Funktionelle Magnetresonanztomographie mittels simultaner EEG-Registrierung interiktaler Spikes bei fokaler Epilepsie: Vergleich der on-, off- mit der häufigkeitskorrelierten Datenanalyse

Obwohl die funktionelle Magnetresonanztomographie (fMRI) interiktaler Spikes mit simultaner EEG-Ableitung bei Patienten mit fokalen Anfallsleiden seit einigen Jahren zur Lokalisation beteiligter Hirnstrukturen untersucht wird, ist sie nach wie vor eine experimentelle Methode. Um zuverlässig Ergebnisse zu erhalten, ist insbesondere die Verbesserung des Signal-zu-Rausch-Verhältnisses in der statistischen Bilddatenauswertung von Bedeutung. Frühere Untersuchungen zur sog. event-related fMRI weisen auf einen Zusammenhang zwischen Häufigkeit von Einzelreizen und nachfolgender hämodynamischer Signalantwort in der fMRI hin. Um einen möglichen Einfluss der Häufigkeit interiktaler Spikes auf die Signalantwort nachzuweisen, wurden 20 Kinder mit fokaler Epilepsie mit der EEG-fMRI untersucht. Von 11 dieser Patienten konnten die Daten ausgewertet werden. In einer zweifachen Analyse mit dem Softwarepaket SPM99 wurden die Bilddaten zuerst ausschließlich je nach Auftreten interiktaler Spikes der „Reiz“- oder „Ruhe“-Bedingung zugeordnet, unabhängig von der jeweiligen Anzahl der Spikes je Messzeitpunkt (on/off-Analyse). In einem zweiten Schritt wurden die „Reiz“- Bedingungen auch differenziert nach jeweiliger Anzahl einzelner Spikes ausgewertet (häufigkeitskorrelierte Analyse). Die Ergebnisse dieser Analysen zeigten bei 5 der 11 Patienten eine Zunahme von Sensitivität und Signifikanzen der in der fMRI nachgewiesenen Aktivierungen. Eine höhere Spezifität konnte hingegen nicht gezeigt werden. Diese Ergebnisse weisen auf eine positive Korrelation von Reizhäufigkeit und nachfolgender hämodynamischer Antwort auch bei interiktalen Spikes hin, welche für die EEG-fMRI nutzbar ist. Bei 6 Patienten konnte keine fMRI-Aktivierung nachgewiesen werden. Mögliche technische und physiologische Ursachen hierfür werden diskutiert.

External drivers of biogeochemical cycles in a tropical montane forest in Ecuador

Successful conservation of tropical montane forest, one of the most threatened ecosystems on earth, requires detailed knowledge of its biogeochemistry. Of particular interest is the response of the biogeochemical element cycles to external influences such as element deposition or climate change. Therefore the overall objective of my study was to contribute to improved understanding of role and functioning of the Andean tropical montane forest. In detail, my objectives were to determine (1) the role of long-range transported aerosols and their transport mechanisms, and (2) the role of short-term extreme climatic events for the element budget of Andean tropical forest. In a whole-catchment approach including three 8-13 ha microcatchments under tropical montane forest on the east-exposed slope of the eastern cordillera in the south Ecuadorian Andes at 1850-2200 m above sea level I monitored at least in weekly resolution the concentrations and fluxes of Ca, Mg, Na, K, NO3-N, NH4-N, DON, P, S, TOC, Mn, and Al in bulk deposition, throughfall, litter leachate, soil solution at the 0.15 and 0.3 m depths, and runoff between May 1998 and April 2003. I also used meteorological data from my study area collected by cooperating researchers and the Brazilian meteorological service (INPE), as well as remote sensing products of the North American and European space agencies NASA and ESA. My results show that (1) there was a strong interannual variation in deposition of Ca [4.4-29 kg ha-1 a-1], Mg [1.6-12], and K [9.8-30]) between 1998 and 2003. High deposition changed the Ca and Mg budgets of the catchments from loss to retention, suggesting that the additionally available Ca and Mg was used by the ecosystem. Increased base metal deposition was related to dust outbursts of the Sahara and an Amazonian precipitation pattern with trans-regional dry spells allowing for dust transport to the Andes. The increased base metal deposition coincided with a strong La Niña event in 1999/2000. There were also significantly elevated H+, N, and Mn depositions during the annual biomass burning period in the Amazon basin. Elevated H+ deposition during the biomass burning period caused elevated base metal loss from the canopy and the organic horizon and deteriorated already low base metal supply of the vegetation. Nitrogen was only retained during biomass burning but not during non-fire conditions when deposition was much smaller. Therefore biomass burning-related aerosol emissions in Amazonia seem large enough to substantially increase element deposition at the western rim of Amazonia. Particularly the related increase of acid deposition impoverishes already base-metal scarce ecosystems. As biomass burning is most intense during El Niño situations, a shortened ENSO cycle because of global warming likely enhances the acid deposition at my study forest. (2) Storm events causing near-surface water flow through C- and nutrient-rich topsoil during rainstorms were the major export pathway for C, N, Al, and Mn (contributing >50% to the total export of these elements). Near-surface flow also accounted for one third of total base metal export. This demonstrates that storm-event related near-surface flow markedly affects the cycling of many nutrients in steep tropical montane forests. Changes in the rainfall regime possibly associated with global climate change will therefore also change element export from the study forest. Element budgets of Andean tropical montane rain forest proved to be markedly affected by long-range transport of Saharan dust, biomass burning-related aerosols, or strong rainfalls during storm events. Thus, increased acid and nutrient deposition and the global climate change probably drive the tropical montane forest to another state with unknown consequences for its functions and biological diversity.

