Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

Spectral Analysis of Long Electroencephalographic Records

Spectral analysis of a 10-min electroencephalogram (EEG) record has made it possible to describe the behavior of EEG rhythms as a dynamic spectrum and find a distinct periodic pattern in this behavior. The data on the dynamic spectra of long EEGs offer a new insight into the estimation of the stability of EEG electrical processes in healthy subjects, inter- and intrahemispheric relationships between the electrical activities of different cortical regions, and estimation of phase relations, which were previously performed on the basis of comparison between single EEG spectral patterns.     

Characteristic Features of EEG Spectral Characteristics in Persons with Deviant Sexual Behavior

The study was performed with participation of 59 right-handed men. The normal group consisted of 19 subjects, and 40 patients with organic brain lesions who had commited sexual offenses were divided into two groups: 19 patients with a diagnosis of paraphilia (pathology of sexual drive) made up the main test group, and 21 patients without such a diagnosis formed the control group. A monopolar EEG was recorded in 16 standard leads in the states of rest (eyes closed) and general activation (eyes open) and during presentation of cognitive tests. The following EEG features manifest in all the frequency ranges and functional states were revealed in the group of patients with paraphilias as compared to the control groups: a substantially increased level of interhemispheric coherence (ICoh) and increased spectral density in the posterotemporal area (T ₅, T ₆), a significantly decreased ICoh level between the F _3/4 and C _3/4 leads in the frontocentral area, and lower spectral densities in the leads Fp ₂, C ₄, and P ₄. Analysis of reactions to loads presented showed that the general arousal in the group of patients with paraphilias was characterized by significantly greater shifts of EEG parameters associated with the desynchronization reaction (as compared to the control groups) and statistically significant disorders of interhemispheric interaction and EEG reactivity in the right hemisphere in the range during performance of a visuospatial (right-hemispheric) task. The results suggest the formation of a stationary activation focus in the right hemisphere with signs of involvement of the limbic structures in patients with paraphilias.     

Topographic Electrophysiological Signatures of fMRI Resting State Networks

Background

fMRI Resting State Networks (RSNs) have gained importance in the present fMRI literature. Although their functional role is unquestioned and their physiological origin is nowadays widely accepted, little is known about their relationship to neuronal activity. The combined recording of EEG and fMRI allows the temporal correlation between fluctuations of the RSNs and the dynamics of EEG spectral amplitudes. So far, only relationships between several EEG frequency bands and some RSNs could be demonstrated, but no study accounted for the spatial distribution of frequency domain EEG.

Methodology/Principal Findings

In the present study we report on the topographic association of EEG spectral fluctuations and RSN dynamics using EEG covariance mapping. All RSNs displayed significant covariance maps across a broad EEG frequency range. Cluster analysis of the found covariance maps revealed the common standard EEG frequency bands. We found significant differences between covariance maps of the different RSNs and these differences depended on the frequency band.

Conclusions/Significance

Our data supports the physiological and neuronal origin of the RSNs and substantiates the assumption that the standard EEG frequency bands and their topographies can be seen as electrophysiological signatures of underlying distributed neuronal networks.     

Statistical Comparison of Band Spectral Power: An Aid in Stochastical Analysis of Brain Electrical Activity Part 1: Approximation of the distribution of broad band power by a χ2-distribution

In this study the distribution of estimated broad band spectral power is evaluated. Under weak assumptions it is possible to appropriate this distribution by a χ2-distribution and to construct tolerance intervals with great statistical accuracy. The theoretical results implicate a new methodical basis for statistical comparison of spectral parameters in EEG analysis.     

