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Concept: Spectral density


Investigating suicides following the death of Robin Williams, a beloved actor and comedian, on August 11th, 2014, we used time-series analysis to estimate the expected number of suicides during the months following Williams' death. Monthly suicide count data in the US (1999-2015) were from the Centers for Disease Control and Prevention Wide-ranging ONline Data for Epidemiologic Research (CDC WONDER). Expected suicides were calculated using a seasonal autoregressive integrated moving averages model to account for both the seasonal patterns and autoregression. Time-series models indicated that we would expect 16,849 suicides from August to December 2014; however, we observed 18,690 suicides in that period, suggesting an excess of 1,841 cases (9.85% increase). Although excess suicides were observed across gender and age groups, males and persons aged 30-44 had the greatest increase in excess suicide events. This study documents associations between Robin Williams' death and suicide deaths in the population thereafter.

Concepts: Disease, Statistics, Death, Demography, Spectral density, Ageing, Time series, Suicide


A method is proposed for theoretical estimation of the level-crossing rate of the underwater acoustic communication signals that are reflected from the ocean surface. The variation in the reflection coefficient of the moving ocean surface causes the intensities of the received signals to fluctuate. In this work, the reflection coefficient is obtained by modeling the time-varying characteristics of the ocean surface based on rough surface scattering theory. The surface of the ocean is modeled by Gaussian processes that are characterized by ocean spectra such as the Pierson-Moskowitz and Durden-Vesecky spectra. Furthermore, Gaussian random functions with a particular correlation time are incorporated to model the surface that continuously varies over time. Then the standard Periodogram analysis is applied to estimate the autocorrelation function. Finally, the level-crossing rate is calculated with the negative curvature of the autocorrelation function. For verification, comparison of the simulated results with the measured data is provided.

Concepts: Scientific method, Variance, Mathematics, Spectral density, Reflection, Correlation function


It has been consistently reported that children with autism spectrum disorders (ASD) show considerable handwriting difficulties, specifically relating to accurate and consistent letter formation, and maintaining appropriate letter size. The aim of this study was to investigate the underlying factors that contribute to these difficulties, specifically relating to motor control. We examined the integrity of fundamental handwriting movements and contributions of neuromotor noise in 26 children with ASD aged 8-13 years (IQ>75), and 17 typically developing controls. Children wrote a series of four cursive letter l’s using a graphics tablet and stylus. Children with ASD had significantly larger stroke height and width, more variable movement trajectory, and higher movement velocities. The absolute level of neuromotor noise in the velocity profiles, as measured by power spectral density analysis, was significantly higher in children with ASD; relatively higher neuromotor noise was found in bands >3Hz. Our findings suggest that significant instability of fundamental handwriting movements, in combination with atypical biomechanical strategies, contribute to larger and less consistent handwriting in children with ASD.

Concepts: Spectral density, Autism, Pervasive developmental disorder, Asperger syndrome, Autism spectrum, PDD-NOS, Sociological and cultural aspects of autism, Spectrum


The gut microbiome is a dynamic system that changes with host development, health, behavior, diet, and microbe-microbe interactions. Prior work on gut microbial time series has largely focused on autoregressive models (e.g. Lotka-Volterra). However, we show that most of the variance in microbial time series is non-autoregressive. In addition, we show how community state-clustering is flawed when it comes to characterizing within-host dynamics and that more continuous methods are required. Most organisms exhibited stable, mean-reverting behavior suggestive of fixed carrying capacities and abundant taxa were largely shared across individuals. This mean-reverting behavior allowed us to apply sparse vector autoregression (sVAR)-a multivariate method developed for econometrics-to model the autoregressive component of gut community dynamics. We find a strong phylogenetic signal in the non-autoregressive co-variance from our sVAR model residuals, which suggests niche filtering. We show how changes in diet are also non-autoregressive and that Operational Taxonomic Units strongly correlated with dietary variables have much less of an autoregressive component to their variance, which suggests that diet is a major driver of microbial dynamics. Autoregressive variance appears to be driven by multi-day recovery from frequent facultative anaerobe blooms, which may be driven by fluctuations in luminal redox. Overall, we identify two dynamic regimes within the human gut microbiota: one likely driven by external environmental fluctuations, and the other by internal processes.

Concepts: Bacteria, Gut flora, Cellular respiration, Escherichia coli, Spectral density, Facultative anaerobic organism, Autoregressive moving average model, Autoregressive model


People’s behaviors synchronize. It is difficult, however, to determine whether synchronized behaviors occur in a mutual direction-two individuals influencing one another-or in one direction-one individual leading the other, and what the underlying mechanism for synchronization is. To answer these questions, we hypothesized a non-leader-follower postural sway synchronization, caused by a reciprocal visuo-postural feedback system operating on pairs of individuals, and tested that hypothesis both experimentally and via simulation. In the behavioral experiment, 22 participant pairs stood face to face either 20 or 70 cm away from each other wearing glasses with or without vision blocking lenses. The existence and direction of visual information exchanged between pairs of participants were systematically manipulated. The time series data for the postural sway of these pairs were recorded and analyzed with cross correlation and causality. Results of cross correlation showed that postural sway of paired participants was synchronized, with a shorter time lag when participant pairs could see one another’s head motion than when one of the participants was blindfolded. In addition, there was less of a time lag in the observed synchronization when the distance between participant pairs was smaller. As for the causality analysis, noise contribution ratio (NCR), the measure of influence using a multivariate autoregressive model, was also computed to identify the degree to which one’s postural sway is explained by that of the other’s and how visual information (sighted vs. blindfolded) interacts with paired participants' postural sway. It was found that for synchronization to take place, it is crucial that paired participants be sighted and exert equal influence on one another by simultaneously exchanging visual information. Furthermore, a simulation for the proposed system with a wider range of visual input showed a pattern of results similar to the behavioral results.

