Related papers: Signal from noise retrieval from one and two-point…
Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding…
In this paper, we explore the two-point zeroth-order gradient estimator and identify the distribution of random perturbations that minimizes the estimator's asymptotic variance as the perturbation stepsize tends to zero. We formulate it as…
We present a method of reliably extracting the flux of individual sources from sky maps in the presence of noise and a source population in which number counts are a steeply falling function of flux. The method is an extension of a standard…
In a recent work, we presented the first application of the Poisson-Wiseman-Anderson method of `matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…
The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the…
In this article we derive the average and the variance of the cross-correlation of a noise wavefield. The noise cross-correlation function (NCF) is widely used to passively estimate the Green's function between two probes and is…
In this paper we study the time dependent Schr\"odinger equation with all possible self-adjoint singular interactions located at the origin, which include the $\delta$ and $\delta'$-potentials as well as boundary conditions of Dirichlet,…
An efficient and accurate image reconstruction algorithm for ultrasound tomography (UST) is described and demonstrated, which can recover accurate sound speed distribution from acoustic time series measurements made in soft tissue. The…
General equations for one- particle Green function in non- magic nuclei have been derived where a pairing mechanism, which is analogous to the Bardeen- Cooper- Schrieffer one, has been singled out explicitely. A "refining" procedure for the…
The Green's function of the discrete Sch\"odinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting appropriate potentials. We show two ways of the expression for the Green's…
The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
The homogeneous Green's function is the difference between an impulse response and its time-reversal. According to existing representation theorems, the homogeneous Green's function associated with source-receiver pairs inside a medium can…
When the available information is noisy zeroth-order (ZO) oracle, stochastic approximation methods are popular for estimating the root of the multivariate gradient equation. Inspired by the Stein's identity, this work establishes a novel…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
The relativistic mean field theory with the Green's function method is taken to study the single-particle resonant states. Different from our previous work [Phys.Rev.C 90,054321(2014)], the resonant states are identified by searching for…