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Numerical simulations of merging black hole binaries produce the most accurate gravitational waveforms. The availability of hundreds of these numerical relativity (NR) waveforms, often containing many higher spherical harmonic modes, allows…
Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for…
This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…
Smoothing is widely used approach for measurement noise reduction in spectral analysis. However, it suffers from signal distortion caused by peak suppression. A locally self-adjustive smoothing method is developed that retains sharp peaks…
Penalized spline smoothing of time series and its asymptotic properties are studied. A data-driven algorithm for selecting the smoothing parameter is developed. The proposal is applied to define a semiparametric extension of the well-known…
LiDARs provide accurate geometric measurements, making them valuable for ego-motion estimation and reconstruction tasks. Although its success, managing an accurate and lightweight representation of the environment still poses challenges.…
Methods for parameter estimation of gravitational-wave data assume that detector noise is stationary and Gaussian. Real data deviates from these assumptions, which causes bias in the inferred parameters and incorrect estimates of the…
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation, Gaussian smoothing and smoothing on a sphere. The methods…
Oceanic processes at fine scales are crucial yet difficult to observe accurately due to limitations in satellite and in-situ measurements. The Surface Water and Ocean Topography (SWOT) mission provides high-resolution Sea Surface Height…
Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…
In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by…
Recent advances in 3D Gaussian Splatting (3DGS) have achieved remarkable success in high-fidelity Novel View Synthesis (NVS), yet the optimization process inevitably introduces noisy Gaussian primitives due to the sparse and incomplete…
Studies of hadron resonances and their properties are limited by the accuracy and consistency of measured datasets, which can originate from many different experiments. We have used Gaussian Processes (GP) to build interpolated datasets,…
In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…
In the absence of external reference position information (e.g. GNSS) SLAM has proven to be an effective method for indoor navigation. The positioning drift can be reduced with regular loop-closures and global relaxation as the backend,…
The increasing sensitivity of gravitational-wave detectors has brought about an increase in the rate of astrophysical signal detections as well as the rate of "glitches"; transient and non-Gaussian detector noise. Temporal overlap of…
Astronomical data often suffer from noise and incompleteness. We extend the common mixtures-of-Gaussians density estimation approach to account for situations with a known sample incompleteness by simultaneous imputation from the current…
The potential of compressed sensing for obtaining sparse time-frequency representations for gravitational wave data analysis is illustrated by comparison with existing methods, as regards i) shedding light on the fine structure of noise…