme Court Act 1970 (NSW) can be utilised to initially attract the jurisdiction of the court and subsequently the inherent jurisdiction specifically utilising the equitable “just and equitable” ground is available to the court to consider and make such a winding up order if appropriate. Variation of such a paradigm may also be available to the court when considering the inherent jurisdiction in relation to corporation matters more generally.

Robust image hashing using higher order spectral features

Robust image hashing seeks to transform a given input image into a shorter hashed version using a key-dependent non-invertible transform. These image hashes can be used for watermarking, image integrity authentication or image indexing for fast retrieval. This paper introduces a new method of generating image hashes based on extracting Higher Order Spectral features from the Radon projection of an input image. The feature extraction process is non-invertible, non-linear and different hashes can be produced from the same image through the use of random permutations of the input. We show that the transform is robust to typical image transformations such as JPEG compression, noise, scaling, rotation, smoothing and cropping. We evaluate our system using a verification-style framework based on calculating false match, false non-match likelihoods using the publicly available Uncompressed Colour Image database (UCID) of 1320 images. We also compare our results to Swaminathan’s Fourier-Mellin based hashing method with at least 1% EER improvement under noise, scaling and sharpening.