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

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

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

Digit recognition using trispectral features

Features derived from the trispectra of DFT magnitude slices are used for multi-font digit recognition. These features are insensitive to translation, rotation, or scaling of the input. They are also robust to noise. Classification accuracy tests were conducted on a common data base of 256× 256 pixel bilevel images of digits in 9 fonts. Randomly rotated and translated noisy versions were used for training and testing. The results indicate that the trispectral features are better than moment invariants and affine moment invariants. They achieve a classification accuracy of 95% compared to about 81% for Hu's (1962) moment invariants and 39% for the Flusser and Suk (1994) affine moment invariants on the same data in the presence of 1% impulse noise using a 1-NN classifier. For comparison, a multilayer perceptron with no normalization for rotations and translations yields 34% accuracy on 16× 16 pixel low-pass filtered and decimated versions of the same data.

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Antiretroviral therapy (ART) adherence among people living with HIV/AIDS (PLHIV) in the north of Vietnam : a multi-method approach

The antiretroviral therapy (ART) program for People Living with HIV/AIDS (PLHIV) in Vietnam has been scaled up rapidly in recent years (from 50 clients in 2003 to almost 38,000 in 2009). ART success is highly dependent on the ability of the patients to fully adhere to the prescribed treatment regimen. Despite the remarkable extension of ART programs in Vietnam, HIV/AIDS program managers still have little reliable data on levels of ART adherence and factors that might promote or reduce adherence. Several previous studies in Vietnam estimated extremely high levels of ART adherence among their samples, although there are reasons to question the veracity of the conclusion that adherence is nearly perfect. Further, no study has quantitatively assessed the factors influencing ART adherence. In order to reduce these gaps, this study was designed to include several phases and used a multi-method approach to examine levels of ART non-adherence and its relationship to a range of demographic, clinical, social and psychological factors. The study began with an exploratory qualitative phase employing four focus group discussions and 30 in-depth interviews with PLHIV, peer educators, carers and health care providers (HCPs). Survey interviews were completed with 615 PLHIV in five rural and urban out-patient clinics in northern Vietnam using an Audio Computer Assisted Self-Interview (ACASI) and clinical records extraction. The survey instrument was carefully developed through a systematic procedure to ensure its reliability and validity. Cultural appropriateness was considered in the design and implementation of both the qualitative study and the cross sectional survey. The qualitative study uncovered several contrary perceptions between health care providers and HIV/AIDS patients regarding the true levels of ART adherence. Health care providers often stated that most of their patients closely adhered to their regimens, while PLHIV and their peers reported that “it is not easy” to do so. The quantitative survey findings supported the PLHIV and their peers’ point of view in the qualitative study, because non-adherence to ART was relatively common among the study sample. Using the ACASI technique, the estimated prevalence of onemonth non-adherence measured by the Visual Analogue Scale (VAS) was 24.9% and the prevalence of four-day not-on-time-adherence using the modified Adult AIDS Clinical Trials Group (AACTG) instrument was 29%. Observed agreement between the two measures was 84% and kappa coefficient was 0.60 (SE=0.04 and p<0.0001). The good agreement between the two measures in the current study is consistent with those found in previous research and provides evidence of cross-validation of the estimated adherence levels. The qualitative study was also valuable in suggesting important variables for the survey conceptual framework and instrument development. The survey confirmed significant correlations between two measures of ART adherence (i.e. dose adherence and time adherence) and many factors identified in the qualitative study, but failed to find evidence of significant correlations of some other factors and ART adherence. Non-adherence to ART was significantly associated with untreated depression, heavy alcohol use, illicit drug use, experiences with medication side-effects, chance health locus of control, low quality of information from HCPs, low satisfaction with received support and poor social connectedness. No multivariate association was observed between ART adherence and age, gender, education, duration of ART, the use of adherence aids, disclosure of ART, patients’ ability to initiate communication with HCPs or distance between clinic and patients’ residence. This is the largest study yet reported in Asia to examine non-adherence to ART and its possible determinants. The evidence strongly supports recent calls from other developing nations for HIV/AIDS services to provide screening, counseling and treatment for patients with depressive symptoms, heavy use of alcohol and substance use. Counseling should also address fatalistic beliefs about chance or luck determining health outcomes. The data suggest that adherence could be enhanced by regularly providing information on ART and assisting patients to maintain social connectedness with their family and the community. This study highlights the benefits of using a multi-method approach in examining complex barriers and facilitators of medication adherence. It also demonstrated the utility of the ACASI interview method to enhance open disclosure by people living with HIV/AIDS and thus, increase the veracity of self-reported data.

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.