Concepts: Scientific method, Psychology, Causality, Spectral density, Experiment, Hypothesis, Theory, Time series


There is an array of numerical techniques available to estimate the period of circadian and other biological rhythms. Criteria for choosing a method include accuracy of period measurement, resolution of signal embedded in noise or of multiple periodicities, and sensitivity to the presence of weak rhythms and robustness in the presence of stochastic noise. Maximum Entropy Spectral Analysis (MESA) has proven itself excellent in all regards. The MESA algorithm fits an autoregressive model to the data and extracts the spectrum from its coefficients. Entropy in this context refers to “ignorance” of the data and since this is formally maximized, no unwarranted assumptions are made. Computationally, the coefficients are calculated efficiently by solution of the Yule-Walker equations in an iterative algorithm. MESA is compared here to other common techniques. It is normal to remove high frequency noise from time series using digital filters before analysis. The Butterworth filter is demonstrated here and a danger inherent in multiple filtering passes is discussed.

Concepts: Spectral density, Circadian rhythm, Noise, Filter, Filters, Infinite impulse response


Real-time optical spectrum analysis is an essential tool in observing ultrafast phenomena, such as the dynamic monitoring of spectrum evolution. However, conventional method such as optical spectrum analyzers disperse the spectrum in space and allocate it in time sequence by mechanical rotation of a grating, so are incapable of operating at high speed. A more recent method all-optically stretches the spectrum in time domain, but is limited by the allowable input condition. In view of these constraints, here we present a real-time spectrum analyzer called parametric spectro-temporal analyzer (PASTA), which is based on the time-lens focusing mechanism. It achieves a frame rate as high as 100 MHz and accommodates various input conditions. As a proof of concept and also for the first time, we verify its applications in observing the dynamic spectrum of a Fourier domain mode-locked laser, and the spectrum evolution of a laser cavity during its stabilizing process.

Concepts: Time, Scientific method, Optics, Light, Observation, Spectral density, Nonlinear optics, Spectrum analyzer


We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria.

Concepts: Statistics, Estimator, Spectral density, Probability theory, Normal distribution, Conditional probability, Subroutine, Nuisance parameter


SUMMARY Campylobacteriosis has been the most common food-associated notifiable infectious disease in Switzerland since 1995. Contact with and ingestion of raw or undercooked broilers are considered the dominant risk factors for infection. In this study, we investigated the temporal relationship between the disease incidence in humans and the prevalence of Campylobacter in broilers in Switzerland from 2008 to 2012. We use a time-series approach to describe the pattern of the disease by incorporating seasonal effects and autocorrelation. The analysis shows that prevalence of Campylobacter in broilers, with a 2-week lag, has a significant impact on disease incidence in humans. Therefore Campylobacter cases in humans can be partly explained by contagion through broiler meat. We also found a strong autoregressive effect in human illness, and a significant increase of illness during Christmas and New Year’s holidays. In a final analysis, we corrected for the sampling error of prevalence in broilers and the results gave similar conclusions.

Concepts: Epidemiology, Disease, Infectious disease, Medical statistics, Infection, Spectral density, Chicken, Prevalence


Patients with severe brain injury are difficult to assess and frequently subject to misdiagnosis. ‘Cognitive motor dissociation’ is a term used to describe a subset of such patients with preserved cognition as detected with neuroimaging methods but not evident in behavioural assessments. Unlike the locked-in state, cognitive motor dissociation after severe brain injury is prominently marked by concomitant injuries across the cerebrum in addition to limited or no motoric function. In the present study, we sought to characterize the EEG signals used as indicators of cognition in patients with disorders of consciousness and examine their reliability for potential future use to re-establish communication. We compared EEG-based assessments to the results of using similar methods with functional MRI. Using power spectral density analysis to detect EEG evidence of task performance (Two Group Test, P ≤ 0.05, with false discovery rate correction), we found evidence of the capacity to follow commands in 21 of 28 patients with severe brain injury and all 15 healthy individuals studied. We found substantial variability in the temporal and spatial characteristics of significant EEG signals among the patients in contrast to only modest variation in these domains across healthy controls; the majority of healthy controls showed suppression of either 8-12 Hz ‘alpha’ or 13-40 Hz ‘beta’ power during task performance, or both. Nine of the 21 patients with EEG evidence of command-following also demonstrated functional MRI evidence of command-following. Nine of the patients with command-following capacity demonstrated by EEG showed no behavioural evidence of a communication channel as detected by a standardized behavioural assessment, the Coma Recovery Scale - Revised. We further examined the potential contributions of fluctuations in arousal that appeared to co-vary with some patients' ability to reliably generate EEG signals in response to command. Five of nine patients with statistically indeterminate responses to one task tested showed a positive response after accounting for variations in overall background state (as visualized in the qualitative shape of the power spectrum) and grouping of trial runs with similar background state characteristics. Our findings reveal signal variations of EEG responses in patients with severe brain injuries and provide insight into the underlying physiology of cognitive motor dissociation. These results can help guide future efforts aimed at re-establishment of communication in such patients who will need customization for brain-computer interfaces.

Concepts: Psychology, Brain, Traumatic brain injury, Cognition, Cognitive science, Spectral density, Electroencephalography, Spectrum