The central notion of this thesis is the minor relation on functions of several arguments. A function f: A^n→B is called a minor of another function g: A^m→B if f can be obtained from g by permutation of arguments, identification of arguments, and introduction of inessential arguments. We first provide some general background and context to this work by presenting a brief survey of basic facts and results concerning different aspects of the minor relation, placing some emphasis on the author’s contributions to the field. The notions of functions of several arguments and minors give immediately rise to the following reconstruction problem: Is a function f: A^n→B uniquely determined, up to permutation of arguments, by its identification minors, i.e., the minors obtained by identifying a pair of arguments? We review known results – both positive and negative – about the reconstructibility of functions from identification minors, and we outline the main ideas of the proofs, which often amount to formulating and solving reconstruction problems for other kinds of mathematical objects. We then turn our attention to functions determined by the order of first occurrence, and we are interested in the reconstructibility of such functions. One of the main results of this thesis states that the class of functions determined by the order of first occurrence is weakly reconstructible. Some reconstructible subclasses are identified; in particular, pseudo-Boolean functions determined by the order of first occurrence are reconstructible. As our main tool, we introduce the notion of minor of permutation. This is a quotient-like construction for permutations that parallels minors of functions and has some similarities to permutation patterns. We develop the theory of minors of permutations, focusing on Galois connections induced by the minor relation and on the interplay between permutation groups and minors of permutations. Our results will then find applications in the analysis of the reconstruction problem of functions determined by the order of first occurrence.

Individual differences in the strength of music preference are among the most intricate psychological phenomena. While one person gets by very well without music, another person needs to listen to music every day and spends a lot of temporal and financial resources on listening to music, attending concerts, or buying concert tickets. Where do these differences come from? The hypothesis presented in this article is that the strength of music preference is mainly informed by the functions that music fulfills in people’s lives (e.g., to regulate emotions, moods, or physiological arousal; to promote self-awareness; to foster social relatedness). Data were collected with a diary study, in which 121 respondents documented the goals they tried to attain and the effects that actually occurred for up to 5 music-listening episodes per day for 10 successive days. As expected, listeners reporting more intense experience of the functional use of music in the past (1) had a stronger intention to listen to music to attain specific goals in specific situations and (2) showed a larger overall strength of music preference. It is concluded that the functional effectiveness of music listening should be incorporated in existing models and frameworks of music preference to produce better predictions of interindividual differences in the strength of music preference. The predictability of musical style/genre preferences is also discussed with regard to the present results.

Neurofeedback (NF) is an important treatment for attention deficit/hyperactivity disorder (ADHD). In ADHD, cognitive control deficits pose considerable problems to patients. However, NF protocols are not yet optimized to enhance cognitive control alongside with clinical symptoms, partly because they are not driven by basic cognitive neuroscience. In this study, we evaluated different EEG theta and/or beta frequency band NF protocols designed to enhance cognitive control. Participants were n = 157 children and adolescents, n = 129 of them were patients with ADHD (n = 28 typically developing (TD) controls). Patients with ADHD were divided into five groups in the order of referral, with four of them taking part in different NF protocols systematically varying theta and beta power. The fifth ADHD group and the TD group did not undergo NF. All NF protocols resulted in reductions of ADHD symptoms. Importantly, only when beta frequencies were enhanced during NF (without any theta regulation or in combination with theta upregulation), consistent enhancing effects in both response inhibition and conflict control were achieved. The theta/beta NF protocol most widely used in clinical settings revealed comparatively limited effects. Enhancements in beta band activity are key when aiming to improve cognitive control functions in ADHD. This calls for a change in the use of theta/beta NF protocols and shows that protocols differing from the current clinical standard are effective in enhancing important facets of cognitive control in ADHD. Further studies need to examine regulation data within the neurofeedback sessions to provide more information about the mechanisms underlying the observed effects.

