Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

The LHC di-photon excess and Gauge Coupling Unification in Extra Z′Z^\prime Heterotic-String Derived Models

The di-photon excess observed at the LHC can be explained as a Standard Model singlet that is produced and decays by heavy vector-like colour triplets and electroweak doublets in one-loop diagrams. The characteristics of the required spectrum are well motivated in heterotic-string constructions that allow for a light $Z^\prime$. Anomaly cancellation of the $U(1)_{Z^\prime}$ symmetry requires the existence of the Standard Model singlet and vector-like states in the vicinity of the $U(1)_{Z^\prime}$ breaking scale. In this paper we show that the agreement with the gauge coupling data at one-loop is identical to the case of the Minimal Supersymmetric Standard Model, owing to cancellations between the additional states. We further show that effects arising from heavy thresholds may push the supersymmetric spectrum beyond the reach of the LHC, while maintaining the agreement with the gauge coupling data. We show that the string inspired model can indeed account for the observed signal and discuss the feasibility of obtaining viable scalar mass spectrum.Comment: 26 pages. 11 figures. Published versio

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Discrepancy of Minimal Riesz Energy Points

We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in S2 were obtained. Our result improves previously known bounds for 0 ≤ s< 2 and s≠ 1 in S2, where s= 0 is Wolff’s result, and for d- t< s< d with t≈ 2.5 when d≥ 3 and s≠ d- 1

Service level agreement framework for differentiated survivability in GMPLS-based IP-over-optical networks

In the next generation optical internet, GMPLS based IP-over-optical networks, ISPs will be required to support a wide variety of applications each having their own requirements. These requirements are contracted by means of the SLA. This paper describes a recovery framework that may be included in the SLA contract between ISP and customers in order to provide the required level of survivability. A key concern with such a recovery framework is how to present the different survivability alternatives including recovery techniques, failure scenario and layered integration into a transparent manner for customers. In this paper, two issues are investigated. First, the performance of the recovery framework when applying a proposed mapping procedure as an admission control mechanism in the edge router considering a smart-edge simple-core GMPLS-based IP/WDM network is considered. The second issue pertains to the performance of a pre-allocated restoration and its ability to provide protected connections under different failure scenarios

Characterization of islamic ceramic production techniques in northeast iberian peninsula: The case of medieval albarracin (spain)

Ceramic objects found in the Islamic Taifa of Albarracin (Spain), 12th century CE, were studied to ascertain the main characteristics and influences of its manufacture. Production centers even from small kingdoms can add new insights in medieval ceramic technology. Several types of decorated ceramics, such as tin-opacified glazed, monochrome glazed and cuerda seca, were investigated. Ceramic bodies were analyzed by ICP-Optical Emission Spectrometry, and glazes were studied by Scanning Electron Microscopy with Energy Dispersive X-ray Spectrometry. All the ceramic bodies showed the use of Ca-rich pastes, although three groups could be distinguished and related to their decoration. Lead and silicon were the main components of the glazes, as well as scattered tin oxide in the case of white or green opacified glazes. Some features, such as calcareous bodies, double firing for tin-opacified glazes, glaze components, and coloring oxides, were common in Albarracin samples and other Islamic production centers in the Iberian Peninsula. However, some differences were also highlighted in lead/silica proportions and cuerda seca decoration, and several influences from northern or southern pottery centers. Lead isotope ratios, measured by ICP-Quadrupole Mass Spectrometry, revealed two different sources or suppliers of lead raw materials according to the type of glaze to be prepared. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Naturalness and Dark Matter Properties of the BLSSM

In this report, we compare the naturalness and Dark Matter (DM) properties of the Minimal Supersymmetric Standard Model (MSSM) and the $B-L$ Supersymmetric Standard Model (BLSSM), with universality in both cases. We do this by adopting standard measures for the quantitative analysis of the Fine-Tuning (FT), at both low (i.e. supersymmetric (SUSY)) and high (i.e. unification) scales. We will see a similar level of FT for both models in these scenarios, with a slightly better FT for the BLSSM at SUSY scales and MSSM at Grand Unification Theory (GUT) scales. When including DM relic constraints, we drastically confine the MSSM's parameter space, whereas we still find a large parameter space available for the non-minimal scenario.Comment: Prepared for proceedings for DIS2017, talk presented by Simon Kin