TY - JOUR A1 - Mironchenko, Andrii T1 - Well-posedness and properties of the flow for semilinear evolution equations JF - Mathematics of Control, Signals, and Systems N2 - We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general C0 -semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers’ equation with nonlinear local dynamics and both distributed and boundary disturbances. KW - Well-posedness KW - Evolution equations KW - Boundary control systems KW - Infinite-dimensional systems KW - Analytic systems Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2024022307494197431619 VL - 36 IS - 3 SP - 483 EP - 523 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Herbold, Steffen A1 - Tunkel, Steffen T1 - Differential testing for machine learning: an analysis for classification algorithms beyond deep learning JF - Empirical Software Engineering N2 - Differential testing is a useful approach that uses different implementations of the same algorithms and compares the results for software testing. In recent years, this approach was successfully used for test campaigns of deep learning frameworks. There is little knowledge about the application of differential testing beyond deep learning. Within this article, we want to close this gap for classification algorithms. We conduct a case study using Scikit-learn, Weka, Spark MLlib, and Caret in which we identify the potential of differential testing by considering which algorithms are available in multiple frameworks, the feasibility by identifying pairs of algorithms that should exhibit the same behavior, and the effectiveness by executing tests for the identified pairs and analyzing the deviations. While we found a large potential for popular algorithms, the feasibility seems limited because, often, it is not possible to determine configurations that are the same in other frameworks. The execution of the feasible tests revealed that there is a large number of deviations for the scores and classes. Only a lenient approach based on statistical significance of classes does not lead to a huge amount of test failures. The potential of differential testing beyond deep learning seems limited for research into the quality of machine learning libraries. Practitioners may still use the approach if they have deep knowledge about implementations, especially if a coarse oracle that only considers significant differences of classes is sufficient. KW - Machine learning KW - Software testing KW - Differential testing Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023033121421148821912 VL - 28 IS - 2 SP - 1 EP - 38 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Rudolf, Daniel A1 - Schär, Philip T1 - Dimension-independent spectral gap of polar slice sampling JF - Statistics and Computing N2 - Polar slice sampling, a Markov chain construction for approximate sampling, performs, under suitable assumptions on the target and initial distribution, provably independent of the state space dimension. We extend the aforementioned result of Roberts and Rosenthal (Stoch Model 18(2):257–280, 2002) by developing a theory which identifies conditions, in terms of a generalized level set function, that imply an explicit lower bound on the spectral gap even in a general slice sampling context. Verifying the identified conditions for polar slice sampling yields a lower bound of 1/2 on the spectral gap for arbitrary dimension if the target density is rotationally invariant, log-concave along rays emanating from the origin and sufficiently smooth. The general theoretical result is potentially applicable beyond the polar slice sampling framework. KW - MCMC KW - Slice Sampling KW - Spectral gap Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2024011821064231531382 VL - 34 IS - 1 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Weißgerber, Thomas A1 - Ben Amor, Mehdi A1 - Fellicious, Christofer A1 - Granitzer, Michael T1 - PyPads: Transparent Machine Learning Experiment Tracking JF - Datenbank-Spektrum N2 - Despite algorithmic advancements in the field of machine learning, a need for improvement in the infrastructure supporting machine learning development and research has become increasingly apparent. Machine learning experiments usually tend to be more ad-hoc in nature, and results are communicated most often in the form of a publication. Experimental details are often omitted due to size or time constraints, or simply because the complexity in terms of technical setup or parametrization became intractable. Even access to code bases, disregard important properties of the environment and experimental setup, like for example random generators or computing infrastructure. At the same time, tracking and communicating an often inherently exploratory scientific process is a task with considerable effort. We explored different venues to tackle these issues from a data science engineering point of view. The efforts resulted in PyPads, a framework providing an infrastructure to extend experimental setups with logging, communication and analysis features in a mostly non-intrusive way. PyPads can be extended to different Python-based frameworks, utilizing community driven, descriptive metadata in an effort to harmonize library specific logs in an ontology. Meanwhile, we also try to emphasize similarities to practices in software engineering, which have turned out to be essential in practical applications. KW - Machine