Der Begriff des ›Prototypen‹ ist der deutschsprachigen Musiktheorie nicht fremd, ohne dass jedoch seine Implikationen umfassend rezipiert worden wären. Für die Entwicklung der cognitive sciences hat die Prototypentheorie seit den 1970er Jahren eine wichtige Rolle gespielt, indem sie Prozesse der Kategorisierung untersuchte und diese ins Zentrum der Kognition stellte: »We have categories for everything we can think about. To change the concept of category itself is to change our understanding of the world.« (Lakoff) Ausgehend von einer kurzen Einführung in das Prinzip einer Kategorienbildung mit unscharfen Grenzen, nichtäquivalenten Exemplaren und flexibler Gewichtung von Merkmalen, skizziert der Beitrag das Potenzial der Prototypentheorie für die Klärung bzw. Weiterentwicklung musiktheoretischer Begriffe und schlägt Kriterien zur Beurteilung ihrer Nützlichkeit vor. / The term ›prototype‹ is not unknown in German music theory. Its implications, however, haven’t been thoroughly adopted yet. Prototype theory has played an important part in the development of cognitive sciences since the 1970s by enabling researchers to examine processes of categorization and place them in the center of cognition: »We have categories for everything we can think about. To change the concept of category itself is to change our understanding of the world.« (Lakoff) The article begins with a brief introduction into the concept of categories with vague boundaries, non-equivalent samples and adjustable emphasis of characteristics. It outlines the potential of prototype theory to clarify or further develop music theory terms. Finally, there are suggestions for criteria to evaluate their usefulness.

In dieser Dissertation erweitern wir die Ideen des Yangian-Bootstrap-Algorithmus auf Feynman-Diagramme mit massiven Teilchen. Ausgehend von der massiven dual-konformen Symmetrie der N = 4 Super-Yang-Mills Theorie auf dem Coulomb-Zweig konstruieren wir einen Satz von bilokalen Yangian Level-Eins Generatoren und zeigen, dass sie eine unendliche Anzahl von planaren ein- und zwei-Schleifen-Diagrammen vernichten. Wir beschreiben außerdem wie der dual-konforme Level-Eins Impuls-Operator auf eine massive Verallgemeinerung des gewöhnlichen spezial-konformen Generators im Impulsraum abgebildet wird. Als nächstes wenden wir den Yangian-Bootstrap-Algorithmus mit großem Erfolg auf eine Reihe von massiven Ein-Schleifen-Diagrammen mit verallgemeinerten Propagatorexponenten und in beliebiger Anzahl von Raumdimensionen an. Im Spezialfall der dual-konformen Integrale, deren Propagatorexponenten sich zur Raumdimension addieren, finden wir neue sehr einfache Darstellungen durch hypergeometrische Funktionen, die eine natürliche Verallgemeinerung für Diagramme mit beliebig vielen äußeren Punkten erlauben. Außerdem diskutieren wir Aspekte des Yangian-Bootstrap-Algorithmus in Minkowski-Raumzeit am Beispiel des masselosen Box-Integrals. Wir zeigen, dass dessen Yangian-Symmetrie gemeinsam mit seinen diskreten Permutationssymmetrien das Box-Integrals bis auf 12 unbestimmte Konstanten komplett festlegt. Schließlich schlagen wir vor, dass das Auftreten von Yangian-Symmetrie in massiven Fischnetz-Diagrammen mit deren Rolle als Ein-Spur-Streuamplituden in einer massiven Fischnetz-Theorie zusammenhängen könnte. In Analogie mit der masselosen Fischnetz-Theorie zeigen wir, wie diese Theorie als Deformation der N = 4 Super-Yang-Mills Theorie auf dem Coulomb-Zweig definiert werden kann. Wir diskutieren eine bestimmte Klasse von planaren Grenzfällen, in der die off-shell Streuamplituden der Theorie eine massive dual-konforme Symmetrie sowie Yangian-Symmetrie aufweisen. / In this dissertation, we extend the ideas of the Yangian bootstrap algorithm to massive Feynman diagrams. Based on the massive dual-conformal symmetry of Coulomb branch N = 4 super-Yang-Mills theory, we construct a set of bi-local Yangian level-one generators and show that they annihilate infinite classes of massive planar Feynman integrals at one and two loops. We also describe how the dual-conformal level-one momentum generator maps to a massive deformation of the ordinary momentum space special conformal generator. We then apply the Yangian bootstrap to a set of massive one-loop integrals with generalised propagator powers and in an arbitrary number of space dimensions to great success. In the special case of dual-conformal integrals, whose propagator powers sum to the space dimension, we find very simple novel hypergeometric structures, suggesting a natural generalisation to diagrams with an arbitrary number of external points. In the particular case of the massless box integral we also discuss elements of the Yangian bootstrap in Minkowski space. We show that its Yangian and discrete permutation symmetries constrain it up to 12 undetermined constants. We then derive the values of these constants via analytic continuation from the box integral in the Euclidean region. Finally, we provide evidence that the appearance of Yangian symmetry for massive fishnet diagrams is related to their role as colour-ordered scattering amplitudes in a massive fishnet theory. We show how to construct this theory from Coulomb branch N = 4 super-Yang-Mills theory, paralleling the original construction of the massless fishnet theory. We discuss how a particular class of planar limits leads to the emergence of massive dual-conformal symmetry as well as massive Yangian symmetry for the theory’s off-shell scattering amplitudes.

