Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum C(l), this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual C(l)'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales l = 7 and l = 8. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.

Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum C(l), this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual C(l)'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales l = 7 and l = 8. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.

Power spectrum measurements by numerical methods. Internal research project 85-440.

Mode of access: Internet.

Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Power quality analysis applying a hybrid methodology with wavelet transforms and neural networks

A hybrid system to automatically detect, locate and classify disturbances affecting power quality in an electrical power system is presented in this paper. The disturbances characterized are events from an actual power distribution system simulated by the ATP (Alternative Transients Program) software. The hybrid approach introduced consists of two stages. In the first stage, the wavelet transform (WT) is used to detect disturbances in the system and to locate the time of their occurrence. When such an event is flagged, the second stage is triggered and various artificial neural networks (ANNs) are applied to classify the data measured during the disturbance(s). A computational logic using WTs and ANNs together with a graphical user interface (GU) between the algorithm and its end user is then implemented. The results obtained so far are promising and suggest that this approach could lead to a useful application in an actual distribution system. (C) 2009 Elsevier Ltd. All rights reserved.

Shannon information and power law analysis of the chromosome code

This paper studies the information content of the chromosomes of twenty-three species. Several statistics considering different number of bases for alphabet character encoding are derived. Based on the resulting histograms, word delimiters and character relative frequencies are identified. The knowledge of this data allows moving along each chromosome while evaluating the flow of characters and words. The resulting flux of information is captured by means of Shannon entropy. The results are explored in the perspective of power law relationships allowing a quantitative evaluation of the DNA of the species.

Power law analysis of financial index dynamics

Power law PL and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.

Identificação da actividade do sistema nervoso simpático e parassimpático em dados de pupilometria, utilizando a Singular Spectrum Analysis

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Influence of inter-electrode distance, contraction type, and muscle on the relationship between the sEMG power spectrum and contraction force.

INTRODUCTION: Spectral frequencies of the surface electromyogram (sEMG) increase with contraction force, but debate still exists on whether this increase is affected by various methodological and anatomical factors. This study aimed to investigate the influence of inter-electrode distance (IED) and contraction modality (step-wise vs. ramp) on the changes in spectral frequencies with increasing contraction strength for the vastus lateralis (VL) and vastus medialis (VM) muscles. METHODS: Twenty healthy male volunteers were assessed for isometric sEMG activity of the VM and VL, with the knee at 90° flexion. Subjects performed isometric ramp contractions in knee extension (6-s duration) with the force gradually increasing from 0 to 80 % MVC. Also, subjects performed 4-s step-wise isometric contractions at 10, 20, 30, 40, 50, 60, 70, and 80 % MVC. Interference sEMG signals were recorded simultaneously at different IEDs: 10, 20, 30, and 50 mm. The mean (F mean) and median (F median) frequencies and root mean square (RMS) of sEMG signals were calculated. RESULTS: For all IEDs, contraction modalities, and muscles tested, spectral frequencies increased significantly with increasing level of force up to 50-60 % MVC force. Spectral indexes increased systematically as IED was decreased. The sensitivity of spectral frequencies to changes in contraction force was independent of IED. The behaviour of spectral indexes with increasing contraction force was similar for step-wise and ramp contractions. CONCLUSIONS: In the VL and VM muscles, it is highly unlikely that a particular inter-electrode distance or contraction modality could have prevented the observation of the full extent of the increase in spectral frequencies with increasing force level.

On-axis joint transform correlation based on a four-level power spectrum

We propose a method to obtain a single centered correlation with use of a joint transform correlator. We analyze the required setup to carry out the whole process optically, and we also present experimental results.

3D noise power spectrum applied on clinical mdct scanners: effects of reconstruction algorithms and reconstruction filters

The noise power spectrum (NPS) is the reference metric for understanding the noise content in computed tomography (CT) images. To evaluate the noise properties of clinical multidetector (MDCT) scanners, local 2D and 3D NPSs were computed for different acquisition reconstruction parameters.A 64- and a 128-MDCT scanners were employed. Measurements were performed on a water phantom in axial and helical acquisition modes. CT dose index was identical for both installations. Influence of parameters such as the pitch, the reconstruction filter (soft, standard and bone) and the reconstruction algorithm (filtered-back projection (FBP), adaptive statistical iterative reconstruction (ASIR)) were investigated. Images were also reconstructed in the coronal plane using a reformat process. Then 2D and 3D NPS methods were computed.In axial acquisition mode, the 2D axial NPS showed an important magnitude variation as a function of the z-direction when measured at the phantom center. In helical mode, a directional dependency with lobular shape was observed while the magnitude of the NPS was kept constant. Important effects of the reconstruction filter, pitch and reconstruction algorithm were observed on 3D NPS results for both MDCTs. With ASIR, a reduction of the NPS magnitude and a shift of the NPS peak to the low frequency range were visible. 2D coronal NPS obtained from the reformat images was impacted by the interpolation when compared to 2D coronal NPS obtained from 3D measurements.The noise properties of volume measured in last generation MDCTs was studied using local 3D NPS metric. However, impact of the non-stationarity noise effect may need further investigations.

