Die Aktivität des Hippocampus im Tiefschlaf ist geprägt durch sharp wave-ripple Komplexe (SPW-R): kurze (50–100 ms) Phasen mit erhöhter neuronaler Aktivität, moduliert durch eine schnelle “Ripple”-Oszillation (140–220 Hz). SPW-R werden mit Gedächtniskonsolidierung in Verbindung gebracht, aber ihr Ursprung ist unklar. Sowohl exzitatorische als auch inhibitorische Neuronpopulationen könnten die Oszillation generieren. Diese Arbeit analysiert Ripple-Oszillationen in inhibitorischen Netzwerkmodellen auf mikro-, meso- und makroskopischer Ebene und zeigt auf, wie die Ripple-Dynamik von exzitatorischem Input, inhibitorischer Kopplungsstärke und dem Rauschmodell abhängt. Zuerst wird ein stark getriebenes Interneuron-Netzwerk mit starker, verzögerter Kopplung analysiert. Es wird eine Theorie entwickelt, die die Drift-bedingte Feuerdynamik im Mean-field Grenzfall beschreibt. Die Ripple-Frequenz und die Dynamik der Membranpotentiale werden analytisch als Funktion des Inputs und der Netzwerkparameter angenähert. Die Theorie erklärt, warum die Ripple-Frequenz im Verlauf eines SPW-R-Ereignisses sinkt (intra-ripple frequency accommodation, IFA). Weiterhin zeigt eine numerische Analyse, dass ein alternatives Modell, basierend auf einem transienten Störungseffekt in einer schwach gekoppelten Interneuron-Population, unter biologisch plausiblen Annahmen keine IFA erzeugen kann. IFA kann somit zur Modellauswahl beitragen und deutet auf starke, verzögerte inhibitorische Kopplung als plausiblen Mechanismus hin. Schließlich wird die Anwendbarkeit eines kürzlich entwickelten mesoskopischen Ansatzes für die effiziente Simulation von Ripples in endlich großen Netzwerken geprüft. Dabei wird das Rauschen nicht im Input der Neurone beschrieben, sondern als stochastisches Feuern entsprechend einer Hazard-Rate. Es wird untersucht, wie die Wahl des Hazards die dynamische Suszeptibilität einzelner Neurone, und damit die Ripple-Dynamik in rekurrenten Interneuron-Netzwerken beeinflusst. / Hippocampal activity during sleep or rest is characterized by sharp wave-ripples (SPW-Rs): transient (50–100 ms) periods of elevated neuronal activity modulated by a fast oscillation — the ripple (140–220 Hz). SPW-Rs have been linked to memory consolidation, but their generation mechanism remains unclear. Multiple potential mechanisms have been proposed, relying on excitation and/or inhibition as the main pacemaker. This thesis analyzes ripple oscillations in inhibitory network models at micro-, meso-, and macroscopic scales and elucidates how the ripple dynamics depends on the excitatory drive, inhibitory coupling strength, and the noise model. First, an interneuron network under strong drive and strong coupling with delay is analyzed. A theory is developed that captures the drift-mediated spiking dynamics in the mean-field limit. The ripple frequency as well as the underlying dynamics of the membrane potential distribution are approximated analytically as a function of the external drive and network parameters. The theory explains why the ripple frequency decreases over the course of an event (intra-ripple frequency accommodation, IFA). Furthermore, numerical analysis shows that an alternative inhibitory ripple model, based on a transient ringing effect in a weakly coupled interneuron population, cannot account for IFA under biologically realistic assumptions. IFA can thus guide model selection and provides new support for strong, delayed inhibitory coupling as a mechanism for ripple generation. Finally, a recently proposed mesoscopic integration scheme is tested as a potential tool for the efficient numerical simulation of ripple dynamics in networks of finite size. This approach requires a switch of the noise model, from noisy input to stochastic output spiking mediated by a hazard function. It is demonstrated how the choice of a hazard function affects the linear response of single neurons and therefore the ripple dynamics in a recurrent interneuron network.

In meshfree methods, partial differential equations are solved on an unstructured cloud of points distributed throughout the computational domain. In collocated meshfree methods, the differential operators are directly approximated at each grid point based on a local cloud of neighboring points. The set of neighboring nodes used to construct the local approximation is determined using a variable search radius. The variable search radius establishes an implicit nodal connectivity and hence a mesh is not required. As a result, meshfree methods have the potential flexibility to handle problem sets where the computational grid may undergo large deformations as well as where the grid may need to undergo adaptive refinement. In this work we develop the sharp interface formulation of the immersed boundary method for collocated meshfree approximations. We use the framework to implement three meshfree methods: General Finite Differences (GFD), Smoothed Particle Hydrodynamics (SPH), and Moving Least Squares (MLS). We evaluate the numerical accuracy and convergence rate of these methods by solving the 2D Poisson equation. We demonstrate that GFD is computationally more efficient than MLS and show that its accuracy is superior to a popular corrected form of SPH and comparable to MLS. We then use GFD to solve several canonic steady state fluid flow problems on meshfree grids generated using uniform and variable radii Poisson disk algorithm.

