On units of central division algebras over algebraic number fields

Der erste Teil meiner Diplomarbeit beschäftigt sich mit algebraischen Zahlkörpern. Um mehr über den Zahlkörper zu erfahren, betrachtet man seine Vervollständigungen bezüglich seiner inäquivalenten Bewertungen gleichzeitig. Die geeignete Methode hierfür sind die Adele und Idele. Man kann den Körper kanonisch als diskreten Unterring der Adele auffassen und erhält des weiteren, dass die Adele modulo dem Körper kompakt sind. Ebenso kann man die Einheiten des Körpers als Unterring der Idele auffassen. Damit kann man beweisen, dass die Norm eins Idele modulo der Einheitengruppe des Körpers kompakt sind. Daraus lässt sich der Dirichletsche Einheitensatz sowie die Endlichkeit der Klassenzahl folgern. Im zweiten Teil werden die Ideen des ersten Teiles auf den Fall von endlich dimensionalen Algebren übertragen. Wie im Fall des Zahlkörpers erhält man, dass die Adele modulo der Algebra kompakt sind. Im Fall der Gruppe der Idele muss man sich auf Divisionsalgebren beschränken. Wiederum erhält man, dass die Idele mit Norm eins modulo der Einheitengruppe der Divisionsalgebra kompakt sind. Damit lässt sich eine Verallgemeinerung des Dirichletschen Einheitensatzes beweisen, nämlich dass die Einheitengruppe einer Ordnung einer Divisionsalgebra endlich erzeugt ist.In the first part of my thesis I study algebraic number fields. To do so I introduce valuations and completions. The aim is to find out more about an algebraic number field by studying its completions simultaneously. The natural language to deal with the completions is that of adeles and ideles. There is an embedding of the field into the ring of adeles and one can show, that the ring of adeles modulo this field is compact. When studying the unit group of the adeles, which is the group of ideles, one can prove something similar. In fact one shows that the group of norm one ideles modulo the field is compact. This leads to a proof of Dirichlets Unit Theorem and one can show the finiteness of the class number, which are both important results in algebraic number theory. The second part of my thesis generalizes the methodological approach introduced in the first part. As in the case of a field, one has that the adele ring of an algebra modulo the algebra itself is compact. When turning our attention to the group of ideles, one has to restrict to the case of a division algebra. One can define the norm one ideles and show that the group of norm one ideles modulo the division algebra itself is compact. Using this result one can generalize Dirichlets Unit Theorem and show that the unit group of an order of a division algebra is finitely generated

Tennessee Williams, the Playwright-Painter: Vieux Carré and Something Cloudy, Something Clear at the Crossroads between Text and Image

