The radiation belts of the Earth, filled with energetic electrons, comprise complex and dynamic systems that pose a significant threat to satellite operation. While various models of electron flux both for low and relativistic energies have been developed, the behavior of medium energy (120-600 keV) electrons, especially in the MEO region, remains poorly quantified. At these energies, electrons are driven by both convective and diffusive transport, and their prediction usually requires sophisticated 4D modeling codes. In this paper, we present an alternative approach using the Light Gradient Boosting (LightGBM) machine learning algorithm. The Medium Energy electRon fLux In Earth's outer radiatioN belt (MERLIN) model takes as input the satellite position, a combination of geomagnetic indices and solar wind parameters including the time history of velocity, and does not use persistence. MERLIN is trained on >15 years of the GPS electron flux data and tested on more than 1.5 years of measurements. Tenfold cross validation yields that the model predicts the MEO radiation environment well, both in terms of dynamics and amplitudes o f flux. Evaluation on the test set shows high correlation between the predicted and observed electron flux (0.8) and low values of absolute error. The MERLIN model can have wide space weather applications, providing information for the scientific community in the form of radiation belts reconstructions, as well as industry for satellite mission design, nowcast of the MEO environment, and surface charging analysis.

According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.

Heat waves are increasingly common in many countries across the globe, and also in Germany, where this study is set. Heat poses severe health risks, especially for vulnerable groups such as the elderly and children. This case study explores visitors' behavior and perceptions during six weekends in the summer of 2018 at a 6-month open-air horticultural show. Data from a face-to-face survey (n = 306) and behavioral observations ( n = 2750) were examined by using correlation analyses, ANOVA, and multiple regression analyses. Differences in weather perception, risk awareness, adaptive behavior, and activity level were observed between rainy days (maximum daily temperature, 25 degrees C), warmsummer days (25 degrees-30 degrees C), and hot days (>30 degrees C). Respondents reported a high level of heat risk awareness, butmost (90%) were unaware of actual heat warnings. During hot days, more adaptive measures were reported and observed. Older respondents reported taking the highest number of adaptive measures. We observed the highest level of adaptation in children, but they also showed the highest activity level. From our results we discuss how to facilitate individual adaptation to heat stress at open-air events by taking the heterogeneity of visitors into account. To mitigate negative health outcomes for citizens in the future, we argue for tailored risk communication aimed at vulnerable groups. <br /> SIGNIFICANCE STATEMENT: People around the world are facing higher average temperatures. While higher temperatures make open-air events a popular leisure time activity in summer, heat waves are a threat to health and life. Since there is not much research on how visitors of such events perceive different weather conditions-especially hot temperatures-we explored this in our case study in southern Germany at an open-air horticultural show in the summer of 2018. We discovered deficits both in people's awareness of current heat risk and the heat adaptation they carry out themselves. Future research should further investigate risk perception and adaptation behavior of private individuals, whereas event organizers and authorities need to continually focus on risk communication and facilitate individual adaptation of their visitors.

In X-ray computed tomography (XCT), an X-ray beam of intensity I0 is transmitted through an object and its attenuated intensity I is measured when it exits the object. The attenuation of the beam depends on the attenuation coefficients along its path. The attenuation coefficients provide information about the structure and composition of the object and can be determined through mathematical operations that are referred to as reconstruction. The standard reconstruction algorithms are based on the filtered backprojection (FBP) of the measured data. While these algorithms are fast and relatively simple, they do not always succeed in computing a precise reconstruction, especially from under-sampled data. Alternatively, an image or volume can be reconstructed by solving a system of linear equations. Typically, the system of equations is too large to be solved but its solution can be approximated by iterative methods, such as the Simultaneous Iterative Reconstruction Technique (SIRT) and the Conjugate Gradient Least Squares (CGLS). This dissertation focuses on the development of a novel iterative algorithm, the Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT). After its reconstruction principle is explained, its performance is assessed for real parallel- and cone-beam CT (including under-sampled) data and compared to that of other established algorithms. Finally, it is demonstrated how the shape of the measured object can be modelled into DIRECTT to achieve even better reconstruction results.

A paradigm shift in quantum thermometry is proposed. To date, thermometry has relied on local estimation, which is useful to reduce statistical fluctuations once the temperature is very well known. In order to estimate temperatures in cases where few measurement data or no substantial prior knowledge are available, we build instead a method for global quantum thermometry. Based on scaling arguments, a mean logarithmic error is shown here to be the correct figure of merit for thermometry. Its full minimization provides an operational and optimal rule to postprocess measurements into a temperature reading, and it establishes a global precision limit. We apply these results to the simulated outcomes of measurements on a spin gas, finding that the local approach can lead to biased temperature estimates in cases where the global estimator converges to the true temperature. The global framework thus enables a reliable approach to data analysis in thermometry experiments.