Related papers: Asymptotics of the $k$-free diffraction measure vi…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
We develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically…
We describes a new approach for performing quantitative structure-factor analysis and density measurements of liquids using x-ray diffraction with a pink-spectrum x-ray source. The methodology corrects for the pink beam effect by performing…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
We study the problem of discrete distribution estimation in KL divergence and provide concentration bounds for the Laplace estimator. We show that the deviation from mean scales as $\sqrt{k}/n$ when $n \ge k$, improving upon the best prior…
The combination of interaction-free measurement and the quantum Zeno effect has been shown to both increase the signal-to-noise ratio of imaging, and decrease the light intensity flux through the imaged object. So far though, this has only…
We analyze the diffraction of elementary systems as the electron by light gratings when they are described by charge distributions instead of the usual point-like form. The treatment of the problem is based on the introduction, in analogy…
Strong intensity attenuation limits the use of conventional diffraction-free optical elements. We show a possible solution to the exponential intensity attenuation limiting the use of Fresnel-type diffraction-free nanometer-scale optics by…
This work is concerned with optical imaging in strongly diffusive environments. We consider a typical setting in optical coherence tomography where a sample is probed by a collection of wavefields produced by a laser and propagating through…
The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…
We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural…
Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity…
We compute the variance asymptotics for the number of real zeros of trigonometric polynomials with random dependent Gaussian coefficients and show that under mild conditions, the asymptotic behavior is the same as in the independent…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
De-diffraction (DD), a new procedure to totally cancel diffraction effects from wave-fields is presented, whereby the full field from an aperture is utilized and a truncated geometrical field is obtained, allowing infinitely sharp focusing…
We present a method to measure the spectral density of in-band optical transmission impairments without coherent electrical reception and digital signal processing at the receiver. We determine the method's accuracy by numerical simulations…
This paper presents a method for estimating the characteristics of a diffuse source from interferometric measurements in the context of SAR tomography. The proposed method is based on the use of central moments of the reflectivity density…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
Interaction-free measurement is shown to arise from the forward-scattered wave accompanying absorption: a "quantum silhouette" of the absorber. Accordingly, the process is not free of interaction. For a perfect absorber the…
In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fraction as soon as it ``appears'' for the first time and no later.…