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Institute
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.
Blockchains in public administration : a RADIUS on blockchain framework for public administration
(2023)
The emergence of blockchain technology has generated a great deal of attention, as reflected in numerous scientific and journalistic articles. However, the implementation of blockchain for public administrations in Germany has encountered a setback owing to unsuccessful initiatives. Initial enthusiasm was followed by disillusionment. Nevertheless, technology continues to evolve. This paper examines whether the use of a blockchain can still optimize the processes of public administrations. Not only the failed projects are analysed, but also more current applications of the technology and their potential relevance for the administration, especially in the state of Hesse.
To answer if blockchains are promising to administrations, a Design Science Research (DSR) research approach is chosen. The DSR method is a research-based approach that aims to create new and innovative solutions to real-world problems through the development and evaluation of artefacts such as models, methods, or prototypes. For this work, the implementation of a framework to realize an Authentication, Authorization, and Accounting (AAA) system on the blockchain was identified as profitable. The framework aims to implement the aforementioned AAA tasks using a blockchain. The Remote Authentication Dial-In User Service (RADIUS) protocol has been identified as a potential protocol of the AAA system. The goal is to create a way to implement the system either entirely on a blockchain or as a hybrid system. Various blockchain technologies will be considered. Suitable for development, the framework AAA-me is named.
The development of AAA-me has shown that the desired framework for implementing RADIUS on the blockchain is possible in various degrees of implementation. Previous work mostly relied on full development. Additionally, it has been shown that AAA-me can be used to perform hybrid integration at different implementation levels. This makes AAA-me stand out from the few hybrid previous approaches. Furthermore, AAA-me was investigated in different laboratory environments. This was to determine the expected resilience against Single Point of Failure (SPOF). The results of the lab investigation indicated that a RADIUS system on top of a blockchain can provide benefits in terms of security and performance. In the lab environment, times were measured within which a series of authorization requests were processed. In addition, it was illustrated how a RADIUS system implemented using blockchain can protect itself against Man-in-the-Middle (MITM) attacks.
Finally, in collaboration with the Hessian Central Office for Data Processing (German: Hessische Zentrale für Datenverarbeitung) (HZD), another test lab demonstrated how a RADIUS system on the blockchain can integrate with the existing IT systems of the German state of Hesse. Based on these findings, this work reevaluated the applicability of blockchain technology for public administration processes.
The work has thus shown that the use of a blockchain can still be purposeful. However, it has also been shown that an implementation can bring many problems with it. The small number of blockchain developers and engineers also poses the risk of finding people to develop and maintain a system. In addition, one faces the problem of determining an architecture now that will be applied to many projects in the future. However, each project can, in turn, have an impact on the choice of architecture. Once one has solved this problem and a blockchain infrastructure is available, it can be established quickly and be more SPOF resistant, for example, for Public Key Infrastructure (PKI) systems.
AAA-me was only applied in lab and test environments. As a result, no real data ran over its own infrastructure. This allowed the necessary flexibility for development. However, system-related properties could appear in real situations that are not detectable here in this way. Furthermore, the initial stage of AAA-me’s development is still in its infancy. Many manual adjustments need to be made in order for this to integrate with an existing RADIUS system. Also, no system security effort in and of itself has been carried out in the lab environments. Thus, vulnerabilities can quickly open up on web servers due to misconfigurations and missing updates. For the above reasons, productive use should be discouraged unless major developments are carried out.
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)ˢ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of s-harmonic functions. As an application, we infer that the weak maximum principle fails in eccentric ellipsoids for s ∈ (1; √3 + 3/2) in any dimension n ≥ 2. We build a counterexample in terms of the torsion function times a polynomial of degree 2. Using point inversion transformations, it follows that a variety of bounded and unbounded domains do not satisfy positivity preserving properties either and we give some examples.
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. We investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets.
Adaptive, synchronous, and mobile online education: developing the ASYMPTOTE learning environment
(2022)
The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online learning tools. As one example for online learning in mathematics education, the ASYMPTOTE system is introduced. It will be freely available by May 2022. ASYMPTOTE is aimed at the adaptive and synchronous delivery of online education by taking a mobile learning approach. Its core is the so-called digital classroom, which not only allows students to interact with each other or with the teacher but also enables teachers to monitor their students’ work progress in real time. With respect to the theoretical framework, this article analyses to what extent the ASYMPTOTE system meets the requirements of online learning. Overall, the digital classroom can be seen as a promising tool for teachers to carry out appropriate formative assessment and—partly—to maintain personal and content-related interaction at a distance. Moreover, we highlight the availability of this tool. Due to its mobile learning approach, almost all students will be able to participate in lessons conducted with ASYMPTOTE.