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Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like…
In this paper, we propose a new protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying…
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…
Absorption imaging with quasi-resonant laser light is a commonly used technique to probe ultra-cold atomic gases in various geometries. Here we investigate some non-trivial aspects of this method when it is applied to in situ diagnosis of a…
This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression…
In characterization of quantum systems, adapting measurement settings based on data while it is collected can generally outperform in efficiency conventional measurements that are carried out independently of data. The existing methods for…
The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid…
When modelling strong gravitational lenses, i.e., where there are multiple images of the same source, the most widely used parameterisation for the mass profile in the lens galaxy is the singular power-law model $\rho(r)\propto…
Most statistical inference from cosmic large-scale structure relies on two-point statistics, i.e.\ on the galaxy-galaxy correlation function (2PCF) or the power spectrum. These statistics capture the full information encoded in the Fourier…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. We investigate here the accuracy of the tight-coupling approximation commonly used to…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
In homogenization theory and multiscale modeling, typical functions satisfy the scaling law $f^{\epsilon}(x) = f(x,x/\epsilon)$, where $f$ is periodic in the second variable and $\epsilon$ is the smallest relevant wavelength,…
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…
In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…
Consistency training has proven to be an advanced semi-supervised framework and achieved promising results in medical image segmentation tasks through enforcing an invariance of the predictions over different views of the inputs. However,…
We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a…
We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) $q$-derivatives. Both theories can be formulated in two different frames, called fractional…