The hippocampus is a brain area fundamental for cognitive functions, such as learning, memory, spatial navigation and emotion regulation, and is mainly affected in Alzheimer’s disease (AD). AD is an irreversible neurodegenerative disease, characterized by pathological protein aggregations and cognitive impairments. To date, there is no treatment for Alzheimer’s disease. The search for a therapy is urgently needed to alleviate the suffering of patients and relieve the burden on society. Neural stem cells (NSCs) in the hippocampal neurogenic niche sustain continuous neurogenesis in adulthood. Adult hippocampal neurogenesis (AHN) is functionally associated with many cognitive and emotional functions in humans and rodents. In particular, hippocampal neurogenesis is impaired in AD patients and AD mouse models and may be a putative therapeutic target for curing AD. In my project, endogenous hippocampal neurogenesis is manipulated in the 3xTg AD mouse model by a chronic, genetically-driven expansion of hippocampal NSCs. Exploiting intrinsic NSCs potential to generate newborn neurons increases the neurogenesis in 3xTg AD mice. The boosted neurogenesis ameliorates the anxiety-like behavior, improves spatial navigational performances and restores the connectivity of the hippocampal network in AD. Altogether, this study demonstrates the beneficial effect of enhancing neurogenesis by exploiting the endogenous NSCs reserve to rescue AD phenotypes and elucidates the functional contribution of neurogenesis to learning and memory. The findings support and highlight the therapeutic potential of enhancing neurogenesis in the treatments of neurodegenerative diseases.

Alterations in executive functions have repeatedly been found in individuals suffering from eating and weight disorders. However, less is known about how these cognitive processes might contribute to the etiology of the disorders, as large prospective population-based studies have been missing. Here, we comment on the results of Steegers et al. (2021), a study that helped to fill this gap with a focus on set-shifting abilities predicting symptoms of anorexia nervosa (AN) in children. The main goal of this commentary is to encourage further interpretation of the population-based data beyond its relevance to AN. More specifically, we discuss the role of impaired inhibition as a risk factor for weight gain and obesity.

