Related papers: On the Injectivity of Euler Integral Transforms wi…
The Euler characteristic $\chi =|V|-|E|$ and the total length $\mathcal{L}$ are the most important topological and geometrical characteristics of a metric graph. Here, $|V|$ and $|E|$ denote the number of vertices and edges of a graph. The…
It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.
Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…
Can transformers generalize efficiently on problems that require dealing with examples with different levels of difficulty? We introduce a new task tailored to assess generalization over different complexities and present results that…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
We present an explicit piecewise linear map from a flat Klein bottle (i.e. one that is locally isometric to the Euclidean plane) into Euclidean 3-space an that is an isometric immersion -- a path isometry that is locally injective. The…
We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, provided that the singular foliation defined by the closures of…
Electrical Capacitance Tomography (ECT) is an imaging technique providing the distribution of permittivity in a medium by the mean of electrodes. As for any imaging systems, the reachable spatial resolution is a key parameter. In this paper…
We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with…
Baer's Criterion of injectivity implies that injectivity of a module is a factorization property w.r.t. a single monomorphism. Using the notion of a cotorsion pair, we study generalizations and dualizations of factorization properties in…
Acousto-electric tomography (AET) is a hybrid imaging modality that combines electrical impedance tomography with focused ultrasound perturbations to obtain interior power density measurements, which provide additional information that can…
Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…
Symbolic Extension Entropy Theorem (SEET) describes the possibility of a lossless digitalization of a dynamical system by extending it to a subshift. It gives an estimate on the entropy of symbolic extensions (and the necessary number of…
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…
Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the boundary of a conductive medium (the data) are taken according to a prescribed protocol set and inverted to map the internal…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
Purpose: The main purpose of this study was to assess the reliability of shape and heterogeneity features in both Positron Emission Tomography (PET) and low-dose Computed Tomography (CT) components of PET/CT. A secondary objective was to…
Although perturbative quantum field theory is highly successful, it possesses a number of well-known analytic problems, from ultraviolet and infrared divergencies to the divergence of the perturbative expansion itself. As a consequence, it…
We propose a notion of integral Menger curvature for compact, $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies that the set is $C^{1,\alpha}$ embedded manifold with the H{\"o}lder…