Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

MIMO and SISO identification of radiation force terms for models of marine structures in waves

This paper presents a discussion on the use of MIMO and SISO techniques for identification of the radiation force terms in models for surface vessels. We compare and discuss two techniques recently proposed in literature for this application: time domain identification and frequency domain identification. We compare the methods in terms of estimates model order, accuracy of the fit, use of the available information, and ease of use and implementation.

Natural convection heat transfer in a baffled triangular enclosure

To reduce the natural convection heat loss from enclosures many researchers used convection suppression devices in the past. In this study a single baffle is used under the top tip to investigate numerically the natural convection heat loss in an attic shaped enclosure which is a cost effective approach. The case considered here is one inclined wall of the enclosure is uniformly heated while the other inclined wall is uniformly cooled with adiabatic bottom wall. The finite volume method has been used to discretize the governing equations, with the QUICK scheme approximating the advection term. The diffusion terms are discretized using central-differencing with second order accuracy. A wide range of governing parameters are studied (Rayleigh number, aspect ratio, baffle length etc.). It is observed that the heat transfer due to natural convection in the enclosure reduces when the baffle length is increased. Effects of other parameters on heat transfer and flow field are described in this study.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Clinical Accuracy of the MedGem Indirect Calorimeter for Measuring Resting Energy Expenditure in Cancer Patients

OBJECTIVE: To compare, in patients with cancer and in healthy subjects, measured resting energy expenditure (REE) from traditional indirect calorimetry to a new portable device (MedGem) and predicted REE. DESIGN: Cross-sectional clinical validation study. SETTING: Private radiation oncology centre, Brisbane, Australia. SUBJECTS: Cancer patients (n = 18) and healthy subjects (n = 17) aged 37-86 y, with body mass indices ranging from 18 to 42 kg/m(2). INTERVENTIONS: Oxygen consumption (VO(2)) and REE were measured by VMax229 (VM) and MedGem (MG) indirect calorimeters in random order after a 12-h fast and 30-min rest. REE was also calculated from the MG without adjustment for nitrogen excretion (MGN) and estimated from Harris-Benedict prediction equations. Data were analysed using the Bland and Altman approach, based on a clinically acceptable difference between methods of 5%. RESULTS: The mean bias (MGN-VM) was 10% and limits of agreement were -42 to 21% for cancer patients; mean bias -5% with limits of -45 to 35% for healthy subjects. Less than half of the cancer patients (n = 7, 46.7%) and only a third (n = 5, 33.3%) of healthy subjects had measured REE by MGN within clinically acceptable limits of VM. Predicted REE showed a mean bias (HB-VM) of -5% for cancer patients and 4% for healthy subjects, with limits of agreement of -30 to 20% and -27 to 34%, respectively. CONCLUSIONS: Limits of agreement for the MG and Harris Benedict equations compared to traditional indirect calorimetry were similar but wide, indicating poor clinical accuracy for determining the REE of individual cancer patients and healthy subjects.

Speaker identification using higher order spectral phase features and their effectiveness vis-a-vis Mel-Cepstral features

The effectiveness of higher-order spectral (HOS) phase features in speaker recognition is investigated by comparison with Mel Cepstral features on the same speech data. HOS phase features retain phase information from the Fourier spectrum unlikeMel–frequency Cepstral coefficients (MFCC). Gaussian mixture models are constructed from Mel– Cepstral features and HOS features, respectively, for the same data from various speakers in the Switchboard telephone Speech Corpus. Feature clusters, model parameters and classification performance are analyzed. HOS phase features on their own provide a correct identification rate of about 97% on the chosen subset of the corpus. This is the same level of accuracy as provided by MFCCs. Cluster plots and model parameters are compared to show that HOS phase features can provide complementary information to better discriminate between speakers.

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.

Analysis of cardiac and epileptic signals using higher order spectra

The theory of nonlinear dyamic systems provides some new methods to handle complex systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers are applying the concepts from this theory to bio-signal analysis. In this work, the complex dynamics of the bio-signals such as electrocardiogram (ECG) and electroencephalogram (EEG) are analyzed using the tools of nonlinear systems theory. In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The Electrocardiogram (ECG) is an important biosignal 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. 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 computerbased intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and four classes of arrhythmia. This thesis presents some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. Several features were extracted from the HOS and subjected 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. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, seven features were extracted from the heart rate signals using HOS and fed to a support vector machine (SVM) for classification. The performance evaluation protocol in this thesis uses 330 subjects consisting of five different kinds of cardiac disease conditions. The classifier achieved a sensitivity of 90% and a specificity of 89%. This system is ready to run on larger data sets. In EEG analysis, the search for hidden information for identification of seizures has a long history. Epilepsy is a pathological condition characterized by spontaneous and unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic early detection of the seizure onsets would help the patients and observers to take appropriate precautions. 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, these features are used to train both a Gaussian mixture model (GMM) classifier and a Support Vector Machine (SVM) classifier. Results show that the classifiers were able to achieve 93.11% and 92.67% classification accuracy, respectively, with selected HOS based features. About 2 hours of EEG recordings from 10 patients were used in this study. This thesis introduces unique bispectrum and bicoherence plots for various cardiac conditions and for normal, background and epileptic EEG signals. These plots reveal distinct patterns. The patterns are useful for visual interpretation by those without a deep understanding of spectral analysis such as medical practitioners. It includes original contributions in extracting features from HRV and EEG signals using HOS and entropy, in analyzing the statistical properties of such features on real data and in automated classification using these features with GMM and SVM classifiers.

Striving to realise the European idea : judging the news media’s accounts of how the Berlin Wall gave impetus to a new order across Europe

The 1990 European Community was taken by surprise, by the urgency of demands from the newly-elected Eastern European governments to become member countries. Those governments were honouring the mass social movement of the streets, the year before, demanding free elections and a liberal economic system associated with “Europe”. The mass movement had actually been accompanied by much activity within institutional politics, in Western Europe, the former “satellite” states, the Soviet Union and the United States, to set up new structures – with German reunification and an expanded EC as the centre-piece. This paper draws on the writer’s doctoral dissertation on mass media in the collapse of the Eastern bloc, focused on the Berlin Wall – documenting both public protests and institutional negotiations. For example the writer as a correspondent in Europe from that time, recounts interventions of the German Chancellor, Helmut Kohl, at a European summit in Paris nine days after the “Wall”, and separate negotiations with the French President, Francois Mitterrand -- on the reunification, and EU monetary union after 1992. Through such processes, the “European idea” would receive fresh impetus, though the EU which eventuated, came with many altered expectations. It is argued here that as a result of the shock of 1989, a “social” Europe can be seen emerging, as a shared experience of daily life -- especially among people born during the last two decades of European consolidation. The paper draws on the author’s major research, in four parts: (1) Field observation from the strategic vantage point of a news correspondent. This includes a treatment of evidence at the time, of the wishes and intentions of the mass public (including the unexpected drive to join the European Community), and those of governments, (e.g. thoughts of a “Tienanmen Square solution” in East Berlin, versus the non-intervention policies of the Soviet leader, Mikhail Gorbachev). (2) A review of coverage of the crisis of 1989 by major news media outlets, treated as a history of the process. (3) As a comparison, and a test of accuracy and analysis; a review of conventional histories of the crisis appearing a decade later.(4) A further review, and test, provided by journalists responsible for the coverage of the time, as reflection on practice – obtained from semi-structured interviews.

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

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.