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The adaptive non-harmonic (ANH) model is a powerful tool to compactly represent oscillating signals with time-varying amplitude and phase, and non-sinusoidal oscillating morphology. Given good estimators of instantaneous amplitude and phase…
Alzheimer's disease gradually affects several components including the cerebral dimension with brain atrophies, the cognitive dimension with a decline in various functions and the functional dimension with impairment in the daily living…
This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss nontrivial features of stellar systems. Taking…
A new alternate method for evaluating linear response theory is formally developed, and results are presented. This method involves the time-evolution of the system using TDHF and is constructed directly on top of a static Hartree-Fock…
This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…
Complex architectures for wireless communications, digital electronics and space-based navigation interlink several oscillator-based devices such as clocks, transponders and synthesizers. Estimators characterizing their stability are…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
We develop a fully spatio-temporal numerical model, based on stochastic simulations, simulating the generation of spatio-temporal multimode spontaneous parametric down conversion, the propagation of the signal and idler beams through a…
We extend the method of multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of…
We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination…
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…
We consider a neural field model which consists of a network of an arbitrary number of Wilson-Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time delayed, excitatory coupling. We extend previous work on this…
Many methods aim to enhance time series forecasting by decomposing the series through intricate model structures and prior knowledge, yet they are inevitably limited by computational complexity and the robustness of the assumptions. Our…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI),…
We investigate a late-fusion approach to piano transcription, combined with a strong temporal prior in the form of a handcrafted Hidden Markov Model (HMM). The network architecture under consideration is compact in terms of its number of…
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
Leveraging spatio-temporal correlations among wind farms can significantly enhance the accuracy of ultra-short-term wind power forecasting. However, the complex and dynamic nature of these correlations presents significant modeling…
High-dimensional and incomplete (HDI) data, characterized by massive node interactions, have become ubiquitous across various real-world applications. Second-order latent factor models have shown promising performance in modeling this type…