TY - JOUR A1 - Zubaer, Abdullah Al A1 - Granitzer, Michael A1 - Mitrović, Jelena T1 - Performance analysis of large language models in the domain of legal argument mining JF - Frontiers in Artificial Intelligence N2 - Generative pre-trained transformers (GPT) have recently demonstrated excellent performance in various natural language tasks. The development of ChatGPT and the recently released GPT-4 model has shown competence in solving complex and higher-order reasoning tasks without further training or fine-tuning. However, the applicability and strength of these models in classifying legal texts in the context of argument mining are yet to be realized and have not been tested thoroughly. In this study, we investigate the effectiveness of GPT-like models, specifically GPT-3.5 and GPT-4, for argument mining via prompting. We closely study the model's performance considering diverse prompt formulation and example selection in the prompt via semantic search using state-of-the-art embedding models from OpenAI and sentence transformers. We primarily concentrate on the argument component classification task on the legal corpus from the European Court of Human Rights. To address these models' inherent non-deterministic nature and make our result statistically sound, we conducted 5-fold cross-validation on the test set. Our experiments demonstrate, quite surprisingly, that relatively small domain-specific models outperform GPT 3.5 and GPT-4 in the F1-score for premise and conclusion classes, with 1.9% and 12% improvements, respectively. We hypothesize that the performance drop indirectly reflects the complexity of the structure in the dataset, which we verify through prompt and data analysis. Nevertheless, our results demonstrate a noteworthy variation in the performance of GPT models based on prompt formulation. We observe comparable performance between the two embedding models, with a slight improvement in the local model's ability for prompt selection. This suggests that local models are as semantically rich as the embeddings from the OpenAI model. Our results indicate that the structure of prompts significantly impacts the performance of GPT models and should be considered when designing them. KW - natural language processing (NLP) KW - argument mining KW - legal data KW - European Court of Human Rights (ECHR) KW - sequence classification KW - GPT-4 KW - ChatGPT KW - large language models Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-18326 SN - 2624-8212 VL - 2023 IS - 6 PB - Frontiers CY - Lausanne ER - TY - JOUR A1 - Hackl, Veronika A1 - Müller, Alexandra Elena A1 - Granitzer, Michael A1 - Sailer, Maximilian T1 - Is GPT-4 a reliable rater? Evaluating consistency in GPT-4's text ratings JF - Frontiers in Education N2 - This study reports the Intraclass Correlation Coefficients of feedback ratings produced by OpenAI's GPT-4, a large language model (LLM), across various iterations, time frames, and stylistic variations. The model was used to rate responses to tasks related to macroeconomics in higher education (HE), based on their content and style. Statistical analysis was performed to determine the absolute agreement and consistency of ratings in all iterations, and the correlation between the ratings in terms of content and style. The findings revealed high interrater reliability, with ICC scores ranging from 0.94 to 0.99 for different time periods, indicating that GPT-4 is capable of producing consistent ratings. The prompt used in this study is also presented and explained. KW - artificial intelligence KW - GPT-4 KW - large language model KW - prompt engineering KW - feedback KW - higher education Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-18348 SN - 2504-284X VL - 2023 IS - 8 PB - Frontiers CY - Lausanne ER - TY - BOOK ED - Hennemann, Moritz ED - Lewinski, Kai von ED - Wawra, Daniela ED - Widjaja, Thomas T1 - Data disclosure BT - global developments and perspectives T3 - Global and comparative data law (edited by Moritz Hennemann; Lea Katharina Kumkar; Linda Kuschel; Björn Steinrötter) KW - Personenbezogene Daten KW - Datenübermittlung KW - Datenschutz KW - Rechtsvergleich Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023031216403784842331 VL - 2023 IS - volume 2 PB - Walter de Gruyter CY - Berlin/Boston ER - TY - JOUR A1 - Kaiser, Tobias T1 - Growth of log-analytic functions JF - Archiv der Mathematik N2 - We show that unary log-analytic functions are polynomially bounded. In the higher dimensional case, globally a log-analytic function can have exponential growth. We show that a log-analytic function is polynomially bounded on a definable set which contains the germ of every ray at infinity. KW - Log-analytic functions KW - Polynomially bounded KW - Exponential growth Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023091614564557203657 