Disertační práce se zabývá asymptotickou stabilitou zpožděných diferenciálních rovnic a jejich diskretizací. V práci jsou uvažovány lineární zpožděné diferenciální rovnice s~konstantním i neohraničeným zpožděním. Jsou odvozeny nutné a postačující podmínky popisující oblast asymptotické stability jak pro exaktní, tak i diskretizovanou lineární neutrální diferenciální rovnici s konstantním zpožděním. Pomocí těchto podmínek jsou porovnány oblasti asymptotické stability odpovídajících exaktních a diskretizovaných rovnic a vyvozeny některé vlastnosti diskrétních oblastí stability vzhledem k měnícímu se kroku použité diskretizace. Dále se zabýváme lineární zpožděnou diferenciální rovnicí s neohraničeným zpožděním. Je uveden popis jejích exaktních a diskrétních oblastí asymptotické stability spolu s asymptotickým odhadem jejich řešení. V závěru uvažujeme lineární diferenciální rovnici s více neohraničenými zpožděními.

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.

Diese Dissertation hat zwei Teile. Im ersten Teil untersuchen wir die Modulräume von Kurven mit multiplen Spinstrukturen. Wir stellen eine neue Kompaktifizierung dieser Räume mit geometrisch sinnvollem Grenzverhalten vor. Die irreduziblen Komponenten dieser Räume werden vollstandig klassifiziert. Die Ergebnisse aus diesem ersten Teil der Dissertation sind fundamental für die Degenerationstechniken im zweiten Teil. Im zweiten Teil untersuchen wir eine Reihe von Problemen, die von der klassischen Geometrie inspiriert werden. Unser Hauptaugenmerk liegt hierbei auf dem Fall von zwei Hyperebenen, die eine kanonische Kurve in jedem Schnittpunkt tangential berühren. Wir fragen, ob eingemensamer Tangentialpunk existieren kann. Unsere Analyse zeigt, dass so ein gemeinsamer Punkt nur in Kodimension 1 im Modulraum existieren kann. Wir berechen dann weiter die Klasse dieses Divisors. Insbesonders zeigen wir, dass diese Klasse eine hinreichend kleine Steigung hat, sodass die kanonischen Klassen von Modulräumen von Kurven mit zwei ungeraden Spinstrukturen gross ist, wenn der Genus grösser ist als neun. Falls die zugehörigen groben Modulräume gutartige Singularitäten haben, dann haben sie in diesem Intervall maximale Kodaria Dimension. / This thesis has two parts. In Part I we consider the moduli spaces of curves with multiple spin structures and provide a compactification using geometrically meaningful limiting objects. We later give a complete classification of the irreducible components of these spaces. The moduli spaces built in this part provide the basis for the degeneration techniques required in the second part. In the second part we consider a series of problems inspired by projective geometry. Given two hyperplanes tangential to a canonical curve at every point of intersection, we ask if there can be a common point of tangency. We show that such a common point can appear only in codimension 1 in moduli and proceed to compute the class of this divisor. We then study the general properties of curves in this divisor. Our divisor class has small enough slope to imply that the canonical class of the moduli space of curves with two odd spin structures is big when the genus is greater than 9. If the corresponding coarse moduli spaces have mild enough singularities, then they have maximal Kodaira dimension in this range.

