Related papers: The Effects of Noise and Sampling on the Spectral …
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Oscillation of sessile drops is important to many applications. In the present study, the natural oscillation of a sessile drop on flat surfaces with free contact lines (FCL) is investigated through numerical and theoretical analysis. The…
Current self-supervised denoising methods for paired noisy images typically involve mapping one noisy image through the network to the other noisy image. However, after measuring the spectral bias of such methods using our proposed Image…
The Integrated Sachs-Wolfe (ISW) effect is a direct signature of the presence of dark energy in the universe, in the absence of spatial curvature. A powerful method for observing the ISW effect is through cross-correlation of the Cosmic…
Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a…
Noise correlations are studied for systems of hard-core bosons in one-dimensional lattices. We use an exact numerical approach based on the Bose-Fermi mapping and properties of Slater determinants. We focus on the scaling of the noise…
The effect of random surface roughness on quantum size effect in thin films is discussed. The conductivity of quantized metal films is analyzed for different types of experimentally identified correlation functions of surface…
Supervised machine learning approaches require the formulation of a loss functional to be minimized in the training phase. Sequential data are ubiquitous across many fields of research, and are often treated with Euclidean distance-based…
In Stage-IV imaging surveys, a significant amount of the cosmologically useful information is due to sources whose images overlap with those of other sources on the sky. The cosmic shear signal is primarily encoded in the estimated shapes…
In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
Noise power estimation is a key issue in modern wireless communication systems. It allows resource allocation by detecting white spectral spaces effectively, and gives control over the communication process by adjusting transmission power.…
We consider the optical fiber channel modelled by the nonlinear Schr\"{o}dinger equation with additive white Gaussian noise and with large signal-to-noise ratio. For the small dispersion case we present the approach to analyze the…
We consider a stochastic partial differential equation (SPDE) on a lattice \partial_t X=(\Delta-m^2)X-\lambda X^p+\eta where $\eta$ is a space-time L\'evy noise. A perturbative (in the sense of formal power series) strong solution is given…
The synchronized phase of globally coupled nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results…
The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Universe. In this Letter we present some of the initial results on…
We measure the two point correlation function (CF) of 1357 galaxy clusters with a mass of $\log_{10}{M_{200}}\geq 13.6$~\hm~and at a redshift of $z \leq 0.125$. This work differs from previous analyses in that it utilizes a spectroscopic…
The Continuous Spontaneous Localisation (CSL) model is the most studied among collapse models, which describes the breakdown of the superposition principle for macroscopic systems. Here, we derive an upper bound on the parameters of the…