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.

The electron antineutrino angular correlation coefficient a in free neutron decay: Testing the standard model with the aSPECT-spectrometer

The beta-decay of free neutrons is a strongly over-determined process in the Standard Model (SM) of Particle Physics and is described by a multitude of observables. Some of those observables are sensitive to physics beyond the SM. For example, the correlation coefficients of the involved particles belong to them. The spectrometer aSPECT was designed to measure precisely the shape of the proton energy spectrum and to extract from it the electron anti-neutrino angular correlation coefficient "a". A first test period (2005/ 2006) showed the “proof-of-principles”. The limiting influence of uncontrollable background conditions in the spectrometer made it impossible to extract a reliable value for the coefficient "a" (publication: Baessler et al., 2008, Europhys. Journ. A, 38, p.17-26). A second measurement cycle (2007/ 2008) aimed to under-run the relative accuracy of previous experiments (Stratowa et al. (1978), Byrne et al. (2002)) da/a =5%. I performed the analysis of the data taken there which is the emphasis of this doctoral thesis. A central point are background studies. The systematic impact of background on a was reduced to da/a(syst.)=0.61 %. The statistical accuracy of the analyzed measurements is da/a(stat.)=1.4 %. Besides, saturation effects of the detector electronics were investigated which were initially observed. These turned out not to be correctable on a sufficient level. An applicable idea how to avoid the saturation effects will be discussed in the last chapter.

Hyperbranched polyether polyols as building blocks for complex macromolecular architectures

The present thesis deals with the development of new branched polymer architectures containing hyperbranched polyglycerol. Materials investigated include hyperbranched oligomers, hyperbranched polyglycerols containing functional initiator-cores at the focal point, well-defined linear-hyperbranched block copolymers and also negatively charged hyperbranched polyelectrolytes.rnHyperbranched oligoglycerols (DPn = 7 and 14) have been synthesized for the first time. The materials show narrow polydispersity (Mw/Mn ca. 1.45) and a very low content in cyclic homopolymers. 13C NMR evidences the dendritic structure of the oligomers and the DB could be calculated (44% and 52%). These new oligoglycerols were compared with the industrial products obtained by polycondensation which exhibit narrow polydispersity (Mw/Mn<1.3) butrnmultimodal distribution in SEC. Detailed 13C NMR and Maldi-ToF studies reveal the presence of branched units and cyclic compounds. In comparison, the hyperbranched oligoglycerols comprise a very low proportion of cyclic homopolymer which render them very interesting materials for biomedical applications for example.rnThe site isolation of the core moiety in dendritic structure offers intriguing potential with respect to peculiar electro-optical properties. Various initiator-cores (n-alkyl amines, UVabsorbing amines and benzophenone) for the ROMBP of glycidol have been tested. The bisglycidolized amine initiator-cores show the best control over the molecular weight and the molecular weight distribution. The photochemical analyses of the naphthalene containingrnhyperbranched polyglycerols show a slight red shift, a pronounced hypochromic effect (decrease of the intensity of the band) compared with the parent model compound and the formation of a relative compact structure. The benzophenone containing polymers adopt an open structure in polar solvents. The fluorescence measurements show a clear “dendritic effect” on the fluorescence intensities and the quantum yield of the encapsulated benzophenone.rnA convenient 3-step strategy has been developed for the preparation of well-defined amphiphilic, linear-hyperbranched block copolymers via hypergrafting. The procedure represents a combination of carbanionic polymerization with the alkoxide-based, controlled ring-opening multibranching polymerization of glycidol. Materials consisting of a polystyrene linear block and a hyperbranched polyglycerol block exhibit narrow polydispersity (1.01-1.02rnfor 5.4% to 27% wt. PG and 1.74 for 52% wt. PG) with a high grafting efficiency. The strategy was also extended to materials with a linear polyisoprene block.rnDetailed investigations of the solution properties of the block copolymers with linear polystyrene blocks show that block copolymer micelles are stabilized by the highly branched block. The morphology of the aggregates is depending on the solvent: in chloroform monodisperse spherical shape aggregates and in toluene ellipsoidal aggregates are formed. On graphite these aggregates show interesting features, giving promising potential applications with respect to the presence of a very dense, functional and stable hyperbranched block.rnThe bulk morphology of the linear-hyperbranched block copolymers has been investigated. The materials with a linear polyisoprene block only behave like complex liquids due to the low Tg and the disordered nature of both components. For the materials with polystyrene, only the sample with 27% wt. hyperbranched polyglycerol forms some domains showing lamellae.rnThe preparation of hyperbranched polyelectrolytes was achieved by post-modification of the hydroxyl groups via Michael addition of acrylonitrile, followed by hydrolysis. In aqueous solution materials form large aggregates with size depending on the pH value. After deposition on mica the structures observed by AFM show the coexistence of aggregates andrnunimers. For the low molecular weight sample (PG 520 g·mol-1) extended and highly ordered terrace structures were observed. Materials were also successfully employed for the fabrication of composite organic-inorganic multilayer thin films, using electrostatic layer-bylayer self-assembly coupled with chemical vapor deposition.

Tailoring molecular weight of the conjugated model polymer MEH-PPV and its structure-property relations

In der vorliegenden Arbeit wurden Struktur-Eigenschaftsbeziehungen des konjugierten Modell-Polymers MEH-PPV untersucht. Dazu wurde Fällungs-fraktionierung eingesetzt, um MEH-PPV mit unterschiedlichem Molekulargewicht (Mw) zu erhalten, insbesondere MEH-PPV mit niedrigem Mw, da dieses für optische Wellenleiterbauelemente optimal geeignet ist Wir konnten feststellen, dass die Präparation einer ausreichenden Menge von MEH-PPV mit niedrigem Mw und geringer Mw-Verteilung wesentlich von der geeigneten Wahl des Lösungsmittels und der Temperatur während der Zugabe des Fällungsmittels abhängt. Alternativ dazu wurden UV-induzierte Kettenspaltungseffekte untersucht. Wir folgern aus dem Vergleich beider Vorgehensweisen, dass die Fällungsfraktionierung verglichen mit der UV-Behandlung besser geeignet ist zur Herstellung von MEH-PPV mit spezifischem Mw, da das UV-Licht Kettendefekte längs des Polymerrückgrats erzeugt. 1H NMR and FTIR Spektroskopie wurden zur Untersuchung dieser Kettendefekte herangezogen. Wir konnten außerdem beobachten, dass die Wellenlängen der Absorptionsmaxima der MEH-PPV Fraktionen mit der Kettenlänge zunehmen bis die Zahl der Wiederholeinheiten n  110 erreicht ist. Dieser Wert ist signifikant größer als früher berichtet. rnOptische Eigenschaften von MEH-PPV Wellenleitern wurden untersucht und es konnte gezeigt werden, dass sich die optischen Konstanten ausgezeichnet reproduzieren lassen. Wir haben die Einflüsse der Lösungsmittel und Temperatur beim Spincoaten auf Schichtdicke, Oberflächenrauigkeit, Brechungsindex, Doppelbrechung und Wellenleiter-Dämpfungsverlust untersucht. Wir fanden, dass mit der Erhöhung der Siedetemperatur der Lösungsmittel die Schichtdicke und die Rauigkeit kleiner werden, während Brechungsindex, Doppelbrechung sowie Wellenleiter-Dämpfungsverluste zunahmen. Wir schließen daraus, dass hohe Siedetemperaturen der Lösungsmittel niedrige Verdampfungsraten erzeugen, was die Aggregatbildung während des Spincoatings begünstigt. Hingegen bewirkt eine erhöhte Temperatur während der Schichtpräparation eine Erhöhung von Schichtdicke und Rauhigkeit. Jedoch nehmen Brechungsindex und der Doppelbrechung dabei ab.rn Für die Schichtpräparation auf Glassubstraten und Quarzglas-Fasern kam das Dip-Coating Verfahren zum Einsatz. Die Schichtdicke der Filme hängt ab von Konzentration der Lösung, Transfergeschwindigkeit und Immersionszeit. Mit Tauchbeschichtung haben wir Schichten von MEH-PPV auf Flaschen-Mikroresonatoren aufgebracht zur Untersuchung von rein-optischen Schaltprozessen. Dieses Verfahren erweist sich insbesondere für MEH-PPV mit niedrigem Mw als vielversprechend für die rein-optische Signalverarbeitung mit großer Bandbreite.rn Zusätzlich wurde auch die Morphologie dünner Schichten aus anderen PPV-Derivaten mit Hilfe von FTIR Spektroskopie untersucht. Wir konnten herausfinden, dass der Alkyl-Substitutionsgrad einen starken Einfluss auf die mittlere Orientierung der Polymerrückgrate in dünnen Filmen hat.rn

Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.

Sustainable improvement of water networks : to achieve best decisions for rehabilitation plans using advanced GIS and statistical techniques

Many of developing countries are facing crisis in water management due to increasing of population, water scarcity, water contaminations and effects of world economic crisis. Water distribution systems in developing countries are facing many challenges of efficient repair and rehabilitation since the information of water network is very limited, which makes the rehabilitation assessment plans very difficult. Sufficient information with high technology in developed countries makes the assessment for rehabilitation easy. Developing countries have many difficulties to assess the water network causing system failure, deterioration of mains and bad water quality in the network due to pipe corrosion and deterioration. The limited information brought into focus the urgent need to develop economical assessment for rehabilitation of water distribution systems adapted to water utilities. Gaza Strip is subject to a first case study, suffering from severe shortage in the water supply and environmental problems and contamination of underground water resources. This research focuses on improvement of water supply network to reduce the water losses in water network based on limited database using techniques of ArcGIS and commercial water network software (WaterCAD). A new approach for rehabilitation water pipes has been presented in Gaza city case study. Integrated rehabilitation assessment model has been developed for rehabilitation water pipes including three components; hydraulic assessment model, Physical assessment model and Structural assessment model. WaterCAD model has been developed with integrated in ArcGIS to produce the hydraulic assessment model for water network. The model have been designed based on pipe condition assessment with 100 score points as a maximum points for pipe condition. As results from this model, we can indicate that 40% of water pipeline have score points less than 50 points and about 10% of total pipes length have less than 30 score points. By using this model, the rehabilitation plans for each region in Gaza city can be achieved based on available budget and condition of pipes. The second case study is Kuala Lumpur Case from semi-developed countries, which has been used to develop an approach to improve the water network under crucial conditions using, advanced statistical and GIS techniques. Kuala Lumpur (KL) has water losses about 40% and high failure rate, which make severe problem. This case can represent cases in South Asia countries. Kuala Lumpur faced big challenges to reduce the water losses in water network during last 5 years. One of these challenges is high deterioration of asbestos cement (AC) pipes. They need to replace more than 6500 km of AC pipes, which need a huge budget to be achieved. Asbestos cement is subject to deterioration due to various chemical processes that either leach out the cement material or penetrate the concrete to form products that weaken the cement matrix. This case presents an approach for geo-statistical model for modelling pipe failures in a water distribution network. Database of Syabas Company (Kuala Lumpur water company) has been used in developing the model. The statistical models have been calibrated, verified and used to predict failures for both networks and individual pipes. The mathematical formulation developed for failure frequency in Kuala Lumpur was based on different pipeline characteristics, reflecting several factors such as pipe diameter, length, pressure and failure history. Generalized linear model have been applied to predict pipe failures based on District Meter Zone (DMZ) and individual pipe levels. Based on Kuala Lumpur case study, several outputs and implications have been achieved. Correlations between spatial and temporal intervals of pipe failures also have been done using ArcGIS software. Water Pipe Assessment Model (WPAM) has been developed using the analysis of historical pipe failure in Kuala Lumpur which prioritizing the pipe rehabilitation candidates based on ranking system. Frankfurt Water Network in Germany is the third main case study. This case makes an overview for Survival analysis and neural network methods used in water network. Rehabilitation strategies of water pipes have been developed for Frankfurt water network in cooperation with Mainova (Frankfurt Water Company). This thesis also presents a methodology of technical condition assessment of plastic pipes based on simple analysis. This thesis aims to make contribution to improve the prediction of pipe failures in water networks using Geographic Information System (GIS) and Decision Support System (DSS). The output from the technical condition assessment model can be used to estimate future budget needs for rehabilitation and to define pipes with high priority for replacement based on poor condition. rn

Synthese von grenzflächenaktiven Monomeren zur Herstellung von funktionalen Metall-Chalkogenid,Polymer-Hybridnanopartikeln

