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Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…
We develop a framework to uncover and analyze dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive data sets to eliminate erroneous data segments,…
Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to…
The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and…
We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We…
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
We introduce a generalization of the Kuramoto model by explicit consideration of time-dependent parameters. The oscillators' natural frequencies and/or couplings are supposed to be influenced by external, time-dependant fields, with…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
Epilepsy is a common, chronic neurological disorder characterized by recurrent seizures caused by sudden bursts of abnormal electrical activity in the brain. Seizures can often be unpredictable, leading to uncertainty and anxiety for people…
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…
Discovering causal relationships between different variables from time series data has been a long-standing challenge for many domains such as climate science, finance, and healthcare. Given the complexity of real-world relationships and…
The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a…
The identification of time-varying \textit{in situ} signals is crucial for characterizing the dynamics of quantum processes occurring in highly isolated environments. Under certain circumstances, they can be identified from time-resolved…
We introduce a new method of Bayesian wavelet shrinkage for reconstructing a signal when we observe a noisy version. Rather than making the common assumption that the wavelet coefficients of the signal are independent, we allow for the…
In quantum mechanics courses, students often solve the Schr\"odinger equation for the harmonic oscillator with time-independent parameters. However, time-dependent quantum harmonic oscillators are relevant in modeling several problems as,…
We simulate the process of continuous homodyne detection of the radiative emission from a quantum system, and we investigate how a Bayesian analysis can be employed to determine unknown parameters that govern the system evolution.…