Statistical problems related to excitation threshold and reset value of membrane potentials

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für spikende Neuronen ist das Folgende. Zwischen den Spikes verhält sich das Membranpotential wie ein Diffusionsprozess X der durch die SDGL dX_t= beta(X_t) dt+ sigma(X_t) dB_t gegeben ist, wobei (B_t) eine Standard-Brown'sche Bewegung bezeichnet. Spikes erklärt man wie folgt. Sobald das Potential X eine gewisse Exzitationsschwelle S überschreitet entsteht ein Spike. Danach wird das Potential wieder auf einen bestimmten Wert x_0 zurückgesetzt. In Anwendungen ist es manchmal möglich, einen Diffusionsprozess X zwischen den Spikes zu beobachten und die Koeffizienten der SDGL beta() und sigma() zu schätzen. Dennoch ist es nötig, die Schwellen x_0 und S zu bestimmen um das Modell festzulegen. Eine Möglichkeit, dieses Problem anzugehen, ist x_0 und S als Parameter eines statistischen Modells aufzufassen und diese zu schätzen. In der vorliegenden Arbeit werden vier verschiedene Fälle diskutiert, in denen wir jeweils annehmen, dass das Membranpotential X zwischen den Spikes eine Brown'sche Bewegung mit Drift, eine geometrische Brown'sche Bewegung, ein Ornstein-Uhlenbeck Prozess oder ein Cox-Ingersoll-Ross Prozess ist. Darüber hinaus beobachten wir die Zeiten zwischen aufeinander folgenden Spikes, die wir als iid Treffzeiten der Schwelle S von X gestartet in x_0 auffassen. Die ersten beiden Fälle ähneln sich sehr und man kann jeweils den Maximum-Likelihood-Schätzer explizit angeben. Darüber hinaus wird, unter Verwendung der LAN-Theorie, die Optimalität dieser Schätzer gezeigt. In den Fällen OU- und CIR-Prozess wählen wir eine Minimum-Distanz-Methode, die auf dem Vergleich von empirischer und wahrer Laplace-Transformation bezüglich einer Hilbertraumnorm beruht. Wir werden beweisen, dass alle Schätzer stark konsistent und asymptotisch normalverteilt sind. Im letzten Kapitel werden wir die Effizienz der Minimum-Distanz-Schätzer anhand simulierter Daten überprüfen. Ferner, werden Anwendungen auf reale Datensätze und deren Resultate ausführlich diskutiert.

Exploring physical processes related to past climate proxies: lake sediments and stable water isotopes

