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

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum 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, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

Homo- and heteronuclear meso,meso-(E)-Ethene-1,2-diyl-Linked Diporphyrins : preparation, X-ray crystal structure, electronic absorption and emission spectra and density functional theory calculations

Homo-and heteronuclear meso,meso-(E)-ethene-1,2-diyl-linked diporphyrins have been prepared by the Suzuki coupling of porphyrinylboronates and iodovinylporphyrins. Combinations comprising 5,10,15-triphenylporphyrin (TriPP) on both ends of the ethene-1,2-diyl bridge M 210 (M 2=H 2/Ni, Ni 2, Ni/Zn, H 4, H 2Zn, Zn 2) and 5,15-bis(3,5-di-tert-butylphenyl)porphyrinato-nickel(II) on one end and H 2, Ni, and ZnTriPP on the other (M 211), enable the first studies of this class of compounds possessing intrinsic polarity. The compounds were characterized by electronic absorption and steady state emission spectra, 1H NMR spectra, and for the Ni 2 bis(TriPP) complex Ni 210, single crystal X-ray structure determination. The crystal structure shows ruffled distortions of the porphyrin rings, typical of Ni II porphyrins, and the (E)-C 2H 2 bridge makes a dihedral angle of 50° with the mean planes of the macrocycles. The result is a stepped parallel arrangement of the porphyrin rings. The dihedral angles in the solid state reflect the interplay of steric and electronic effects of the bridge on interporphyrin communication. The emission spectra in particular, suggest energy transfer across the bridge is fast in conformations in which the bridge is nearly coplanar with the rings. Comparisons of the fluorescence behaviour of H 410 and H 2Ni10 show strong quenching of the free base fluorescence when the complex is excited at the lower energy component of the Soret band, a feature associated in the literature with more planar conformations. TDDFT calculations on the gas-phase optimized geometry of Ni 210 reproduce the features of the experimental electronic absorption spectrum within 0.1 eV. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Infrared spectra of Mg-SiO smokes : comparison with analytical electron microscopy studies

An important component of current models for interstellar and circumstellar evolution is the infrared (IR)spectral data collected from stellar outflows around oxygen-rich stars and from the general interstellar medium [1]. IR spectra from these celestial bodies are usually interpreted as showing the general properties of sub-micron sized silicate grains [2]. Two major features at 10 and 20 microns are reasonably attributed to amorphous olivine or pyroxene (e.g. Mg2Si04 or MgSi03) on the basis of comparisons with natural standards and vapor condensed silicates [3-6]. In an attempt to define crystallisation rates for spectrally amorphous condensates, Nuth and Donn [5] annealed experimentally produced amorphous magnesium silicate smokes at 1000K. On analysing these smokes at various annealing times, Nuth and Donn [5] showed that changes in crystallinity measured by bulk X-ray diffraction occured at longer annealing times (days) than changes measured by IR spectra (a few hours). To better define the onset of crystallinity in these magnesium silicates, we have examined each annealed product using a JEOL 1OOCX analytical electron microscope (AEM). In addition, the development of chemical diversity with annealing has been monitored using energy dispersive spectroscopy of individual grains from areas <20nm in diameter. Furthermore, the crystallisation kinetics of these smokes under ambient, room temperature conditions have been examined using bulk and fourier transform infrared (FTIR)spectra.

Near infrared (NIR) absorption spectra correlates with subchondral bone micro-CT parameters in osteoarthritic rat models

Determining the properties and integrity of subchondral bone in the developmental stages of osteoarthritis, especially in a form that can facilitate real-time characterization for diagnostic and decision-making purposes, is still a matter for research and development. This paper presents relationships between near infrared absorption spectra and properties of subchondral bone obtained from 3 models of osteoarthritic degeneration induced in laboratory rats via: (i) menisectomy (MSX); (ii) anterior cruciate ligament transaction (ACL); and (iii) intra-articular injection of mono-ido-acetate (1 mg) (MIA), in the right knee joint, with 12 rats per model group (N = 36). After 8 weeks, the animals were sacrificed and knee joints were collected. A custom-made diffuse reflectance NIR probe of diameter 5 mm was placed on the tibial surface and spectral data were acquired from each specimen in the wavenumber range 4000–12 500 cm− 1. After spectral acquisition, micro computed tomography (micro-CT) was performed on the samples and subchondral bone parameters namely: bone volume (BV) and bone mineral density (BMD) were extracted from the micro-CT data. Statistical correlation was then conducted between these parameters and regions of the near infrared spectra using multivariate techniques including principal component analysis (PCA), discriminant analysis (DA), and partial least squares (PLS) regression. Statistically significant linear correlations were found between the near infrared absorption spectra and subchondral bone BMD (R2 = 98.84%) and BV (R2 = 97.87%). In conclusion, near infrared spectroscopic probing can be used to detect, qualify and quantify changes in the composition of the subchondral bone, and could potentially assist in distinguishing healthy from OA bone as demonstrated with our laboratory rat models.

Kinetic study of goethite dehydration and the effect of aluminium substitution on the dehydrate

Goethite and Al-substituted goethite were synthesized and were characterized using XRD and XRF. The kinetic study of goethite dehydrate was investigated by TG and DTG at different heating rates (2, 5, 10, 15, 20 ◦C/min) and the effect of Al substitution for Fe on dehydrate was studied. The results showed that two types of absorbed water with the same Ed values of 3.4, 6.2 kJ/mol were confirmed on goethite and Alsubstituted goethite. Three types of hydroxyl units were proved, one being on the surface and the other two being in the structure of goethite. The substitution of Al for Fe in the structure of goethite decreases the desorption rate of hydroxyl, increases the dehydroxylation temperature, broadens the desorption peaks in DTG curves, and improves the Ed values from 19.4, 20.4, 26.1 kJ/mol to 21.6, 30, 33.6 kJ/mol when Al substitution comes to 9.1%.