Simulating global properties of electroencephalograms with minimal random neural networks

The human electroencephalogram (EEG) is globally characterized by a 1/f power spectrum superimposed with certain peaks, whereby the "alpha peak" in a frequency range of 8-14 Hz is the most prominent one for relaxed states of wakefulness. We present simulations of a minimal dynamical network model of leaky integrator neurons attached to the nodes of an evolving directed and weighted random graph (an Erdos-Renyi graph). We derive a model of the dendritic field potential (DFP) for the neurons leading to a simulated EEG that describes the global activity of the network. Depending on the network size, we find an oscillatory transition of the simulated EEG when the network reaches a critical connectivity. This transition, indicated by a suitably defined order parameter, is reflected by a sudden change of the network's topology when super-cycles are formed from merging isolated loops. After the oscillatory transition, the power spectra of simulated EEG time series exhibit a 1/f continuum superimposed with certain peaks. (c) 2007 Elsevier B.V. All rights reserved.

Effects of non-uniform crosswind fields on scintillometry measurements

The effects of a non-uniform wind field along the path of a scintillometer are investigated. Theoretical spectra are calculated for a range of scenarios where the crosswind varies in space or time and compared to the ‘ideal’ spectrum based on a constant uniform crosswind. It is verified that the refractive-index structure parameter relation with the scintillometer signal remains valid and invariant for both spatially and temporally-varying crosswinds. However, the spectral shape may change significantly preventing accurate estimation of the crosswind speed from the peak of the frequency spectrum and retrieval of the structure parameter from the plateau of the power spectrum. On comparison with experimental data, non-uniform crosswind conditions could be responsible for previously unexplained features sometimes seen in observed spectra. By accounting for the distribution of crosswind, theoretical spectra can be generated that closely replicate the observations, leading to a better understanding of the measurements. Spatial variability of wind speeds should be expected for paths other than those that are parallel to the surface and over flat, homogenous areas, whilst fluctuations in time are important for all sites.

Evidence for a respiratory component, similar to mammalian respiratory sinus arrhythmia, in the heart rate variability signal from the rattlesnake, Crotalus durissus terrificus

Autonomic control of heart rate variability and the central location of vagal preganglionic neurones (VPN) were examined in the rattlesnake ( Crotalus durissus terrificus), in order to determine whether respiratory sinus arrhythmia (RSA) occurred in a similar manner to that described for mammals. Resting ECG signals were recorded in undisturbed snakes using miniature datalogging devices, and the presence of oscillations in heart rate (f(H)) was assessed by power spectral analysis (PSA). This mathematical technique provides a graphical output that enables the estimation of cardiac autonomic control by measuring periodic changes in the heart beat interval. At fH above 19 min(-1) spectra were mainly characterised by low frequency components, reflecting mainly adrenergic tonus on the heart. By contrast, at f(H) below 19 min(-1) spectra typically contained high frequency components, demonstrated to be cholinergic in origin. Snakes with a f(H) > 19 min(-1) may therefore have insufficient cholinergic tonus and/or too high an adrenergic tonus acting upon the heart for respiratory sinus arrhythmia ( RSA) to develop. A parallel study monitored f(Hd) simultaneously with the intraperitoneal pressures associated with lung inflation. Snakes with a fH < 19 min(-1) exhibited a high frequency (HF) peak in the power spectrum, which correlated with ventilation rate (f(V)). Adrenergic blockade by propranolol infusion increased the variability of the ventilation cycle, and the oscillatory component of the f(H) spectrum broadened accordingly. Infusion of atropine to effect cholinergic blockade abolished this HF component, confirming a role for vagal control of the heart in matching f(H) and f(V) in the rattlesnake. A neuroanatomical study of the brainstem revealed two locations for vagal preganglionic neurones (VPN). This is consistent with the suggestion that generation of ventilatory components in the heart rate variability (HRV) signal are dependent on spatially distinct loci for cardiac VPN. Therefore, this study has demonstrated the presence of RSA in the HRV signal and a dual location for VPN in the rattlesnake. We suggest there to be a causal relationship between these two observations.

