Related papers: Noise in Disordered Systems: Higher Order Spectra …
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…
The application of large deep learning models in weather forecasting has led to significant advancements in the field, including higher-resolution forecasting and extended prediction periods exemplified by models such as Pangu and Fuxi.…
We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spectral norm of H on the scale n^{-2/3} in the limit…
We calculate analytically the asymptotic form of quasi-normal frequencies for massive scalar perturbations of large black holes in AdS_5. We solve the wave equation, which reduces to a Heun equation, perturbatively and calculate the wave…
Hyperspectral images are high-dimensional datasets comprising hundreds of contiguous spectral bands, enabling detailed analysis of materials and surfaces. Hyperspectral anomaly detection (HAD) refers to the technique of identifying and…
In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise…
Detection of the \hi~ 21-cm power spectrum is one of the key science drivers of several ongoing and upcoming low-frequency radio interferometers. However, the major challenge in such observations come from bright foregrounds, whose accurate…
The NMR spectra of paramagnetic substances can feature shifts over thousands of ppm. In high magnetic field instruments, this corresponds to extreme offsets, which make it challenging or impossible to achieve uniform excitation without…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is…
We construct foreground simulations comprising spatially correlated extragalactic and diffuse Galactic emission components and calculate the `intrinsic' (instrument-free) two-dimensional spatial power spectrum and the cylindrically and…
Matrix perturbation bounds (such as Weyl and Davis-Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectral norm of the noise matrix and are sharp in worst case…
Load modeling is an important issue in modeling a power system. The approach of ambient signals-based load modeling (ASLM) was recently proposed to better track the time-varying changes of load models. To improve computation efficiency and…
Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a…
This paper covers predicting high-resolution electricity peak demand features given lower-resolution data. This is a relevant setup as it answers whether limited higher-resolution monitoring helps to estimate future high-resolution peak…
We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a…
The power spectrum of redshifted 21 cm emission brightness temperature fluctuations is a powerful probe of the Epoch of Reionization (EoR). However, bright foreground emission presents a significant impediment to its unbiased recovery from…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…