Development of phase retrieval algorithm and techniques for optical spectrum analysis

Coherent anti-Stokes Raman scattering is the powerful method of laser spectroscopy in which significant successes are achieved. However, the non-linear nature of CARS complicates the analysis of the received spectra. The objective of this Thesis is to develop a new phase retrieval algorithm for CARS. It utilizes the maximum entropy method and the new wavelet approach for spectroscopic background correction of a phase function. The method was developed to be easily automated and used on a large number of spectra of different substances.. The algorithm was successfully tested on experimental data.

Fourier self-deconvolution in coherent anti-Stokes Raman scattering spectrum analysis

Coherent anti-Stokes Raman scattering (CARS) microscopy is rapidly developing into a unique microscopic tool in biophysics, biology and the material sciences. The nonlinear nature of CARS spectroscopy complicates the analysis of the received spectra. There were developed mathematical methods for signal processing and for calculations spectra. Fourier self-deconvolution is a special high pass FFT filter which synthetically narrows the effective trace bandwidth features. As Fourier self-deconvolution can effectively reduce the noise, which may be at a higher spatial frequency than the peaks, without losing peak resolution. The idea of the work is to experiment the possibility of using wavelet decomposition in spectroscopic for background and noise removal, and Fourier transformation for linenarrowing.

Intrapartum hypoxia and power spectral analysis of fetal heart rate variability

Reliable detection of intrapartum fetal acidosis is crucial for preventing morbidity. Hypoxia-related changes of fetal heart rate variability (FHRV) are controlled by the autonomic nervous system. Subtle changes in FHRV that cannot be identified by inspection can be detected and quantified by power spectral analysis. Sympathetic activity relates to low-frequency FHRV and parasympathetic activity to both low- and high-frequency FHRV. The aim was to study whether intra partum fetal acidosis can be detected by analyzing spectral powers of FHRV, and whether spectral powers associate with hypoxia-induced changes in the fetal electrocardiogram and with the pH of fetal blood samples taken intrapartum. The FHRV of 817 R-R interval recordings, collected as a part of European multicenter studies, were analyzed. Acidosis was defined as cord pH ≤ 7.05 or scalp pH ≤ 7.20, and metabolic acidosis as cord pH ≤ 7.05 and base deficit ≥ 12 mmol/l. Intrapartum hypoxia increased the spectral powers of FHRV. As fetal acidosis deepened, FHRV decreased: fetuses with significant birth acidosis had, after an initial increase, a drop in spectral powers near delivery, suggesting a breakdown of fetal compensation. Furthermore, a change in excess of 30% of the low-to-high frequency ratio of FHRV was associated with fetal metabolic acidosis. The results suggest that a decrease in the spectral powers of FHRV signals concern for fetal wellbeing. A single measure alone cannot be used to reveal fetal hypoxia since the spectral powers vary widely intra-individually. With technical developments, continuous assessment of intra-individual changes in spectral powers of FHRV might aid in the detection of fetal compromise due to hypoxia.

Relative influence of age, resting heart rate and sedentary life style in short-term analysis of heart rate variability

In order to assess the relative influence of age, resting heart rate (HR) and sedentary life style, heart rate variability (HRV) was studied in two different groups. The young group (YG) consisted of 9 sedentary subjects aged 15 to 20 years (YG-S) and of 9 nonsedentary volunteers (YG-NS) also aged 15 to 20. The elderly sedentary group (ESG) consisted of 16 sedentary subjects aged 39 to 82 years. HRV was assessed using a short-term procedure (5 min). R-R variability was calculated in the time-domain by means of the root mean square successive differences. Frequency-domain HRV was evaluated by power spectrum analysis considering high frequency and low frequency bands. In the YG the effort tolerance was ranked in a bicycle stress test. HR was similar for both groups while ESG showed a reduced HRV compared with YG. Within each group, HRV displayed a negative correlation with HR. Although YG-NS had better effort tolerance than YG-S, their HR and HRV were not significantly different. We conclude that HRV is reduced with increasing HR or age, regardless of life style. The results obtained in our short-term study agree with others of longer duration by showing that age and HR are the main determinants of HRV. Our results do not support the idea that changes in HRV are related to regular physical activity.