Um eine Folge von Ereignissen aus unserem Gedächtnis abzurufen, ist zunächst ein Mechanismus erforderlich, der geordnete Sequenzen abspeichert. Hierbei stehen wir vor dem Problem, dass Ereignisse in unserem Leben auf einer Zeitskala von Sekunden oder mehr stattfinden. Auf der anderen Seite basiert das Lernen von Sequenzen auf der Plastizität von Synapsen im Gehirn, die durch die Abfolge von Aktionspotentialen von Nervenzellen im Millisekunden-Bereich gesteuert wird. Um dieses zeitliche Problem zu lösen, betrachten wir den Hippocampus, eine Struktur im Gehirn von Vertebraten, die für das explizite Gedächtnis (Fakten, Ereignisse, Sequenzen) entscheidende Bedeutung hat. In Nagetieren ist der Hippocampus sehr gut untersucht. Dort wurden Neurone gefunden, die nur dann aktiv sind, wenn das Tier innerhalb einer bestimmten Region seiner Umgebung ist: im sogenannten “Ortsfeld” des entsprechenden Neurons. Während der Bewegung durch ein Ortsfeld verschiebt sich die Phase der Nervenimpulse zu immer früheren Phasen der EEG-Oszillation. Dieses Phänomen wird als “Phasenpräzession” bezeichnet. Theoretische und experimentelle Untersuchungen zeigen, dass Phasenpräzession eine Lösung für unser Dilemma bietet: es führt zu einer zeitlich komprimierten Darstellung der Sequenz von Orten. In der vorliegenden Arbeit untersuche ich den Mechanismus und die Funktion von Phasenpräzession im Hinblick auf die Ausbreitung neuronaler Aktivität von einer Hirnregion zu einer anderen. Phasenpräzession konnte bereits in mehreren Regionen des Gehirns beobachtet werden. Bisher war unklar, ob Phasenpräzession in jeder dieser Regionen eigenständig entsteht, oder ob die Phasenpräzession von einer vorgeschalteten Population von Neuronen “vererbt” werden kann. Schliesslich diskutiere ich auf Grundlage der aktuellen Literatur, ob Phasenpräzession das Verhalten beeinflusst und gebe einen Ausblick auf zukünftige Forschungsmöglichkeiten auf diesem Gebiet. / The process of faithfully retrieving episodes from our memory requires a neural mechanism capable of initially forming ordered and reliable behavioral sequences. These behavioral sequences take place on a timescale of seconds or more, whereas the timescale of neural plasticity and learning is in the order of tens of milliseconds. To shed light on this dilemma, we turn to studies of hippocampal place cells in rodents, i.e., cells that selectively increase their firing rates in locations of the environment known as the place fields. Within a field, the firing phases of a place cell precess monotonically relative to the ongoing theta rhythm. This phenomenon, termed "phase precession", leads to a temporally compressed representation of the behavioral sequences experienced by the rodent, and the compressed timescale matches the requirements of neural plasticity. In this thesis, I study the mechanisms and functions of phase precession by proposing a framework that relies on the concept of inheritance: the simple idea that patterns of neural activity can be propagated from one region to another. Indeed, phase precession has been observed in several regions of the hippocampus and entorhinal cortex, and an important open question is whether phase precession emerges independently in each region, or conversely, whether phase precession can be "inherited" from an upstream neu ronal population. These results suggest that the presence of phase precession in different stages of the hippocampal circuit and other regions of the brain is indicative of a common source, a fact that can help us better understand the temporal spiking patterns in the brain. Finally, I critically review the current evidence for a behavioral role for phase precession and suggest a roadmap for future research in this field.

Wir beweisen, dass die Tannaka Gruppe und Darstellung Jacobische Varietäten der Dimension bis zu 5 charakterisieren. Außerdem zeigen wir, dass dies in allen Dimensionen für nicht-hyperelliptische Jacobische Varietäten auf dem bielliptischen Prym-Locus gilt. Wir erhalten dieses Ergebnis durch Untersuchung des Theta-Divisors von bielliptischen Prym Varietäten: Wir berechnen den Grad der Gauß-Abbildung, die Chern-Mather-Klasse und die charakteristische Klasse. Dazu gehört auch die Untersuchung von Entartungen mit Hilfe der Theorie der zulässigen Abdeckungen von Beauville. Auf dem Weg dorthin erhalten wir ähnliche Ergebnisse für den Theta-Divisor zyklischer Nodalkurven. Schließlich berechnen wir den Grad der Gauß-Abbildung auf einer allgemeinen Abelschen Varietät der bekannten irreduziblen Komponenten des Andreotti-Mayer-Locus. Wir tun dies unter Verwendung der Lagrangeschen Spezialisierung. Wir beweisen auch eine allgemeine Formel, die den ersten Koeffizienten der Lagrangeschen Spezialisierung mit der Samuel-Multiplizität der Singularität in Beziehung setzt. / We prove that the Tannakian group and representation characterize Jacobians amongst principally polarized abelian varieties of dimension up to 5. More generally, we show that this holds in all dimensions, for non-hyperelliptic Jacobians, on the bielliptic Prym locus. We obtain this result by studying the theta divisor of bielliptic Pryms: We compute the degree of the Gauss map, the Chern-Mather class and the characteristic cycle. This involves also looking at degenerations of Prym varieties using Beauville's theory of admissible covers. Along the way, we obtain similar results for the theta divisor of cyclic nodal curves. Finally, we compute the degree of the Gauss map on a general principally polarized abelian variety of all known irreducible components of the Andreotti-Mayer locus. We do this using Lagrangian specialization. We also prove a general formula relating the first coefficient of the Lagrangian specialization to the Samuel multiplicity of the singularity.

