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Motivation: Gene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
Two-dimensional terahertz spectroscopy (2DTS) is a low-frequency analogue of two-dimensional optical spectroscopy that is rapidly maturing as a probe of a wide variety of condensed matter systems. However, a persistent problem of 2DTS is…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
In the realm of quantum-effect devices and materials, two-dimensional electron gases (2DEGs) stand as fundamental structures that promise transformative technologies. However, the presence of impurities and defects in 2DEGs poses…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
Recently, electromagnetic surrogate solvers, trained on solutions of Maxwell's equations under specific simulation conditions, enabled fast inference of computationally expensive simulations. However, conventional electromagnetic surrogate…
A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is…
3D Gaussian Splatting (3DGS) has emerged as a dominant novel-view synthesis technique, but its high memory consumption severely limits its applicability on edge devices. A growing number of 3DGS compression methods have been proposed to…
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore…
The sparsity-restricted maximum likelihood estimator (SMLE) has received considerable attention for feature screening in ultrahigh-dimensional regression. SMLE is a computationally convenient method that naturally incorporates the joint…
Multitemporal spectral unmixing (SU) is a powerful tool to process hyperspectral image (HI) sequences due to its ability to reveal the evolution of materials over time and space in a scene. However, significant spectral variability is often…
Deep learning has emerged as the preferred modeling approach for automatic ECG analysis. In this study, we investigate three elements aimed at improving the quantitative accuracy of such systems. These components consistently enhance…
This paper presents a novel extended dynamic programming approach for energy minimization (EDP) to solve the correspondence problem for stereo and motion. A significant speedup is achieved using a recursive minimum search strategy (RMS).…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The…
We focus on the problem of estimating the change in the dependency structures of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth…
Electroencephalogram (EEG) signals generally exhibit low signal-to-noise ratio (SNR) and high inter-subject variability, making generalization across subjects and domains challenging. Recent advances in deep learning, particularly…