In dieser Arbeit wurde gezeigt, wie oberflächenfunktionalisierte Polystyrolnanopartikel zur Herstellung von Metallchalkogenid/Polymer-Hybridnanopartikeln eingesetzt werden können. Dazu wurden zunächst phosphonsäure- und phosphorsäurefunktionalisierte Surfmere synthetisiert, die anschließend bei der Miniemulsionspolymerisation von Styrol verwendet wurden. Die Surfmere dienten dabei zugleich zur Stabilisierung und als Comonomer. Die oberflächenfunktionalisierten Polystyrolnanopartikel wurden anschließend als Trägerpartikel für die Kristallisation von Metalloxiden eingesetzt. Dabei wurden Metalloxid/Polymer-Hybridnanopartikel mit einer „himbeerartigen“ Morphologie erhalten. Um die vielseitige Modifizierbarkeit der phosphonat- und phosphat¬funktionalisierten Polystyrolpartikel zu demonstrieren, wurden Cer-, Eisen- sowie Zinkoxid auf der Partikeloberfläche kristallisiert. Dazu wurden sowohl wässrige als auch alkoholische Metalloxid-Präkursorlösungen eingesetzt. Die synthetisierten Metall¬oxid/Polymer-Hybridpartikel wurden detailliert mit REM, TEM und PXRD analysiert. Die Untersuchung des Kristallisationsmechanismus hatte erwiesen, dass die komplexierten Metallkationen auf der Partikeloberfläche als Nukleationszentren wirkten und die Zutropfrate des Fällungsreagenz entscheidend für die Oberflächenkristallisation ist. Durch Mischungsexperimente von Metalloxidnanopartikeln und den oberflächen¬funktionalisierten Polymerpartikeln konnte die Hybridpartikelbildung über Hetero¬koagulation ausgeschlossen werden. Außerdem wurde festgestellt, dass die Polarität der funktionellen Gruppe über die Stärke der Komplexierung der Metalloxid-Präkursor bestimmt. Darüber hinaus wurde ein Modell zur Erklärung der kolloidalen Stabilisierung der Metalloxid/Polymer-Hybridsysteme aufgestellt und ein Zusammenhang zwischen dem gemessenen Zeta-Potential und der Oberflächenbedeckung der Polymerpartikel durch Metalloxid gefunden. Mit der Methode der Oberflächenkristallisation konnten frühe Stadien der Nukleation auf der Partikeloberfläche fixiert werden. Weiterhin wurden die individuellen physikalisch-chemischen Eigenschaften der hergestellten Metall¬oxid/Polymer-Hybridnano¬partikel untersucht. Dabei zeigten die CeO2/Polymer-Hybridpartikel eine hohe katalytische Aktivität bezüglich der photokatalytischen Oxidation von Rhodamin B, die als Modellreaktion durchgeführt wurde. Des Weiteren wurde die Magnetisierung der Magnetit/Polymer-Hybridpartikel gemessen. Die Fe3O4-Hybrid¬partikelsysteme wiesen eine vergleichbare Sättigungsmagnetisierung auf. Die Zinkoxid/Polymer-Hybridsysteme zeigten eine starke Lumineszenz im sichtbaren Bereich bei Anregung mit UV-Licht. Die Metalloxid/Polymer-Hybridpartikel, die mit den phosphonat- oder phosphatfunktion¬alisierten Polystyrolpartikeln hergestellt wurden, zeigten keine signifikanten Unterschiede in ihren physikochemischen Eigenschaften. Im Allgemeinen lässt sich schlussfolgern, dass sowohl Phosphonat- als auch Phosphatgruppen gleichermaßen für die Oberflächenkristallisation von Metalloxiden geeignet sind. Die Zink¬oxid/Polymer-Hybridsysteme stellen eine Ausnahme dar. Die Verwendung der phosphonat¬funktionalisierten Polystyrolpartikel führte zur Entstehung einer Zinkhydroxidphase, die neben der Zinkoxidphase gebildet wurde. Aufgrund dessen zeigten die ZnO/RPO3H2-Hybridpartikel eine geringere Lumineszenz im sichtbaren Bereich als die ZnO/RPO4H2-Hybridsysteme.rnDie Erkenntnisse, die bei der Oberflächenkristallisation von Metalloxiden gewonnen wurden, konnten erfolgreich auf Cadmiumsulfid übertragen werden. Dabei konnte Cadmiumsulfid auf der Oberfläche von phosphonatfunktionalisierten Polystyrolpartikeln kristallisiert werden. Mit Hilfe des RPO3H2-Surfmers konnten phosphonatfunktion¬alisierte Polystyrolpartikel mit superparamagnetischem Kern synthetisiert werden, die zur Herstellung von multifunktionalen CdS/Polymer-Hybridpartikeln mit Magnetitkern verwendet wurden. Die Kristallphase und die Oberflächenbedeckung der multi¬funktionalen Hybridsysteme wurden mit den CdS/Polymer-Hybridsystemen ohne magnetischen Kern verglichen. Dabei konnte nachgewiesen werden, dass in beiden Fällen Cadmiumsulfid in der Greenockit-Modifikation gebildet wurde. Die multifunktionalen CdS/Polymer-Hybridpartikel mit superparamagnetischem Kern konnten sowohl mit einem optischen als auch einem magnetischen Stimulus angeregt werden.rnrn