Kognitive Kontrolle bezieht sich auf eine Vielzahl mentaler Fähigkeiten, die es uns erlauben im täglichen Leben zielgerichtete Entscheidungen zu treffen und sich flexibel an sich ständig ändernde Umweltanforderungen anzupassen. Das Ziel der vorliegenden Dissertation war es heraus zu finden, ob Kernfunktionen im Bereich der Konfliktüberwachung, Konfliktkontrolle, Fehlerverarbeitung und die daraus resultierenden Verhaltensanpassungen durch ein einheitliches Kontrollnetzwerk geleistet werden, oder ob spezifische Mechanismen die möglicherweise durch unabhängige neuronale Kontrollschleifen realisiert sind, die Flexibilität unserer Anpassungsfähigkeit steuern. Studie 1 und Studie 2 untersuchen sowohl generelle aus auch spezifische Aspekte der Konflikt- und Fehlerverarbeitung mit Hilfe klassischer Konfliktparadigmen und dem Einsatz von Zeit-Frequenz-analytischen Auswertungsmethoden. Studie 1 untersucht anhand 3 verschiedener Konfliktparadigmen (Simon, Flanker, NoGo) die Modulation der Theta Aktivität (4-8 Hz) und verortet diese grob innerhalb des medial frontalen Cortex (MFC), einer Struktur die durch eine Vielzahl von Studien als entscheidend bei der Konfliktverarbeitung angesehen wird. Die gefundene Theta Aktivität wurde in Studie 2 genutzt, um auch dynamische Netzwerkaktivierungen bei der Bearbeitung von Reiz- und Reaktionskonflikten zu beobachten. Es konnte gezeigt werden, dass ein vermutetes Netzwerk bestehend aus MFC, lateralen präfrontalen Cortices und motorischen Arealen bei der Lösung von Reaktionskonflikten beteiligt ist. In Studie 3 wird eine Simon-Aufgabe, die innerhalb von belohnenden oder bestrafenden Kontexten durchgeführt wurde, genutzt um zu zeigen, dass Konflikt- und Fehlerverarbeitung differentiell durch die Kontextmanipulation beeinflusst werden. Entgegen voriger Annahmen scheinen mehrere neuronale Kontrollsysteme an der Lösung von Konflikten und daraus resultierenden Verhaltensanpassungen beteiligt zu sein. / Cognitive control refers to a set of mental abilities that allow us goal-directed behavior in everyday life and to flexibly adapt to permanently changing environmental demands. The goal of the present dissertation was to investigate whether core functions in the area of conflict monitoring, conflict control, error processing and behavioral adjustments caused by these processes are enabled via a unitary control network or whether specific mechanisms that are possibly realized via independent control loops are responsible for the flexibility of our adaptability. Study 1 and 2 investigate general as well as specific aspects of conflict and error processing by using classic conflict paradigms and time-frequency-analytic methods. Study 1 compares the modulation of theta activity (4-8 Hz) across 3 conflict paradigms (Simon, Flanker, NoGo) and roughly situates it within medial frontal cortex (MFC), a structure which has been characterized as crucial for conflict processing in manifold studies. The found theta activity has been used in study 2, to observe dynamic network activations during processing of stimulus and response conflicts. Data confirmed that a hypothesized network consisting of MFC, lateral prefrontal cortices and motor areas is involved in conflict resolution. In study 3 we used a Simon task which was executed either during a rewarding or a punishing context assessing the influence of motivational contexts on conflict adaptation revealing that conflict and error processing were influenced differentially by the context manipulation. Against previous assumptions, several neuronal control systems seem to be engaged during conflict resolution and resulting behavioral adjustments.

Published Article / The role of the Projection Principle within Chomsky's Government-Binding (GB) Theory is to preserve the subcategorisation properties of lexical items at all levels of syntactic representation, viz. D-structure, S-structure, and Lexical Form. Arguments have been made that the Projection Principle is a new concept that is simply an extension of theTransformational Component (XFM) and Emonds' Structure-Preserving Constraint (SPC), and that it does not deserve the high status it has been accorded in GB theory. This paper provides evidence, based on sentences involving movement operations, that the Projection Principle is innovative and that it convincingly addresses what theXFMandSPChave failed to address.