Spectral fluorescence signatures in the characterization of phytoplankton community composition

Fluorescence spectral signatures from 28 algal cultures aredescribed.The cultures are split into four groups accordingto their accessory pigments. Phycocyanin and phycoerythrin,characteristic pigments of cyanobacteria, form groups I andII. The characteristic pigment found in group III is chlorophyllb (green and rasinophyte algae) and in group IV it is chlorophyllc (diatoms, dinophytes and some other algae).This preliminarycatalogue of spectral signatures was used to characterize fivenatural phytoplankton communities from brackish water environmentsas a comparison with phytoplankton species found in the samples.Accessory pigments such as phycocyanin and phycoerythrin, characterizinggroups I and II, can be used for identification without confusion.Distinguishing between groups III and IV is more complicated,because their accessory pigments do not have their own fluorescence.These groups can be characterized by increased fluorescenceof chlorophyll a induced by energy excited through chlorophyllb and c. The possibilities of applying the spectral fluorescencesignatures approach to the characterization of natural communitiesare discussed.     

Spectral unmixing of coral reef benthos under ideal conditions

Hyperspectral remote sensing has shown promise for detailed discrimination of coral reef substratum types, but, by necessity, it samples at pixel scales larger than reef substratum patch sizes. Spectral unmixing techniques have been successful in resolving subpixel areal cover in terrestrial environments. However, the application of spectral unmixing on coral reefs is fundamentally challenging, due not only to the water column, but also to the potentially large number of spectrally similar and ecologically significant end-member (substratum) classes involved. A controlled ex-situ experiment was conducted using field-spectrometer data to assess the accuracy of spectral unmixing techniques to estimate the areal cover of small-scale (<0.25 m²) assemblages of reef substrata (e.g., changes in cover between massive corals, branching corals, bleached corals, macroalgae, and coralline red algae). Mixture compositions were obtained precisely by analysis of digital images collected by a camera calibrated to the field of view of the spectrometer. Linear unmixing techniques were applied to derive estimates of substratum proportions using the full spectral resolution data and various transformations of it, including derivatives and down sampling (merging adjacent wavelengths into broader spectral bands). Comparison of actual and estimated substratum proportions indicate that spectral unmixing may be a practical approach for estimating subpixel-scale cover of coral reef substrata. In the most accurate treatment, coefficients of determination across all mixture sets were high for most end-member classes (37 of 52 cases with r ² >0.64, i.e. r >0.8). The most successful analyses were based on derivatives of down-sampled data, implying that spectral unmixing benefits more from spectral smoothing and judicious choice of band locations than from high spectral resolution per se. Although these results show that changes in coral and algal cover can be determined by unmixing their spectra, the method is not yet an operational remote sensing tool. Primary empirical research is needed before taking the next step, which is to incorporate a water column, of variable depth, above the sea bed.     

An estimate of spin diffusion in a spin subset: Application to iterative distance calculation from 3D 15N NOESY-HMQC

Summary A method for quantification of distances between amide hydrogens using only the 3D NOESY-HMQC experiment recorded on a ¹⁵N-labelled protein is presented. This method is based on an approximate expression of the NOE intensities between amide hydrogens obtained from continuum modelling of the non-amide spins; this expression is used in a distance calculation algorithm. The algorithm has been named CROWD, standing for Continuum approximation of Relaxati On path Ways between Dilute spins. This approximation as well as the CROWD algorithm are tested on a simulated case; the CROWD algorithm is then applied to experimental data, measured on a fragment of bacteriorhodopsin.     

Temperature Dependent Soret Spectral Band Shifts Accompany Human CN-Mesohemoglobin Assembly

The interaction between human apohemoglobin A and CN-Mesohemin, a monomeric non-native heme derivative, was probed by Soret spectrophotometric titrations in 0.05 M potassium phosphate buffer, pH 7 at varied temperatures. Hypsochromic shifts in the absorbance maxima were observed at all temperatures below 10°C. First derivative spectroscopy of CN-Mesohemin titrations was used to provide further evidence of a spectral shift upon CN-Mesohemoglobin assembly. Findings of Soret Spectral shifts demonstrate a preference for the α chain heme site by CN-Mesohemin indicative of semi-α-hemoglobin intermediate formation. CN-Mesohemin, a derivative with peripheral 2,4 ethyl groups, does not possess the extended conjugation seen for native CN-Protohemin with its 2,4 vinyl groups. Indeed, reduced polarity of CN-Mesohemin over that of CN-Protohemin resulted in distinct temperature dependencies. Molecular visualization and protein-ligand interaction analysis targeted a functionally diverse residue unique to the α-chain. Tyrosine-42 (a polar/non-polar amino acid) appeared to play a prominent role in the assembly process.     

Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media

The resistive or non-resistive nature of the extracellular space in the brain is still debated, and is an important issue for correctly modeling extracellular potentials. Here, we first show theoretically that if the medium is resistive, the frequency scaling should be the same for electroencephalogram (EEG) and magnetoencephalogram (MEG) signals at low frequencies (<10 Hz). To test this prediction, we analyzed the spectrum of simultaneous EEG and MEG measurements in four human subjects. The frequency scaling of EEG displays coherent variations across the brain, in general between 1/f and 1/f ², and tends to be smaller in parietal/temporal regions. In a given region, although the variability of the frequency scaling exponent was higher for MEG compared to EEG, both signals consistently scale with a different exponent. In some cases, the scaling was similar, but only when the signal-to-noise ratio of the MEG was low. Several methods of noise correction for environmental and instrumental noise were tested, and they all increased the difference between EEG and MEG scaling. In conclusion, there is a significant difference in frequency scaling between EEG and MEG, which can be explained if the extracellular medium (including other layers such as dura matter and skull) is globally non-resistive.     

Electroencephalographic Correlates of Mental Performance of Emotional Personal and Scenic Situations: I. Characteristics of Local Synchronization

An electroencephalogram (EEG) was recorded in 19 standard derivations in two groups of subjects (student actors and nonactors) during emotionally positive and negative mental recalls of personal experiences (test 1) or mental reproduction of scenic situations (test 2), as well as during mental count of time. Statistical comparison of EEG spectral power estimations in the frequency bands , , ₁, ₂, ₁, and ₂ showed that the induction of emotionally positive and emotionally negative states led to statistically significant changes in the EEG absolute power (local synchronization) simultaneously in many derivations and frequency bands. Analysis of all possible comparisons and changes in frequency bands showed that bilateral prefrontal and temporal cortical areas are most active during the internal induction of emotional states. Emotionally positive states were characterized, predominantly, by higher local EEG power than emotionally negative states. The EEG power changes accompanying internal induction of emotionally negative and positive states were of the same order in the case of reproduction of a presented situation (scenic material), whereas, in the case of recall of personal experience, emotionally negative states were accompanied by substantially weaker EEG spectral changes than emotionally positive states. The internal induction of emotional states on the basis of scenic material was accompanied by a pronounced increase in the power of the EEG range over the whole cortical surface. EEG reactions to induction of emotional states were generally stronger in actors than in nonactors. In case of emotional induction on the basis of scenic material, qualitative differences in the EEG reactions were also revealed between the groups. The findings are discussed in comparison with known data of investigations into regional cerebral blood flow during internal emotional induction and EEG studies of internal and external emotional induction.     

