@phdthesis{Grum2021,
  author    = {Grum, Marcus},
  title     = {Construction of a concept of neuronal modeling},
  year      = {2021},
  abstract  = {The business problem of having inefficient processes, imprecise process analyses, and simulations as well as non-transparent artificial neuronal network models can be overcome by an easy-to-use modeling concept. With the aim of developing a flexible and efficient approach to modeling, simulating, and optimizing processes, this paper proposes a flexible Concept of Neuronal Modeling (CoNM). The modeling concept, which is described by the modeling language designed and its mathematical formulation and is connected to a technical substantiation, is based on a collection of novel sub-artifacts. As these have been implemented as a computational model, the set of CoNM tools carries out novel kinds of Neuronal Process Modeling (NPM), Neuronal Process Simulations (NPS), and Neuronal Process Optimizations (NPO). The efficacy of the designed artifacts was demonstrated rigorously by means of six experiments and a simulator of real industrial production processes.},
  language  = {en}
}
@phdthesis{Schuette2011,
  author    = {Sch{\"u}tte, Moritz},
  title     = {Evolutionary fingerprints in genome-scale networks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57483},
  school      = {Universit{\"a}t Potsdam},
  year      = {2011},
  abstract  = {Mathematical modeling of biological phenomena has experienced increasing interest since new high-throughput technologies give access to growing amounts of molecular data. These modeling approaches are especially able to test hypotheses which are not yet experimentally accessible or guide an experimental setup. One particular attempt investigates the evolutionary dynamics responsible for today's composition of organisms. Computer simulations either propose an evolutionary mechanism and thus reproduce a recent finding or rebuild an evolutionary process in order to learn about its mechanism. The quest for evolutionary fingerprints in metabolic and gene-coexpression networks is the central topic of this cumulative thesis based on four published articles. An understanding of the actual origin of life will probably remain an insoluble problem. However, one can argue that after a first simple metabolism has evolved, the further evolution of metabolism occurred in parallel with the evolution of the sequences of the catalyzing enzymes. Indications of such a coevolution can be found when correlating the change in sequence between two enzymes with their distance on the metabolic network which is obtained from the KEGG database. We observe that there exists a small but significant correlation primarily on nearest neighbors. This indicates that enzymes catalyzing subsequent reactions tend to be descended from the same precursor. Since this correlation is relatively small one can at least assume that, if new enzymes are no "genetic children" of the previous enzymes, they certainly be descended from any of the already existing ones. Following this hypothesis, we introduce a model of enzyme-pathway coevolution. By iteratively adding enzymes, this model explores the metabolic network in a manner similar to diffusion. With implementation of an Gillespie-like algorithm we are able to introduce a tunable parameter that controls the weight of sequence similarity when choosing a new enzyme. Furthermore, this method also defines a time difference between successive evolutionary innovations in terms of a new enzyme. Overall, these simulations generate putative time-courses of the evolutionary walk on the metabolic network. By a time-series analysis, we find that the acquisition of new enzymes appears in bursts which are pronounced when the influence of the sequence similarity is higher. This behavior strongly resembles punctuated equilibrium which denotes the observation that new species tend to appear in bursts as well rather than in a gradual manner. Thus, our model helps to establish a better understanding of punctuated equilibrium giving a potential description at molecular level. From the time-courses we also extract a tentative order of new enzymes, metabolites, and even organisms. The consistence of this order with previous findings provides evidence for the validity of our approach. While the sequence of a gene is actually subject to mutations, its expression profile might also indirectly change through the evolutionary events in the cellular interplay. Gene coexpression data is simply accessible by microarray experiments and commonly illustrated using coexpression networks where genes are nodes and get linked once they show a significant coexpression. Since the large number of genes makes an illustration of the entire coexpression network difficult, clustering helps to show the network on a metalevel. Various clustering techniques already exist. However, we introduce a novel one which maintains control of the cluster sizes and thus assures proper visual inspection. An application of the method on Arabidopsis thaliana reveals that genes causing a severe phenotype often show a functional uniqueness in their network vicinity. This leads to 20 genes of so far unknown phenotype which are however suggested to be essential for plant growth. Of these, six indeed provoke such a severe phenotype, shown by mutant analysis. By an inspection of the degree distribution of the A.thaliana coexpression network, we identified two characteristics. The distribution deviates from the frequently observed power-law by a sharp truncation which follows after an over-representation of highly connected nodes. For a better understanding, we developed an evolutionary model which mimics the growth of a coexpression network by gene duplication which underlies a strong selection criterion, and