Fractal descriptors based on Fourier spectrum applied to texture analysis

This work proposes the development and study of a novel technique lot the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal dimension calculus. The power spectrum of the Fourier transform of the image is plotted against the frequency in a log-log scale and a multiscale transform is applied to this curve. The obtained values are taken as the fractal descriptors of the image. The validation of the proposal is performed by the use of the descriptors for the classification of a dataset of texture images whose real classes are previously known. The classification precision is compared to other fractal descriptors known in the literature. The results confirm the efficiency of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.

Compressed sensing based cyclic feature spectrum sensing for cognitive radios

Spectrum sensing is currently one of the most challenging design problems in cognitive radio. A robust spectrum sensing technique is important in allowing implementation of a practical dynamic spectrum access in noisy and interference uncertain environments. In addition, it is desired to minimize the sensing time, while meeting the stringent cognitive radio application requirements. To cope with this challenge, cyclic spectrum sensing techniques have been proposed. However, such techniques require very high sampling rates in the wideband regime and thus are costly in hardware implementation and power consumption. In this thesis the concept of compressed sensing is applied to circumvent this problem by utilizing the sparsity of the two-dimensional cyclic spectrum. Compressive sampling is used to reduce the sampling rate and a recovery method is developed for re- constructing the sparse cyclic spectrum from the compressed samples. The reconstruction solution used, exploits the sparsity structure in the two-dimensional cyclic spectrum do-main which is different from conventional compressed sensing techniques for vector-form sparse signals. The entire wideband cyclic spectrum is reconstructed from sub-Nyquist-rate samples for simultaneous detection of multiple signal sources. After the cyclic spectrum recovery two methods are proposed to make spectral occupancy decisions from the recovered cyclic spectrum: a band-by-band multi-cycle detector which works for all modulation schemes, and a fast and simple thresholding method that works for Binary Phase Shift Keying (BPSK) signals only. In addition a method for recovering the power spectrum of stationary signals is developed as a special case. Simulation results demonstrate that the proposed spectrum sensing algorithms can significantly reduce sampling rate without sacrifcing performance. The robustness of the algorithms to the noise uncertainty of the wireless channel is also shown.

O EFEITO DO CONTROLE RESPIRATÓRIO EM VARIÁVEIS ELETROFISIOLÓGICAS DA ATENÇÃO

A prática do ioga tem se tornado cada vez mais popular, não apenas pelos benefícios físicos, mas principalmente pelo bem-estar psicológico trazido pela sua prática. Um dos componentes do ioga é o Prãnãyama, ou controle da respiração. A atenção e a respiração são dois mecanismos fisiológicos e involuntários requeridos para a execução do Prãnãyama. O principal objetivo desse estudo foi verificar se variáveis contínuas do EEG (potência de diferentes faixas que o compõem) seriam moduladas pelo controle respiratório, comparando-se separadamente as duas fases do ciclo respiratório (inspiração e expiração), na situação de respiração espontânea e controlada. Fizeram parte do estudo 19 sujeitos (7 homens/12 mulheres, idade média de 36,89 e DP = ± 14,46) que foram convidados a participar da pesquisa nas dependências da Faculdade de Saúde da Universidade Metodista de São Paulo. Para o registro do eletroencefalograma foi utilizado um sistema de posicionamento de cinco eletrodos Ag AgCl (FPz, Fz, Cz, Pz e Oz) fixados a uma touca de posicionamento rápido (Quick-Cap, Neuromedical Supplies®), em sistema 10-20. Foram obtidos valores de máxima amplitude de potência (espectro de potência no domínio da frequência) nas frequências teta, alfa e beta e delta e calculada a razão teta/beta nas diferentes fases do ciclo respiratório (inspiração e expiração), separadamente, nas condições de respiração espontânea e de controle respiratório. Para o registro do ciclo respiratório, foi utilizada uma cinta de esforço respiratório M01 (Pletismógrafo). Os resultados mostram diferenças significativas entre as condições de respiração espontânea e de controle com valores das médias da razão teta/beta menores na respiração controlada do que na respiração espontânea e valores de média da potência alfa sempre maiores no controle respiratório. Diferenças significativas foram encontradas na comparação entre inspiração e expiração da respiração controlada com diminuição dos valores das médias da razão teta/beta na inspiração e aumento nos valores das médias da potência alfa, sobretudo na expiração. Os achados deste estudo trazem evidências de que o controle respiratório modula variáveis eletrofisiológicas relativas à atenção refletindo um estado de alerta, porém mais relaxado do que na situação de respiração espontânea.

Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

O EFEITO DO CONTROLE RESPIRATÓRIO EM VARIÁVEIS ELETROFISIOLÓGICAS DA ATENÇÃO

A prática do ioga tem se tornado cada vez mais popular, não apenas pelos benefícios físicos, mas principalmente pelo bem-estar psicológico trazido pela sua prática. Um dos componentes do ioga é o Prãnãyama, ou controle da respiração. A atenção e a respiração são dois mecanismos fisiológicos e involuntários requeridos para a execução do Prãnãyama. O principal objetivo desse estudo foi verificar se variáveis contínuas do EEG (potência de diferentes faixas que o compõem) seriam moduladas pelo controle respiratório, comparando-se separadamente as duas fases do ciclo respiratório (inspiração e expiração), na situação de respiração espontânea e controlada. Fizeram parte do estudo 19 sujeitos (7 homens/12 mulheres, idade média de 36,89 e DP = ± 14,46) que foram convidados a participar da pesquisa nas dependências da Faculdade de Saúde da Universidade Metodista de São Paulo. Para o registro do eletroencefalograma foi utilizado um sistema de posicionamento de cinco eletrodos Ag AgCl (FPz, Fz, Cz, Pz e Oz) fixados a uma touca de posicionamento rápido (Quick-Cap, Neuromedical Supplies®), em sistema 10-20. Foram obtidos valores de máxima amplitude de potência (espectro de potência no domínio da frequência) nas frequências teta, alfa e beta e delta e calculada a razão teta/beta nas diferentes fases do ciclo respiratório (inspiração e expiração), separadamente, nas condições de respiração espontânea e de controle respiratório. Para o registro do ciclo respiratório, foi utilizada uma cinta de esforço respiratório M01 (Pletismógrafo). Os resultados mostram diferenças significativas entre as condições de respiração espontânea e de controle com valores das médias da razão teta/beta menores na respiração controlada do que na respiração espontânea e valores de média da potência alfa sempre maiores no controle respiratório. Diferenças significativas foram encontradas na comparação entre inspiração e expiração da respiração controlada com diminuição dos valores das médias da razão teta/beta na inspiração e aumento nos valores das médias da potência alfa, sobretudo na expiração. Os achados deste estudo trazem evidências de que o controle respiratório modula variáveis eletrofisiológicas relativas à atenção refletindo um estado de alerta, porém mais relaxado do que na situação de respiração espontânea.

Application of higher order statistics/spectra in biomedical signals : a review

For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.

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.

Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

The unfinished landscape fractal geometry and the aesthetics of ecological design

During the late 20th century it was proposed that a design aesthetic reflecting current ecological concerns was required within the overall domain of the built environment and specifically within landscape design. To address this, some authors suggested various theoretical frameworks upon which such an aesthetic could be based. Within these frameworks there was an underlying theme that the patterns and processes of Nature may have the potential to form this aesthetic — an aesthetic based on fractal rather than Euclidean geometry. In order to understand how fractal geometry, described as the geometry of Nature, could become the referent for a design aesthetic, this research examines the mathematical concepts of fractal Geometry, and the underlying philosophical concepts behind the terms ‘Nature’ and ‘aesthetics’. The findings of this initial research meant that a new definition of Nature was required in order to overcome the barrier presented by the western philosophical Nature¯culture duality. This new definition of Nature is based on the type and use of energy. Similarly, it became clear that current usage of the term aesthetics has more in common with the term ‘style’ than with its correct philosophical meaning. The aesthetic philosophy of both art and the environment recognises different aesthetic criteria related to either the subject or the object, such as: aesthetic experience; aesthetic attitude; aesthetic value; aesthetic object; and aesthetic properties. Given these criteria, and the fact that the concept of aesthetics is still an active and ongoing philosophical discussion, this work focuses on the criteria of aesthetic properties and the aesthetic experience or response they engender. The examination of fractal geometry revealed that it is a geometry based on scale rather than on the location of a point within a three-dimensional space. This enables fractal geometry to describe the complex forms and patterns created through the processes of Wild Nature. Although fractal geometry has been used to analyse the patterns of built environments from a plan perspective, it became clear from the initial review of the literature that there was a total knowledge vacuum about the fractal properties of environments experienced every day by people as they move through them. To overcome this, 21 different landscapes that ranged from highly developed city centres to relatively untouched landscapes of Wild Nature have been analysed. Although this work shows that the fractal dimension can be used to differentiate between overall landscape forms, it also shows that by itself it cannot differentiate between all images analysed. To overcome this two further parameters based on the underlying structural geometry embedded within the landscape are discussed. These parameters are the Power Spectrum Median Amplitude and the Level of Isotropy within the Fourier Power Spectrum. Based on the detailed analysis of these parameters a greater understanding of the structural properties of landscapes has been gained. With this understanding, this research has moved the field of landscape design a step close to being able to articulate a new aesthetic for ecological design.

