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.

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

Hadronic correlation functions with quark-disconnected contributions in lattice QCD

One of the fundamental interactions in the Standard Model of particle physicsrnis the strong force, which can be formulated as a non-abelian gauge theoryrncalled Quantum Chromodynamics (QCD). rnIn the low-energy regime, where the QCD coupling becomes strong and quarksrnand gluons are confined to hadrons, a perturbativernexpansion in the coupling constant is not possible.rnHowever, the introduction of a four-dimensional Euclidean space-timernlattice allows for an textit{ab initio} treatment of QCD and provides arnpowerful tool to study the low-energy dynamics of hadrons.rnSome hadronic matrix elements of interest receive contributionsrnfrom diagrams including quark-disconnected loops, i.e. disconnected quarkrnlines from one lattice point back to the same point. The calculation of suchrnquark loops is computationally very demanding, because it requires knowledge ofrnthe all-to-all propagator. In this thesis we use stochastic sources and arnhopping parameter expansion to estimate such propagators.rnWe apply this technique to study two problems which relay crucially on therncalculation of quark-disconnected diagrams, namely the scalar form factor ofrnthe pion and the hadronic vacuum polarization contribution to the anomalousrnmagnet moment of the muon.rnThe scalar form factor of the pion describes the coupling of a charged pion torna scalar particle. We calculate the connected and the disconnected contributionrnto the scalar form factor for three different momentum transfers. The scalarrnradius of the pion is extracted from the momentum dependence of the form factor.rnThe use ofrnseveral different pion masses and lattice spacings allows for an extrapolationrnto the physical point. The chiral extrapolation is done using chiralrnperturbation theory ($chi$PT). We find that our pion mass dependence of thernscalar radius is consistent with $chi$PT at next-to-leading order.rnAdditionally, we are able to extract the low energy constant $ell_4$ from thernextrapolation, and ourrnresult is in agreement with results from other lattice determinations.rnFurthermore, our result for the scalar pion radius at the physical point isrnconsistent with a value that was extracted from $pipi$-scattering data. rnThe hadronic vacuum polarization (HVP) is the leading-order hadronicrncontribution to the anomalous magnetic moment $a_mu$ of the muon. The HVP canrnbe estimated from the correlation of two vector currents in the time-momentumrnrepresentation. We explicitly calculate the corresponding disconnectedrncontribution to the vector correlator. We find that the disconnectedrncontribution is consistent with zero within its statistical errors. This resultrncan be converted into an upper limit for the maximum contribution of therndisconnected diagram to $a_mu$ by using the expected time-dependence of therncorrelator and comparing it to the corresponding connected contribution. Wernfind the disconnected contribution to be smaller than $approx5%$ of thernconnected one. This value can be used as an estimate for a systematic errorrnthat arises from neglecting the disconnected contribution.rn