Non-linear structures as probes of the cosmological standard model

Non-linear structures provide an important test of the cosmological standard model. In this thesis, we investigate both analytic approaches to describing statistical properties of cosmic non-linear structures and a comparison of observational with simulated data. In the first part, we focus on analytic derivations in the framework of kinetic field theory (KFT), a novel theory to cosmic structure formation based on statistical field theory of classical particles. We investigate ways to derive the probability density function (PDF) of the cosmic density field within this framework. For this purpose, we introduce different models and explore approaches to derive the density PDF from the generating functional of KFT directly. We then use parts of these results in order to obtain an analytic derivation of the halo mass function. Unlike the standard approach, we derive the halo mass function from the present day non-linear density field directly. We use two models of the density PDF for this purpose, the lognormal and the generalised normal distribution, and fix their parameters by the predictions of KFT. We then derive the halo mass function using excursion set theory with correlated random walks. We obtain a closed form expression for the halo mass function, with only one free parameter, i.e. the halo overdensity Delta. For a choice of Delta = 2.9, our results agree well with those of simulations. In the last part, we investigate a concrete example of non-linear structure, i.e. the substructure distribution in the massive galaxy cluster Abell 2744. We compare it to that of haloes of the Millennium XXL simulation in order to test its compatibility with the cosmological standard model LambdaCDM. We identify structures in both the mass map of Abell 2744 and comparable mass maps of the MXXL haloes by a method based on the wavelet transform. This allows us to find three haloes in the MXXL simulation with a substructure distribution similar to Abell 2744 thus corroborating its concordance with LambdaCDM. We add a thorough discussion of our results and put them into context with the findings of other recent works

xLength: Predicting Expected Ski Jump Length Shortly after Take-Off Using Deep Learning

With tracking systems becoming more widespread in sports research and regular training and competitions, more data are available for sports analytics and performance prediction. We analyzed 2523 ski jumps from 205 athletes on five venues. For every jump, the dataset includes the 3D trajectory, 3D velocity, skis’ orientation, and metadata such as wind, starting gate, and ski jumping hill data. Using this dataset, we aimed to predict the expected jump length (xLength) inspired by the expected goals metric in soccer (xG). We evaluate the performance of a fully connected neural network, a convolutional neural network (CNN), a long short-term memory (LSTM), and a ResNet architecture to estimate the xLength. For the prediction of the jump length one second after take-off, we achieve a mean absolute error (MAE) of 5.3 m for the generalization to new athletes and an MAE of 5.9 m for the generalization to new ski jumping hills using ResNet architectures. Additionally, we investigated the influence of the input time after the take-off on the predictions’ accuracy. As expected, the MAE becomes smaller with longer inputs. Due to the real-time transmission of the sensor’s data, xLength can be updated during the flight phase and used in live TV broadcasting. xLength could also be used as an analysis tool for experts to quantify the quality of the take-off and flight phases