Intraspecific Variation in the Mating System of Spectral Tarsiers

Historically, a species’ social system was perceived to be a fixed attribute and deviations were usually treated as aberrant or maladaptive. Over the last few decades, socioecologists have started to recognize that variation in social systems is normal and adaptive. Here I explore how ecological variation affects the mating system of a nocturnal primate, the spectral tarsier, Tarsius spectrum. Several studies of the spectral tarsier have illustrated variation in this species’ mating system. Although most groups exhibit a monogamous mating system, a small proportion of the population consistently exhibits a polygynous mating system. I conducted this study at Tangkoko Nature Reserve in Sulawesi, Indonesia during 2007. I found that group size was highly variable, ranging from 2 individuals to as many as 8 individuals per sleeping site. Although most groups (21 of 26) were composed of a single adult male and a single adult female, ca. 19% of the groups contained 2 adult females. Three of the 5 groups with 2 adult females contained 2 young infants. As might be expected, polygynous groups were larger than were monogamous groups. The mean group size of monogamous groups was 2.9, whereas the mean group size of polygynous groups was 6.0. Polygynous groups were also more likely to use Ficus caulocarpa trees than were the monogamous groups. Polygynous groups consistently used more sleeping sites as well as larger diameter sleeping trees, than did monogamous groups. The large-diameter fig trees are ideal homes for the spectral tarsiers in that they offer multiple entrances and exits as well as protection from the elements. Polygynous and monogamous groups exhibited no differences in insect biomass available, home range size, or height of sleeping tree. These results support the hypothesis that ecological variation is an important determinant of mating system within spectral tarsiers.     

2‐D mapping of skin chromophores in the spectral range 500 – 700 nm

The multi‐spectral imaging technique has been used for distant mapping of in‐vivo skin chromophores by analyzing spectral data at each reflected image pixel and constructing 2‐D maps of the relative concentrations of oxy‐/deoxy‐haemoglobin and melanin. Instead of using a broad visible‐NIR spectral range, this study focuses on narrowed spectral band 500–700 nm, speeding‐up the signal processing procedure. Regression analysis confirmed that superposition of three Gaussians is optimal analytic approximation for the oxy‐haemoglobin absorption tabular spectrum in this spectral band, while superposition of two Gaussians fits well for deoxy‐haemoglobin absorption and exponential function – for melanin absorption. The proposed approach was clinically tested for three types of in‐vivo skin provocations: ultraviolet irradiance, chemical reaction with vinegar essence and finger arterial occlusion. Spectral range 500–700 nm provided better sensitivity to oxy‐haemoglobin changes and higher response stability to melanin than two reduced ranges 500–600 nm and 530–620 nm. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enabling adoption of 2D-NMR for the higher order structure assessment of monoclonal antibody therapeutics

The increased interest in using monoclonal antibodies (mAbs) as a platform for biopharmaceuticals has led to the need for new analytical techniques that can precisely assess physicochemical properties of these large and very complex drugs for the purpose of correctly identifying quality attributes (QA). One QA, higher order structure (HOS), is unique to biopharmaceuticals and essential for establishing consistency in biopharmaceutical manufacturing, detecting process-related variations from manufacturing changes and establishing comparability between biologic products. To address this measurement challenge, two-dimensional nuclear magnetic resonance spectroscopy (2D-NMR) methods were introduced that allow for the precise atomic-level comparison of the HOS between two proteins, including mAbs. Here, an inter-laboratory comparison involving 26 industrial, government and academic laboratories worldwide was performed as a benchmark using the NISTmAb, from the National Institute of Standards and Technology (NIST), to facilitate the translation of the 2D-NMR method into routine use for biopharmaceutical product development. Two-dimensional ¹H,¹⁵N and ¹H,¹³C NMR spectra were acquired with harmonized experimental protocols on the unlabeled Fab domain and a uniformly enriched-¹⁵N, 20%-¹³C-enriched system suitability sample derived from the NISTmAb. Chemometric analyses from over 400 spectral maps acquired on 39 different NMR spectrometers ranging from 500 MHz to 900 MHz demonstrate spectral fingerprints that are fit-for-purpose for the assessment of HOS. The 2D-NMR method is shown to provide the measurement reliability needed to move the technique from an emerging technology to a harmonized, routine measurement that can be generally applied with great confidence to high precision assessments of the HOS of mAb-based biotherapeutics.     

