Related papers: Gaussian Bounds for Noise Correlation of Resilient…
We consider a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise (PSN). We study the fluctuations of the work done to maintain this system in a nonequilibrium…
It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of…
We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the…
We address the dynamics of entanglement and quantum discord for two non interacting qubits initially prepared in a maximally entangled state and then subjected to a classical colored noise, i.e. coupled with an external environment…
We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the…
We have built a highly sensitive torsion balance to investigate small forces between closely spaced gold coated surfaces. Such forces will occur between the LISA proof mass and its housing. These forces are not well understood and…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational…
The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >=…
Progress in experimental techniques at nanoscale made measurements of noise in molecular junctions possible. These data are important source of information not accessible through average flux measurements. Emergence of optoelectronics,…
We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…
We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums of region-stabilizing (determined by the points of the process within some specified regions) score functions and provide a bound on…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…
Motivated by recent experiments with Josephson qubits we propose a new phenomenological model for 1/f noise due to collective excitations of interacting defects in the qubit's environment. At very low temperatures the effective dynamics of…
The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive…
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…
In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the…
Harris's correlation inequality states that any two monotone functions on the Boolean hypercube are positively correlated. Talagrand \cite{Talcorr} started a line of works in search of quantitative versions of this fact by providing a lower…