Spatially varying ground motion effects on seismic response of adjacent structures considering soil-structure interaction

Spatial variation of seismic ground motions is caused by incoherence effect, wave passage, and local site conditions. This study focuses on the effects of spatial variation of earthquake ground motion on the responses of adjacent reinforced concrete (RC) frame structures. The adjacent buildings are modeled considering soil-structure interaction (SSI) so that the buildings can be interacted with each other under uniform and non-uniform ground motions. Three different site classes are used to model the soil layers of SSI system. Based on fast Fourier transformation (FFT), spatially correlated non-uniform ground motions are generated compatible with known power spectrum density function (PSDF) at different locations. Numerical analyses are carried out to investigate the displacement responses and the absolute maximum base shear forces of adjacent structures subjected to spatially varying ground motions. The results are presented in terms of related parameters affecting the structural response using three different types of soil site classes. The responses of adjacent structures have changed remarkably due to spatial variation of ground motions. The effect can be significant on rock site rather than clay site.

On the effect of Reynolds number for flow past three side-by-side square cylinders for unequal gap spacings

Flow patterns and aerodynamic characteristics behind three side-by-side square cylinders has been found depending upon the unequal gap spacing (g1 = s1/d and g2 = s2/d) between the three cylinders and the Reynolds number (Re) using the Lattice Boltzmann method. The effect of Reynolds numbers on the flow behind three cylinders are numerically studied for 75 ≤ Re ≤ 175 and chosen unequal gap spacings such as (g1, g2) = (1.5, 1), (3, 4) and (7, 6). We also investigate the effect of g2 while keeping g1 fixed for Re = 150. It is found that a Reynolds number have a strong effect on the flow at small unequal gap spacing (g1, g2) = (1.5, 1.0). It is also found that the secondary cylinder interaction frequency significantly contributes for unequal gap spacing for all chosen Reynolds numbers. It is observed that at intermediate unequal gap spacing (g1, g2) = (3, 4) the primary vortex shedding frequency plays a major role and the effect of secondary cylinder interaction frequencies almost disappear. Some vortices merge near the exit and as a result small modulation found in drag and lift coefficients. This means that with the increase in the Reynolds numbers and unequal gap spacing shows weakens wakes interaction between the cylinders. At large unequal gap spacing (g1, g2) = (7, 6) the flow is fully periodic and no small modulation found in drag and lift coefficients signals. It is found that the jet flows for unequal gap spacing strongly influenced the wake interaction by varying the Reynolds number. These unequal gap spacing separate wake patterns for different Reynolds numbers: flip-flopping, in-phase and anti-phase modulation synchronized, in-phase and anti-phase synchronized. It is also observed that in case of equal gap spacing between the cylinders the effect of gap spacing is stronger than the Reynolds number. On the other hand, in case of unequal gap spacing between the cylinders the wake patterns strongly depends on both unequal gap spacing and Reynolds number. The vorticity contour visualization, time history analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and force statistics are systematically discussed for all chosen unequal gap spacings and Reynolds numbers to fully understand this valuable and practical problem.