Learning KW - Reproducibility KW - Open Science KW - Automated Logging KW - Python Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2024021511222778687954 VL - 24 IS - 1 SP - 53 EP - 62 PB - Springer Nature CY - Berlin ER - TY - THES A1 - Mexis, Nico T1 - A Comprehensive Comparison of Fuzzy Extractor Schemes Employing Different Error Correction Codes N2 - This thesis deals with fuzzy extractors, security primitives often used in conjunction with Physical Unclonable Functions (PUFs). A fuzzy extractor works in two stages: The generation phase and the reproduction phase. In the generation phase, an Error Correction Code (ECC) is used to compute redundant bits for a given PUF response, which are then stored as helper data, and a key is extracted from the response. Then, in the reproduction phase, another (possibly noisy) PUF response can be used in conjunction with this helper data to extract the original key. It is clear that the performance of the fuzzy extractor is strongly dependent on the underlying ECC. Therefore, a comparison of ECCs in the context of fuzzy extractors is essential in order to make them as suitable as possible for a given situation. It is important to note that due to the plethora of various PUFs with different characteristics, it is very unrealistic to propose a single metric by which the suitability of a given ECC can be measured. First, we give a brief introduction to the topic, followed by a detailed description of the background of the ECCs and fuzzy extractors studied. Then, we summarise related work and describe an implementation of the ECCs under consideration. Finally, we carry out the actual comparison of the ECCs and the thesis concludes with a summary of the results and suggestions for future work. N2 - Diese Arbeit befasst sich mit Fuzzy Extractors, Sicherheitsprimitiven, die häufig in Verbindung mit Physical Unclonable Functions (PUFs) verwendet werden. Ein Fuzzy Extractor arbeitet in zwei Phasen: Der Generierungsphase und der Reproduktionsphase. In der Generierungsphase wird ein Fehlerkorrekturverfahren (ECC) verwendet, um redundante Bits für eine gegebene PUF-Antwort zu berechnen, die dann als Hilfsdaten gespeichert werden, und ein Schlüssel wird aus der Antwort extrahiert. In der Reproduktionsphase kann dann eine andere (möglicherweise verrauschte) PUF-Antwort zusammen mit diesen Hilfsdaten verwendet werden, um den ursprünglichen Schlüssel zu extrahieren. Es ist klar, dass die Leistung des Fuzzy Extractors stark von der Leistung des zugrunde liegenden ECC abhängt. Daher ist es unerlässlich, ECCs in Verbindung mit Fuzzy Extractors zu vergleichen, um sie für eine bestimmte Situation so geeignet wie möglich zu machen. Es ist wichtig, darauf hinzuweisen, dass es aufgrund der Vielzahl verschiedener PUFs mit unterschiedlichen Eigenschaften sehr unrealistisch ist, eine einzige Metrik vorzuschlagen, mit der die Eignung eines bestimmten ECCs gemessen werden kann. Wir beginnen mit einer kurzen Einführung in das Thema, gefolgt von einer detaillierten Beschreibung des Hintergrunds der untersuchten ECCs und Fuzzy Extractors. Anschließend fassen wir verwandte Arbeiten zusammen und beschreiben eine Implementierung der untersuchten ECCs. Schließlich führen wir den eigentlichen Vergleich der ECCs durch und schließen die Arbeit mit einer Zusammenfassung der Ergebnisse und Vorschlägen für zukünftige Arbeiten ab. T2 - Ein umfassender Vergleich von Fuzzy Extractors unter Verwendung verschiedener Fehlerkorrekturverfahren KW - Fuzzy extractor KW - Error correction KW - Vorwärtsfehlerkorrektur KW - Codierungstheorie KW - Physical unclonable function KW - Biometrie Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-12914 VL - 2023 ER - TY - JOUR A1 - Erdogan, Gülsah A1 - Hassen, Wiem Fekih T1 - Charging scheduling of hybrid energy storage systems for EV charging stations JF - Energies N2 - The growing demand for electric vehicles (EV) in the last decade and the most recent European Commission regulation to only allow EV on the road from 2035 involved the necessity to design a cost-effective and sustainable EV charging station (CS). A crucial challenge for charging stations arises from matching fluctuating power supplies and meeting peak load demand. The overall objective of this paper is to optimize the charging scheduling of a hybrid energy storage system (HESS) for EV charging stations while maximizing PV power usage and reducing grid energy costs. This goal is achieved by forecasting the PV power and the load demand using different deep learning (DL) algorithms such as the recurrent neural network (RNN) and long short-term memory (LSTM). Then, the predicted data are adopted to design a scheduling algorithm that determines the optimal charging time slots for the HESS. The findings demonstrate the efficiency of the proposed approach, showcasing a root-mean-square error (RMSE) of 5.78% for real-time PV power forecasting and 9.70% for real-time load demand forecasting. Moreover, the proposed scheduling algorithm reduces the total grid energy cost by 12.13%. KW - scheduling optimization KW - HESS KW - PV power KW - load demand KW - RNN KW - LSTM KW - GRU KW - cost reduction Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-14128 VL - 2023 IS - 16 PB - MDPI CY - Basel ER - TY - JOUR A1 - Frühwirth, Lorenz A1 - Juhos, Michael A1 - Prochno, Joscha T1 - The large deviation behavior of lacunary sums JF - Monatshefte für Mathematik