Optische Mikroskopie an elektrostatisch stabilisierten kolloidalen Suspensionen unter dem Einfluss geladener Wände - ausgewählte Gleichgewichts- und Nichtgleichgewichtsphänomene

Das Verhalten kolloidaler Suspensionen unter räumlich beschränkter Geometrie ist von großer Bedeutung für die statistische Physik wie auch für die Technologie. Von speziellem Interesse sind Modellsysteme geladener kolloidaler Sphären aufgrund ihrer langreichweitigen und veränderbaren Wechselwirkungen. In dieser Arbeit wurde ein experimenteller Aufbau für die optische mikroskopische Untersuchung solcher, zwischen ebenen Wänden beschränkter Systeme realisiert. Anhand von Piezo-Aktuatoren kann die Zellgeometrie flexibel und präzise eingestellt werden. Unter Verwendung eines Pumpkreislaufs mit einer Ionentauschersäule können kolloidale Suspensionen unter stark entsalzten Bedingungen effizient präpariert werden. Anhand dieses Aufbaus wurde zunächst das Gleichgewichtsphasendiagramm monodisperser geladener kolloidaler Sphären zwischen parallelen Wänden untersucht. Es wurden quantitative Resultate für den Grenzfall starker Entsalzung erzielt, welche mit theoretischen Grundzustandsvorhersagen übereinstimmen. In Doppellagensystemen konnte die Existenz transienter kolloidaler Moiré-Rotationsmuster demonstriert werden, welche besondere zweidimensionale Kristallstrukturen mit komplexer Basis darstellen. Es wurden ferner Nichtgleichgewichtsphänomene untersucht, welche durch Gradienten von lokal freigesetzten Elektrolyten verursacht werden. Durch hauptsächlich diffusioosmotischen Partikeltransport entlang einer einzelnen geladenen Substratoberfläche konnten die Bildung kristalliner Ordnung sowie komplexe, selbstorganisierte Bewegungszustände in einem verdünnten kolloidalen Monolagenfluid bei kleinen Reynolds-Zahlen induziert werden. Interessante Perspektiven für die zukünftige Verwendung des experimentellen Aufbaus ergeben sich aus Beobachtungen verschiedener weiterer Phänomene.

Predictability in Social Science, The statistical mechanics approach.

The subject of this work concerns the study of the immigration phenomenon, with emphasis on the aspects related to the integration of an immigrant population in a hosting one. Aim of this work is to show the forecasting ability of a recent finding where the behavior of integration quantifiers was analyzed and investigated with a mathematical model of statistical physics origins (a generalization of the monomer dimer model). After providing a detailed literature review of the model, we show that not only such a model is able to identify the social mechanism that drives a particular integration process, but it also provides correct forecast. The research reported here proves that the proposed model of integration and its forecast framework are simple and effective tools to reduce uncertainties about how integration phenomena emerge and how they are likely to develop in response to increased migration levels in the future.

