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The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Progressive neurodegenerative diseases, including Alzheimer's disease (AD), multiple sclerosis (MS), Parkinson's disease (PD), and amyotrophic lateral sclerosis (ALS), exhibit complex, nonlinear trajectories that challenge deterministic…

Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about…

High spatial frequency information, including fine details like textures, significantly contributes to the accuracy of semantic segmentation. However, according to the Nyquist-Shannon Sampling Theorem, high-frequency components are…

Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode…

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD), which is a template-free method that represents the combination of different intrinsic modes on a time-frequency map (i.e., the Hilbert spectrum). The…

This paper describes a method for decomposing steady-state instrument data into excitation and formant filter components. The input data, taken from several series of recordings of acoustical instruments is analyzed in the frequency domain,…

We give a novel convergence theory for two-level hybrid Schwarz domain-decomposition (DD) methods for finite-element discretisations of the high-frequency Helmholtz equation. This theory gives sufficient conditions for the preconditioned…

We experimentally disentangle the contributions of different quantum paths in high-order harmonic generation (HHG) from the spectrally and spatially resolved harmonic spectra. By adjusting the laser intensity and focusing position, we…

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…

General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…

This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…

In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and…

The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…

Learning systems deployed in nonstationary and safety-critical environments often suffer from instability, slow convergence, or brittle adaptation when learning dynamics evolve over time. While modern optimization, reinforcement learning,…

We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix…

Computational spectral imaging (CSI) achieves real-time hyperspectral imaging through co-designed optics and algorithms, but typical CSI methods suffer from a bulky footprint and limited fidelity. Therefore, Spectral Deconvolution imaging…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

Depression and Attention Deficit Hyperactivity Disorder (ADHD) stand out as the common mental health challenges today. In affective computing, speech signals serve as effective biomarkers for mental disorder assessment. Current research,…