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Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic…
The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal…
High-dimensional time series are characterized by a large number of measurements and complex dependence, and often involve abrupt change points. We propose a new procedure to detect change points in the mean of high-dimensional time series…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
This work presents the application of the Complex Orthogonal Decomposition (C.O.D.) to a simple spatio-temporal signal. C.O.D. has been introduced rst in the article of B. Feeny, entitled "A Complex Orthogonal Decomposition for Wave Motion…
We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate…
In the present paper, details are given on the implementation of a wavelet-based analysis tailored to the processing of acoustical signals. The family of the suitable wavelets (`Reimann wavelets') are obtained in the time domain from a…
This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is…
This study investigates temporal variability in U.S. climate using harmonic decomposition techniques, specifically Fourier and wavelet transforms. Monthly temperature, precipitation, and drought index data from the National Oceanic and…
The wavelength and system-resolution dependencies of dynamic optical coherence tomography (DOCT) are investigated experimentally and numerically. Experimental investigations demonstrate significant wavelength dependency for the DOCT values…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…
A diagnostics method based on a continuous wavelet transform is proposed. This method makes it possible to diagnose the presence of synchronization of the oscillations of a self-excited oscillator locked by an external force with a linearly…
In an oscillatory medium, a region which oscillates faster than its surroundings can act as a source of outgoing waves. Such pacemaker-generated waves can synchronize the whole medium and are present in many chemical and biological systems,…
Tracking individual cells in live-cell imaging provides fundamental insights, inevitable for studying causes and consequences of phenotypic heterogeneity, responses to changing environmental conditions or stressors. Microbial cell tracking,…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
TEMPO (Time-dependent Evolution of Multiple Pulse Operations) offers accessible and efficient simulations of pulse sequences in Python, using the suite of master equation solvers available in the Quantum Toolbox in Python (QuTiP). It…
We show that, by using the quantum orthogonal functions invariant, we are able to solve a coupled of time dependent harmonic oscillators where all the time dependent frequencies are arbitrary. We do so, by transforming the time dependent…
In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing…
Cardiovascular system study using ECG signals have evolved tremendously in the domain of electronics and signal processing. However, there are certain floating challenges unresolved in the analysis and detection of abnormal performances of…