“Snatching the eternal out of the desperately fleeting is the great magic trick of human existence”, Tennessee Williams wrote in 1951 in an essay devoted to The Rose Tattoo, entitled “The Timeless World of a Play” (61). What the statement reveals is the American playwright’s conception of art as a means of fighting against the passing of time, against the “awful sense of impermanence” (61) that never stopped haunting him. But the stage is not the only place where, as Williams wrote in the same essay, “time is arrested in the sense of being confined” (61). The sketches and paintings he made throughout his life reveal the same obsession with time, the same desire to freeze the intensity of the moment into the work of art. Two paintings, made in 1975 and 1977, shed new light on two of his late plays, Vieux Carré and Something Cloudy, Something Clear. Written at the end of his life, both plays are attempts at capturing the totality of experience. In them, Williams intertwines past and present, life and art, combining movement and stasis to achieve a synthesis his paintings echo, or mirror, though in a very different way. The examination of these unknown paintings in relation to the plays is meant to engage us in a dialogue between texts and images. What the dialogical perspective reveals is a temporality that is circular rather than linear, anachronistic rather than chronological. Williams the painter and Williams the playwright blur the limits of space and time to reach that region where the distinctions between text and image collapse as one becomes the mirror of the other, its “horizon,” as Jean-Luc Nancy writes in Au Fond des images. There, words fail and figures dissolve; there, silence and haziness confront the reader/spectator with the timelessness of art, not as something eternal or transcendent, but rather as a magic interval where the intensity of the vanishing moment can be captured. In the scripts of his plays as well as in his paintings, Williams faces us with the mystery of time, with an elusiveness that he considers as the only true essence of his art. Through a comparative analysis of two of his paintings with two of his late plays, I intend to show how the verbal and the visual interconnect in Williams’s art, how his texts as well as his paintings convey a sense of “intense immobility” that is the artist’s way of beating “the game of being against non-being” (Williams 2009, 61).« Snatching the eternal out of the desperately fleeting is the great magic trick of human existence » : Tennessee Williams écrivit cette phrase en 1951 dans un essai intitulé « The Timeless World of a Play » (61). L’affirmation met au jour une conception de l’art comme moyen de lutter contre le passage du temps, contre une « affreuse sensation d’impermanence » (61) qui n’a jamais quitté le dramaturge. Or, la scène n’est pas le seul endroit où, selon Williams, « le temps, soudain pris au piège, s’arrête » (61). Les dessins et tableaux qu’il réalisa tout au long de sa vie trahissent la même hantise du temps qui passe, le même désir de fixer l’intensité du moment dans l’œuvre d’art. Deux tableaux, peints en 1975 et 1977, permettent ainsi de porter un regard nouveau sur deux pièces écrites à la fin de sa carrière. Intitulées Vieux Carré et Something Cloudy, Something Clear, elles ont ceci de commun qu’elles apparaissent comme des tentatives de capturer la totalité d’une existence, d’enfermer la petite éternité d’une vie dans les limites de la représentation. Dans chacune d’elles, Williams mêle le passé et le présent, la vie et l’art, combinant les notions de mouvement et de stase pour opérer une synthèse dont ses images peintes sont l’écho, ou, pourrait-on dire aussi, le miroir. L’analyse de ces deux pièces au prisme de deux peintures méconnues de Williams invite à un dialogue fructueux entre les textes et les images. De cette approche dialogique émerge une temporalité plus circulaire que linéaire, plus anachronique que chronologique. Williams le peintre et Williams le dramaturge brouillent les limites spatio-temporelles pour créer ce lieu intermédiaire où les distinctions entre texte et image s’annulent, l’un devenant le miroir de l’autre, son « horizon d’interprétation », pour reprendre l’expression de Jean-Luc Nancy. Là, les mots manquent et les formes s’évanouissent ; là encore, le silence et l’indistinction confrontent le spectateur à l’intemporalité de l’art, non pas comme quelque chose d’éternel ou de transcendant, mais plutôt comme un intervalle magique où l’intensité du moment fuyant se révèle, comme une évanescence capturée dans les mailles de la représentation. Dans les textes de ses pièces, comme dans ses tableaux, Williams met le spectateur/lecteur face au mystère du temps, de ce temps objet d’une quête artistique vitale dans une œuvre où les images n’ont jamais cessé d’accompagner les mots

Quand le théâtre s’inspire du cinéma : Jean Cocteau, Sergueï Eisenstein et Tennessee Williams

La fascination de Tennessee Williams pour le cinéma a laissé des traces dans son théâtre. Les projections sur écran envisagées dans les indications scéniques de The Glass Menagerie ou l’importance accordée à la musique dans nombre de ses pièces n’en sont que quelques illustrations. Or, au delà du simple apport technique, les avancées de l’art cinématographique de la première moitié du XXe siècle invitent à repenser le rapport entre le réel et sa représentation, rapport que Williams n’a cessé d’explorer tout au long de sa carrière. Ses écrits autobiographiques sont parsemés de références à des films et à des réalisateurs qui ont joué un rôle essentiel dans l’élaboration de son « nouveau théâtre plastique ». L’analyse de sa pièce la plus connue, A Streetcar Named Desire, à la lumière de ces écrits révèle des influences diverses. Cocteau et Eisenstein affleurent ainsi à la surface de l’écriture dans une pièce où les univers des deux réalisateurs se rencontrent, ouvrant de nouvelles perspectives d’interprétation sur une œuvre dont il reste encore beaucoup à découvrir.Tennessee Williams’s lifelong fascination with cinema left marks on his theatre. The use of projections in The Glass Menagerie and the role played by music in many of his plays are cases in point. Yet, the influence of cinema on Williams’s writing goes far beyond the mere transposition of new technological devices onto the stage. For cinema brought about new ways of representing the world, thus providing the playwright with the means of escaping from the realist tradition and creating the “new, plastic theatre” he advocated as early as 1944. His autobiographical essays are peppered with references to famous filmmakers who helped him shape his language for the stage. The examination of his most famous play – A Streetcar Named Desire – reveals the influence of Cocteau and Eisenstein’s films and theories, giving us a new insight into Williams’s creative process

