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During the last few decades, the rapid separation of the Small Aral Sea from the isolated basin has changed its hydrological and ecological conditions tremendously. In the present study, we developed and validated the hybrid model for the Syr Darya River basin based on a combination of state-of-the-art hydrological and machine learning models. Climate change impact on freshwater inflow into the Small Aral Sea for the projection period 2007–2099 has been quantified based on the developed hybrid model and bias corrected and downscaled meteorological projections simulated by four General Circulation Models (GCM) for each of three Representative Concentration Pathway scenarios (RCP). The developed hybrid model reliably simulates freshwater inflow for the historical period with a Nash–Sutcliffe efficiency of 0.72 and a Kling–Gupta efficiency of 0.77. Results of the climate change impact assessment showed that the freshwater inflow projections produced by different GCMs are misleading by providing contradictory results for the projection period. However, we identified that the relative runoff changes are expected to be more pronounced in the case of more aggressive RCP scenarios. The simulated projections of freshwater inflow provide a basis for further assessment of climate change impacts on hydrological and ecological conditions of the Small Aral Sea in the 21st Century.
Cyber-physical systems achieve sophisticated system behavior exploring the tight interconnection of physical coupling present in classical engineering systems and information technology based coupling. A particular challenging case are systems where these cyber-physical systems are formed ad hoc according to the specific local topology, the available networking capabilities, and the goals and constraints of the subsystems captured by the information processing part. In this paper we present a formalism that permits to model the sketched class of cyber-physical systems. The ad hoc formation of tightly coupled subsystems of arbitrary size are specified using a UML-based graph transformation system approach. Differential equations are employed to define the resulting tightly coupled behavior. Together, both form hybrid graph transformation systems where the graph transformation rules define the discrete steps where the topology or modes may change, while the differential equations capture the continuous behavior in between such discrete changes. In addition, we demonstrate that automated analysis techniques known for timed graph transformation systems for inductive invariants can be extended to also cover the hybrid case for an expressive case of hybrid models where the formed tightly coupled subsystems are restricted to smaller local networks.
In this work, an approach of paleoclimate reconstruction for tropical East Africa is presented. After giving a short summary of modern climate conditions in the tropics and the East African climate peculiarity, the potential of reconstructing climate from paleolake sediments is discussed. As demonstrated, the hydrologic sensitivity of high-elevated closed-basin lakes in the Central Kenya Rift yields valuable guaranties for the establishment of long-term climate records. Temporal fluctuations of the limnological characteristics saved in the lake sediments are used to define variations in the Quaternary climate history. Based on diatom analyses in radiocarbon- and 40Ar/39Ar-dated sediments, a chronology of paleoecologic fluctuations is developed for the Central Kenya Rift -lakes Nakuru, Elmenteita and Naivasha. At least during the penultimate interglacial (around 140 to 60 kyr BP) and during the last interglacial (around 12 to 4 kyr BP), these lakes experienced several transgression-regression cycles on time intervals of about 11,000 years. Additionally, a long-term trend of lake evolution is found suggesting the general succession from deep freshwater lakes towards more saline waters during the last million years. Using ecologic transfer functions and a simple lake-balance model, the observed paleohydrologic fluctuations are linked to potential precipitation-evaporation changes in the lake basins. Though also tectonic influences on the drainage pattern and the effect of varied seepage are investigated, it can be shown that already a small increase in precipitation of about 30±10 % may have affected the hydrologic budget of the intra-rift lakes within the reconstructed range. The findings of this study help to assess the natural climate variability of East Africa. They furthermore reflect the sensitivity of the Central Kenya Rift -lakes to fluctuations of large-scale climate parameters, such as solar radiation and sea-surface temperatures of the Indian Ocean.
