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Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
The ensemble of Euclidean gluon field configurations represented by the domain wall network is considered. A single domain wall is given by the sine-Gordon kink for the angle between chromomagnetic and chromoelectric components of the gauge…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
The question of unique continuation of harmonic functions in a domain $\Omega$ $\subset$ R d with boundary $\partial$$\Omega$, satisfying Dirichlet boundary conditions and with normal derivatives vanishing on a subset $\omega$ of the…
In this work we study the mutual benefits of two common computer vision tasks, self-supervised depth estimation and semantic segmentation from images. For example, to help unsupervised monocular depth estimation, constraints from semantic…
In this paper, we will consider generalised eigenfunctions of the Laplacian on some surfaces of infinite area. We will be interested in lower bounds on the number of nodal domains of such eigenfunctions which are included in a given bounded…
Let $\Omega\subset \mathbb{R}^{n+1}$ be an open set, not necessarily connected, with an $n$-dimensional uniformly rectifiable boundary. We show that $\partial\Omega$ may be approximated in a "Big Pieces" sense by boundaries of chord-arc…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
As the vast majority of network measures are defined for one-mode networks, two-mode networks often have to be projected onto one-mode networks to be analyzed. A number of issues arise in this transformation process, especially when…
Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining the bound (Hoffman colorings) for several notions of graph…
In-painting networks use existing pixels to generate appropriate pixels to fill "holes" placed on parts of an image. A 2-D in-painting network's input usually consists of (1) a three-channel 2-D image, and (2) an additional channel for the…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence measure over product bases. Any coherence…
Quantum entanglement is a useful resource for implementing communication tasks. However, for the resource to be useful in practice, it needs to be accessible by parties with bounded computational resources. Computational entanglement…
A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures $\mu$ in $n$-dimensional Euclidean space for all $n\geq 2$ in terms of…
Lower bounds are obtained on the maximum field strength in one or both phases in a body containing two-phases. These bounds only incorporate boundary data that can be obtained from measurements at the surface of the body, and thus may be…
Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…
We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…