Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Cardiac health diagnosis using higher order spectra and support vector machine

The Electrocardiogram (ECG) is an important bio-signal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. 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. The HRV signal can be used as a base signal to observe the heart's functioning. These signals are non-linear and non-stationary in nature. So, higher order spectral (HOS) analysis, which is more suitable for non-linear systems and is robust to noise, was used. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, we have extracted seven features from the heart rate signals using HOS and fed them to a support vector machine (SVM) for classification. Our performance evaluation protocol uses 330 subjects consisting of five different kinds of cardiac disease conditions. We demonstrate a sensitivity of 90% for the classifier with a specificity of 87.93%. Our system is ready to run on larger data sets.

Statistical analyses of weigh-in-motion data for bridge live load development

This paper discusses the statistical analyses used to derive bridge live loads models for Hong Kong from a 10-year weigh-in-motion (WIM) data. The statistical concepts required and the terminologies adopted in the development of bridge live load models are introduced. This paper includes studies for representative vehicles from the large amount of WIM data in Hong Kong. Different load affecting parameters such as gross vehicle weights, axle weights, axle spacings, average daily number of trucks etc are first analyzed by various stochastic processes in order to obtain the mathematical distributions of these parameters. As a prerequisite to determine accurate bridge design loadings in Hong Kong, this study not only takes advantages of code formulation methods used internationally but also presents a new method for modelling collected WIM data using a statistical approach.

Developing a research method to test a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). The paper begins with an update on a key development in a new early/first-order procurement decision making model that deploys production cost/benefit theory and theories concerning transaction costs from the New Institutional Economics, in order to identify a procurement mode that is likely to deliver the best ratio of production costs and transaction costs to production benefits, and therefore deliver superior VfM relative to alternative procurement modes. In doing so, the new procurement model is also able to address the uncertainty concerning the relative merits of Public-Private Partnerships (PPP) and non-PPP procurement approaches. The main aim of the paper is to develop competition as a dependent variable/proxy for VfM and a hypothesis (overarching proposition), as well as developing a research method to test the new procurement model. Competition reflects both production costs and benefits (absolute level of competition) and transaction costs (level of realised competition) and is a key proxy for VfM. Using competition as a proxy for VfM, the overarching proposition is given as: When the actual procurement mode matches the predicted (theoretical) procurement mode (informed by the new procurement model), then actual competition is expected to match potential competition (based on actual capacity). To collect data to test this proposition, the research method that is developed in this paper combines a survey and case study approach. More specifically, data collection instruments for the surveys to collect data on actual procurement, actual competition and potential competition are outlined. Finally, plans for analysing this survey data are briefly mentioned, along with noting the planned use of analytical pattern matching in deploying the new procurement model and in order to develop the predicted (theoretical) procurement mode.

Application of higher order spectra to identify epileptic EEG

Epilepsy is characterized by the spontaneous and seemingly unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic system that detects seizure onsets would allow patients or the people near them to take appropriate precautions, and could provide more insight into this phenomenon. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, we made a comparative study of the performance of Gaussian mixture model (GMM) and Support Vector Machine (SVM) classifiers using the features derived from HOS and from the power spectrum. Results show that the selected HOS based features achieve 93.11% classification accuracy compared to 88.78% with features derived from the power spectrum for a GMM classifier. The SVM classifier achieves an improvement from 86.89% with features based on the power spectrum to 92.56% with features based on the bispectrum.

Pattern recognition using invariants defined from higher order spectra : 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants

Shape discrimination using invariants defined from higher-order spectra

An approach to pattern recognition using invariant parameters based on higher-order spectra is presented. In particular, bispectral invariants are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale- and amplification-invariant. A minimal set of these invariants is selected as the feature vector for pattern classification. Pattern recognition using higher-order spectral invariants is fast, suited for parallel implementation, and works for signals corrupted by Gaussian noise. The classification technique is shown to distinguish two similar but different bolts given their one-dimensional profiles

A general procedure for the derivation of principal domains of higher-order spectra

A general procedure to determine the principal domain (i.e., nonredundant region of computation) of any higher-order spectrum is presented, using the bispectrum as an example. The procedure is then applied to derive the principal domain of the trispectrum of a real-valued, stationary time series. These results are easily extended to compute the principal domains of other higher-order spectra

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies