Intrinsic mode entropy based on multivariate empirical mode decomposition and its application to neural data analysis

Entropy, a measure of the regularity of a time series, has long been used to quantify the complexity of brain dynamics. Given the multiple spatiotemporal scales inherent in the brain, traditional entropy analysis based on a single scale is not adequate to accurately describe the underlying nonlinear dynamics. Intrinsic mode entropy (IMEn) is a recent development with appealing properties to estimate entropy over multiple time scales. It is a multiscale entropy measure that computes sample entropy (SampEn) over different scales of intrinsic mode functions extracted by empirical mode decomposition (EMD) method. However, it suffers from both mode-misalignment and mode-mixing problems when applied to multivariate time series data. In this paper, we address these two problems by employing the recently introduced multivariate empirical mode decomposition (MEMD). First, we extend the MEMD to multi-channel multi-trial neural data to ensure the IMEn matched at different scales. Second, for the discriminant analysis of IMEn, we propose to improve the discriminative ability by including variance that has not been used before in entropy analysis. Finally, we apply the proposed approach to the multi-electrode local field potentials (LFPs) simultaneously collected from visual cortical areas of macaque monkeys while performing a generalized flash suppression task. The results have shown that the entropy of LFP is indeed scale-dependent and is closely related to the perceptual conditions. The discriminative results of the perceptual conditions, revealed by support vector machine, show that the accuracy based on IMEn and variance reaches 83.05%, higher than that only by IMEn (76.27%). These results suggest that our approach is sensitive to capture the complex dynamics of neural data.     

Information quantification of empirical mode decomposition and applications to field potentials

The empirical mode decomposition (EMD) method can adaptively decompose a non-stationary time series into a number of amplitude or frequency modulated functions known as intrinsic mode functions. This paper combines the EMD method with information analysis and presents a framework of information-preserving EMD. The enhanced EMD method has been exploited in the analysis of neural recordings. It decomposes a signal and extracts only the most informative oscillations contained in the non-stationary signal. Information analysis has shown that the extracted components retain the information content of the signal. More importantly, a limited number of components reveal the main oscillations presented in the signal and their instantaneous frequencies, which are not often obvious from the original signal. This information-coupled EMD method has been tested on several field potential datasets for the analysis of stimulus coding in visual cortex, from single and multiple channels, and for finding information connectivity among channels. The results demonstrate the usefulness of the method in extracting relevant responses from the recorded signals. An investigation is also conducted on utilizing the Hilbert phase for cases where phase information can further improve information analysis and stimulus discrimination. The components of the proposed method have been integrated into a toolbox and the initial implementation is also described.     

Temporal associations between daytime physical activity and sleep in children

Objectives

We examined temporal associations between objectively-measured physical activity (PA) during the day and in the evening, and sleep quantity and quality.

Study Design

PA and sleep were measured by actigraphs for an average of one week in an epidemiological cohort study of 275 eight-year-old children.

Results

For each one standard deviation (SD) unit of increased PA during the day, sleep duration was decreased by 0.30, sleep efficiency by 0.16, and sleep fragmentation increased by 0.08 SD units that night. For each one SD unit increase in sleep duration and efficiency the preceding night, PA the following day decreased by 0.09 and 0.16 SD units, respectively. When we contrasted days with a high amount of moderate to vigorous activity during the day or in the evening to days with a more sedentary profile, the results were essentially similar. However, moderate to vigorous PA in the evening shortened sleep latency.

Conclusions

The relationship between a higher level of PA and poorer sleep is bidirectional. These within-person findings challenge epidemiological findings showing that more active people report better sleep. Since only a few studies using objective measurements of both PA and sleep have been conducted in children, further studies are needed to confirm/refute these results.     

A search for associations between weather and the onset of human parturition

Weather data were examined for association with hospital records indicating the time at which pregnant women at term first experienced labor contractions (onsets). There is a considerable advantage, compared with mortality and morbidity, to using this response to infer weather influences. Three tests were used. First, the time series of daily onsets was analyzed to determine if characteristics known to exist in time series of weather data — variability and persistence — were evident in daily onsets. Second, the frequency distributions of nine weather variables were stratified, mostly by terciles, and onset means calculated for each of these divisions. Response means much different from average were then used to specify the nature of weather at such times. Third, the weather data were organized as weather types — pre- and post-cold frontal and general cold frontal — and onsets at these times were compared with those at non-frontal times. The time series characteristics were not found, but the other analysis revealed subsets of days on which onsets were above average, and in some cases the results were statistically significant. One such subset consists of winter days with low pressure, temperature markedly lower than the day before, and high wind speeds. On such days onsets were 34% above average. They were also above average during the 48 hours before and after cold front passage, and especially so in the 12 hours prior to the front. These findings constitute a weak, but statistically significant indication that human parturition is influenced by weather. Follow-up studies are urged.     

Weekly headache periodicity and the effect of weather changes on headache

A weekly periodicity in the occurrence of headache was found in 53 patients with migraine and in 20 with tension headache during an observation period of four weeks. In the migraine group the frequency was highest on Thursday and on Saturday and lowest on Sunday–Monday, and in patients with tension headache it was lowest on Sunday–Tuesday and highest on Friday. During the observation period several climatic factors were recorded. After correction for the weekly periodicity a highly significant correlation was found in the migraine group between headache frequency, on the one hand, and atmospheric pressure and outdoor temperature recorded 1–3 days later, on the other.     

Weather and emotional state: a search for associations between weather and calls to telephone counseling services

Previous research has revealed that an emotional response to weather might be indicated by calls to telephone counseling services. We analyzed call frequency from such "hotlines", each serving communities in a major metropolitan area of the United States (Detroit, Washington DC, Dallas and Seattle). The periods examined were all, or parts of, the years 1997 and 1998. Associations with subjectively derived synoptic weather types for all cities except Seattle, as well as with individual weather elements [cloudiness (sky cover), precipitation, windspeed, and interdiurnal temperature change] for all four cities, were investigated. Analysis of variance and t-tests (significance of means) were applied to test the statistical significance of differences. Although statistically significant results were obtained in scattered instances, the total number was within that expected by chance, and there was little in the way of consistency to these associations. One clear exception was the increased call frequency during destructive (severe) weather, when there is obvious concern about the damage done by it.     

Antepartum fetal heart rate feature extraction and classification using empirical mode decomposition and support vector machine

Background  

Cardiotocography (CTG) is the most widely used tool for fetal surveillance. The visual analysis of fetal heart rate (FHR) traces largely depends on the expertise and experience of the clinician involved. Several approaches have been proposed for the effective interpretation of FHR. In this paper, a new approach for FHR feature extraction based on empirical mode decomposition (EMD) is proposed, which was used along with support vector machine (SVM) for the classification of FHR recordings as 'normal' or 'at risk'.     

Extraction of single-trial cortical beta oscillatory activities in EEG signals using empirical mode decomposition

Background  

Brain oscillatory activities are stochastic and non-linearly dynamic, due to their non-phase-locked nature and inter-trial variability. Non-phase-locked rhythmic signals can vary from trial-to-trial dependent upon variations in a subject's performance and state, which may be linked to fluctuations in expectation, attention, arousal, and task strategy. Therefore, a method that permits the extraction of the oscillatory signal on a single-trial basis is important for the study of subtle brain dynamics, which can be used as probes to study neurophysiology in normal brain and pathophysiology in the diseased.     

A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition

Transient neural assemblies mediated by synchrony in particular frequency ranges are thought to underlie cognition. We propose a new approach to their detection, using empirical mode decomposition (EMD), a data-driven approach removing the need for arbitrary bandpass filter cut-offs. Phase locking is sought between modes. We explore the features of EMD, including making a quantitative assessment of its ability to preserve phase content of signals, and proceed to develop a statistical framework with which to assess synchrony episodes. Furthermore, we propose a new approach to ensure signal decomposition using EMD. We adapt the Hilbert spectrum to a time-frequency representation of phase locking and are able to locate synchrony successfully in time and frequency between synthetic signals reminiscent of EEG. We compare our approach, which we call EMD phase locking analysis (EMDPL) with existing methods and show it to offer improved time-frequency localisation of synchrony. Action Editor: Carson C. Chow     

The time factor in mortality: weather associations in a subtropical environment

 Mortality rates for a decade in Brisbane are analysed for dependence upon atmospheric factors. Time filters are applied to both the dependent and independent variables, and several models are developed to enable prediction, especially for weekly intervals. Statistically, deaths are observed to increase with colder and less humid weather with winds from a westerly, direction. Overall, taking account of both synoptic and seasonal influences, >90% of cumulative deviations from mean death rates are explained. Some differences are also noted in the association of death with the weather between sexes, age groups and causes of death. Received: 2 November 1995 / Accepted: 26 December 1996     

Linkage analysis versus association analysis: distinguishing between two models that explain disease-marker associations.

Human genetics researchers have been intrigued for many years by weak-to-moderate associations between markers and diseases. However, in most cases of association, the cause of this phenomenon is still not known. Recently, interest has grown in pursuing association studies for complex diseases, either instead of or in addition to linkage studies. Hence, it is timely to reconsider what a disease-marker association, particularly in the weak-to-moderate range (relative risk < 10), can tell us about disease etiology. To this end, this study accomplishes three aims: (1) It formulates two different models explaining weak-to-moderate associations and derives the relationship between them. One is a linkage disequilibrium model, and the other is a susceptibility, or pure association, model. The importance of drawing the distinction between these two models and the implications for our understanding of the genetics of human disease will also be discussed. It will be argued that the linkage disequilibrium model represents true linkage but that the susceptibility model does not. (2) It examines two family-based association tests proposed recently by Parsian et al. and Spielman et al. and derives formulas for their behavior under the two models described above. It demonstrates that these tests yield almost identical results under these two models. It shows that, whereas these tests can confirm an association, they cannot determine whether the association is caused by the linkage disequilibrium model or the susceptibility model. The study also characterizes the probabilities yielded by the family association tests in the presence of weak-to-moderate associations, which will aid researchers using these tests. (3) It proposes two approaches, both based on linkage analysis, which can distinguish between the two models described above. One approach involves a straightforward linkage analysis of the data; the other involves a partitioned association-linkage (PAL) test, as suggested by Greenberg. Formulas are derived for testing identity by descent in affected sib pairs by using both approaches. (4) Finally, the formulas and arguments are illustrated with two examples from the literature and one computer-simulated data set.     

Developmental associations between traits: covariance and beyond

Statistical associations between phenotypic traits often result from shared developmental processes and include both covariation between the trait values and more complex associations between higher moments of the joint distribution of traits. In this article, an analytical technique for calculating the covariance between traits is presented on the basis of (1). the distribution of underlying genetic and environmental variation that jointly influences the traits and (2). the mechanics of how these underlying factors influence the development of each trait. It is shown that epistasis can produce patterns of covariation between traits that are not seen in additive models. Applying this approach to a trait in parents and the same trait in their offspring allows us to study the consequences of epistasis for the evolution of additive genetic variance and heritability. This analysis is then extended to the study of more complicated associations between traits. It is shown that even traits that are not correlated may exhibit developmental associations that influence their joint evolution.     

Correlations between weather conditions and common vole (Microtus arvalis) densities identified by regression tree analysis

Population dynamics of fluctuating and cyclic rodent populations can be impacted by particular weather parameters. In temperate areas there are interrelations between different weather parameters, which make identification difficult. However, this is necessary because small rodents are relevant for both the food web and crop damage especially in the face of climate change. We used both, boosted regression tree and classification and regression tree methods to identify weather conditions correlating with the active burrow index (ABI) of common voles (Microtus arvalis) from 1974 to 1998 in the high outbreak risk area of Central Germany. Highest ABI occurred in perennial crops in fall with a maximum of more than 2000 active burrows per 1000 m². Boosted regression tree analysis showed that between 12 and 20 weather parameters could have a relative influence on vole ABIs ranging from 2% to 19%. Classification and regression tree analysis highlighted that the number of days with snow cover in December and March, rainfall amount in spring and maximum temperature in October seem to be key indicators for ABIs in the following year in spring. Monthly maximum temperatures of February to June and the amount of precipitation in April and July were correlated to ABIs in fall. Quantitative validation showed an agreement of ABI distribution on regional scale >85%. This represents the first study to identify complex weather conditions including single parameter thresholds correlated with common vole abundance in a temperate area. The results have the potential to aid the development of predictive models for small rodent dynamics and they inspire further detailed search for regulative mechanisms of small mammal dynamics.     

Binding mode analysis between membrane dipeptidase and its substrates

Membrane dipeptidase (MDP) is a membrane-bound glycoprotein involved in the hydrolysis of dipeptides, showing specific activity for dipeptides. Recent study showed that membrane dipeptidase was the receptor for a lung-targeting peptide identified by in vivo phage display and the crystal structure of the cilastatin-liganded human renal dipeptidase was determined. We performed a pharmacophore-based virtual screening and molecular docking in order to characterize MDP binding interactions with its substrates. A ligand-based pharmacophore model represented only a slight enrichment because of a lacked variety and centralization of ligand features. Molecular docking study was used to incorporate ligand conformational changes in the binding sites and the performance was much better than pharmacophore model; only 10% of compound library needed to be screened in order to detect all included active compounds. In addition, we found that one of the crystallographically observed water molecules plays an important role in the binding modes between MDP and its substrate.     

Cryopreservation of oocytes and embryos: optimization by theoretical versus empirical analysis

Embryos and oocytes were first successfully cryopreserved more than 30 years ago. This procedure has come to be an important, almost essential component in the practice of assisted reproduction in animals and humans. Literally millions of animals of more than 20 species and undoubtedly hundreds of thousands of children have been born from frozen embryos. Nevertheless, there still remain shortcomings with methods used to cryopreserve oocytes and embryos. A wide variety of approaches has been used to try to improve and optimize methods of cryopreservation. These approaches range from the very basic to the completely empirical. Some investigators make use of rigorous mathematical formulations to define and describe the behavior of oocytes and embryos at subzero temperatures. Others conduct "trial-and-error" studies to improve the results by dint of many replicate experiments in which they examine the effects of various protective compounds, macromolecular supplements, and compare different cooling and warming conditions. This review considers both extremes.     

DNA-based patents: an empirical analysis

The perception of rising litigation rates is driving the push for patent reform.     

Temporal change of gas metabolism by hydrogen-syntrophic methanogenic bacterial associations in anoxic paddy soil

Abstract Interspecies H₂ transfer within methanogenic bacterial associations (MBA) accounted for 95–97% of the conversion of ¹⁴CO₂ to ¹⁴CH₄ in anoxic paddy soil. Only 3–5% of the ¹⁴CH₄ were produced from the turnover of dissolved H₂. The H₂-syntrophic MBA developed within 5 days after the paddy soil had been submerged and placed under anoxic atmosphere. Afterwards, both the contribution of MBA to H₂-dependent methanogenesis and the turnover of dissolved H₂ did not change significantly for up to 7 months of incubation. However, while the rates of H₂-dependent methanogenesis stayed relatively constant, the rates of total methanogenesis decreased. The contribution of MBA to H₂-dependent methanogenesis was further enhanced to 99% when the temperature was shifted from 30°C to 17°C, or when the soil had been planted with rice. This enhancement was partially due to an increased utilization of dissolved H₂ by chloroform-insensitive non-methanogenic bacteria, most probably homoacetogens, so that CH₄ production was almost completely restricted to H₂-syntrophic MBA. The activity of MBA, as measured by the conversion of ¹⁴CO₂ to ¹⁴CH₄, was stimulated by glucose, lactate, and ethanol to a similar or greater extent than by exogenous H₂. Propionate and acetate had no effect.     

Nuclear architecture of human pachytene spermatocytes: quantitative analysis of associations between nucleolar and XY bivalents

Summary Nucleolar association and heterochromatin coalescence have both been invoked as mechanisms involved in the origin of chromosomal associations between nucleolar bivalents themselves, as well as between these bivalents and the XY pair, during meiotic prophase in human spermatocytes. However, these mechanisms do not satisfactorily explain how associating bivalents meet each other within the nuclear space. To elucidate this problem, we have characterized different types of nucleolar-nucleolar and nucleolar-XY bivalent associations, and their frequencies, in light and electron microscope serial sections of spermatocyte nuclei. In the pachytene nucleus, nucleolar bivalent associations were found to involve only one nucleolar sphere of RNP granules connected through a fibrillar center to a chromatin mass composed of two, or more, nucleolar-bivalent short arms. Structural relationships between these elements were examined using 3D computer models of various nucleolar associations. XY and nucleolar bivalents were usually located towards the nuclear periphery associated with the inner face of the nuclear envelope. Some nucleolar bivalents, whether single or associated appeared beside or over XY chromatin. When nucleolar-bivalent short arms (BK) were found over nucleolar or over XY chromatin, their telomeres were unattached to the nuclear envelope and the corresponding synaptonemal complexes were not observed. Ninety nucleoli were found in sixty pachytene nuclei. Thirty six percent of these nucleoli were bound to associated BKs and the remaining 64% to single BKs. Over 40% of individual spermatocytes showed at least one cluster of associated BKs and about 20% presented single or multiple BKs associated with the XY pair. The frequencies of random BK associations, over the total or restricted areas of the nuclear envelope, were calculated according to a probabilistic nuclear model. A correspondence was found in comparing the observed frequencies of associated BKs with those calculated on the basis of bouquet formation. Such an analysis strongly suggests that the occurrence of associations between nucleolar bivalents may arise at random within the bouquet. Thus, the architecture of the meiocyte nucleus, particularly the organization of the bouquet, may be the primary mechanism by which nucleolar bivalents meet each other and, consequently, become associated either through common nucleolus formation or by heterochromatin coalescence.