One of the most striking features of ecological systems is their ability to undergo sudden outbreaks in the population numbers of one or a small number of species. The similarity of outbreak characteristics, which is exhibited in totally different and unrelated (ecological) systems naturally leads to the question whether there are universal mechanisms underlying outbreak dynamics in Ecology. It will be shown into two case studies (dynamics of phytoplankton blooms under variable nutrients supply and spread of epidemics in networks of cities) that one explanation for the regular recurrence of outbreaks stems from the interaction of the natural systems with periodical variations of their environment. Natural aquatic systems like lakes offer very good examples for the annual recurrence of outbreaks in Ecology. The idea whether chaos is responsible for the irregular heights of outbreaks is central in the domain of ecological modeling. This question is investigated in the context of phytoplankton blooms. The dynamics of epidemics in networks of cities is a problem which offers many ecological and theoretical aspects. The coupling between the cities is introduced through their sizes and gives rise to a weighted network which topology is generated from the distribution of the city sizes. We examine the dynamics in this network and classified the different possible regimes. It could be shown that a single epidemiological model can be reduced to a one-dimensional map. We analyze in this context the dynamics in networks of weighted maps. The coupling is a saturation function which possess a parameter which can be interpreted as an effective temperature for the network. This parameter allows to vary continously the network topology from global coupling to hierarchical network. We perform bifurcation analysis of the global dynamics and succeed to construct an effective theory explaining very well the behavior of the system.
Forage availability has been suggested as one driver of the observed decline in honey bees. However, little is known about the effects of its spatiotemporal variation on colony success. We present a modeling framework for assessing honey bee colony viability in cropping systems. Based on two real farmland structures, we developed a landscape generator to design cropping systems varying in crop species identity, diversity, and relative abundance. The landscape scenarios generated were evaluated using the existing honey bee colony model BEEHAVE, which links foraging to in-hive dynamics. We thereby explored how different cropping systems determine spatiotemporal forage availability and, in turn, honey bee colony viability (e.g., time to extinction, TTE) and resilience (indicated by, e.g., brood mortality). To assess overall colony viability, we developed metrics,P(H)andP(P,)which quantified how much nectar and pollen provided by a cropping system per year was converted into a colony's adult worker population. Both crop species identity and diversity determined the temporal continuity in nectar and pollen supply and thus colony viability. Overall farmland structure and relative crop abundance were less important, but details mattered. For monocultures and for four-crop species systems composed of cereals, oilseed rape, maize, and sunflower,P(H)andP(P)were below the viability threshold. Such cropping systems showed frequent, badly timed, and prolonged forage gaps leading to detrimental cascading effects on life stages and in-hive work force, which critically reduced colony resilience. Four-crop systems composed of rye-grass-dandelion pasture, trefoil-grass pasture, sunflower, and phacelia ensured continuous nectar and pollen supply resulting in TTE > 5 yr, andP(H)(269.5 kg) andP(P)(108 kg) being above viability thresholds for 5 yr. Overall, trefoil-grass pasture, oilseed rape, buckwheat, and phacelia improved the temporal continuity in forage supply and colony's viability. Our results are hypothetical as they are obtained from simplified landscape settings, but they nevertheless match empirical observations, in particular the viability threshold. Our framework can be used to assess the effects of cropping systems on honey bee viability and to develop land-use strategies that help maintain pollination services by avoiding prolonged and badly timed forage gaps.
Die Projektierung und Abwicklung sowie die statische und dynamische Analyse von Geschäftsprozessen im Bereich des Verwaltens und Regierens auf kommunaler, Länder- wie auch Bundesebene mit Hilfe von Informations- und Kommunikationstechniken beschäftigen Politiker und Strategen für Informationstechnologie ebenso wie die Öffentlichkeit seit Langem.
Der hieraus entstandene Begriff E-Government wurde in der Folge aus den unterschiedlichsten technischen, politischen und semantischen Blickrichtungen beleuchtet.
Die vorliegende Arbeit konzentriert sich dabei auf zwei Schwerpunktthemen:
• Das erste Schwerpunktthema behandelt den Entwurf eines hierarchischen Architekturmodells, für welches sieben hierarchische Schichten identifiziert werden können. Diese erscheinen notwendig, aber auch hinreichend, um den allgemeinen Fall zu beschreiben.
Den Hintergrund hierfür liefert die langjährige Prozess- und Verwaltungserfahrung als Leiter der EDV-Abteilung der Stadtverwaltung Landshut, eine kreisfreie Stadt mit rund 69.000 Einwohnern im Nordosten von München. Sie steht als Repräsentant für viele Verwaltungsvorgänge in der Bundesrepublik Deutschland und ist dennoch als Analyseobjekt in der Gesamtkomplexität und Prozessquantität überschaubar.
