A Fourier integral formula for logarithmic energy

A formula which expresses logarithmic energy of Borel measures on R^n in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz energy is reinvented.Comment: 14 page

Point Source Approximation Methods in Inverse Obstacle Reconstruction Problems

Wir untersuchen verschiedene Punktquellenverfahren zur Lösung inverser Objektrekonstruktionsprobleme für die Laplace- und Helmholtz-Gleichung. Dabei stellen wir einen Zweischritt-Algorithmus vor, der durch eine geeignete Wahl von Approximationsgebieten zunächst die Umgebung des Objekts rekonstruiert. In einem zweiten Schritt wird durch Adaption des Approximationsgebietes das unbekannte Gebiet selbst rekonstruiert. Wir formulieren den Zweischrittalgorithmus für die Punktquellenmethode, die Methode singulärer Quellen und die Probe Methode. Hierbei zeigen wir Rekonstruktionsergebnisse für die Laplace und die Helmholtzgleichung in zwei bzw. drei Dimensionen. Schließlich vergleichen wir die Punktquellenverfahren mit der Faktorisierungs- und der Linear Sampling Methode sowohl für exakte als auch für fehlerbehaftete Daten.We consider point source approximation methods for the solution of inverse object reconstruction problems for the Laplace and the Helmholtz equation. We present a two-step algorithm to reconstruct the neighbourhood of the obstacle by a proper choice of approximation domains, first. Then we reconstruct the obstacle in the second step of the algorithm by varying the approximation domains adaptively. We formulate this two-step algorithm for the point source method, the singular sources method and the probe method. Moreover we show numerical examples both for the Laplace and the Helmholtz equation in two and three dimensions, respectively. Finally, we compare the point source approximation methods with the factorisation and the linear sampling method both for exact data and noisy data

Neuronal Signal Modulation By Dendritic Geometry

Neurons are the basic units in nervous systems. They transmit signals along neurites and at synapses in electrical and chemical forms. Neuronal morphology, mainly dendritic geometry, is famous for anatomical diversity, and names of many neuronal types reflect their morphologies directly. Dendritic geometries, as well as distributions of ion channels on cell membranes, contribute significantly to distinct behaviours of electrical signal filtration and integration in different neuronal types (even in the cases of receiving identical inputs in vitro). In this thesis I mainly address the importance of dendritic geometry, by studying its effects on electrical signal modulation at the level of single neurons via mathematical and computational approaches. By ‘geometry’, I consider both branching structures of entire dendritic trees and tapered structures of individual dendritic branches. The mathematical model of dendritic membrane potential dynamics is established by generalising classical cable theory. It forms the theoretical benchmark for this thesis to study neuronal signal modulation on dendritic trees with tapered branches. A novel method to obtain analytical response functions in algebraically compact forms on such dendrites is developed. It permits theoretical analysis and accurate and efficient numerical calculation on a neuron as an electrical circuit. By investigating simplified but representative dendritic geometries, it is found that a tapered dendrite amplifies distal signals in comparison to the non-tapered dendrite. This modulation is almost a local effect, which is merely influenced by global dendritic geometry. Nonetheless, global geometry has a stronger impact on signal amplitudes, and even more on signal phases. In addition, the methodology employed in this thesis is perfectly compatible with other existing methods dealing with neuronal stochasticity and active behaviours. Future works of large-scale neural networks can easily adapt this work to improve computational efficiency, while preserving a large amount of biophysical details

Morality, Law, and the Socialist Sexual Self in the German Democratic Republic, 1945-1972.

While many existing accounts attribute the emergence of a new sexual sensibility in the German Democratic Republic (GDR) to the liberalization of laws regarding contraception and abortion that accompanied the beginning of Erich Honecker’s tenure as First Secretary of the Socialist Unity Party (SED) in the early 1970s, "Morality, Law, and the Socialist Sexual Self in the German Democratic Republic, 1945-1972" revisits the 1950s and 1960s as a crucible for sexual change. In the absence of Western-style civil society and the overt commodification of sexuality, the presence or absence of a “sexual revolution” in the GDR must be assessed with different yardsticks. Despite the depredations of Stalinism and Nazism and the conservative moral climate of the early Cold War years, the spirit of Weimar-era progressive sex reform continued to inform the tenor of sexual change in the legal realm and in marital counseling, albeit in a muted fashion. Indeed, it was in part because of this legacy that the SED came to respect the inviolability of the right to private same-sex sexual intimacy despite its ostensible commitment to abolishing the concepts of the rights-bearing individual and the public-private divide from liberal jurisprudence. While many observers have criticized the East German polity for having failed to abide by its rhetorical commitment to gender equality, the SED promulgated new norms regarding the age of marital consent and no-fault divorce as part of a sincere effort to change the gendered dynamics of domestic life. This endeavor, however, was undermined by the regime’s willful obliviousness to the discordance between official and popular mores. By inviting citizens to submit petitions (Eingaben) and visit an expanded network of marital counseling centers, the regime facilitated the proliferation of discourse on sexual topics that many in the regime would rather have left unspoken. Through an amalgam of ideological and medical measures designed to shape the socialist sexual self, the SED effectively redefined the terms of biopolitical interventions under state-socialist auspices in ways that were not reducible to demographic concerns alone.PHDHistoryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/97942/1/ehuneke_1.pd

Les portraits de Marie-Thérèse

In the Austrian monarchy, Maria Theresa is the first and only woman of the Habsburg dynasty to rule and impose herself in a context of wars and reforms. In a situation of multiform crises (territorial dynasty, etc.), the representation and dissemination of the image of the sovereign through portraits is an essential aspect of royal politics. These portraits and their analysis are at the heart of this book