Exact computation of the adjacency graph of an arrangement of quadrics

Präsentiert wird ein vollständiger, exakter und effizienter Algorithmus zur Berechnung des Nachbarschaftsgraphen eines Arrangements von Quadriken (Algebraische Flächen vom Grad 2). Dies ist ein wichtiger Schritt auf dem Weg zur Berechnung des vollen 3D Arrangements. Dabei greifen wir auf eine bereits existierende Implementierung zur Berechnung der exakten Parametrisierung der Schnittkurve von zwei Quadriken zurück. Somit ist es möglich, die exakten Parameterwerte der Schnittpunkte zu bestimmen, diese entlang der Kurven zu sortieren und den Nachbarschaftsgraphen zu berechnen. Wir bezeichnen unsere Implementierung als vollständig, da sie auch die Behandlung aller Sonderfälle wie singulärer oder tangentialer Schnittpunkte einschließt. Sie ist exakt, da immer das mathematisch korrekte Ergebnis berechnet wird. Und schließlich bezeichnen wir unsere Implementierung als effizient, da sie im Vergleich mit dem einzigen bisher implementierten Ansatz gut abschneidet. Implementiert wurde unser Ansatz im Rahmen des Projektes EXACUS. Das zentrale Ziel von EXACUS ist es, einen Prototypen eines zuverlässigen und leistungsfähigen CAD Geometriekerns zu entwickeln. Obwohl wir das Design unserer Bibliothek als prototypisch bezeichnen, legen wir dennoch größten Wert auf Vollständigkeit, Exaktheit, Effizienz, Dokumentation und Wiederverwendbarkeit. Über den eigentlich Beitrag zu EXACUS hinaus, hatte der hier vorgestellte Ansatz durch seine besonderen Anforderungen auch wesentlichen Einfluss auf grundlegende Teile von EXACUS. Im Besonderen hat diese Arbeit zur generischen Unterstützung der Zahlentypen und der Verwendung modularer Methoden innerhalb von EXACUS beigetragen. Im Rahmen der derzeitigen Integration von EXACUS in CGAL wurden diese Teile bereits erfolgreich in ausgereifte CGAL Pakete weiterentwickelt.

Investigation of a superthermal ultracold neutron source based on a solid deuterium converter for the TRIGA Mainz reactor

Research in fundamental physics with the free neutron is one of the key tools for testing the Standard Model at low energies. Most prominent goals in this field are the search for a neutron electric dipole moment (EDM) and the measurement of the neutron lifetime. Significant improvements of the experimental performance using ultracold neutrons (UCN) require reduction of both systematic and statistical errors.rnThe development and construction of new UCN sources based on the superthermal concept is therefore an important step for the success of future fundamental physics with ultracold neutrons. rnSignificant enhancement of today available UCN densities strongly correlates with an efficient use of an UCN converter material. The UCN converter here is to be understood as a medium which reduces the velocity of cold neutrons (CN, velocity of about 600 m/s) to the velocity of UCN (velocity of about 6 m/s).rnSeveral big research centers around the world are presently planning or constructing new superthermal UCN sources, which are mainly based on the use of either solid deuterium or superfluid helium as UCN converter.rnThanks to the idea of Yu.Pokotilovsky, there exists the opportunity to build competitive UCN sources also at small research reactors of the TRIGA type. Of course these smaller facilities don't promise high UCN densities of several 1000 UCN/cm³, but they are able to provide densities around 100 UCN/cm³ for experiments.rnIn the context of this thesis, it was possible to demonstrate succesfully the feasibility of a superthermal UCN source at the tangential beamport C of the research reactor TRIGA Mainz. Based on a prototype for the future UCN source at the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRMII) in munich, which was planned and built in collaboration with the Technical University of Munich, further investigations and improvements were done and are presented in this thesis. rnIn parallel, a second UCN source for the radial beamport D was designed and built. The comissioning of this new source is foreseen in spring 2010.rnAt beamport D with its higher thermal neutron flux, it should be possible to increase the available UCN densities of 4 UCN/cm³ by minimum one order of magnitude.

Resonance properties of different neuronal populations in the immature mouse neocortex

Subthreshold resonance is a characteristic membrane property of different neuronal classes, is critically involved in the generation of network oscillations, and tunes the integration of synaptic inputs to particular frequency ranges. In order to investigate whether resonance properties of distinct neuronal populations in the immature neocortex contribute to these network oscillations, I performed whole-cell patch-clamp recordings from visually identified neurons in tangential and coronal neocortical slices from postnatal day (P) P0-P7 C57Bl/6 and P6-P13 GAD67-GFP knock-in mice. Subthreshold resonance was analyzed by sinusoidal current injection of varying frequency. All Cajal-Retzius cells showed subthreshold resonance with an average frequency of 2.6 ± 0.1 Hz (n=60), which was massively reduced by ZD7288, a blocker of hyperpolarization-activated cation currents. About 65.6% (n=61) of the supragranular pyramidal neurons showed subthreshold resonance with an average frequency of 1.4 ± 0.1 Hz (n=40). Application of 1 mM Ni2+ suppressed subthreshold resonance, suggesting that low-threshold Ca2+ currents contribute to resonance in these neurons. About 63.6% (n=77) of the layer V pyramidal neurons showed subthreshold resonance with an average frequency of 1.4 ± 0.2 Hz (n=49), which was abolished by ZD7288. Only 44.1% (n=59) of the subplate neurons showed subthreshold resonance with an average frequency of 1.3 ± 0.2 Hz (n=26) and a small resonance strength. Finally, 50% of the investigated GABAergic interneurons showed subthreshold resonance with an average frequency of 2.0 ± 0.2 Hz (n=42). Membrane hyperpolarization to –86 mV attenuated the frequency and strength of subthreshold resonance. Subthreshold resonance was virtually abolished in the presence of 1 mM Ni2+, suggesting that t-type Ca2+ currents are critically involved in the generation of resonance, while ZD7288 had no effect. Application of 0.4 µM TTX suppressed subthreshold resonance at depolarized, but not hyperpolarized membrane potential, suggesting that persistent Na+ current contribute to the amplification of membrane resonance. rnIn summary, these results demonstrate that all investigated neuronal subpopulations reveal resonance behavior, with either hyperpolarization-activated cation or low-threshold Ca2+ currents contributing to the subthreshold resonance. GABAergic interneurons also express subthreshold resonance at low frequencies, with t-type Ca2+ and persistent Na+ currents underlying the generation of membrane resonance. The membrane resonance of immature neurons may contribute to the generation of slow oscillatory activity pattern in the immature neocortex and enhance the temporal precision of synaptic integration in developing cortical neurons.rn