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Cone photoreceptor cells are wavelength-sensitive neurons in the retinas of vertebrate eyes and are responsible for color vision. The spatial distribution of these nerve cells is commonly referred to as the cone photoreceptor mosaic. By applying the principle of maximum entropy, we demonstrate the universality of retinal cone mosaics in vertebrate eyes by examining various species, namely, rodent, dog, monkey, human, fish, and bird. We introduce a parameter called retinal temperature, which is conserved across the retinas of vertebrates. The virial equation of state for two-dimensional cellular networks, known as Lemaître’s law, is also obtained as a special case of our formalism. We investigate the behavior of several artificially generated networks and the natural one of the retina concerning this universal, topological law.

This bachelor thesis developed a pipeline for automatic processing of scanned hospital letters: HospLetExtractor. Hospital letters can contain valuable information about potential adverse drug reactions and useful case information relevant to pharmacovigilance. To make this data accessible, this thesis presents a pipeline consisting of image pre-processing, optical character recognition and post-processing. Pre-processing deskews the images, removes lines and rectangles, reduces noise and applies super-resolution. For the post-processing a spell checking system was set up including a newly built word frequency dictionary for german medical terms based on a created corpus of german medical texts. Furthermore, classical and deep learning models for the classification of hospital letters were compared, in which the transformer-based models performed best. In order to train and test the models, a new gold standard was created. By making these medical documents accessible for automatic analysis, hopefully a contribution can be made to expand the scope of pharmacovigilance.

We introduce a Cannings model with directional selection via a paintbox construction and establish a strong duality with the line counting process of a new Cannings ancestral selection graph in discrete time. This duality also yields a formula for the fixation probability of the beneficial type. Haldane’s formula states that for a single selectively advantageous individual in a population of haploid individuals of size N the probability of fixation is asymptotically (as N→∞) equal to the selective advantage of haploids sN divided by half of the offspring variance. For a class of offspring distributions within Kingman attraction we prove this asymptotics for sequences sN obeying N−1≪sN≪N−1/2, which is a regime of “moderately weak selection”. It turns out that for sN≪N−2/3 the Cannings ancestral selection graph is so close to the ancestral selection graph of a Moran model that a suitable coupling argument allows to play the problem back asymptotically to the fixation probability in the Moran model, which can be computed explicitly.

Background: Prostate cancer is a major health concern in aging men. Paralleling an aging society, prostate cancer prevalence increases emphasizing the need for efcient diagnostic algorithms.
Methods: Retrospectively, 106 prostate tissue samples from 48 patients (mean age,
66 ± 6.6 years) were included in the study. Patients sufered from prostate cancer (n = 38) or benign prostatic hyperplasia (n = 10) and were treated with radical prostatectomy or Holmium laser enucleation of the prostate, respectively. We constructed tissue microarrays (TMAs) comprising representative malignant (n = 38) and benign (n = 68) tissue cores. TMAs were processed to histological slides, stained, digitized and assessed for the applicability of machine learning strategies and open–source tools in diagnosis of prostate cancer. We applied the software QuPath to extract features for shape, stain intensity, and texture of TMA cores for three stainings, H&E, ERG, and PIN-4. Three machine learning algorithms, neural network (NN), support vector machines (SVM), and random forest (RF), were trained and cross-validated with 100 Monte Carlo random splits into 70% training set and 30% test set. We determined AUC values for single color channels, with and without optimization of hyperparameters by exhaustive grid search. We applied recursive feature elimination to feature sets of multiple color transforms.
Results: Mean AUC was above 0.80. PIN-4 stainings yielded higher AUC than H&E and
ERG. For PIN-4 with the color transform saturation, NN, RF, and SVM revealed AUC of 0.93 ± 0.04, 0.91 ± 0.06, and 0.92 ± 0.05, respectively. Optimization of hyperparameters improved the AUC only slightly by 0.01. For H&E, feature selection resulted in no increase of AUC but to an increase of 0.02–0.06 for ERG and PIN-4.
Conclusions: Automated pipelines may be able to discriminate with high accuracy between malignant and benign tissue. We found PIN-4 staining best suited for classifcation. Further bioinformatic analysis of larger data sets would be crucial to evaluate the reliability of automated classifcation methods for clinical practice and to evaluate potential discrimination of aggressiveness of cancer to pave the way to automatic precision medicine.

Unified probabilistic deep continual learning through generative replay and open set recognition
(2022)

Modern deep neural networks are well known to be brittle in the face of unknown data instances and recognition of the latter remains a challenge. Although it is inevitable for continual-learning systems to encounter such unseen concepts, the corresponding literature appears to nonetheless focus primarily on alleviating catastrophic interference with learned representations. In this work, we introduce a probabilistic approach that connects these perspectives based on variational inference in a single deep autoencoder model. Specifically, we propose to bound the approximate posterior by fitting regions of high density on the basis of correctly classified data points. These bounds are shown to serve a dual purpose: unseen unknown out-of-distribution data can be distinguished from already trained known tasks towards robust application. Simultaneously, to retain already acquired knowledge, a generative replay process can be narrowed to strictly in-distribution samples, in order to significantly alleviate catastrophic interference.

We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right-hand side are available. A natural approach is to take the average of the measurements as an approximation of the right-hand side and to estimate the data error as the inverse of the square root of the number of measurements. We calculate the optimal convergence rate (as the number of measurements tends to infinity) under classical source conditions and introduce a modified discrepancy principle, which asymptotically attains this rate.

In online video games toxic interactions are very prevalent and often
even considered an imperative part of gaming.
Most studies analyse the toxicity in video games by analysing the messages that are sent during a match, while only a few focus on other interactions. We focus specifically on the in-game events to try to identify toxic matches, by constructing a framework that takes a list of time-based events and projects them into a graph structure which we can then analyse with current methods in the field of graph representation learning.
Specifically we use a Graph Neural Network and Principal Neighbour-
hood Aggregation to analyse the graph structure to predict the toxicity of a match.
We also discuss the subjectivity behind the term toxicity and why the
process of only analysing in-game messages with current state-of-the-art NLP methods isn’t capable to infer if a match is perceived as toxic or not.