Some notes on the distribution and certain modifications of Mahalanobis' generalized distance (D)

Different modifications of Mahalanobis' generalized distance (D²) utilized in anthropological research are given, and it is shown that they all derive from the distribution of D² when the distances between the populations investigated are real. To investigate whether observed distances are real, testing of D² for significance is stressed. It is demonstrated that D² ought to be tested for significance according to its relation to the F-distribution, but that it may be related to the chi-squared distribution as an approximation when the numbers of individuals in the samples are very large. The great disadvantages of utilizing this approximation for smaller numbers of individuals in the samples are demonstrated, as well as the dependence of D² on sample size and the number of measurements used when testing for significance.     

Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

EEG Spectral Characteristics in Junior Schoolchildren with Learning Problems

EEG spectral characteristics were studied in two age groups (7–8.5 and 8.5–10 years) of mentally healthy children and children with learning problems at rest and during performance of a Raven test. It was shown that slow frequencies are more pronounced in the EEG of 7- to 8.5-year-old children with learning problems than in EEG of healthy children of the same age group. An immature form of EEG activation, i.e., an increase not only in the but also in the frequencies during activity, was characteristic of these children. The reaction of the activation of the definitive type develops between the 8.5–10 years of age. This reaction is correlated with an increase in the efficiency of the sensory perceptive and sensorimotor activity. The distinctive feature of children with learning problems between 8.5–10 years of age is a greater expression of slow frequencies in the baseline EEG of the frontal (in particular, left frontal) areas of the cortex. The obtained results are considered as a reflection of a retardation of the functional maturation of the brain structures responsible for the deficit of involuntary and voluntary attention and the disorder of a systemic organization of perception and analytical–synthetic brain activity as compared to the normal age characteristics. Possible neurophysiological mechanisms responsible for learning problems in junior schoolchildren are discussed on the basis of the obtained results and evidence from the literature.     

The reflection of different aspects of brain activation in the electroencephalogram: Quantitative electroencephalography of the states of rest with the eyes open and closed

The rest states with the eyes open (RSEO) and closed (RSEC) were subjected to quantitative EEG study as states similar in the pattern of mental activity and subjective assessments but different in the EEG pattern. The mean values of the spectral power and EEG coherence function were compared in 74 subjects for the following bands: Δ, ?, α₁, α₂, β₁, β₂, and γ. Upon the transition from the RSEC to the RSEO, the EEG local power significantly decreased over the whole cortex for the α, ?, and β bands. A simultaneous decrease in the EEG power in all the bands (including β and γ) was most pronounced (as judged by relative changes and tests of significance of difference) in the parietooccipital derivations immediately related to the cortical zones where an increase in the neuronal activity upon opening the eyes is most probable. A significant increase in the EEG power was observed only for the γ band in frontal derivations F ₃ and F ₄. Significant differences in the mean EEG coherence in the RSEO-RSEC comparison were present in many derivation pairs, especially in the α₂, β₁, β₂, and γ bands. For each of these bands, the number of differences determined on the basis of Fisher test was more than 70% of the maximum possible number. In the overwhelming majority of cases, the coherence was lower in the RSEO; however, in the caudal cortical zones, a higher coherence in the α₁, ?, and Δ bands in the RSEO was rather typical. The results confirmed that the two states under study differ in a number of averaged EEG parameters with high statistical significance and may be used as reference states during performance of tasks with the eyes open and closed, respectively. The differences between the RSEC and the RSEO may be caused by the fact that the RSEC is a functional state oriented predominantly to the analysis of internal information (internally oriented), and the RSEO, predominantly to the analysis of information coming from the outside (externally oriented). The pattern of the observed EEG differences points to a combination of effects both localized in the visual zone and reflecting changes in the network cortical activity, i.e., simultaneous, although nonuniform, changes over all the main zones of the cortex. Comparison of the results with published estimations of differences in the local cerebral blood flow (ICBF) between the RSEO and the RSEC shows that increase in the ICBF may be associated with a local decrease in the EEG spectral power in any frequency band, including the high-frequency β and γ bands, or several frequency bands simultaneously.