Long-Range Effects in Layered Spin Structures

We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled rotator model with short-range and mean-field interactions. This latter model has been studied in the past because of its interesting dynamical and statistical properties related to exotic features of long-range interactions. It is suggested that experiments could be conducted such that within a specific temperature range the presence of long-range interactions crucially affect the behavior of the system

The octonionic eigenvalue problem

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.Comment: 21 page

Quaternionic Diffusion by a Potential Step

In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.Comment: 10 pages, 1 figur

Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

Oral contraceptives combined with interferon β in multiple sclerosis

Objective: To test the effect of oral contraceptives (OCs) in combination with interferon b (IFN-b) on disease activity in patients with relapsing-remitting multiple sclerosis (RRMS). Methods: One hundred fifty women with RRMS were randomized in a 1:1:1 ratio to receive IFNb-1a subcutaneously (SC) only (group 1), IFN-b-1a SC plus ethinylstradiol 20 mg and desogestrel 150 mg (group 2), or IFN-b-1a SC plus ethinylestradiol 40 mg and desogestrel 125 mg (group 3). The primary endpoint was the cumulative number of combined unique active (CUA) lesions on brain MRI at week 96. Secondary endpoints included MRI and clinical and safety measures. Results: The estimated number of cumulative CUA lesions at week 96 was 0.98 (95% confidence interval [CI] 0.81–1.14) in group 1, 0.84 (95% CI 0.66–1.02) in group 2, and 0.72 (95% CI 0.53–0.91) in group 3, with a decrease of 14.1% (p 5 0.24) and 26.5% (p 5 0.04) when comparing group 1 with groups 2 and 3, respectively. The number of patients with no gadoliniumenhancing lesions was greater in group 3 than in group 1 (p 5 0.03). No significant differences were detected in other secondary endpoints. IFN-b or OC discontinuations were equally distributed across groups. Conclusions: Our results translate the observations derived from experimental models to patients, supporting the anti-inflammatory effects of OCs with high-dose estrogens, and suggest possible directions for future research

Monitoring spatial sustainable development: Semi-automated analysis of satellite and aerial images for energy transition and sustainability indicators

Solar panels are installed by a large and growing number of households due to the convenience of having cheap and renewable energy to power house appliances. In contrast to other energy sources solar installations are distributed very decentralized and spread over hundred-thousands of locations. On a global level more than 25% of solar photovoltaic (PV) installations were decentralized. The effect of the quick energy transition from a carbon based economy to a green economy is though still very difficult to quantify. As a matter of fact the quick adoption of solar panels by households is difficult to track, with local registries that miss a large number of the newly built solar panels. This makes the task of assessing the impact of renewable energies an impossible task. Although models of the output of a region exist, they are often black box estimations. This project's aim is twofold: First automate the process to extract the location of solar panels from aerial or satellite images and second, produce a map of solar panels along with statistics on the number of solar panels. Further, this project takes place in a wider framework which investigates how official statistics can benefit from new digital data sources. At project completion, a method for detecting solar panels from aerial images via machine learning will be developed and the methodology initially developed for BE, DE and NL will be standardized for application to other EU countries. In practice, machine learning techniques are used to identify solar panels in satellite and aerial images for the province of Limburg (NL), Flanders (BE) and North Rhine-Westphalia (DE).Comment: This document provides the reader with an overview of the various datasets which will be used throughout the project. The collection of satellite and aerial images as well as auxiliary information such as the location of buildings and roofs which is required to train, test and validate the machine learning algorithm that is being develope

Statistical analysis of probability density functions for photometric redshifts through the KiDS-ESO-DR3 galaxies

Despite the high accuracy of photometric redshifts (zphot) derived using Machine Learning (ML) methods, the quantification of errors through reliable and accurate Probability Density Functions (PDFs) is still an open problem. First, because it is difficult to accurately assess the contribution from different sources of errors, namely internal to the method itself and from the photometric features defining the available parameter space. Second, because the problem of defining a robust statistical method, always able to quantify and qualify the PDF estimation validity, is still an open issue. We present a comparison among PDFs obtained using three different methods on the same data set: two ML techniques, METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts) and ANNz2, plus the spectral energy distribution template fitting method, BPZ. The photometric data were extracted from the KiDS (Kilo Degree Survey) ESO Data Release 3, while the spectroscopy was obtained from the GAMA (Galaxy and Mass Assembly) Data Release 2. The statistical evaluation of both individual and stacked PDFs was done through quantitative and qualitative estimators, including a dummy PDF, useful to verify whether different statistical estimators can correctly assess PDF quality. We conclude that, in order to quantify the reliability and accuracy of any zphot PDF method, a combined set of statistical estimators is required.Comment: Accepted for publication by MNRAS, 20 pages, 14 figure