VL - 120 IS - 6 SP - 605 EP - 614 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Strunk, Kim Simon A1 - Strich, Franz T1 - Building professional holding environments for crowd work job crafting through online communities JF - Information Systems Journal N2 - Work is increasingly being organised via online platforms outside guiding organisational structures. Instead of having colleagues at work, crowd workers connect in online communities. We investigate how crowd workers build professional holding environments in online communities to compensate for the lack of organisational structures and we consider how they craft their crowd work activities to enhance their work experience and reduce its long-term precarity. Following a qualitative research design, this paper uses 675 forum interactions collected across six online communities. Based on our findings, we propose the concept of professional holding environments and provide a model for building such holding environments and job crafting in online communities. We thereby expand previous research on holding environments comprised of family members and friends by revealing the impact of professional online communities and their role in professionalisation and crafting supportive social structures in online crowd work. KW - crowd work KW - holding environments KW - job crafting KW - online communities Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16315 VL - 33 SP - 1239 EP - 1274 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Frühwirth, Lorenz A1 - Prochno, Joscha T1 - Hölder’s inequality and its reverse — a probabilistic point of view JF - Mathematische Nachrichten N2 - In this article, we take a probabilistic look at Hölder's inequality, considering the ratio of terms in the classical Hölder inequality for random vectors in ℝ𝑛. We prove a central limit theorem for this ratio, which then allows us to reverse the inequality up to a multiplicative constant with high probability. The models of randomness include the uniform distribution on 𝓁𝑛𝑝 balls and spheres. We also provide a Berry–Esseen–type result and prove a large and a moderate deviation principle for the suitably normalized Hölder ratio. KW - Berry–Esseen bound KW - central limit theorem KW - Hölder’s inequality KW - 𝓁 𝑛 𝑝 ball KW - large deviation principle KW - moderate deviation principle KW - reverse inequality Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023062315175042989607 VL - 296 IS - 12 SP - 5493 EP - 5512 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Schwartz, Niels T1 - Topology of closure systems in algebraic lattices JF - Algebra universalis N2 - Algebraic lattices are spectral spaces for the coarse lower topology. Closure systems in algebraic lattices are studied as subspaces. Connections between order theoretic properties of a closure system and topological properties of the subspace are explored. A closure system is algebraic if and only if it is a patch closed subset of the ambient algebraic lattice. Every subset X in an algebraic lattice P generates a closure system〈X〉P . The closure system〈Y 〉P generated by the patch closure Y of X is the patch closure of〈X〉P. If X is contained in the set of nontrivial prime elements of P then〈X〉P is a frame and is a coherent algebraic frame if X is patch closed in P. Conversely, if the algebraic lattice P is coherent then its set of nontrivial prime elements is patch closed. KW - Poset KW - Complete lattice KW - Algebraic lattice KW - Frame KW - Closure system KW - Closure operator KW - Spectral space KW - Specialization KW - Coarse lower topology KW - Scott topology KW - Patch topology Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023090808111682406614 VL - 84 IS - 2 SP - 1 EP - 33 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Piwoni, Eunike A1 - Mußotter, Marlene T1 - The evolution of the civic–ethnic distinction as a partial success story: Lessons for the nationalism–patriotism distinction JF - Nations and Nationalism N2 - This article brings, for the first time, two of the most pivotal distinctions in nationalism studies into extended dialogue: the civic–ethnic distinction (CED) and the nationalism–patriotism distinction (NPD). By reviewing both the evolution of those distinctions over the previous decades and the ways in which they have been used in quantitative empirical research, we argue that the CED's evolution has been a partial success story, whereas discourse around the NPD has not seen substantial development. Despite lingering inconsistencies, researchers drawing on the CED have been successful in addressing different lines of critique and in using the CED as a heuristic for investigating notions of nationhood as expressed in public perceptions. In contrast, there has been only limited dialogue