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The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
We extend frequency-domain blind source separation based on independent vector analysis to the case where there are more microphones than sources. The signal is modelled as non-Gaussian sources in a Gaussian background. The proposed…
In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point:…
Intensity interferometry removes the stringent requirements on mechanical precision and atmospheric corrections that plague all amplitude interferometry techniques at the cost of severely limited sensitivity. A new idea we recently…
We present a quantum sensing scheme achieving the ultimate quantum sensitivity in the estimation of the transverse displacement between two photons interfering at a balanced beam splitter, based on transverse-momentum sampling measurements…
Long-baseline optical interferometry uses the power spectrum and bispectrum constructs as fundamental observables. Noise arising in the detection of the fringe pattern gives rise to both variance and biases in the power spectrum and…
The optical interferometry has been widely used in various high precision applications. Usually, the minimum precision of an interferometry is limited by various technique noises in practice. To suppress such kind of noises, we propose a…
Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase…
In this work we present a new algorithm for data deconvolution that allows the retrieval of the target function with super-resolution with a simple approach that after a precis e measurement of the instrument response function (IRF), the…
The same machine learning model running on different edge devices may produce highly-divergent outputs on a nearly-identical input. Possible reasons for the divergence include differences in the device sensors, the device's signal…
We prove an upper bound for the convergence rate of the homogenization limit $\epsilon\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $\epsilon$ is a…
We devise a systematic method to determine the Fisher information required for resolving two incoherent point sources with a diffraction-limited linear imaging device. The resulting Cram\'er-Rao bound gives the lowest variance achievable…
It has been recently suggested that optical interferometers may not require a phase-stable optical link between the stations if instead sources of quantum-mechanically entangled pairs could be provided to them, enabling extra-long baselines…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Current pulsar timing array (PTA) analyses do not take full advantage of pulsar distance information, thereby missing out on improved angular resolution and on a potential factor-of-two gain in detection sensitivity for individual…
The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…
This paper studies the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements collected by a uniform array of sensors. We prove novel stability bounds for…