Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Large-Size AlGaN/GaN HEMT Large-Signal Electrothermal Characterization and Modeling for Wireless Digital Communications

The rapid growth in high data rate communication systems has introduced new high spectral efficient modulation techniques and standards such as LTE-A (long term evolution-advanced) for 4G (4th generation) systems. These techniques have provided a broader bandwidth but introduced high peak-to-average power ratio (PAR) problem at the high power amplifier (HPA) level of the communication system base transceiver station (BTS). To avoid spectral spreading due to high PAR, stringent requirement on linearity is needed which brings the HPA to operate at large back-off power at the expense of power efficiency. Consequently, high power devices are fundamental in HPAs for high linearity and efficiency. Recent development in wide bandgap power devices, in particular AlGaN/GaN HEMT, has offered higher power level with superior linearity-efficiency trade-off in microwaves communication. For cost-effective HPA design to production cycle, rigorous computer aided design (CAD) AlGaN/GaN HEMT models are essential to reflect real response with increasing power level and channel temperature. Therefore, large-size AlGaN/GaN HEMT large-signal electrothermal modeling procedure is proposed. The HEMT structure analysis, characterization, data processing, model extraction and model implementation phases have been covered in this thesis including trapping and self-heating dispersion accounting for nonlinear drain current collapse. The small-signal model is extracted using the 22-element modeling procedure developed in our department. The intrinsic large-signal model is deeply investigated in conjunction with linearity prediction. The accuracy of the nonlinear drain current has been enhanced through several issues such as trapping and self-heating characterization. Also, the HEMT structure thermal profile has been investigated and corresponding thermal resistance has been extracted through thermal simulation and chuck-controlled temperature pulsed I(V) and static DC measurements. Higher-order equivalent thermal model is extracted and implemented in the HEMT large-signal model to accurately estimate instantaneous channel temperature. Moreover, trapping and self-heating transients has been characterized through transient measurements. The obtained time constants are represented by equivalent sub-circuits and integrated in the nonlinear drain current implementation to account for complex communication signals dynamic prediction. The obtained verification of this table-based large-size large-signal electrothermal model implementation has illustrated high accuracy in terms of output power, gain, efficiency and nonlinearity prediction with respect to standard large-signal test signals.

Electrophysiological analysis of the olfactory signal transduction cascade in the hawkmoth Manduca sexta

Neben der Verbreitung von gefährlichen Krankheiten sind Insekten für enorme agrarwirtschaftliche Schäden verantwortlich. Ein Großteil der Verhaltensweisen bei Insekten wird über den Geruchssinn gesteuert, der somit einen möglichen Angriffspunkt zur Bekämpfung von Schadinsekten darstellt. Hierzu ist es allerdings nötig, die Mechanismen der olfaktorischen Signalübertragung im Detail zu verstehen. Neben den duftstoffbindenden olfaktorischen Rezeptoren spielt hier auch ein konservierter Korezeptor (Orco) eine entscheidende Rolle. Inwieweit bei diesen Proteinen ionotrope bzw. metabotrope Prozesse involviert sind ist bislang nicht vollständig aufgeklärt. Um weitere Einzelheiten aufzuklären wurden daher Einzelsensillenableitungen am Tabakschwärmer Manduca sexta durchgeführt. Orco-Agonisten und Antagonisten wurden eingesetzt, um die Funktion des Korezeptors besser zu verstehen. Bei dem Einsatz des Orco-Agonisten VUAA1 konnte keine Verstärkung der Pheromonantworten bzw. eine Sensitivierung beobachtet werden, wie im Falle einer ionotropen Signalweiterleitung zu erwarten gewesen wäre. Ein ionotroper Signalweg über den OR/Orco-Komplex in M. sexta ist daher unwahrscheinlich. Der Orco-Antagonist OLC15 beeinflusste die gleichen Parameter wie VUAA1 und konnte die von VUAA1 generierte Spontanaktivität blocken. Daher ist es wahrscheinlich, dass dieser einen spezifischen Orco-Blocker darstellt. Sowohl VUAA1 als auch OLC15 hatten großen Effekt auf die langanhaltende Pheromonantwort, welches die Vermutung nahelegt, dass Orco modulierend auf die Sensitivität der Nervenzelle einwirkt. Von OLC15 abweichende Effekte durch die getesteten Amiloride HMA und MIA auf die Pheromonantwort lassen nicht auf eine spezifische Wirkung dieser Agenzien auf Orco schließen und zusätzliche Wirkorte sind anzunehmen. Um die These eines metabotropen Signalwegs zu überprüfen wurde ebenfalls der G-Protein-Blocker GDP-β-S eingesetzt. Alle Parameter der Pheromonantwort die innerhalb der ersten Millisekunden analysiert wurden wiesen eine Reduktion der Sensitivität auf. Im Gegensatz dazu hatte GDP-β-S keinen Effekt auf die langanhaltende Pheromonantwort. Somit scheint ausschließlich die schnelle Pheromonantwort über einen Ligand-bindenden G-Protein-gesteuerten Rezeptor gesteuert zu werden.