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Imaging with optical resolution through highly scattering media is a long sought-after goal with important applications in deep tissue imaging. Although being the focus of numerous works, this goal was considered impractical until recently.…
An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius \r{ho} such that there exist…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
Compressed sensing (CS) using overcomplete wavelet dictionaries has been a well-investigated topic in the recent times for image and vision applications. In this paper, different overcomplete wavelet transforms have been studied to estimate…
We introduce a new volume definition on normed vector spaces. We show that the induced $k$-area functionals are convex for all $k$. In the particular case $k=2$, our theorem implies that Busemann's 2-volume density is convex, which was…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency…
A simple and effective method for imaging through ground-level atmospheric turbulence.
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
Light microscopy as well as image acquisition and processing suffer from physical and technical prejudices which preclude a correct interpretation of biological observations which can be reflected in, e.g., medical and pharmacological…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of a point with respect to a measure is defined as the infimum…
We give a deterministic method of quasi-polynomial complexity to approximate the volume of the intersection of the unit hypercube with two specific sets. The method can actually be applied (without losing the quasi-polynomial complexity) to…
Let $f:[0,1)^d \to {\mathbb R}$ be an integrable function. An objective of many computer experiments is to estimate $\int_{[0,1)^d} f(x) dx$ by evaluating f at a finite number of points in [0,1)^d. There is a design issue in the choice of…
We extend the notion of convexity of functions defined on global nonpositive curvature spaces by introducing (geodesically) $h$-convex functions. We prove estimates of Hermite-Hadamard type via Katugampola's fractional integrals. We obtain…
We present an unsupervised method for co-segmentation of a set of 3D shapes from the same class with the aim of segmenting the input shapes into consistent semantic parts and establishing their correspondence across the set. Starting from…