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Observations of time-resolved thermal emission from tidally locked exoplanets can tell us about their atmospheric temperature structure. Telescopes such as JWST and ARIEL will improve the quality and availability of these measurements. This…
Environmental data often take the form of a collection of curves observed sequentially over time. An example of this includes daily pollution measurement curves describing the concentration of a particulate matter in ambient air. These…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
As the complexity increases in modern power systems, power quality analysis considering interharmonics has become a challenging and important task. This paper proposes a novel decomposition and estimation method for instantaneous power…
Detailed investigations of time series features across climates, continents and variable types can progress our understanding and modelling ability of the Earth's hydroclimate and its dynamics. They can also improve our comprehension of the…
Soil assessment is important for mobile robot planning and navigation on natural and planetary environments. Terramechanic characteristics can be inferred from the thermal behaviour of soils under the influence of sunlight using remote…
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…
Causality implies that by measuring an absorption spectrum, the time-dependent linear response function can be retrieved. Recent experiments suggest a link between the shape of spectral lines observed in absorption spectroscopy with the…
This topic review communicates working experiences regarding interaction of a multiplicity of processes. Our experiences come from climate change modelling, materials science, cell physiology and public health, and macroeconomic modelling.…
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
We demonstrate the real-time detection of dynamical phase transitions (DPTs) in lattice-confined spinor gases subject to a priori unknown time-variant interactions, via the temporal behaviors of both the system energy and spinor phases…
Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lema\^itre-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered.…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The phenomenon of Hilbert space fragmentation, whereby dynamical constraints fragment Hilbert space into many disconnected sectors, provides a simple mechanism by which thermalization can be arrested. However, little is known about how…
Technological advances in high performance computing and maturing physical models allow scientists to simulate weather and climate evolutions with an increasing accuracy. While this improved accuracy allows us to explore complex dynamical…
Rapid changes in Earth's cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets.…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…