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Bei altersbedingt abnehmender kognitiver Funktion stellt das steigende Renteneintrittsalter Arbeitgeber und -nehmer vor wachsende Herausforderungen. Der Aufbau der kognitiven Reserve (CR) durch geistig stimulierende Aktivitäten verspricht eine Resilienz gegenüber neuropathologisch bedingten kognitiven Defiziten. In der vorliegenden Arbeit wird die Rolle der CR in Bezug auf die kognitive Leistungsfähigkeit und die neuronale Informationsverarbeitung gesunder Erwachsener im Berufsalter untersucht. Unter Ableitung des Elektroenzephalogramms bearbeiteten Probanden mittleren und hohen Erwerbsalters (34-45 J. und 46-62 J.) im 2-Jahres-Abstand Aufgaben zu drei Domänen exekutiver Funktionen: Arbeitsgedächtnis (AG), kognitive Flexibilität und Inhibitionskontrolle. Hoch-CR-Probanden wiesen aufgabenübergreifend schnellere Reaktionen und geringere Fehlerraten auf. Reduzierte Leistung ließ sich in der Gering-CR-Gruppe tendenziell bei älteren Probanden und in anspruchsvollen Aufgabenbedingungen beobachten. Nach 2 Jahren zeigten Gering-CR-Ältere eine numerisch abnehmende AG-Kapazität, während Hoch-CR-Ältere ihre hohe Leistung steigern konnten. Die P3-Amplitude variierte in Abhängigkeit von der CR und dem Alter. Hoch-CR-Jüngere wiesen im Vergleich zu Gering-CR-Jüngeren höhere P3-Amplituden auf, während Hoch-CR-Ältere im Gegensatz zu Gering-CR-Älteren kleinere P3-Amplituden generierten. Zudem legten kürzere P3-Latenzen in der Hoch-CR-Gruppe eine schnellere neuronale Verarbeitungsgeschwindigkeit nahe. In der Aufgabe zur kognitiven Flexibilität ließ sich bei Gering-CR-Probanden ein Anterior-Shift der P3 beobachten. Die Untersuchungsergebnisse konnten nach 2 Jahren repliziert werden. Alterungsrelevante Leistungsvariablen und neuronale Informationsverarbeitungsprozesse zeigten sich bereits im Berufsalter sensitiv gegenüber der CR. Das mittlere Erwachsenenalter sollte bei der Erarbeitung und Evaluation CR-basierter Maßnahmen zur Prävention kognitiver Defizite stärker berücksichtigt werden. / The increasing retirement date accompanied by an age-associated decline of cognitive functions poses growing challenges to employers and employees. The cognitive reserve (CR) promises a resilience to brain damage-associated cognitive deficits through intellectually stimulating lifestyle activities. The present study examines the role of CR relating to cognitive performance and neuronal information processing of healthy adults in working age. Using an electroencephalogram, subjects of middle and high working age (34-45 years and 46-62 years of age, respectively) completed tasks on three domains of executive functions: working memory, cognitive flexibility and inhibition control. Follow-up assessments were conducted after two years. High-CR subjects performed better across tasks than Low-CR subjects, with faster reaction times and lower error rates. Reduced performance in the Low-CR group tended to be more common among older participants and during the more challenging task conditions. In addition, after two years, Low-CR older workers showed a decreased working memory capacity while older High-CR individuals improved their higher performance. The P3 amplitude of the event-related brain potential varied systematically as a function of CR and age. High-CR younger individuals revealed higher P3 amplitudes compared to Low-CR younger individuals, while High-CR older individuals generated smaller P3 amplitudes than Low-CR older individuals. The shorter P3 peak-latencies of the High-CR group suggested moreover a difference in neural processing speed. When testing cognitive flexibility an anterior shift of the P3 was observed in older Low-CR subjects. The results were almost completely replicated after two years. Age-related performance variables and neuronal information processes revealed to be sensitive to CR already at working age. These findings recommend more research on early adulthood in the development and evaluation of CR-based programs to prevent cognitive deficits.

Die Notwendigkeit einer Untersuchung über Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht ergibt sich einerseits aus den aktuellen bildungspolitischen Forderungen, andererseits aus den reichhaltigen bildungsphilosophischen Traditionen im deutschsprachigem Raum(KMK 2012, 11). Das Ziel der vorliegenden Arbeit besteht vor allem in der Reflexion von Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht. Diese Reflexion ist durch drei Fragen bestimmt: Was kann man als Lehrer über Beziehungshaltigkeit wissen? Wie kann man als Lehrer handeln, so dass die Schüler Beziehungen zwischen mathematischen Inhalten erkennen bzw. selbständig herstellen? Um handeln zu können, muss man die Wirklichkeit oder die Praxis (bzw. Empirie) kennen, in der man handelt. In diesem Sinne ist die vorliegende Arbeit aufgebaut. Dabei wird ein Versuch unternommen, die klassische Aufteilung zwischen Theorie und Empirie bzw. Praxis des Mathematikunterrichts aufzubrechen, um eine Verzahnung zwischen diesen zu verstärken. Das Herzstück der Arbeit bilden zwei ausgearbeitete und in der schulischen Arbeit erprobte Aufgabennetze (Pythagorasbaum und Rund ums Sechseck), die den Rahmen zur Reflexion bieten. / The need for a study on relations sustainability and networks in mathematics stems, on the one hand, from current education policy requirements, and, on the other, from the rich philosophical traditions of education in the German-speaking countries (KMK 2012, 11). The goal of the present work consists, above all, in reflecting on relations sustainability and networks in mathematics lessons. This reflection is guided by three questions: What can one know, as a teacher, about relations sustainability? How can one act a teacher to ensure that students recognise relationships between mathematical content, or independently produce such relations? In order to act, one must know the reality or practice (e.g. empiricism) in which one acts. The project is focused on the development and testing of worked examples of concrete task networks ("Pythagoras’ tree" and "Around the hexagon").