Search results for "Euclid"

A practical MRI-based reconstruction method for a new endocavitary and interstitial gynaecological template

2015

Purpose: There are perineal templates for interstitial implants such as MUPIT and Syed applicators. Their limitations are the intracavitary component deficit and the necessity to use computed tomography (CT) for treatment planning since both applicators are non-magnetic resonance imaging (MRI) compatibles. To overcome these problems, a new template named Template Benidorm (TB) has been recently developed. Titanium needles are usually reconstructed based on their own artifacts, mainly in T1-weighted sequence, using the void on the tip as the needle tip position. Nevertheless, patient tissues surrounding the needles present heterogeneities that complicate the accurate identification of these …

Differential of metric valued Sobolev maps

2020

We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is $\mathbb{R}$.

Uniformization of two-dimensional metric surfaces

2014

We establish uniformization results for metric spaces that are homeomorphic to the Euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and sufficient condition for such spaces to be QC equivalent to the Euclidean plane, disk, or sphere. Moreover, we show that if such a QC parametrization exists, then the dilatation can be bounded by 2. As an application, we show that the Euclidean upper bound for measures of balls is a sufficient condition for the existence of a 2-QC parametrization. This result gives a new approach to the Bonk-Kleiner theorem on parametrizations of Ahlfors 2-regular spheres by qu…

On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups

2002

Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the `Bestvina-Brady group', or `Artin kernel', Gamma_K. We show that Gamma_K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known.

Stationary sets of the mean curvature flow with a forcing term

2020

We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space $\mathbb R^n$ of dimension at least 2. Our main results states that tangential balls in $\mathbb R^n$ under any flat flow with a bounded forcing term will experience fattening, which generalizes the result by Fusco, Julin and Morini from the planar case to higher dimensions. Then, as in the planar case, we are able to characterize stationary sets in $\mathbb R^n$ for a constant forcing term as finite unions of equisized balls with mutually positive distance.

Gaussian processes retrieval of crop traits in Google Earth Engine based on Sentinel-2 top-of-atmosphere data.

2022

The unprecedented availability of optical satellite data in cloud-based computing platforms, such as Google Earth Engine (GEE), opens new possibilities to develop crop trait retrieval models from the local to the planetary scale. Hybrid retrieval models are of interest to run in these platforms as they combine the advantages of physically-based radiative transfer models (RTM) with the flexibility of machine learning regression algorithms. Previous research with GEE primarily relied on processing bottom-of-atmosphere (BOA) reflectance data, which requires atmospheric correction. In the present study, we implemented hybrid models directly into GEE for processing Sentinel-2 (S2) Level-1C (L1C)…

I poligoni stellati: origini storiche ed implicazioni didattiche

2019

The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.

Rectifiability and singular integrals

1995

Hadronic light-by-light contribution to $(g-2)_\mu$ from lattice QCD with SU(3) flavor symmetry

2020

We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_\mu$ at the SU(3) flavor-symmetric point $m_\pi=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computin…

Cluster-Based RF Fingerprint Positioning Using LTE and WLAN Outdoor Signals

2015

In this paper we evaluate user-equipment (UE) positioning performance of three cluster-based RF fingerprinting methods using LTE and WLAN signals. Real-life LTE and WLAN data were collected for the evaluation purpose using consumer cellular-mobile handset utilizing ‘Nemo Handy’ drive test software tool. Test results of cluster-based methods were compared to the conventional grid-based RF fingerprinting. The cluster-based methods do not require grid-cell layout and training signature formation as compared to the gridbased method. They utilize LTE cell-ID searching technique to reduce the search space for clustering operation. Thus UE position estimation is done in short time with less comput…