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A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
Traditional shape descriptors have been gradually replaced by convolutional neural networks due to their superior performance in feature extraction and classification. The state-of-the-art methods recognize object shapes via image…
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…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
We study Fourier bases on invariant measures generated by affine iterated function systems in ${\mathbb R}^d$ with integer coefficients. We show that, for simple digit sets, these systems satisfy the open set condition and have no overlap.…
Magnetic Resonance Imaging (MRI) typically recruits multiple sequences (defined here as "modalities"). As each modality is designed to offer different anatomical and functional clinical information, there are evident disparities in the…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…
This paper focuses on visual motion-based invariants that result in a representation of 3D points in which the stationary environment remains invariant, ensuring shape constancy. This is achieved even as the images undergo constant change…
A certain real number, depending on two neighbouring sides of a quadrilateral and the diagonal meeting these two sides at their common point, is shown to be invariant under affinity. As an application we demonstrate a nice formula for the…
Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schr\"odinger quantization and reduce effectively the quantized problem from $n^{2}$ to $n$…
Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be…
Shape effects in magnetic particles are widely studied, because of the ability of the shape and the size to control the parameters of a sample during its production. Experiments with nano-sized samples show that the shape can affect also…
We put forward and demonstrate experimentally a {\it quantum-inspired} protocol that allows to quantify the degree of similarity between two spatial shapes embedded in two optical beams without the need to measure the amplitude and phase…
We propose a nonrigid registration approach for diffusion tensor images using a multicomponent information-theoretic measure. Explicit orientation optimization is enabled by incorporating tensor reorientation, which is necessary for…
We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…