International Telemetering Conference Proceedings / October 28-31, 1996 / Town and Country Hotel and Convention Center, San Diego, California / The use of high bit rates in the missile testing environment requires that the receiving telemetry system(s) have the correct signal margin for no PCM bit errors. This requirement plus the fact that the use of “redundant systems” are no longer considered optimum support scenarios has made it necessary to select the minimum number of tracking sites that will gather the data with the required signal margin. A very basic link analysis can be made by using the maximum and minimum gain values from the transmitting antenna pattern. Another way of evaluating the transmitting antenna gain is to base the gain on the highest percentile appearance of the highest gain value. This paper discusses the mathematical analysis the WSMR Telemetry Branch uses to determine the signal margin resulting from a radiating source along a nominal trajectory. The mathematical analysis calculates the missile aspect angles (Theta, Phi, and Alpha) to the telemetry tracking system that yields the transmitting antenna gain. The gain is obtained from the Antenna Radiation Distribution Table (ARDT) that is stored in a computer file. An entire trajectory can be evaluated for signal margin before an actual flight. The expected signal strength level can be compared to the actual signal strength level from the flight. This information can be used to evaluate any plume effects.

Compared to other structures, such as the amygdala, the lateral septum’s (LS) role in the regulation of anxiety and/or behavioural defense is relatively understudied. Thus, the overarching goal of this thesis was to further investigate its contribution to rats’ anxiety-related behaviours. In Chapter 2, we demonstrate, for the first time, that while the dorsal LS does not mediate rats’ appetitive motivation or anxiety in the novelty induced suppression of feeding (NISF) paradigm, it does modulate their defensive behaviours in the elevated plus maze (EPM) and shock probe burying tests (SPBT). In Chapter 3, we are the first to show that bilateral infusions of histamine, a neurochemical previously linked to anxiety, into the LS reduce rats’ anxiety-related behaviours in the EPM and NISF. In addition, we report a novel double dissociation between lateral septal H1 and H2, and H3 receptors in their regulation of rats’ defensive behaviours in those two paradigms. More specifically, the H1 and H2 receptors contribute to rats’ hyponeophagia in the NISF but not their open arm exploration in the EPM, while the H3 receptors modulate rats’ defensive behaviors in the EPM but not in the NISF. Finally, in Chapter 4, we report for the first time that infusions of histamine into the LS, which produce behavioural anxiolysis, increase rather than decrease the frequency of reticular-elicited hippocampal theta activity, a putative neurophysiological correlate of anxiolytic-drug action. Altogether, the data in this thesis increase our understanding of how the LS contributes to rats’ defensive behaviours and adds to the existing literature regarding the neurobiology of fear/anxiety. More importantly though, the data presented here could ultimately aid in the development of novel drugs to treat anxiety disorders in humans. / Thesis (Ph.D, Neuroscience Studies) -- Queen's University, 2013-12-17 17:27:34.014

Compared to other structures, such as the amygdala, the lateral septum’s (LS) role in the regulation of anxiety and/or behavioural defense is relatively understudied. Thus, the overarching goal of this thesis was to further investigate its contribution to rats’ anxiety-related behaviours. In Chapter 2, we demonstrate, for the first time, that while the dorsal LS does not mediate rats’ appetitive motivation or anxiety in the novelty induced suppression of feeding (NISF) paradigm, it does modulate their defensive behaviours in the elevated plus maze (EPM) and shock probe burying tests (SPBT). In Chapter 3, we are the first to show that bilateral infusions of histamine, a neurochemical previously linked to anxiety, into the LS reduce rats’ anxiety-related behaviours in the EPM and NISF. In addition, we report a novel double dissociation between lateral septal H1 and H2, and H3 receptors in their regulation of rats’ defensive behaviours in those two paradigms. More specifically, the H1 and H2 receptors contribute to rats’ hyponeophagia in the NISF but not their open arm exploration in the EPM, while the H3 receptors modulate rats’ defensive behaviors in the EPM but not in the NISF. Finally, in Chapter 4, we report for the first time that infusions of histamine into the LS, which produce behavioural anxiolysis, increase rather than decrease the frequency of reticular-elicited hippocampal theta activity, a putative neurophysiological correlate of anxiolytic-drug action. Altogether, the data in this thesis increase our understanding of how the LS contributes to rats’ defensive behaviours and adds to the existing literature regarding the neurobiology of fear/anxiety. More importantly though, the data presented here could ultimately aid in the development of novel drugs to treat anxiety disorders in humans. / Thesis (Ph.D, Neuroscience Studies) -- Queen's University, 2013-12-17 17:27:34.014