Thesis advisor: Solomon Friedberg / Kazhdan and Patterson constructed generalized theta representations on covers of general linear groups as multi-residues of the Borel Eisenstein series. For the double covers, these representations and their (degenerate-type) unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for GL(r). In this thesis, we study two other types of models that the theta representations may support. We first discuss semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondly, we determine the unipotent orbits attached to theta functions, in the sense of Ginzburg. We also determine the covers for which these models are unique. We also describe briefly some applications of these unique models in Rankin-Selberg integrals for covering groups. / Thesis (PhD) — Boston College, 2017. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

L'objet de cette thèse est d'étudier les systèmes linéaires sur le champ algébrique des fibrés quasi-paraboliques sur une courbe algébrique. Dans la première partie nous montrons que la puissance $\ell$-ième du fibré déterminant sur l'espace de modules des fibrés paraboliques semi-stables (au sens de Seshadri) est un système linéaire sans points de base, dès que $\ell$ est supérieur ou égal à un entier $\ell_0$, que nous déterminons et qui ne dépend que du rang des fibrés vectoriels sous-jacents. Ce résultat repose sur l'existence d'un analogue (quasi-)parabolique du schéma des quotients de Grothendieck. Dans la seconde partie nous étudions le lieu de base des systèmes linéaires sur le champ algébrique des fibrés quasi-paraboliques. Le théorème obtenu dans la première partie sur le fibré déterminant parabolique nous permet d'identifier ce lieu de base et le sous-champ fermé des fibrés quasi-paraboliques instables, pour un choix de poids déterminé par le système linéaire.

In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.

In order to investigate the temporal characteristics of cognitive processing, we apply multivariate phase synchronization analysis to event-related potentials. The experimental design combines a semantic incongruity in a sentence context with a physical mismatch (color change). In the ERP average, these result in an N400 component and a P300-like positivity, respectively. The synchronization analysis shows an effect of global desynchronization in the theta band around 288ms after stimulus presentation for the semantic incongruity, while the physical mismatch elicits an increase of global synchronization in the alpha band around 204ms. Both of these effects clearly precede those in the ERP average. Moreover, the delay between synchronization effect and ERP component correlates with the complexity of the cognitive processes.

The light-harvesting like (LiL) proteins are a widely spread group of proteins within photosynthetic organisms. They are membrane proteins composed of one to four transmembrane helices and – in homology to the light-harvesting complexes of algae and higher plants – at least one of these transmembrane helices contains the chlorophyll a/b-binding (CAB) domain. Opposite to the light-harvesting antenna complexes, LiL proteins are stress induced and they have been shown to be involved in protection of the photosynthetic apparatus. The work presented in this thesis is focused on understanding the function of one-helical LiL proteins of the cryptophyte algae Guillardia theta and the cyanobacterium Synechocystis sp. PCC 6803. G. theta contains two genes encoding LiL proteins, one is localized in the plastid (hlipP), the other in the nucleomorph (HlipNm). Both genes are expressed in normal growth condition, but they are not induced by high light. Immunostaining indicated that HlipNm is translated, but not light-induced. These proteins therefore seem not to be involved in photoprotective mechanisms of G. theta. In the cyanobacterium Synechocystis sp. PCC 6803 four one-helical LiL proteins were identified, they are called Small CAB-like Proteins (SCPs); a fifth LiL (ScpA) is fused with the ferrochelatase (FC), an enzyme involved in the heme synthesis. Our analysis revealed that SCPs are involved in the de novo assembly/repair cycle of Photosystem II, stabilizing the chlorophyll pigments at their protein scaffold. The in vitro characterization of the recombinant FC showed that ScpA is involved in the product-release of the catalytic domain of the enzyme, thereby regulating substrate availability for chlorophyll- or heme- biosynthesis. Finally, using a transcriptomic and metabolomic approaches, I was able to show that deletion of all SCP genes has profound impact on the cell organization and metabolism. In SCP-depleted cells, production of reactive oxygen species (ROS) is increased, while the amount of Photosystem II per cell volume is decreased, causing a macronutrient-deficient phenotype. Therefore, SCPs are important for stress protection and help to maintain a metabolic equilibrium within the cell.

<p>Forebrain cholinergic projection systems innervate the entire cortex and hippocampus. These cholinergic systems are involved in a wide range of cognitive and behavioral functions, including learning and memory, attention, and sleep-waking modulation. However, the <italic>in vivo</italic> physiological mechanisms of cholinergic functions, particularly their fast dynamics and the consequent modulation on the hippocampus and cortex, are not well understood. In this dissertation, I investigated these issues using a number of convergent approaches.</p><p> First, to study fast acetylcholine (ACh) dynamics and its interaction with field potential theta oscillations, I developed a novel technique to acquire second-by-second electrophysiological and neurochemical information simultaneously with amperometry. Using this technique on anesthetized rats, I discovered for the first time the tight <italic>in vivo</italic> coupling between phasic ACh release and theta oscillations on fine spatiotemporal scales. In addition, with electrophysiological recording, putative cholinergic neurons in medial setpal area (MS) were found with firing rate dynamics matching the phasic ACh release. </p><p> Second, to further elucidate the dynamic activities and physiological functions of cholinergic neurons, putative cholinergic MS neurons were identified in behaving rats. These neurons had much higher firing rates during rapid-eye-movement (REM) sleep, and brief responses to auditory stimuli. Interestingly, their firing promoted theta/gamma oscillations, or small-amplitude irregular activities (SIA) in a state-dependent manner. These results suggest that putative MS cholinergic neurons may be a generalized hippocampal activation/arousal network. </p><p> Third, I investigated the hypothesis that ACh enhances cortical and hippocampal immediate-early gene (IEG) expression induced by novel sensory experience. Cholinergic transmission was manipulated with pharmacology or lesion. The resultant cholinergic impairment suppressed the induction of <italic>arc</italic>, a representative IEG, suggesting that ACh promotes IEG induction. </p><p> In conclusion, my results have revealed that the firing of putative cholinergic neurons promotes hippocampal activation, and the consequent phasic ACh release is tightly coupled to theta oscillations. These fast cholinergic activities may provide exceptional opportunities to dynamically modulate neural activity and plasticity on much finer temporal scales than traditionally assumed. By the subsequent promotion of IEG induction, ACh may further substantiate its function in neural plasticity and memory consolidation.</p> / Dissertation

Es werden effiziente Algorithmen vorgestellt, die auf algebraischen Methoden beruhen um die Unerfüllbarkeit aussagenlogischer 4-SAT Formeln zu zertifizieren. Die Algorithmen werden implementiert und auf praktische Weise hinsichtlich der Laufzeit mit Backtracking-Algorithmen verglichen.

Thesis (Ph.D.)--Mississippi State University. Department of Instructional Systems, Leadership, and Workforce Development. / Title from title screen. Includes bibliographical references.

We describe combinatorial techniques for studying log Calabi-Yau surfaces. These can be viewed as generalizing the techniques for studying toric varieties in terms of their character and cocharacter lattices. These lattices are replaced by certain integral linear manifolds described in [GHK11], and monomials on toric varieties are replaced with the canonical theta functions defined in [GHK11] using ideas from mirror symmetry. We classify deformation classes of log Calabi-Yau surfaces in terms of the geometry of these integral linear manifolds. We then describe the tropicalizations of theta functions and use them to generalize the dual pairing between the character and cocharacter lattices. We use this to describe generalizations of dual cones, Newton and polar polytopes, Minkowski sums, and finite Fourier series expansions. We hope that these techniques will generalize to higher rank cluster varieties. / text

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