N2 - We study the large deviation behavior of lacunary sums (Sn /n)n∈N with Sn :=∑[k=1...n] f (a(k)U), n ∈ |N, where U is uniformly distributed on [0, 1], (a(k))k∈|N is an Hadamard gap sequence, and f : |R → |R is a 1-periodic, (Lipschitz-)continuous mapping. In the case of large gaps, we show that the normalized partial sums satisfy a large deviation principle at speed n and with a good rate function which is the same as in the case of independent and identically distributed random variables U(k), k ∈ |N, having uniform distribution on [0, 1]. When the lacunary sequence (a(k))k∈|N is a geometric progression, then we also obtain large deviation principles at speed n, but with a good rate function that is different from the independent case, its form depending in a subtle way on the interplay between the function f and the arithmetic properties of the gap sequence. Our work generalizes some results recently obtained by Aistleitner, Gantert, Kabluchko, Prochno, and Ramanan [Large deviation principles for lacunary sums, preprint, 2020] who initiated this line of research for the case of lacunary trigonometric sums. KW - Hadamard gap sequence KW - Large deviation principle KW - Large gap condition KW - Geometric progression Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2022081723261050522140 VL - 2022 IS - 199 SP - 113 EP - 133 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Harks, Tobias A1 - Schwarz, Julian T1 - Generalized Nash equilibrium problems with mixed-integer variables JF - Mathematical Programming N2 - We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few results are known in the literature. We present a new approach to characterize equilibria via a convexification technique using the Nikaido–Isoda function. To any given instance of the GNEP, we construct a set of convexified instances and show that a feasible strategy profile is an equilibrium for the original instance if and only if it is an equilibrium for any convexified instance and the convexified cost functions coincide with the initial ones. We develop this convexification approach along three dimensions: We first show that for quasi-linear models, where a convexified instance exists in which for fixed strategies of the opponent players, the cost function of every player is linear and the respective strategy space is polyhedral, the convexification reduces the GNEP to a standard (non-linear) optimization problem. Secondly, we derive two complete characterizations of those GNEPs for which the convexification leads to a jointly constrained or a jointly convex GNEP, respectively. These characterizations require new concepts related to the interplay of the convex hull operator applied to restricted subsets of feasible strategies and may be interesting on their own. Note that this characterization is also computationally relevant as jointly convex GNEPs have been extensively studied in the literature. Finally, we demonstrate the applicability of our results by presenting a numerical study regarding the computation of equilibria for three classes of GNEPs related to integral network flows and discrete market equilibria. KW - Generalized Nash equilibrium problem KW - Mixed-integer nonlinear problem KW - Non-convex games KW - Complementarity and equilibrium problems and variational inequalities (finite dimensions) KW - Mixed integer programming KW - Noncooperative games Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2405152117292.567771401889 SN - 0025-5610 SN - 1436-4646 VL - 209 IS - 1 SP - 231 EP - 277 PB - Springer Berlin Heidelberg CY - Berlin/Heidelberg ER - TY - JOUR A1 - Kreuzer, Martin A1 - Long, Le Ngoc A1 - Robbiano, Lorenzo T1 - Re-embeddings of affine algebras via Gröbner fans of linear ideals JF - Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry N2 - Given an affine algebra R=K[x1,⋯,xn]/Iover a field  K , where I is an ideal in the polynomial ring P=K[x1,⋯,xn], we examine the task of effectively calculating re-embeddings of  I , i.e., of presentations R=P′/I′such that P′=K[y1,⋯,ym]has fewer indeterminates. For cases when the number of indeterminates  n is large and Gröbner basis computations are infeasible, we have introduced the method of Z -separating re-embeddings in Kreuzer et al. (J Algebra Appl 21, 2022) and Kreuzer, et al. (São Paulo J Math Sci, 2022). This method tries to detect polynomials of a special shape in  I which allow us to eliminate the indeterminates in the tuple  Z by a simple substitution process. Here we improve this approach by showing that suitable candidate tuples  Z can be found using the Gröbner fan of the linear part of  I . Then we describe a method to compute the Gröbner fan of a linear ideal, and we improve this computation in the case of binomial linear ideals using a cotangent equivalence relation. Finally, we apply the improved technique in the case of the defining ideals of border basis schemes. KW - Re-embedding KW - Optimal embedding KW - Gröbner fan KW - Cotangent space KW - Border basis scheme Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2024041316352253862922 SN - 0138-4821 SN - 2191-0383 VL - 65 IS - 4 SP - 827 EP - 851 PB - Springer Berlin Heidelberg CY - Berlin/Heidelberg ER - TY - JOUR A1 - Prochno, Joscha A1 - Rudolf, Daniel T1 - The minimal spherical dispersion JF - The Journal of Geometric Analysis N2 - We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy in (Anz Österreich Akad Wiss Math Nat Kl 132:3–10, 1995). In particular, we see that the inverse N(ε,d)of the minimal spherical dispersion is, for fixed ε>0, linear in the dimension d of the ambient space. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere. In terms of the corresponding inverse N~(ε,d), our bounds are optimal with respect to the dependence on ε. KW - Dispersion KW - Expected dispersion KW - Spherical cap KW - Spherical dispersion KW - VC-dimension Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2405020842543.936733306281 SN - 1050-6926 SN - 1559-002X VL - 34 IS - 3 PB - Springer US CY - New York ER - TY - THES A1 - Klement, Felix T1 - Strengthening Security Foundations in Next-G Wireless Telecommunication Systems N2 - Digital transformation fundamentally impacts our everyday lives and creates significant efficiency gains in the economy. At the same time, however, it is also increasing the complexity of wireless networks, particularly in the case of the sixth generation (6G) mobile communications standard. The use of different technologies in these networks poses an increasing challenge and increases the risk of security threats and vulnerabilities. Wireless communication networks are particularly vulnerable to cyber attacks as they are an integral part of critical infrastructures. Robust methods must, therefore, be developed to overcome these challenges. Consequently, this dissertation is focused on the security fundamentals of next-generation (Next-G) wireless telecommunication systems. It addresses the security challenges resulting from emerging and innovative concepts within these systems. We use case studies for in-depth investigation and analysis, with a particular focus on the Open Radio Access Network (O-RAN) approach. The aim of this concept is to enable open and interoperable network architectures, in contrast to traditional RAN systems, which are often proprietary and manufacturer-specific. In this respect, it is essential to address fundamental questions, like the efficient assessment of the threat landscape, the impact of potential attacks, and the mechanisms that can be used to ensure security at the system level. Initially, an empirical approach is developed to analyze threats within telecommunications systems, such as the O-RAN. The procedure we have developed enables automated, programmatically executable vulnerability management. This methodology is further enhanced by integrating Natural Language Processing (NLP), leading to the creation of a fully automated, iteratively executable framework for security analysis within O-RANs. The framework allows for the direct incorporation of our methods into the deployment process, facilitating rapid and efficient comparison of all components against the latest security vulnerabilities. The current approach of fully deploying all components in virtualized environments, such as cloud infrastructures, introduces new and unprecedented security challenges. In response, we investigate current deployment strategies within the O-RAN infrastructure and establish best practices to mitigate these security issues. In the course of the dissertation, we identify security vulnerabilities in wireless telecommunication systems by executing different attack scenarios. We present a detailed procedure for carrying out the attacks as well as effective methodologies for detecting or avoiding the vulnerabilities we have identified. In the first study, we analyze the security of a key component, the Near-Real-Time RAN Intelligent Controller (Near-RT RIC), within O-RAN. We show how a subscription Denial of Service (DoS) attack can render current implementations of this component unusable. In the second analysis, we investigate the robustness of new standards in wireless networks against jamming attacks using the open-source connectivity standard Matter. The final section of this dissertation explores innovative security research approaches for enhancing the system security of future communication systems. Initially, a novel concept is introduced that facilitates the comprehensive and efficient management and assurance of security within O-RAN systems through the use of Security Platforms (SPs). Furthermore, two developed methodologies for this approach are presented: firstly, a method for programmatically analyzing eXtended Applications (xApps) to identify vulnerabilities, and secondly, an approach for conducting comparative assessments of these vulnerabilities. Additionally, a strategy is proposed to ensure that only secure xApps, such as those that have been pre-tested, are deployed for use in Near-RT RIC. Overall, this dissertation makes an important contribution to the research of security principles for next-generation wireless telecommunication systems. With the help of our approaches for a better and more concrete assessment of threats in such networks, we directly contribute to a clearer and better manageable picture of the vulnerability landscape. Our two publications on vulnerability research also provide valuable insights for securing future problems in the respective areas. In summary, with our approaches to system security, with which security principles can be implemented and integrated into modern system approaches such as O-RAN, we contribute to ensuring a secure transition to 6G. KW - Security KW - Next-G KW - 6G KW - Open RAN Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-18669 ER -