between theoretical and empirical approaches to the NPD. The article illustrates how research drawing on the NPD could profit from the CED's evolution. We close by providing a conceptual roadmap to guide the path towards more terminological clarity and to construct more theoretically robust measures for nationalism and patriotism. We specifically suggest that nationalism and patriotism should be consistently understood as ideal types that citizens can simultaneously hold to varying degrees. KW - civic nationalism KW - civic–ethnic distinction KW - ethnic–civic KW - national attachments KW - nationalism–patriotism distinction KW - nationhood KW - national identity KW - political psychology KW - surveys Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16266 VL - 29 IS - 3 SP - 906 EP - 921 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Urhahne, Detlef A1 - Wijnia, Lisette T1 - Theories of Motivation in Education: an Integrative Framework JF - Educational Psychology Review N2 - Several major theories have been established in research on motivation in education to describe, explain, and predict the direction, initiation, intensity, and persistence of learning behaviors. The most commonly cited theories of academic motivation include expectancy-value theory, social cognitive theory, self-determination theory, interest theory, achievement goal theory, and attribution theory. To gain a deeper understanding of the similarities and differences among these prominent theories, we present an integrative framework based on an action model (Heckhausen & Heckhausen, 2018). The basic model is deliberately parsimonious, consisting of six stages of action: the situation, the self, the goal, the action, the outcome, and the consequences. Motivational constructs from each major theory are related to these determinants in the course of action, mainly revealing differences and to a lesser extent commonalities. In the integrative model, learning outcomes represent a typical indicator of goal-directed behavior. Associated recent meta-analyses demonstrate the empirical relationship between the motivational constructs of the six central theories and academic achievement. They provide evidence for the explanatory value of each theory for students’ learning. KW - Motivation to learn KW - Action model KW - Academic achievement KW - Meta-analysis Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023092911454443208560 VL - 35 IS - 2 SP - 1 EP - 35 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Sommer, Tim T1 - Romantic objects, Victorian collections : scribal relics and the authorial body JF - Literature Compass N2 - Over the course of the nineteenth century, literary manuscripts came to be seen as tangible evidence of the creative process and as a key to the personality of the author. The material traces of writing were understood to outlive their creators and promise to resurrect the authorial body through the magic of the relic. This article reconstructs how authorial script gradually transformed into a collectible object pursued as a memento and a commodity. Letters, drafts, and fair copies by major modern writers found their way into the collections of British aristocrats and American industrialists at the same time that hunting for literary autographs diversified into a middle-class pursuit. Surveying recent scholarship on nineteenth-century collecting and material culture, the essay offers a condensed cultural history of the literary manuscript as a collectible and draws attention to how collectors and collecting feature in fictional texts of the period. It focuses on the artefactual mobility and custodial afterlives of Romantic papers in Victorian literature and culture, exploring a form of collecting which crossed boundaries between periods and national literary traditions. KW - archive KW - authorship KW - collecting KW - literary manuscripts KW - relics KW - Romanticism KW - Victorianism Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16248 VL - 21 IS - 1-3 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Ertel, Florence A1 - Donig, Simon A1 - Eckl, Markus A1 - Gassner, Sebastian A1 - Göler, Daniel A1 - Rehbein, Malte T1 - Using web archives for an explorative study of the web presence of German parties during the European election 2019 JF - Quality & Quantity N2 - In the digital age, political science is faced with a shift of election campaigns and politi- cal discourse to digital or virtual arenas. Because the internet is a highly volatile medium and online content can become inaccessible after the campaign season, new challenges for research arise as well as the need for the preservation of online content. Moreover, the sheer volume of data researchers have to deal with has reached levels where traditional methods are being highly