Related papers: Fake uniformity in a shape inversion formula
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
This article introduces a method for adjusting macro-particle weights within a particle distribution while preserving statistical and physical properties. The method allows the weights of the new macro-particle distribution to be determined…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\"ul\H{o}p-Tsutsui) form. This enables…
We formulate empirically the rapidity density distribution of produced particles in multiple particle production. The assumed mechanism is that the produced particles are emitted isotropically from several emitting centers, located on the…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
The emptiness formation probability in the six-vertex model with domain wall boundary conditions is considered. This correlation function allows one to address the problem of limit shapes in the model. We apply the quantum inverse…
Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf)…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
The information content and properties of the cross section for atom scattering from a defect on a flat surface are investigated. Using the Sudden approximation, a simple expression is obtained that relates the cross section to the…
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…