Aerosol-cloud interactions studied with a chemistry-climate model

This study aims at a comprehensive understanding of the effects of aerosol-cloud interactions and their effects on cloud properties and climate using the chemistry-climate model EMAC. In this study, CCN activation is regarded as the dominant driver in aerosol-cloud feedback loops in warm clouds. The CCN activation is calculated prognostically using two different cloud droplet nucleation parameterizations, the STN and HYB CDN schemes. Both CDN schemes account for size and chemistry effects on the droplet formation based on the same aerosol properties. The calculation of the solute effect (hygroscopicity) is the main difference between the CDN schemes. The kappa-method is for the first time incorporated into Abdul-Razzak and Ghan activation scheme (ARG) to calculate hygroscopicity and critical supersaturation of aerosols (HYB), and the performance of the modied scheme is compared with the osmotic coefficient model (STN), which is the standard in the ARG scheme. Reference simulations (REF) with the prescribed cloud droplet number concentration have also been carried out in order to understand the effects of aerosol-cloud feedbacks. In addition, since the calculated cloud coverage is an important determinant of cloud radiative effects and is influencing the nucleation process two cloud cover parameterizations (i.e., a relative humidity threshold; RH-CLC and a statistical cloud cover scheme; ST-CLC) have been examined together with the CDN schemes, and their effects on the simulated cloud properties and relevant climate parameters have been investigated. The distinct cloud droplet spectra show strong sensitivity to aerosol composition effects on cloud droplet formation in all particle sizes, especially for the Aitken mode. As Aitken particles are the major component of the total aerosol number concentration and CCN, and are most sensitive to aerosol chemical composition effect (solute effect) on droplet formation, the activation of Aitken particles strongly contribute to total cloud droplet formation and thereby providing different cloud droplet spectra. These different spectra influence cloud structure, cloud properties, and climate, and show regionally varying sensitivity to meteorological and geographical condition as well as the spatiotemporal aerosol properties (i.e., particle size, number, and composition). The changes responding to different CDN schemes are more pronounced at lower altitudes than higher altitudes. Among regions, the subarctic regions show the strongest changes, as the lower surface temperature amplifies the effects of the activated aerosols; in contrast, the Sahara desert, where is an extremely dry area, is less influenced by changes in CCN number concentration. The aerosol-cloud coupling effects have been examined by comparing the prognostic CDN simulations (STN, HYB) with the reference simulation (REF). Most pronounced effects are found in the cloud droplet number concentration, cloud water distribution, and cloud radiative effect. The aerosol-cloud coupling generally increases cloud droplet number concentration; this decreases the efficiency of the formation of weak stratiform precipitation, and increases the cloud water loading. These large-scale changes lead to larger cloud cover and longer cloud lifetime, and contribute to high optical thickness and strong cloud cooling effects. This cools the Earth's surface, increases atmospheric stability, and reduces convective activity. These changes corresponding to aerosol-cloud feedbacks are also differently simulated depending on the cloud cover scheme. The ST-CLC scheme is more sensitive to aerosol-cloud coupling, since this scheme uses a tighter linkage of local dynamics and cloud water distributions in cloud formation process than the RH-CLC scheme. For the calculated total cloud cover, the RH-CLC scheme simulates relatively similar pattern to observations than the ST-CLC scheme does, but the overall properties (e.g., total cloud cover, cloud water content) in the RH simulations are overestimated, particularly over ocean. This is mainly originated from the difference in simulated skewness in each scheme: the RH simulations calculate negatively skewed distributions of cloud cover and relevant cloud water, which is similar to that of the observations, while the ST simulations yield positively skewed distributions resulting in lower mean values than the RH-CLC scheme does. The underestimation of total cloud cover over ocean, particularly over the intertropical convergence zone (ITCZ) relates to systematic defficiency of the prognostic calculation of skewness in the current set-ups of the ST-CLC scheme.rnOverall, the current EMAC model set-ups perform better over continents for all combinations of the cloud droplet nucleation and cloud cover schemes. To consider aerosol-cloud feedbacks, the HYB scheme is a better method for predicting cloud and climate parameters for both cloud cover schemes than the STN scheme. The RH-CLC scheme offers a better simulation of total cloud cover and the relevant parameters with the HYB scheme and single-moment microphysics (REF) than the ST-CLC does, but is not very sensitive to aerosol-cloud interactions.

Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

Efficiency limits for silicon/perovskite tandem solar cells: a theoretical model

The primary goal of this work is related to the extension of an analytic electro-optical model. It will be used to describe single-junction crystalline silicon solar cells and a silicon/perovskite tandem solar cell in the presence of light-trapping in order to calculate efficiency limits for such a device. In particular, our tandem system is composed by crystalline silicon and a perovskite structure material: metilammoniumleadtriiodide (MALI). Perovskite are among the most convenient materials for photovoltaics thanks to their reduced cost and increasing efficiencies. Solar cell efficiencies of devices using these materials increased from 3.8% in 2009 to a certified 20.1% in 2014 making this the fastest-advancing solar technology to date. Moreover, texturization increases the amount of light which can be absorbed through an active layer. Using Green’s formalism it is possible to calculate the photogeneration rate of a single-layer structure with Lambertian light trapping analytically. In this work we go further: we study the optical coupling between the two cells in our tandem system in order to calculate the photogeneration rate of the whole structure. We also model the electronic part of such a device by considering the perovskite top cell as an ideal diode and solving the drift-diffusion equation with appropriate boundary conditions for the silicon bottom cell. We have a four terminal structure, so our tandem system is totally unconstrained. Then we calculate the efficiency limits of our tandem including several recombination mechanisms such as Auger, SRH and surface recombination. We focus also on the dependence of the results on the band gap of the perovskite and we calculare an optimal band gap to optimize the tandem efficiency. The whole work has been continuously supported by a numerical validation of out analytic model against Silvaco ATLAS which solves drift-diffusion equations using a finite elements method. Our goal is to develop a simpler and cheaper, but accurate model to study such devices.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.

Statistical shape modeling of pathological scoliotic vertebrae: A comparative analysis

Statistical shape models (SSMs) have been used widely as a basis for segmenting and interpreting complex anatomical structures. The robustness of these models are sensitive to the registration procedures, i.e., establishment of a dense correspondence across a training data set. In this work, two SSMs based on the same training data set of scoliotic vertebrae, and registration procedures were compared. The first model was constructed based on the original binary masks without applying any image pre- and post-processing, and the second was obtained by means of a feature preserving smoothing method applied to the original training data set, followed by a standard rasterization algorithm. The accuracies of the correspondences were assessed quantitatively by means of the maximum of the mean minimum distance (MMMD) and Hausdorf distance (H(D)). Anatomical validity of the models were quantified by means of three different criteria, i.e., compactness, specificity, and model generalization ability. The objective of this study was to compare quasi-identical models based on standard metrics. Preliminary results suggest that the MMMD distance and eigenvalues are not sensitive metrics for evaluating the performance and robustness of SSMs.

Single fluoroscopic image based 2D/3D reconstruction of a scaled, patient-specific vertebral model

Purpose Accurate three-dimensional (3D) models of lumbar vertebrae can enable image-based 3D kinematic analysis. The common approach to derive 3D models is by direct segmentation of CT or MRI datasets. However, these have the disadvantages that they are expensive, timeconsuming and/or induce high-radiation doses to the patient. In this study, we present a technique to automatically reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image. Methods Our technique is based on a hybrid 2D/3D deformable registration strategy combining a landmark-to-ray registration with a statistical shape model-based 2D/3D reconstruction scheme. Fig. 1 shows different stages of the reconstruction process. Four cadaveric lumbar spine segments (total twelve lumbar vertebrae) were used to validate the technique. To evaluate the reconstruction accuracy, the surface models reconstructed from the lateral fluoroscopic images were compared to the associated ground truth data derived from a 3D CT-scan reconstruction technique. For each case, a surface-based matching was first used to recover the scale and the rigid transformation between the reconstructed surface model Results Our technique could successfully reconstruct 3D surface models of all twelve vertebrae. After recovering the scale and the rigid transformation between the reconstructed surface models and the ground truth models, the average error of the 2D/3D surface model reconstruction over the twelve lumbar vertebrae was found to be 1.0 mm. The errors of reconstructing surface models of all twelve vertebrae are shown in Fig. 2. It was found that the mean errors of the reconstructed surface models in comparison to their associated ground truths after iterative scaled rigid registrations ranged from 0.7 mm to 1.3 mm and the rootmean squared (RMS) errors ranged from 1.0 mm to 1.7 mm. The average mean reconstruction error was found to be 1.0 mm. Conclusion An accurate, scaled 3D reconstruction of the lumbar vertebra can be obtained from a single lateral fluoroscopic image using a statistical shape model based 2D/3D reconstruction technique. Future work will focus on applying the reconstructed model for 3D kinematic analysis of lumbar vertebrae, an extension of our previously-reported imagebased kinematic analysis. The developed method also has potential applications in surgical planning and navigation.