Unveiling age-independent spectral markers of propofol-induced loss of consciousness by decomposing the electroencephalographic spectrum into its periodic and aperiodic components

Background: Induction of general anesthesia with propofol induces radical changes in cortical network organization, leading to unconsciousness. While perioperative frontal electroencephalography (EEG) has been widely implemented in the past decades, validated and age-independent EEG markers for the timepoint of loss of consciousness (LOC) are lacking. Especially the appearance of spatially coherent frontal alpha oscillations (8-12 Hz) marks the transition to unconsciousness.Here we explored whether decomposing the EEG spectrum into its periodic and aperiodic components unveiled markers of LOC and investigated their age-dependency. We further characterized the LOC-associated alpha oscillations by parametrizing the adjusted power over the aperiodic component, the center frequency, and the bandwidth of the peak in the alpha range. Methods: In this prospective observational trial, EEG were recorded in a young (18-30 years) and an elderly age-cohort (>= 70 years) over the transition to propofol-induced unconsciousness. An event marker was set in the EEG recordings at the timepoint of LOC, defined with the suppression of the lid closure reflex. Spectral analysis was conducted with the multitaper method. Aperiodic and periodic components were parametrized with the FOOOF toolbox. Aperiodic parametrization comprised the exponent and the offset. The periodic parametrization consisted in the characterization of the peak in the alpha range with its adjusted power, center frequency and bandwidth. Three time-segments were defined: preLOC (105 - 75 s before LOC), LOC (15 s before to 15 s after LOC), postLOC (190 - 220 s after LOC). Statistical significance was determined with a repeated-measures ANOVA. Results: Loss of consciousness was associated with an increase in the aperiodic exponent (young: p = 0.004, elderly: p = 0.007) and offset (young: p = 0.020, elderly: p = 0.004) as well as an increase in the adjusted power (young: p < 0.001, elderly p = 0.011) and center frequency (young: p = 0.008, elderly: p < 0.001) of the periodic alpha peak. We saw age-related differences in the aperiodic exponent and offset after LOC as well as in the power and bandwidth of the periodic alpha peak during LOC. Conclusion: Decomposing the EEG spectrum over induction of anesthesia into its periodic and aperiodic components unveiled novel age-independent EEG markers of propofol-induced LOC: the aperiodic exponent and offset as well as the center frequency and adjusted power of the power peak in the alpha range

The Impact of Dance Movement Interventions on Psychological Health in Older Adults without Dementia: A Systematic Review and Meta-Analysis

Background: Lifestyle-based multimodal interventions that integrate physical, sensory, cognitive and social enrichment are suggested to promote healthy mental aging and resilience against aging and Alzheimer’s disease (AD). Objectives: This meta-analysis examined the efficacy of dance movement interventions (DMI) as an integrated mind–body activity on outcomes of psychological health in older adults. Methods: Pre-registration was carried out with PROSPERO (CRD42021265112). PubMed, Web of Science and PsycINFO were searched for randomized controlled trials (RCT) evaluating the effects of DMI (>4 weeks’ duration) compared to comparators on measures of psychological health (primary outcome) and cognitive function (additional outcome) among older adults without dementia (aged ≥55). Data of 14 primary RCT (n = 983, n-DMI = 494, n-control = 489) were synthesized using a random effects meta-analysis with robust variance estimation. Results: DMI had a small positive effect on overall psychological health (g = 0.30; 95% confidence interval [CI]: 0.06, 0.53; p = 0.02, I2 = 65.04) compared to control conditions. Small effects of DMI on positive and negative psychological domains as well as quality of life were not statistically significant. DMI had a medium positive effect on general cognitive function (g = 0.50; 95% CI: 0.12, 0.89, p = 0.02, I2 = 79.61) over comparators. None of the primary intervention studies evaluated measures of neuroplasticity. Conclusions: We found that DMI was effective in promoting mental health amongst older adults without dementia, suggesting that the multimodal enrichment tool is a potential strategy for health promotion and prevention of AD. High-quality intervention studies are needed to expand evidence on DMI-induced changes in specific psychological domains and identify underlying neurophysiological correlates

