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Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with…
Irregularly sampled multivariate time series are ubiquitous in various fields, particularly in healthcare, and exhibit two key characteristics: intra-series irregularity and inter-series discrepancy. Intra-series irregularity refers to the…
We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST) to model and analyze oscillatory physiological signals. To…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
Dynamic conditional correlation (DCC) is a method that estimates the correlation between two time series across time. Although used primarily in finance so far, DCC has been proposed recently as a model-based estimation method for…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators which are…
Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. While recent advances have enabled graph topology learning from observed signals, existing…
Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication.…
We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…
This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the…
The oscillations of the human heart rate are inherently complex and non-linear -- they are best described by mathematical chaos, and they present a challenge when applied to the practical domain of cardiovascular health monitoring in…
A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise.…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…
Many molecular systems and physical phenomena are controlled by local fluctuations and microscopic dynamical rearrangements of the constitutive interacting units that are often difficult to detect. This is the case, for example, of phase…
We present formulations and numerical algorithms for solving diffeomorphic shape matching problems. We formulate shape matching as a variational problem governed by a dynamical system that models the flow of diffeomorphism $f_t \in…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…
We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal…