Assessing vascular endothelial function using frequency and rank order statistics

Using frequency and rank order statistics (FROS), this study analyzed the fluctuations in arterial waveform amplitudes recorded from an air pressure sensing system before and after reactive hyperemia (RH) induction by temporary blood flow occlusion to evaluate the vascular endothelial function of aged and diabetic subjects. The modified probability-weighted distance (PWD) calculated from the FROS was compared with the dilatation index (DI) to evaluate its validity and sensitivity in the assessment of vascular endothelial function. The results showed that the PWD can provide a quantitative determination of the structural changes in the arterial pressure signals associated with regulation of vascular tone and blood pressure by intact vascular endothelium after the application of occlusion stress. Our study suggests that the use of FROS is a reliable noninvasive approach to the assessment of vascular endothelial degeneration in aging and diabetes.     

Locating wide band acoustic sources using higher order statistics

The conventional array processing algorithms are effective when the propagation model and the array geometry are known and when the additive noise is white or with a known covariance matrix. In several real situations these assumptions are not verified, hence a degradation of their performances. To cope with this problem, we resort to the higher order statistics of the received signals. The interest of the published papers was the separation of the narrow band and uncorrelated acoustic sources. In this paper, we propose a cumulant based algorithm to characterize the wide band and fully correlated signals. This algorithm removes the additive Gaussian noise and then improves the existing narrow band array processing techniques. This method consists in combining the different information contained in the analysis band by using the optimal transformation matrices. The basic idea is based on both the fourth order statistics and the whitening processing of the received data. This leads to cleaned data and then to improve the source separation. The performance of the proposed algorithm is obtained by simulations for several test cases of interest.     

Analysis of speckle in ultrasound images using fractional order statistics and the homodyned k-distribution

It is necessary to identify speckled regions in ultrasound images to control adaptive speckle suppression algorithms, for tissue characterisation, and to estimate the elevational separation of B-scans by speckle decorrelation. Previous authors have proposed classification techniques based on second order powers of the homodyned k-distribution, or lower order powers of the more limited k-distribution. In this paper we explore the speckle discrimination properties of statistics based on arbitrary powers of the ultrasound echo envelope signal using a combination of simulations and theoretical results from the homodyned k-distribution. We conclude that statistics based on powers less than one are surprisingly less effective than some higher powers. A simple discriminant function for speckle is evaluated quantitatively in simulation and qualitatively on sample B-scan images.     

Continuum gamma spectroscopy and order statistics

An analytical function deduced from Order Statistics is able to analytically reproduce lengthy Monte Carlo simulated Energy-Ordered Spectra obtained from heavy ion fusion-evaporation reactions in the case in which the level density is given by Constant Temperature Fermi Gas and the E1 gamma strength by the classical dipole law.     

The universal macroscopic statistics and phase transitions of rank distributions

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian Limit Law” (LLL). Applications of the LLL further establish: (i) a statistical explanation for the universal emergence of Pareto’s law in the context of rank distributions; (ii) a statistical classification of universal macroscopic network topologies; (iii) a statistical classification of universal macroscopic socioeconomic states; (iv) a statistical classification of Zipf’s law, and a characterization of the “self-organized criticality” it manifests.     

Optical-digital processors for morphological and rank order filtering

Non-linear rank order and morphological filtering can be achieved in optical-digital processors. In these processors, all convolutions are performed in inherently parallel optical correlators. Arithmetic and logic operations are made digitally. Due to the threshold decomposition concept, grey scale images are sequentially treated slice by slice. The optical-digital method of local histogram calculation within both binary and weighted neighbourhoods allows local non-linear operations. We derive rank order and morphological filters from optically calculated convolutions. Several configurations of optical convolvers are discussed. Further improvements in the technology of spatial light modulators and encoded light sources are needed before these processors' practical uses will appear.     

Universal order statistics of random walks

We study analytically the order statistics of a time series generated by the positions of a symmetric random walk of n steps with step lengths of finite variance σ(2). We show that the statistics of the gap d(k,n) = M(k,n)-M(k+1,n) between the kth and the (k+1)th maximum of the time series becomes stationary, i.e., independent of n as n → ∞ and exhibits a rich, universal behavior. The mean stationary gap exhibits a universal algebraic decay for large k, ~d(k,∞)-/σ 1/sqrt[2πk], independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, Pr(d(k,∞) = δ) ~/= (sqrt[k]/σ)P(δsqrt[k]/σ), in the regime δ~ (d(k,∞)). The scaling function P(x) is universal and has an unexpected power law tail, P(x) ~ x(-4) for large x. For δ> (d(k,∞)) the scaling breaks down and the pdf gets cut off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multiscaling behavior.     

Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach

The heartbeat rate signal provides an invaluable means of assessing the sympathetic-parasympathetic balance of the human autonomic nervous system and thus represents an ideal diagnostic mechanism for detecting a variety of disorders such as epilepsy, cardiac disease and so forth. The current study analyses the dynamics of the heartbeat rate signal of known epilepsy sufferers in order to obtain a detailed understanding of the heart rate pattern during a seizure event. In the proposed approach, the ECG signals are converted into heartbeat rate signals and the embedology theorem is then used to construct the corresponding multidimensional phase space. The dynamics of the heartbeat rate signal are then analyzed before, during and after an epileptic seizure by examining the maximum Lyapunov exponent and the correlation dimension of the attractors in the reconstructed phase space. In general, the results reveal that the heartbeat rate signal transits from an aperiodic, highly-complex behaviour before an epileptic seizure to a low dimensional chaotic motion during the seizure event. Following the seizure, the signal trajectories return to a highly-complex state, and the complex signal patterns associated with normal physiological conditions reappear.     

Fractionalization, topological order, and quasiparticle statistics

We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions d > or = 2. In d = 2 with genus g, we derive the existence of the minimum topological degeneracy q(g) if the charge is fractionalized in units of 1/q, irrespective of microscopic model or effective theory. Furthermore, if the quasiparticle is either boson or fermion, it must be at least q(2g).     

Multifractal analysis of heartbeat dynamics during meditation training

We investigate the multifractality of heartbeat dynamics during Chinese CHI meditation in healthy young adults. The results show that the range of multifractal singularity spectrum of heartbeat interval time series during meditation is significantly narrower than those in the pre-meditation state of the same subject, which indicates that during meditation the heartbeat becomes regular and the degree of multifractality decreases.     

Empirical analysis on temporal statistics of human correspondence patterns

Recently, extensive empirical evidence shows that the timing of human behaviors obeys non-Possion statistics with heavy-tailed interevent time distribution. In this paper, we empirically study the correspondence pattern of a great Chinese scientist, named Hsue-Shen Tsien. Both the interevent time distribution and response time distributions deviate from the Poisson statistics, showing an approximate power-law decaying. The two power-law exponents are more or less the same (about 2.1), which strongly support the hypothesis in [A. Vázquez, J.G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási, Phys. Rev. E 73 (2006) 036127] that the response time distribution of the tasks could in fact drive the interevent time distribution, and both the two distributions should decay with the same exponent. Our result is against the claim in [A. Vázquez, J.G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási, Phys. Rev. E 73 (2006) 036127], which suggests the human correspondence pattern belongs to a universality class with exponent 1.5.     

Stacked sparse autoencoder in hyperspectral data classification using spectral-spatial,higher order statistics and multifractal spectrum features

This paper proposes a novel classification paradigm for hyperspectral image (HSI) using feature-level fusion and deep learning-based methodologies. Operation is carried out in three main steps. First, during a pre-processing stage, wave atoms are introduced into bilateral filter to smooth HSI, and this strategy can effectively attenuate noise and restore texture information. Meanwhile, high quality spectral-spatial features can be extracted from HSI by taking geometric closeness and photometric similarity among pixels into consideration simultaneously. Second, higher order statistics techniques are firstly introduced into hyperspectral data classification to characterize the phase correlations of spectral curves. Third, multifractal spectrum features are extracted to characterize the singularities and self-similarities of spectra shapes. To this end, a feature-level fusion is applied to the extracted spectral-spatial features along with higher order statistics and multifractal spectrum features. Finally, stacked sparse autoencoder is utilized to learn more abstract and invariant high-level features from the multiple feature sets, and then random forest classifier is employed to perform supervised fine-tuning and classification. Experimental results on two real hyperspectral data sets demonstrate that the proposed method outperforms some traditional alternatives.     