Somit können aus der Analyse sämtlicher Kernabläufe statische und dynamische Strukturen extrahiert und abstrakt modelliert werden.
Die Schwerpunkte liegen in der Darstellung der vorhandenen Bedienabläufe in einer Kommune. Die Transformation der Bedienanforderung in einem hierarchischen System, die Darstellung der Kontroll- und der Operationszustände in allen Schichten wie auch die Strategie der Fehlererkennung und Fehlerbehebung schaffen eine transparente Basis für umfassende Restrukturierungen und Optimierungen.
Für die Modellierung wurde FMC-eCS eingesetzt, eine am Hasso-Plattner-Institut für Softwaresystemtechnik GmbH (HPI) im Fachgebiet Kommunikationssysteme entwickelte Methodik zur Modellierung zustandsdiskreter Systeme unter Berücksichtigung möglicher Inkonsistenzen (Betreuer: Prof. Dr.-Ing. Werner Zorn [ZW07a, ZW07b]).
• Das zweite Schwerpunktthema widmet sich der quantitativen Modellierung und Optimierung von E-Government-Bediensystemen, welche am Beispiel des Bürgerbüros der Stadt Landshut im Zeitraum 2008 bis 2015 durchgeführt wurden. Dies erfolgt auf Basis einer kontinuierlichen Betriebsdatenerfassung mit aufwendiger Vorverarbeitung zur Extrahierung mathematisch beschreibbarer Wahrscheinlichkeitsverteilungen.
Der hieraus entwickelte Dienstplan wurde hinsichtlich der erzielbaren Optimierungen im dauerhaften Echteinsatz verifiziert.
[ZW07a] Zorn, Werner: «FMC-QE A New Approach in Quantitative Modeling», Vortrag anlässlich: MSV'07- The 2007 International Conference on Modeling, Simulation and Visualization Methods WorldComp2007, Las Vegas, 28.6.2007.
[ZW07b] Zorn, Werner: «FMC-QE, A New Approach in Quantitative Modeling», Veröffentlichung, Hasso-Plattner-Institut für Softwaresystemtechnik an der Universität Potsdam, 28.6.2007.
Im Zuge der Covid-19 Pandemie werden zwei Werte täglich diskutiert: Die zuletzt gemeldete Zahl der neu Infizierten und die sogenannte Reproduktionsrate. Sie gibt wieder, wie viele weitere Menschen ein an Corona erkranktes Individuum im Durchschnitt ansteckt. Für die Schätzung dieses Wertes gibt es viele Möglichkeiten - auch das Robert Koch-Institut gibt in seinem täglichen Situationsbericht stets zwei R-Werte an: Einen 4-Tage-R-Wert und einen weniger schwankenden 7-Tage-R-Wert. Diese Arbeit soll eine weitere Möglichkeit vorstellen, einige Aspekte der Pandemie zu modellieren und die Reproduktionsrate zu schätzen.
In der ersten Hälfte der Arbeit werden die mathematischen Grundlagen vorgestellt, die man für die Modellierung benötigt. Hierbei wird davon ausgegangen, dass der Leser bereits ein Basisverständnis von stochastischen Prozessen hat. Im Abschnitt Grundlagen werden Verzweigungsprozesse mit einigen Beispielen eingeführt und die Ergebnisse aus diesem Themengebiet, die für diese Arbeit wichtig sind, präsentiert. Dabei gehen wir zuerst auf einfache Verzweigungsprozesse ein und erweitern diese dann auf Verzweigungsprozesse mit mehreren Typen. Um die Notation zu erleichtern, beschränken wir uns auf zwei Typen. Das Prinzip lässt sich aber auf eine beliebige Anzahl von Typen erweitern.
Vor allem soll die Wichtigkeit des Parameters λ herausgestellt werden. Dieser Wert kann als durchschnittliche Zahl von Nachfahren eines Individuums interpretiert werden und bestimmt die Dynamik des Prozesses über einen längeren Zeitraum. In der Anwendung auf die Pandemie hat der Parameter λ die gleiche Rolle wie die Reproduktionsrate R.