In this Ph. D. thesis we discuss four different problems in analysis: (a) sharp inequalities related to the restriction phenomena for the Fourier transform, with emphasis on some Strichartz-type estimates; (b) extremal approximations of exponential type for the Gaussian and for a class of even functions, with applications to analytic number theory; (c) radial symmetrization approach to convolution-like inequalities for the Boltzmann collision operator; (d) regularity of maximal operators with respect to weak derivatives and weak continuity. / text

A complete two-phase numerical model of film condensation from a mixture of a vapour and a non-condensing gas that is based on the two-dimensional elliptic governing equations with variable physical properties is presented. The model predicts the full viscous flow and heat and mass transfer for the mixture around the tube and in the entire liquid film from the top of the tube to the falling film below the tube. A finite volume method is used with a segregated solution approach and a dynamically moving computational grid that tracks the phase interface sharply. Fundamental balances of mass, energy, and force are enforced accurately at the phase interface. The model was developed in steps and validated against various experimental and theoretical works in the literature for different two-phase flows. The validation tests included stratified flow of liquid and gas in a horizontal channel, falling liquid film over a vertical wall, and condensation of steam from a steam-air mixture in a vertical channel. The model was used to simulate laminar film condensation from a downward flowing steam-air mixture over an isothermal horizontal tube. The validity of this new model is demonstrated by comparisons with previous theoretical and experimental studies. New results are presented on the effects of free-stream-to-tube temperature difference, upstream Reynolds number, free-stream gas mass fraction, and free-stream pressure on the condensate film development, the local and average heat transfer coefficients, and the total condensate mass flow rate. It was found that the temperature difference had the greatest effect on the condensation rate and film thickness. The presence of non-condensing gas in the vapour has a strong negative impact on the condensation process. For the pure steam case, moderate changes in the upstream Reynolds number showed slight increases in condensate mass flow rate with increased Reynolds number. For the mixture case, however, moderate increase in upstream Reynolds number increases significantly the condensate mass flow rate and film thickness. This trend becomes more noticeable as the free-steam gas mass fraction increases. Changing the free-stream pressure demonstrated that property variation had a relatively smaller effect than temperature difference and gas mass fraction changes. / February 2017

This thesis describes statistical approaches of investment portfolio constructions. The theoretic part presents modern portfolio theory and specific statistical methods used to estimate expected revenue and risk of portfolio. These procedures are specifically selection method, modelling volatility using multivariate GARCH model, primarily DCC GARCH procedure and Bayes approach with Jeffrey's and conjugated density. The practical part of the thesis covers application of above mentioned statistical methods of investment portfolio constructions. The maximization of Sharp's ratio was chosen as optimization task. Researched portfolios are created from Austria Traded Index issues of shares where suitable time series of historical daily closed prices. Results attained within assembled portfolios in two year investment interval are later compared.

Total body electrical conductivity (TOBEC) is a noninvasive method for the estimation of lean mass in live subjects. Lipid content can be calculated from the body mass measured and the lean mass estimated from TOBEC. I used live American Kestrels (Falco sparverius) to study the accuracy of this method. TOBEC measurements were compared to actual body content determined by Soxhlet fat extraction using petroleum ether as the solvent. TOBEC estimated 73.7% of the variation in lean mass in a sample of 21 kestrels. The use of restraining devices (Vetrap and cardboard cylinders) altered the TOBEC measurement but only by an average of 1.92% and 0.83%, respectively. TOBEC estimated 83.8% of the variation in lean mass for 21 kestrel carcasses warmed to 39.8oC. No significant difference was found between the slope or elevation of the calibration lines developed using live or dead kestrels. A significant difference was found between measurements taken at two different positions. Body temperature altered the TOBEC measurements by an average of 1.54% (SE = 0.55) for each 10C change over a temperature range of 7.00C (37.3-44.4). The calibration line developed for kestrels was used to estimate lean mass and compute fat mass of migrating kestrels, Sharp-shinned Hawks (Accipiter striatus) and Merlins (Fa/co co/umbarius). The average percent fat mass of kestrels trapped during migration at Cape May, New Jersey, was 6.01 % (SE = 1.92, n = 1 2) for males and 8.51 % (SE = 2.00, n = 13) for females. The difference in lean mass between male and female, and between early, mid-season, and late migrating Sharp-shinned Hawks differed significantly during migration. The fat mass of Sharp-shinned Hawks averaged 5.55% (SE = 0.94, n = 53) for males and 10.92% (SE = 0.80, n = 87) for females. Male Merlins had an average fat mass of 18.05% (SE = 3.35, n = 7) and females averaged 14.19% (SE = 3.15, n = 8).