challenged. This paper puts forth a web harvesting workflow with a strong focus on granular extraction of unstructured information (publication dates) for automated analysis. As our approach is methodological, we would like to point out the benefits that researches in political science may draw from adapting our methodology. We demonstrate this by analysing an event-based web crawl of German parties participating in the election campaign for the European Parliamentary Election in 2019. We employ distant reading methods to generate topic models, which are subsequently evaluated by hermeneutic analysis of a subset of the data. KW - Web archives KW - European parliamentary election KW - Second order elections KW - Distant reading KW - Topic modelling Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023082609050515725791 VL - 58 IS - 1 SP - 603 EP - 625 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Henkel, Anna T1 - Nachhaltige Digitalisierung. Gesellschaftliche Transformation, autonome Materialität und der Fall des Digital Farming JF - Berliner Journal für Soziologie N2 - Nachhaltigkeit und Digitalisierung sind zwei Tendenzen gesellschaftlichen Wandels, die in verschiedene Richtungen weisen. Nachhaltigkeit wird als angestrebte, jedoch im Ergebnis unzureichend bleibende Veränderung gesehen, während Digitalisierung – erwünscht oder auch nicht – schlicht erfolgt. Diese Diskrepanz zu untersuchen, ist eine Herausforderung auch für die soziologische Theorie. Nachdem Nachhaltigkeit und Digitalisierung bislang meist unabhängig voneinander in den Blick genommen wurden, erlaubt eine materialitätstheoretisch erweiterte Gesellschaftstheorie ein soziologisches Zusammendenken und eine Erklärung für die Unterschiedlichkeit der Dynamiken gesellschaftlichen Wandels: In der spezifischen, nämlich autonomen Materialität der modernen Gesellschaft ist Digitalisierung bereits angelegt, während eine nachhaltige Entwicklung eine Transformation dieser Materialität selbst erfordert. Am Fallbeispiel des Digital Farming wird diese These näher ausgeführt. Den Abschluss des Beitrags bilden Überlegungen zu Herausforderungen, Bedingungen und Möglichkeiten einer nachhaltigen Digitalisierung. KW - Digitalisierung KW - Nachhaltigkeit KW - Gesellschaftliche Transformation KW - Gesellschaftstheorie KW - Materialität KW - Systemtheorie KW - Digital Farming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2024010810053745746335 VL - 33 IS - 3 SP - 289 EP - 318 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Kägler, Britta A1 - Schreiner, Eva-Maria T1 - Women, opera and the public stage in eighteenth-century Venice : Fondazione Levi, Venice, 23–24 May 2022 JF - Eighteenth-Century Music Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16410 VL - 20 IS - 1 SP - 116 EP - 119 PB - Cambridge University Press CY - Cambridge ER - TY - JOUR A1 - Rensmann, Lars T1 - Illusions of sovereignty : understanding populist crowds with Hannah Arendt JF - The Review of Politics N2 - This article reconstructs Hannah Arendt's theoretical arguments in relation to current authoritarian-populist crowds, which can be understood as organized mobs of the twenty-first century. Drawn from all classes and originating in societal and political disenfranchisement, in Arendt's understanding they are rebellious nihilists who falsely believe they represent the people as a whole while they exclude any citizens who do not share their tribal nationalism and leader worshiping. Illuminating conditions of their emergence, Arendt also helps to elucidate what drives the populist crowds’ illusions about an uncompromising “sovereign will” they and their leaders claim to embody. Such illusions benefit from broader modern trends eroding differences between facts, opinion, truth, and lies. In public environments suffering from destabilized factual truths, organized lies can easily fill a political vacuum generated by crises of political modernity. Unpacking interrelated theoretical trajectories, it is argued that an Arendtian framework can significantly contribute to the study of present-day authoritarian populism. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16400 VL - 85 IS - 4 SP - 450 EP - 473 PB - Cambridge University Press CY - Cambridge ER - TY - JOUR A1 - Felfeli, Anna A1 - Stahl, Bernhard T1 - Mutual desecuritization as a model of détente? Foreign policy change in the US-Cuban dyad JF - Zeitschrift für Friedens- und Konfliktforschung N2 - In foreign policy dyads characterized by enmity, mutual desecuritization can serve as a crucial asset for détente. But how does “the way out of the emergency mode” function, considering mutual securitizations over decades? Embarking from theoretical insights provided by second generation scholars on securitization and desecuritization studies, the authors generate a theory-based model of détente for dyads. This analytical tool contributes to the study of the dissolution of historically grown, mutual (re-)securitization processes in interstate relations. By clarifying the impact and functioning of the four desecuritizing modes (replacement, silencing, change through stabilization, and rearticulation), our model allows us to trace dynamics of change and assess the sustainability of détente. Especially mutual desecuritization as rearticulation has the potential to substantially change the self-other relation with effects on the social structure of a foreign policy dyad. The heuristic case study of US-Cuban relations serves as a prime example of a complex dyad of enmity which became a subject of change due to the Obama–Castro diplomacy in 2014. The study on US-Cuban foreign policy issues before and after 2014 helps to sharpen our understanding of dynamic securitization and desecuritization processes. The overall analysis demonstrates that the modes of desecuritization during the Obama–Castro diplomacy lifted the process of détente to a new and unprecedented level. KW - Securitization theory KW - Modes of desecuritization KW - Overcoming enmity KW - Rearticulation KW - Change through stabilization Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023110610482836615655 VL - 12 IS - 1 SP - 59 EP - 86 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Thir, Veronika T1 - Co-text, context, and listening proficiency as crucial variables in intelligibility among nonnative users of English JF - Studies in Second Language Acquisition N2 - Research on intelligibility in international encounters has long focused on issues of pronunciation to the detriment of factors such as linguistic co-text and extralinguistic context, which are comparatively well-studied variables in intelligibility research concerning L1 listeners. This paper seeks to expand the scope of international intelligibility research in this respect by reporting on a large-scale study involving 423 nonnative listeners at different proficiency levels, who transcribed words spoken with another nonnative accent under four conditions that varied in the availability of syntactic, semantic, and schematic cues. The results suggest that co-text and context as well as listening proficiency are crucial variables that ought to receive greater attention in research on international intelligibility. The pedagogical implications of these findings are addressed as well. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16374 VL - 45 IS - 5 SP - 1210 EP - 1231 PB - Cambridge University Press CY - Cambridge ER - TY - JOUR A1 - Hevia Fajardo, Mario Alejandro A1 - Sudholt, Dirk T1 - Self-adjusting Population Sizes for Non-elitist Evolutionary Algorithms: why Success Rates Matter JF - Algorithmica N2 - Evolutionary algorithms (EAs) are general-purpose optimisers that come with several parameters like the sizes of parent and offspring populations or the mutation rate. It is well known that the performance of EAs may depend drastically on these parameters. Recent theoretical studies have shown that self-adjusting parameter control mechanisms that tune parameters during the algorithm run can provably outperform the best static parameters in EAs on discrete problems. However, the majority of these studies concerned elitist EAs and we do not have a clear answer on whether the same mechanisms can be applied for non-elitist EAs. We study one of the best-known parameter control mechanisms, the one-fifth success rule, to control the offspring population size λ in the non-elitist (1, λ) EA. It is known that the (1, λ) EA has a sharp threshold with respect to the choice of λ where the expected runtime on the benchmark function OneMax changes from polynomial to exponential time. Hence, it is not clear whether parameter control mechanisms are able to find and maintain suitable values of λ. For OneMax we show that the answer crucially depends on the success rates (i. e. a one-(s + 1)-th success rule). We prove that, if the success rate is appropriately small, the self-adjusting (1, λ) EA optimises OneMax in O(n) expected generations and O(n log n) expected evaluations, the best possible runtime for any unary unbiased black-box algorithm. A small success rate is crucial: we also show that if the success rate is too large, the algorithm has an exponential runtime on OneMax and other functions with similar characteristics. KW - Evolutionary algorithms KW - Parameter control KW - Theory KW - Runtime analysis KW - Non-elitism Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023102616463077837436 VL - 86 IS - 2 SP - 526 EP - 565 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Mußotter, Marlene T1 - On nation, homeland, and democracy: Toward a novel three-factor measurement model