In der zweiten Hälfte dieser Arbeit stellen wir eine Anwendung der Theorie über Multitype Verzweigungsprozesse vor. Professor Yanev und seine Mitarbeiter modellieren in ihrer Veröffentlichung Branching stochastic processes as models of Covid-19 epidemic development die Ausbreitung des Corona Virus' über einen Verzweigungsprozess mit zwei Typen. Wir werden dieses Modell diskutieren und Schätzer daraus ableiten: Ziel ist es, die Reproduktionsrate zu ermitteln. Außerdem analysieren wir die Möglichkeiten, die Dunkelziffer (die Zahl nicht gemeldeter Krankheitsfälle) zu schätzen. Wir wenden die Schätzer auf die Zahlen von Deutschland an und werten diese schließlich aus.
A huge number of applications require coherent radiation in the visible spectral range. Since diode lasers are very compact and efficient light sources, there exists a great interest to cover these applications with diode laser emission. Despite modern band gap engineering not all wavelengths can be accessed with diode laser radiation. Especially in the visible spectral range between 480 nm and 630 nm no emission from diode lasers is available, yet. Nonlinear frequency conversion of near-infrared radiation is a common way to generate coherent emission in the visible spectral range. However, radiation with extraordinary spatial temporal and spectral quality is required to pump frequency conversion. Broad area (BA) diode lasers are reliable high power light sources in the near-infrared spectral range. They belong to the most efficient coherent light sources with electro-optical efficiencies of more than 70%. Standard BA lasers are not suitable as pump lasers for frequency conversion because of their poor beam quality and spectral properties. For this purpose, tapered lasers and diode lasers with Bragg gratings are utilized. However, these new diode laser structures demand for additional manufacturing and assembling steps that makes their processing challenging and expensive. An alternative to BA diode lasers is the stripe-array architecture. The emitting area of a stripe-array diode laser is comparable to a BA device and the manufacturing of these arrays requires only one additional process step. Such a stripe-array consists of several narrow striped emitters realized with close proximity. Due to the overlap of the fields of neighboring emitters or the presence of leaky waves, a strong coupling between the emitters exists. As a consequence, the emission of such an array is characterized by a so called supermode. However, for the free running stripe-array mode competition between several supermodes occurs because of the lack of wavelength stabilization. This leads to power fluctuations, spectral instabilities and poor beam quality. Thus, it was necessary to study the emission properties of those stripe-arrays to find new concepts to realize an external synchronization of the emitters. The aim was to achieve stable longitudinal and transversal single mode operation with high output powers giving a brightness sufficient for efficient nonlinear frequency conversion. For this purpose a comprehensive analysis of the stripe-array devices was done here. The physical effects that are the origin of the emission characteristics were investigated theoretically and experimentally. In this context numerical models could be verified and extended. A good agreement between simulation and experiment was observed. One way to stabilize a specific supermode of an array is to operate it in an external cavity. Based on mathematical simulations and experimental work, it was possible to design novel external cavities to select a specific supermode and stabilize all emitters of the array at the same wavelength. This resulted in stable emission with 1 W output power, a narrow bandwidth in the range of 2 MHz and a very good beam quality with M²<1.5. This is a new level of brightness and brilliance compared to other BA and stripe-array diode laser systems. The emission from this external cavity diode laser (ECDL) satisfied the requirements for nonlinear frequency conversion. Furthermore, a huge improvement to existing concepts was made. In the next step newly available periodically poled crystals were used for second harmonic generation (SHG) in single pass setups. With the stripe-array ECDL as pump source, more than 140 mW of coherent radiation at 488 nm could be generated with a very high opto-optical conversion efficiency. The generated blue light had very good transversal and longitudinal properties and could be used to generate biphotons by parametric down-conversion. This was feasible because of the improvement made with the infrared stripe-array diode lasers due to the development of new physical concepts.
