Detection of multivariate cyclostationarity

This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loe`ve spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program “Return of German scientists from abroad”. The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241

Causality in the association between p300 and alpha event-related desynchronization

Recent findings indicated that both P300 and alpha event-related desynchronization (alpha-ERD) were associated, and similarly involved in cognitive brain functioning, e.g., attention allocation and memory updating. However, an explicit causal influence between the neural generators of P300 and alpha-ERD has not yet been investigated. In the present study, using an oddball task paradigm, we assessed the task effect (target vs. non-target) on P300 and alpha-ERD elicited by stimuli of four sensory modalities, i.e., audition, vision, somatosensory, and pain, estimated their respective neural generators, and investigated the information flow among their neural generators using time-varying effective connectivity in the target condition. Across sensory modalities, the scalp topographies of P300 and alpha-ERD were similar and respectively maximal at parietal and occipital regions in the target condition. Source analysis revealed that P300 and alpha-ERD were mainly generated from posterior cingulate cortex and occipital lobe respectively. As revealed by time-varying effective connectivity, the cortical information was consistently flowed from alpha-ERD sources to P300 sources in the target condition for all four sensory modalities. All these findings showed that P300 in the target condition is modulated by the changes of alpha-ERD, which would be useful to explore neural mechanism of cognitive information processing in the human brain.published_or_final_versio

Design, Evaluation, and Application of Heart Rate Variability Analysis Software (HRVAS)

The analysis of heart rate variability (HRV) has become an increasingly popular and important tool for studying many disease pathologies in the past twenty years. HRV analyses are methods used to non-invasively quantify variability within heart rate. Purposes of this study were to design, evaluate, and apply an easy to use and open-source HRV analysis software package (HRVAS). HRVAS implements four major categories of HRV techniques: statistical and time-domain analysis, frequency-domain analysis, nonlinear analysis, and time-frequency analysis. Software evaluations were accomplished by performing HRV analysis on simulated and public congestive heart failure (CHF) data. Application of HRVAS included studying the effects of hyperaldosteronism on HRV in rats. Simulation and CHF results demonstrated that HRVAS was a dependable HRV analysis tool. Results from the rat hyperaldosteronism model showed that 5 of 26 HRV measures were statistically significant (p\u3c0.05). HRVAS provides a useful tool for HRV analysis to researchers

Applying time-frequency analysis to assess cerebral autoregulation during hypercapnia.

OBJECTIVE: Classic methods for assessing cerebral autoregulation involve a transfer function analysis performed using the Fourier transform to quantify relationship between fluctuations in arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). This approach usually assumes the signals and the system to be stationary. Such an presumption is restrictive and may lead to unreliable results. The aim of this study is to present an alternative method that accounts for intrinsic non-stationarity of cerebral autoregulation and the signals used for its assessment. METHODS: Continuous recording of CBFV, ABP, ECG, and end-tidal CO2 were performed in 50 young volunteers during normocapnia and hypercapnia. Hypercapnia served as a surrogate of the cerebral autoregulation impairment. Fluctuations in ABP, CBFV, and phase shift between them were tested for stationarity using sphericity based test. The Zhao-Atlas-Marks distribution was utilized to estimate the time-frequency coherence (TFCoh) and phase shift (TFPS) between ABP and CBFV in three frequency ranges: 0.02-0.07 Hz (VLF), 0.07-0.20 Hz (LF), and 0.20-0.35 Hz (HF). TFPS was estimated in regions locally validated by statistically justified value of TFCoh. The comparison of TFPS with spectral phase shift determined using transfer function approach was performed. RESULTS: The hypothesis of stationarity for ABP and CBFV fluctuations and the phase shift was rejected. Reduced TFPS was associated with hypercapnia in the VLF and the LF but not in the HF. Spectral phase shift was also decreased during hypercapnia in the VLF and the LF but increased in the HF. Time-frequency method led to lower dispersion of phase estimates than the spectral method, mainly during normocapnia in the VLF and the LF. CONCLUSION: The time-frequency method performed no worse than the classic one and yet may offer benefits from lower dispersion of phase shift as well as a more in-depth insight into the dynamic nature of cerebral autoregulation

Characterization of ictal/non-ictal EEG patterns and Neuronal Networks in Childhood Absence Epilepsy

Childhood absence epilepsy (CAE) is one of the most common pediatric epilepsy syndromes found in children. It is associated with distinct seizure semiology and clear electroencephalographic (EEG) features. In CAE patients, differentiating EEG ictal and non-ictal generalised spikes and waves discharges (GSWDs) is however difficult, since these events have an identical appearance. The differentiation of these two events is very important in a clinical setting as it has a direct effect on diagnosis and management strategies of patients. This study focuses on differentiating ictal and non-ictal discharges at sensor and source level using only surface EEG. Twelve CAE patients having both ictal and non-ictal discharges were selected for this study. For all levels of analysis, frequency ranges of 1-30 Hz containing four important frequency bands (delta, theta, alpha and beta) were used. At sensor level, spectral analysis and functional connectivity (FC) based on imaginary part of coherency, were used to evaluate the spectral changes and channel connectivity at the surface, respectively. At source level, the onset zone for ictal and non-ictal discharges were reconstructed using the eLORETA algorithm, and FC was used again to analyse the neuronal networks. Furthermore, we gave a detailed mathematical background of the EEG, forward and inverse problem, along with the mathematical foundation for the eLORETA algorithm. Additionally, for the first time we prove the correctness of the eLORETA algorithm based on the correct regularization problem. At sensor level, ictal discharges showed significantly higher power compared to non-ictal discharges, followed by FC depicting a desynchronization of channel connections (weaker connectivity) for ictal discharges. At source level, a fascinating observation was that ictal and non-ictal discharges have the same source or onset zone in the brain. However, ictal discharges had a stronger source power compared to non-ictal discharges. FC at source level revealed that the connectivity between certain brain regions and the seeds of interest (source maximum and thalamus) was stronger for ictal discharges, compared to non-ictal discharges. This study clearly shows the significant differences between ictal and non-ictal discharges at sensor and source level using only surface EEG. This study would be a great interest to clinicians, since it could be the potential foundation for future diagnostics research for CAE patients

Exploring the relationship between anxiety sensitivity and heart rate variability

Anxiety sensitivity (AS) is a multifaceted construct based on individual beliefs that anxiety symptoms and sensations will have harmful consequences. In general, literature demonstrates three underlying dimensions of AS: fear of cognitive dyscontrol (i.e., cognitive concerns), fear of physiological anxiety sensations (i.e., physical concerns), and fear of negative evaluation (i.e., social concerns). Elevated AS and underlying dimensions have been shown to underlie psychopathology, including anxiety and depression broadly, and are predictive of fear responding in the context of behavioral challenge paradigms whereby individuals with elevated AS demonstrate higher fear and sympathetic nervous system activation. To date, few studies have investigated AS alongside heart rate variability (HRV), a biomarker of autonomic activity. Like AS, HRV has been well studied in clinical samples. High-frequency heart rate variability (HF-HRV), which indexes parasympathetic activity, has been shown to be lower among clinical samples, relative to controls and during behavioral challenge paradigms designed to induce stress. Lower HF-HRV has shown associations with other traits thought to underlie psychopathology (e.g., worry, difficulty with thought suppression). The present study sought to explore a plausible relationship between AS and HRV. Participants were recruited from the Eastern Michigan University campus community to take part in a brief online screening using the Anxiety Sensitivity Index-3 (ASI-3). Participants with normative (n = 60) and high (n = 60) levels of AS were invited to participate in an in-person study whereby HRV and participant-reported subjective distress were measured at baseline and during engagement in three behavioral challenge paradigms. Challenges were designed to induce mild distress related to underlying AS dimensions (i.e., cognitive, physical, and social concerns). Study findings revealed high AS participants to exhibit significantly greater increases in distress following each challenge, relative to baseline, than normative AS participants. After controlling for variance due to age, HF-HRV was significantly higher among normative AS participants at baseline and during the social challenge, compared with high AS participants. Unexpected findings also arose , whereby, after controlling for age, normative AS participants demonstrated significantly higher low-frequency HRV at baseline and during physical and social challenges, relative to high AS participants.