Proxy data are essential for the investigation of climate variability on time scales larger than the historical meteorological observation period. The potential value of a proxy depends on our ability to understand and quantify the physical processes that relate the corresponding climate parameter and the signal in the proxy archive. These processes can be explored under present-day conditions. In this thesis, both statistical and physical models are applied for their analysis, focusing on two specific types of proxies, lake sediment data and stable water isotopes.rnIn the first part of this work, the basis is established for statistically calibrating new proxies from lake sediments in western Germany. A comprehensive meteorological and hydrological data set is compiled and statistically analyzed. In this way, meteorological times series are identified that can be applied for the calibration of various climate proxies. A particular focus is laid on the investigation of extreme weather events, which have rarely been the objective of paleoclimate reconstructions so far. Subsequently, a concrete example of a proxy calibration is presented. Maxima in the quartz grain concentration from a lake sediment core are compared to recent windstorms. The latter are identified from the meteorological data with the help of a newly developed windstorm index, combining local measurements and reanalysis data. The statistical significance of the correlation between extreme windstorms and signals in the sediment is verified with the help of a Monte Carlo method. This correlation is fundamental for employing lake sediment data as a new proxy to reconstruct windstorm records of the geological past.rnThe second part of this thesis deals with the analysis and simulation of stable water isotopes in atmospheric vapor on daily time scales. In this way, a better understanding of the physical processes determining these isotope ratios can be obtained, which is an important prerequisite for the interpretation of isotope data from ice cores and the reconstruction of past temperature. In particular, the focus here is on the deuterium excess and its relation to the environmental conditions during evaporation of water from the ocean. As a basis for the diagnostic analysis and for evaluating the simulations, isotope measurements from Rehovot (Israel) are used, provided by the Weizmann Institute of Science. First, a Lagrangian moisture source diagnostic is employed in order to establish quantitative linkages between the measurements and the evaporation conditions of the vapor (and thus to calibrate the isotope signal). A strong negative correlation between relative humidity in the source regions and measured deuterium excess is found. On the contrary, sea surface temperature in the evaporation regions does not correlate well with deuterium excess. Although requiring confirmation by isotope data from different regions and longer time scales, this weak correlation might be of major importance for the reconstruction of moisture source temperatures from ice core data. Second, the Lagrangian source diagnostic is combined with a Craig-Gordon fractionation parameterization for the identified evaporation events in order to simulate the isotope ratios at Rehovot. In this way, the Craig-Gordon model can be directly evaluated with atmospheric isotope data, and better constraints for uncertain model parameters can be obtained. A comparison of the simulated deuterium excess with the measurements reveals that a much better agreement can be achieved using a wind speed independent formulation of the non-equilibrium fractionation factor instead of the classical parameterization introduced by Merlivat and Jouzel, which is widely applied in isotope GCMs. Finally, the first steps of the implementation of water isotope physics in the limited-area COSMO model are described, and an approach is outlined that allows to compare simulated isotope ratios to measurements in an event-based manner by using a water tagging technique. The good agreement between model results from several case studies and measurements at Rehovot demonstrates the applicability of the approach. Because the model can be run with high, potentially cloud-resolving spatial resolution, and because it contains sophisticated parameterizations of many atmospheric processes, a complete implementation of isotope physics will allow detailed, process-oriented studies of the complex variability of stable isotopes in atmospheric waters in future research.rn

Interacting bosons and fermions in three-dimensional optical lattice potentials

This thesis reports on the realization, characterization and analysis of ultracold bosonic and fermionic atoms in three-dimensional optical lattice potentials. Ultracold quantum gases in optical lattices can be regarded as ideal model systems to investigate quantum many-body physics. In this work interacting ensembles of bosonic 87Rb and fermionic 40K atoms are employed to study equilibrium phases and nonequilibrium dynamics. The investigations are enabled by a versatile experimental setup, whose core feature is a blue-detuned optical lattice that is combined with Feshbach resonances and a red-detuned dipole trap to allow for independent control of tunneling, interactions and external confinement. The Fermi-Hubbard model, which plays a central role in the theoretical description of strongly correlated electrons, is experimentally realized by loading interacting fermionic spin mixtures into the optical lattice. Using phase-contrast imaging the in-situ size of the atomic density distribution is measured, which allows to extract the global compressibility of the many-body state as a function of interaction and external confinement. Thereby, metallic and insulating phases are clearly identified. At strongly repulsive interaction, a vanishing compressibility and suppression of doubly occupied lattice sites signal the emergence of a fermionic Mott insulator. In a second series of experiments interaction effects in bosonic lattice quantum gases are analyzed. Typically, interactions between microscopic particles are described as two-body interactions. As such they are also contained in the single-band Bose-Hubbard model. However, our measurements demonstrate the presence of multi-body interactions that effectively emerge via virtual transitions of atoms to higher lattice bands. These findings are enabled by the development of a novel atom optical measurement technique: In quantum phase revival spectroscopy periodic collapse and revival dynamics of the bosonic matter wave field are induced. The frequencies of the dynamics are directly related to the on-site interaction energies of atomic Fock states and can be read out with high precision. The third part of this work deals with mixtures of bosons and fermions in optical lattices, in which the interspecies interactions are accurately controlled by means of a Feshbach resonance. Studies of the equilibrium phases show that the bosonic superfluid to Mott insulator transition is shifted towards lower lattice depths when bosons and fermions interact attractively. This observation is further analyzed by applying quantum phase revival spectroscopy to few-body systems consisting of a single fermion and a coherent bosonic field on individual lattice sites. In addition to the direct measurement of Bose-Fermi interaction energies, Bose-Bose interactions are proven to be modified by the presence of a fermion. This renormalization of bosonic interaction energies can explain the shift of the Mott insulator transition. The experiments of this thesis lay important foundations for future studies of quantum magnetism with fermionic spin mixtures as well as for the realization of complex quantum phases with Bose-Fermi mixtures. They furthermore point towards physics that reaches beyond the single-band Hubbard model.