Klima- und Verteilungswirkung eines Verbrenner-Neuzulassungsverbots von Pkw in Deutschland und die Rolle des CO2-Preises

Die Auswirkungen eines Verbrenner-Neuzulassungsverbots von Pkw in Deutschland haben Ariadne-Experten des Instituts für Verkehrsforschung des Deutschen Zentrums für Luft- und Raumfahrt und des Mercator Research Institute on Global Commons and Climate Change jetzt erstmals in Abhängigkeit vom CO2-Preis untersucht. Ihre Berechnungen zeigen: Ein Verbrenner-Neuzulassungsverbot ab 2035 allein reduziert die CO2-Emissionen des Pkw-Verkehrs nur vergleichsweise gering. Die Wirkung des Verbots und die größten Emissionseinsparungen hängen maßgeblich von einem Mix aus Zeitpunkt der Einführung, der CO2-Bepreisung und einem massiv beschleunigten Hochlauf von Nullemissionsfahrzeugen in den Jahren vor dem Verbot ab

Radar internal reflection horizons from multisystem data reflect ice dynamic and surface accumulation history along the Princess Ragnhild Coast, Dronning Maud Land, East Antarctica

Ice shelves, which regulate ice flow from the Antarctic ice sheet towards the ocean, are shaped by spatiotemporal patterns of surface accumulation, surface/basal melt and ice dynamics. Therefore, an ice dynamic and accumulation history are imprinted in the internal ice stratigraphy, which can be imaged by radar in the form of internal reflection horizons (IRHs). Here, IRHs were derived from radar data combined across radar platforms (airborne and ground-based) in coastal eastern Dronning Maud Land (East Antarctica), comprising three ice rises and adjacent two ice shelves. To facilitate interpretation of dominant spatiotemporal patterns of processes shaping the local IRH geometry, traced IRHs are classified into three different types (laterally continuous, discontinuous or absent/IRH-free). Near-surface laterally continuous IRHs reveal local accumulation patterns, reflecting the mean easterly wind direction, and correlate with surface slopes. Areas of current and past increased ice flow and internal deformation are marked by discontinuous or IRH-free zones, and can inform about paleo ice-stream dynamics. The established IRH datasets extend continent-wide mapping efforts of IRHs to an important and climatically sensitive ice marginal region of Antarctica and are ready for integration into ice-flow models to improve predictions of Antarctic ice drainage

The Thrombopoietin Receptor Agonist Eltrombopag Inhibits Human Cytomegalovirus Replication Via Iron Chelation

The thrombopoietin receptor agonist eltrombopag was successfully used against human cytomegalovirus (HCMV)-associated thrombocytopenia refractory to immunomodulatory and antiviral drugs. These effects were ascribed to the effects of eltrombopag on megakaryocytes. Here, we tested whether eltrombopag may also exert direct antiviral effects. Therapeutic eltrombopag concentrations inhibited HCMV replication in human fibroblasts and adult mesenchymal stem cells infected with six different virus strains and drug-resistant clinical isolates. Eltrombopag also synergistically increased the anti-HCMV activity of the mainstay drug ganciclovir. Time-of-addition experiments suggested that eltrombopag interfered with HCMV replication after virus entry. Eltrombopag was effective in thrombopoietin receptor-negative cells, and the addition of Fe3+ prevented the anti-HCMV effects, indicating that it inhibits HCMV replication via iron chelation. This may be of particular interest for the treatment of cytopenias after hematopoietic stem cell transplantation, as HCMV reactivation is a major reason for transplantation failure. Since therapeutic eltrombopag concentrations are effective against drug-resistant viruses, and synergistically increase the effects of ganciclovir, eltrombopag is also a drug-repurposing candidate for the treatment of therapy-refractory HCMV disease

Training Schrödinger’s cat: quantum optimal control

It is control that turns scientific knowledge into useful technology: in physics and engineering itprovides a systematic way for driving a dynamical system from a given initial state into a desired targetstate with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantumtechnologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhancedsensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry,magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantumsimulation. In this communication, state-of-the-art quantum control techniques are reviewed and putinto perspective by a consortium of experts in optimal control theory and applications to spectroscopy,imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketcha roadmap for future developments