LMPIT-inspired Tests for Detecting a Cyclostationary Signal in Noise with Spatio-Temporal Structure

In spectrum sensing for cognitive radio, the presence of a primary user can be detected by making use of the cyclostationarity property of digital communication signals. For the general scenario of a cyclostationary signal in temporally colored and spatially correlated noise, it has previously been shown that an asymptotic generalized likelihood ratio test (GLRT) and locally most powerful invariant test (LMPIT) exist. In this paper, we derive detectors for the presence of a cyclostationary signal in various scenarios with structured noise. In particular, we consider noise that is temporally white and/or spatially uncorrelated. Detectors that make use of this additional information about the noise process have enhanced performance. We have previously derived GLRTs for these specific scenarios; here, we examine the existence of LMPITs. We show that these exist only for detecting the presence of a cyclostationary signal in spatially uncorrelated noise. For white noise, an LMPIT does not exist. Instead, we propose tests that approximate the LMPIT, and they are shown to perform well in simulations. Finally, if the noise structure is not known in advance, we also present hypothesis tests using our framework

Dynamic Specification Tests for Static Factor Models

We derive computationally simple score tests of serial correlation in the levels and squares of common and idiosyncratic factors in static factor models. The implicit orthogonality conditions resemble the orthogonality conditions of models with observed factors but the weighting matrices refl ect their unobservability. We derive more powerful tests for elliptically symmetric distributions, which can be either parametrically or semipametrically specified, and robustify the Gaussian tests against general non-normality. Our Monte Carlo exercises assess the finite sample reliability and power of our proposed tests, and compare them to other existing procedures. Finally, we apply our methods to monthly US stock returns.ARCH, Financial returns, Kalman filter, LM tests, Predictability

Detecting Changes in Global Dynamics with Principal Curves and Information Theory

Two approaches to characterize global dynamics are developed in this dissertation. In particular, the concern is with nonlinear and chaotic time series obtained from physical systems. The objective is to identify the features that adequately characterize a time series, and can consequently be used for fault diagnosis and process monitoring, and for improved control. This study has two parts. The first part is concerned with obtaining a skeletal description of the data using Cluster-linked principal curves (CLPC). A CLPC is a non-parametric hypercurve that passes through the center of the data cloud, and is obtained through the iterative Expectation-Maximization (E-M) principle. The data points are then projected on the curve to yield a distribution of arc lengths along it. It is argued that if some conditions are met, the arc length distribution uniquely characterizes the dynamics. This is demonstrated by testing for stationarity and reversibility based on the arc length distributions. The second part explores the use of mutual information vector to characterize a system. The mutual information vector formed via symbolization is reduced in dimensionality and subjected to K-means clustering algorithm in order to examine stationarity and to compare different processes. The computations required to implement the techniques for online monitoring and fault diagnosis are reasonable enough to be carried out in real time. For illustration purposes time series measurements from a liquid-filled column with an electrified capillary and a fluidized bed are employed

Effects of Neuronic Shutter Observed in the EEG Alpha Rhythm

The posterior alpha (α) rhythm, seen in human electroencephalogram (EEG), is posited to originate from cycling inhibitory/excitatory states of visual relay cells in the thalamus. These cycling states are thought to lead to oscillating visual sensitivity levels termed the “neuronic shutter effect.” If true, perceptual performance should be predictable by observed α phase (of cycling inhibitory/excitatory states) relative to the timeline of afferentiation onto the visual cortex. Here, we tested this hypothesis by presenting contrast changes at near perceptual threshold intensity through closed eyelids to 20 participants (balanced for gender) during times of spontaneous α oscillations. To more accurately and rigorously test the shutter hypothesis than ever before, α rhythm phase and amplitude were calculated relative to each individual’s retina-to-primary visual cortex (V1) conduction delay, estimated from the individual’s C1 visual-evoked potential (VEP) latency. Our results show that stimulus observation rates (ORs) are greater at a trough than a peak of the posterior α rhythm when phase is measured at the individual’s conduction delay relative to stimulus onset. Specifically, the optimal phase for stimulus observation was found to be 272.41°, where ORs are 20.96% greater than the opposing phase of 92.41°. The perception-phase relationship is modulated by α rhythm amplitude and is not observed at lower amplitude oscillations. Collectively, these results provide support to the “neuronic shutter” hypothesis and demonstrate a phase and timing relationship consistent with the theory that cycling excitability in the thalamic relay cells underly posterior α oscillations