Twists of Elliptic Curves

In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set $H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_{\overline{K}}(E)\big)$. The results are illustrated by examples

Explicit construction of rational torsion divisors on Jacobians of curves

In this thesis we describe explicit ways to construct algebraic curves over number fields such that their jacobians admit a certain rational torsion structure. Using these constructions, we give new examples of many different torsion orders over the rational numbers and over some number fields of small degree. While so far only examples of hyperelliptic curves with a torsion point of large order on the jacobian are known, we develop methods that can be applied to a larger class of algebraic curves. With these methods we are able to give series of algebraic curves with a torsion point of an order which is linear and quadratic in the genus. Furthermore, we examine possible orders N of torsion points in a certain family of hyperelliptic curves with real multiplication in the jacobian for some small N

Prediction and understanding of soft proton contamination in XMM-Newton: a machine learning approach

&amp;lt;p&amp;gt;One of the major and unfortunately unforeseen sources of background for the current generation of X-ray telescopes flying mainly in the magnetosphere are soft protons with few tens to hundreds of keV concentrated. One such telescope is the X-ray Multi-Mirror Mission (XMM-Newton) by ESA. Its observing time lost due to the contamination is &amp;amp;#160;about 40%. This affects all the major broad science goals of XMM, ranging from cosmology to astrophysics of neutron stars and black holes. The soft proton background could dramatically impact future X-ray missions such Athena and SMILE missions. Magnetopsheric processes that trigger this background are still poorly understood. We use a machine learning approach to delineate related important parameters and to develop a model to predict the background contamination using 12 years of XMM observations. As predictors we use the location of XMM, solar and geomagnetic activity parameters. We revealed that the contamination is most strongly related to the distance in southern direction, ZGSE, (XMM observations were in the southern hemisphere), the solar wind velocity and the location on the magnetospheric magnetic field lines. We derived simple empirical models for the best two individual predictors and a machine learning model which utilizes an ensemble of the predictors (Extra Trees Regressor) and gives better performance. Based on our analysis, future X-Ray missions in the magnetosphere should minimize observations during &amp;amp;#160;times &amp;amp;#160;associated with high solar wind speed &amp;amp;#160;and avoid closed magnetic field lines, especially at the dusk flank region at least in the southern hemisphere.&amp;amp;#160;&amp;lt;/p&amp;gt;</jats:p

Automatische Auswertung von Elektropherogrammen und Chromatogrammen mit Methoden der digitalen Bildverarbeitung Schlussbericht

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Signatures in a giant radio galaxy of a cosmological shock wave at intersecting filaments of galaxies

SIGLEAvailable from: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Prediction of Soft Proton Intensities in the Near-Earth Space Using Machine Learning

The spatial distribution of energetic protons contributes to the understanding of magnetospheric dynamics. Based upon 17 yr of the Cluster/RAPID observations, we have derived machine-learning-based models to predict the proton intensities at energies from 28 to 962 keV in the 3D terrestrial magnetosphere at radial distances between 6 and 22 RE. We used the satellite location and indices for solar, solar wind, and geomagnetic activity as predictors. The results demonstrate that the neural network (multi-layer perceptron regressor) outperforms baseline models based on the k-nearest neighbors and historical binning on average by ∼80% and ∼33%, respectively. The average correlation between the observed and predicted data is about 56%, which is reasonable in light of the complex dynamics of fast-moving energetic protons in the magnetosphere. In addition to a quantitative analysis of the prediction results, we also investigate parameter importance in our model. The most decisive parameters for predicting proton intensities are related to the location—Z geocentric solar ecliptic direction—and the radial distance. Among the activity indices, the solar wind dynamic pressure is the most important. The results have a direct practical application, for instance, for assessing the contamination particle background in the X-ray telescopes for X-ray astronomy orbiting above the radiation belts. To foster reproducible research and to enable the community to build upon our work we publish our complete code, the data, and the weights of trained models. Further description can be found in the GitHub project at https://github.com/Tanveer81/deep_horizon