A water quality model for shallow river-lake systems and its application in river basin management
(2007)
This work documents the development and application of a new model for simulating mass transport and turnover in rivers and shallow lakes. The simulation tool called 'TRAM' is intended to complement mesoscale eco-hydrological catchment models in studies on river basin management. TRAM aims at describing the water quality of individual water bodies, using problem- and scale-adequate approaches for representing their hydrological and ecological characteristics. The need for such flexible water quality analysis and prediction tools is expected to further increase during the implementation of the European Water Framework Directive (WFD) as well as in the context of climate change research. The developed simulation tool consists of a transport and a reaction module with the latter being highly flexible with respect to the description of turnover processes in the aquatic environment. Therefore, simulation approaches of different complexity can easily be tested and model formulations can be chosen in consideration of the problem at hand, knowledge of process functioning, and data availability. Consequently, TRAM is suitable for both heavily simplified engineering applications as well as scientific ecosystem studies involving a large number of state variables, interactions, and boundary conditions. TRAM can easily be linked to catchment models off-line and it requires the use of external hydrodynamic simulation software. Parametrization of the model and visualization of simulation results are facilitated by the use of geographical information systems as well as specific pre- and post-processors. TRAM has been developed within the research project 'Management Options for the Havel River Basin' funded by the German Ministry of Education and Research. The project focused on the analysis of different options for reducing the nutrient load of surface waters. It was intended to support the implementation of the WFD in the lowland catchment of the Havel River located in North-East Germany. Within the above-mentioned study TRAM was applied with two goals in mind. In a first step, the model was used for identifying the magnitude as well as spatial and temporal patterns of nitrogen retention and sediment phosphorus release in a 100~km stretch of the highly eutrophic Lower Havel River. From the system analysis, strongly simplified conceptual approaches for modeling N-retention and P-remobilization in the studied river-lake system were obtained. In a second step, the impact of reduced external nutrient loading on the nitrogen and phosphorus concentrations of the Havel River was simulated (scenario analysis) taking into account internal retention/release. The boundary conditions for the scenario analysis such as runoff and nutrient emissions from river basins were computed by project partners using the catchment models SWIM and ArcEGMO-Urban. Based on the output of TRAM, the considered options of emission control could finally be evaluated using a site-specific assessment scale which is compatible with the requirements of the WFD. Uncertainties in the model predictions were also examined. According to simulation results, the target of the WFD -- with respect to total phosphorus concentrations in the Lower Havel River -- could be achieved in the medium-term, if the full potential for reducing point and non-point emissions was tapped. Furthermore, model results suggest that internal phosphorus loading will ease off noticeably until 2015 due to a declining pool of sedimentary mobile phosphate. Mass balance calculations revealed that the lakes of the Lower Havel River are an important nitrogen sink. This natural retention effect contributes significantly to the efforts aimed at reducing the river's nitrogen load. If a sustainable improvement of the river system's water quality is to be achieved, enhanced measures to further reduce the immissions of both phosphorus and nitrogen are required.
Point processes are a common methodology to model sets of events. From earthquakes to social media posts, from the arrival times of neuronal spikes to the timing of crimes, from stock prices to disease spreading -- these phenomena can be reduced to the occurrences of events concentrated in points. Often, these events happen one after the other defining a time--series.
Models of point processes can be used to deepen our understanding of such events and for classification and prediction. Such models include an underlying random process that generates the events. This work uses Bayesian methodology to infer the underlying generative process from observed data. Our contribution is twofold -- we develop new models and new inference methods for these processes.
We propose a model that extends the family of point processes where the occurrence of an event depends on the previous events. This family is known as Hawkes processes. Whereas in most existing models of such processes, past events are assumed to have only an excitatory effect on future events, we focus on the newly developed nonlinear Hawkes process, where past events could have excitatory and inhibitory effects. After defining the model, we present its inference method and apply it to data from different fields, among others, to neuronal activity.
The second model described in the thesis concerns a specific instance of point processes --- the decision process underlying human gaze control. This process results in a series of fixated locations in an image. We developed a new model to describe this process, motivated by the known Exploration--Exploitation dilemma. Alongside the model, we present a Bayesian inference algorithm to infer the model parameters.
Remaining in the realm of human scene viewing, we identify the lack of best practices for Bayesian inference in this field. We survey four popular algorithms and compare their performances for parameter inference in two scan path models.
The novel models and inference algorithms presented in this dissertation enrich the understanding of point process data and allow us to uncover meaningful insights.