Formant frequency analysis of children''s spoken and sung vowels using sweeping fundamental frequency production

High-pitched productions present difficulties in formant frequency analysis due to wide harmonic spacing and poorly defined formants. As a consequence, there is little reliable data regarding children's spoken or sung vowel formants. Twenty-nine 11-year-old Swedish children were asked to produce 4 sustained spoken and sung vowels. In order to circumvent the problem of wide harmonic spacing, F₁ and F₂ measurements were taken from vowels produced with a sweeping F₀. Experienced choir singers were selected as subjects in order to minimize the larynx height adjustments associated with pitch variation in less skilled subjects. Results showed significantly higher formant frequencies for speech than for singing. Formants were consistently higher in girls than in boys suggesting longer vocal tracts in these preadolescent boys. Furthermore, formant scaling demonstrated vowel dependent differences between boys and girls suggesting non-uniform differences in male and female vocal tract dimensions. These vowel-dependent sex differences were not consistent with adult data.     

Broken asymmetry of the human heartbeat: loss of time irreversibility in aging and disease

Time irreversibility, a fundamental property of nonequilibrium systems, should be of importance in assessing the status of physiological processes that operate over a wide range of scales. However, measurement of this property in living systems has been limited. We provide a computational method derived from basic physics assumptions to quantify time asymmetry over multiple scales and apply it to the human heartbeat time series in health and disease. We find that the multiscale time asymmetry index is highest for a time series from young subjects and decreases with aging or heart disease. Loss of time irreversibility may provide a new way of assessing the functionality of living systems that operate far from equilibrium.     

Neonatal EEG signal characteristics using time frequency analysis

Time-frequency analysis is a way to represent the energy contents of a signal in the joint time-frequency domain. It provides a good visual way to separate the frequency contents of a multi-component signal, and display the changes of these components with respect to time. This paper outlines investigative work on neonatal EEG signals using time-frequency analysis. The Cohen’s class distributions are discussed, and kernel optimisation for the Cohen’s class distributions is outlined. Segments of EEG with different background continuity states are analysed using a Cohen’s class distribution, and their characteristics are discussed. Through this paper, interesting information that offers insight towards the EEG signal can be visualized from the time frequency analysis.     

First order statistics of speckle produced by weak scattering media

A weak scattering medium produces random phases in a transmitted or reflected wavefront distributed over less than 2π. The far-field speckle pattern has a central maximum. The statistics of intensity in this maximum are calculated and the applications of the results to surface roughness measurement are indicated.     

Velocity measurement by first order statistics of time-differentiated laser speckles

This paper describes a new and very simple technique for the measurement of mean velocities of moving scatterers. Both, basic statistics and experimental results are presented for the velocimetry of scattering objects by the variance of the time-derivative of the intensity in the speckle field.     

Long-range anticorrelations and non-Gaussian behavior of the heartbeat

We find that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range anticorrelations (up to 10(4) heart beats). Furthermore, we find that the histogram for the heartbeat intervals increments is well described by a Lévy stable distribution. For a group of subjects with severe heart disease, we find that the distribution is unchanged, but the long-range correlations vanish. Therefore, the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat.     

Voxelwise analysis of diffusion MRI of cervical spinal cord using tract-based spatial statistics

Robust voxelwise analysis using tract-based spatial statistics (TBSS) together with permutation statistical method is standardly used in analyzing diffusion tensor imaging (DTI) of brain. A similar analytical method could be useful when studying DTI of cervical spinal cord.Based on anatomical data of sixty-four healthy volunteers, white (WM) and gray matter (GM) masks were created and subsequently registered into DTI space. Using TBSS, two skeleton types were created (single line and dilated for WM as well as GM). From anatomical data, percentage rates of overlap were calculated for all skeletons in relation to WM and GM masks.Voxelwise analysis of fractional anisotropy values depending on age and sex was conducted. Correlation of fraction anisotropy values with age of subjects was also evaluated. The two WM skeleton types showed a high overlap rate with WM masks (~94%); GM skeletons showed lower rates (56% and 42%, respectively, for single line and dilated). WM and GM areas where fraction anisotropy values differ between sexes were identified (p < .05). Furthermore, using voxelwise analysis such WM voxels were identified where fraction anisotropy values differ depending on age (p < .05) and in these voxels linear dependence of fraction anisotropy and age (r = −0.57, p < .001) was confirmed by regression analysis. This dependence was not proven when using WM anatomical masks (r = −0.21, p = .10).The analytical approach presented shown to be useful for group analysis of DTI data for cervical spinal cord.