This study is an experimental research to formulate the discharge over sharp-crested rectangular weirs. Firstly, a series of measurements on different weir heights were conducted to find the minimum weir height for which channel bed friction has no effect on discharge capacity. After determining the appropriate weir height, weir width was reduced to collect data on discharge-water head over weir relationship for a variety of different weir openings. Then, the data was analyzed through regression analysis along with utilization of global optimization technique to reach the desired formulation for the discharge. By taking advantage of a newly-introduced &ldquo / weir velocity&rdquo / concept, a simple function was eventually detected for the discharge where no discharge coefficient was involved. The behavior of the weir velocity function obtained in the present study illustrates the transition between the fully contracted and partially contracted weirs. In addition, the proposed weir velocity formulation is simple and robust to calculate the discharge for full range of weir widths.

The thesis provides answers, in one case partial and in the other final, to two conjectures in the area of weighted inequalities for Singular Integral Operators. We study the mapping properties of these operators in weighted Lebesgue spaces with weight w. The novelty of this thesis resides in proving sharp dependence of the operator norm on the Muckenhoupt constant associated to the weigth w for a rich class of Singular Integral operators. The thesis also addresses the end point case p=1, providing counterexamples for the dyadic and continuous settings.

This thesis describes an experimental investigation of the breakup processes involved in the formation of a spray created by a liquid jet injected into a gaseous crossflow. This work is motivated by the utilization of this method to inject fuel in combustors and afterburners of airplane engines. This study aims to develop better understanding of the spray breakup processes and provide better experimental inputs to improve the fidelity of numerical models. This work adresses two key research areas: determining the time required for a liquid column to break up in the crossflow (i.e., primary breakup time) and the effect of injector geometry on spray properties. A new diagnostic technique, the liquid jet light guiding technique that utilizes ability of the liquid jet to act as a waveguide for laser light was developed to determine the location where the liquid column breaks up, in order to obtain the primary breakup time. This study found that the liquid jet Reynolds number was an important factor that governed the primary breakup time and improved the existing correlation. Optical diagnostic techniques such as Phase Doppler Particle Analyzer, Liquid Jet Light Guiding Technique, Particle Image Velocimetry and Imaging techniques were employed to measure the spray properties that include spray penetration, droplet sizes and velocities, velocity field on the surface of the liquid jet and the location of the primary breakup time. These properties were measured for two injectors: one with a sharp transition and the other with a smooth transition. It was found that the spray created by the injector with a sharp transition forms large irregular structures while one with smooth transition produces a smooth liquid jet. The spray transition creates a spray that penetrates deeper into the crossflow, breakup up earlier and produces larger droplets. Additionally, this study reports the phenomenon of the liquid jet splitting into two or more jets in sprays created by the injector with a smooth transition.

Water infiltration into the unsaturated zone especially in a shallow water table environment is affected by air compression ahead of the wetting front and air counterflow. Neglecting air compression in infiltration modeling can overestimate infiltration and infiltration rates, whereas not accounting for air counterflow can underestimate infiltration and infiltration rates due to unrealistic buildup of air pressure resistance ahead of the wetting front. A method, derived on the basis of the Green and Ampt (1911) infiltration model, is introduced to simulate air compression and air counterflow during infiltration into a shallow water table. The method retains the simplicity of the Green and Ampt (1911) model but adds the air pressure resistance term ahead of the wetting front. Infiltration equations are derived on the basis of the Green and Ampt (1911) and Sabeh’s (2004) infiltration model which accounts for air compression and air counterflow. The difference between this method and Sabeh’s (2004) model is that air counterflow, air compression, and infiltration are decoupled and updated with each wetting front increment whereas Sabeh’s (2004) method uses time step as a decoupling mechanism. Air compression ahead of the wetting front is predicted using the perfect gas law. Laboratory experiments showed that the introduced method is reasonably accurate when modeling cumulative infiltration values. Results of laboratory experiments were compared to results of the modeled infiltration methods: original Green and Ampt (1911) model and Green and Ampt with air compression and counterflow. The advantage of this new method is its simplicity. The new method uses parameters that are generally needed for modeling infiltration with the Green and Ampt (1911) approach. Disadvantages of the model are assumptions of the uniform water content and the uniform pressure. Another shortcoming of the model is that it does not account for air compression and air counterflow prior to ponding. Laboratory experiments described in this work and a proposed model can be further used for modeling and studying infiltration with air effects. In addition, this work can be of use to someone studying irrigation techniques of rice or other crops.