for nationalism and patriotism. Evidence from two representative studies JF - Political Psychology N2 - This article calls for revisiting the predominant yet flawed nationalism-patriotism dichotomy, which has to date remained unchallenged. It advocates for a more nuanced triad: nationalism, exclusively referring to the nation; patriotism, revolving around the homeland; and democratic patriotism, with democracy as its object of attachment. This novel conceptual approach explicitly theorizes these three objects of attachment, which have hitherto rarely been considered. In so doing, the article synthesizes the field's predominant research traditions that have not been fully recognized as diverging nor been simultaneously investigated. By responding to calls for more theoretically robust measures, it not only makes a theoretical but also an empirical contribution to the field. Drawing on data from a representative sample (N = 1875) in Germany in 2022, the study introduces a three-factor measurement model of nationalism, patriotism, and democratic patriotism. Taking into account both the antecedents of the triad and its impact on outgroup hostility, the measures are further validated. To establish its applicability in non-German contexts, the model is additionally supported using data from a representative sample (N = 1164) in Denmark in 2022. KW - authoritarianism KW - democracy KW - national attachment KW - nationalism KW - patriotism Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-16352 VL - 45 IS - 6 SP - 903 EP - 921 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Gagin, Stepan A1 - Bettermann, Michael A1 - de Meer, Hermann T1 - Multi-vector optimization scheme for distributed components in energy islands JF - e+i Elektrotechnik und Informationstechnik N2 - Recent advancements in energy systems, such as the emergence of prosumers and sector coupling approaches, introduce additional flexibilities over multiple energy sectors, such as heating, electricity, and mobility. Due to the complexity of such distributed systems, the optimization of energy allocation is a non-trivial task, especially considering constraints and limitations introduced by distributed devices or sub-systems. Additionally, the variety of devices forces approaches to be highly situational and not universally applicable. In this paper, a two-level optimization scheme is proposed, which aims at reducing the optimization complexity of sector-coupled systems. The multi-vector optimization embedded in the two-level optimization scheme is formulated as a mixed-integer linear problem, optimizing the energy flow between domains, which are modeled as an abstraction of a sector. Distributed devices are modeled as components that represent an abstraction of devices connected to an energy domain. The optimization process is evaluated based on the data from a residential complex in Ghent, Belgium. It shows that the approach is capable of minimizing costs, CO2 emissions, and dependency on external resources. KW - Energy optimization KW - Multi-energy systems KW - Sector coupling KW - Energy Management KW - Systems Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023110413071966670578 VL - 140 IS - 5 SP - 460 EP - 470 PB - Springer Nature CY - Berlin ER - TY - JOUR A1 - Fink, Thomas A1 - Forster, Brigitte A1 - Heinrich, Florian T1 - Gabor’s “complex signal” revisited: Complexifying frames and bases JF - PAMM (Proceedings in Applied Mathematics and Mechanics) N2 - In 1946, Dennis Gabor introduced the analytic signal 𝑓 + 𝑖𝐻𝑓 for real-valued signals 𝑓. Here, 𝐻 is the Hilbert transform. This complexification of functions allows for an analysis of their amplitude and phase information and has ever since given well-interpretable insight into the properties of the signals over time. The idea of complexification has been reconsidered with regard to many aspects: examples are the dual tree complex wavelet transform, or via the Riesz transform and the monogenic signal, that is, a multi-dimensional version of the Hilbert transform, which in combination with multi-resolution approaches leads to Riesz wavelets, and others. In this context, we ask two questions: - Which pairs of real orthonormal bases (ONBs), Riesz bases, frames and Parseval frames {𝑓 𝑛 } 𝑛∈ℕ and {𝑔 𝑛 } 𝑛∈ℕ can be “rebricked” to complex-valued ones {𝑓𝑛 + 𝑖𝑔 𝑛 } 𝑛∈ℕ? - And which real operators A allow for rebricking via the ansatz {𝑓𝑛 + 𝑖𝐴𝑓𝑛 } 𝑛∈ℕ? In this short note, we give answers to these questions with regard to a characterization which linear operators A are suitable for rebricking while maintaining the structure of the original real valued family. Surprisingly, the Hilbert transform is not among them. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023091815015485698899 VL - 23 IS - 3 PB - Wiley CY - Hoboken ER -