slight mutational changes in the expression profile. Despite the simplicity of our assumption, we can reproduce the observed properties in A.thaliana as well as in E.coli and S.cerevisiae. The over-representation of high-degree nodes could be identified with mutually well connected genes of similar functional families: zinc fingers (PF00096), flagella, and ribosomes respectively. In conclusion, these four manuscripts demonstrate the usefulness of mathematical models and statistical tools as a source of new biological insight. While the clustering approach of gene coexpression data leads to the phenotypic characterization of so far unknown genes and thus supports genome annotation, our model approaches offer explanations for observed properties of the coexpression network and furthermore substantiate punctuated equilibrium as an evolutionary process by a deeper understanding of an underlying molecular mechanism.},
  language  = {en}
}
@phdthesis{Zhelavskaya2020,
  author    = {Zhelavskaya, Irina},
  title     = {Modeling of the Plasmasphere Dynamics},
  doi       = {10.25932/publishup-48243},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-482433},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xlii, 256},
  year      = {2020},
  abstract  = {The plasmasphere is a dynamic region of cold, dense plasma surrounding the Earth. Its shape and size are highly susceptible to variations in solar and geomagnetic conditions. Having an accurate model of plasma density in the plasmasphere is important for GNSS navigation and for predicting hazardous effects of radiation in space on spacecraft. The distribution of cold plasma and its dynamic dependence on solar wind and geomagnetic conditions remain, however, poorly quantified. Existing empirical models of plasma density tend to be oversimplified as they are based on statistical averages over static parameters. Understanding the global dynamics of the plasmasphere using observations from space remains a challenge, as existing density measurements are sparse and limited to locations where satellites can provide in-situ observations. In this dissertation, we demonstrate how such sparse electron density measurements can be used to reconstruct the global electron density distribution in the plasmasphere and capture its dynamic dependence on solar wind and geomagnetic conditions. First, we develop an automated algorithm to determine the electron density from in-situ measurements of the electric field on the Van Allen Probes spacecraft. In particular, we design a neural network to infer the upper hybrid resonance frequency from the dynamic spectrograms obtained with the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrumentation suite, which is then used to calculate the electron number density. The developed Neural-network-based Upper hybrid Resonance Determination (NURD) algorithm is applied to more than four years of EMFISIS measurements to produce the publicly available electron density data set. We utilize the obtained electron density data set to develop a new global model of plasma density by employing a neural network-based modeling approach. In addition to the location, the model takes the time history of geomagnetic indices and location as inputs, and produces electron density in the equatorial plane as an output. It is extensively validated using in-situ density measurements from the Van Allen Probes mission, and also by comparing the predicted global evolution of the plasmasphere with the global IMAGE EUV images of He+ distribution. The model successfully reproduces erosion of the plasmasphere on the night side as well as plume formation and evolution, and agrees well with data. The performance of neural networks strongly depends on the availability of training data, which is limited during intervals of high geomagnetic activity. In order to provide reliable density predictions during such intervals, we can employ physics-based modeling. We develop a new approach for optimally combining the neural network- and physics-based models of the plasmasphere by means of data assimilation. The developed approach utilizes advantages of both neural network- and physics-based modeling and produces reliable global plasma density reconstructions for quiet, disturbed, and extreme geomagnetic conditions. Finally, we extend the developed machine learning-based tools and apply them to another important problem in the field of space weather, the prediction of the geomagnetic index Kp. The Kp index is one of the most widely used indicators for space weather alerts and serves as input to various models, such as for the thermosphere, the radiation belts and the plasmasphere. It is therefore crucial to predict the Kp index accurately. Previous work in this area has mostly employed artificial neural networks to nowcast and make short-term predictions of Kp, basing their inferences on the recent history of Kp and solar wind measurements at L1. We analyze how the performance of neural networks compares to other machine learning algorithms for nowcasting and forecasting Kp for up to 12 hours ahead. Additionally, we investigate several machine learning and information theory methods for selecting the optimal inputs to a predictive model of Kp. The developed tools for feature selection can also be applied to other problems in space physics in order to reduce the input dimensionality and identify the most important drivers. Research outlined in this dissertation clearly demonstrates that machine learning tools can be used to develop empirical models from sparse data and also can be used to understand the underlying physical processes. Combining machine learning, physics-based modeling and data assimilation allows us to develop novel methods benefiting from these different approaches.},
  language  = {en}
}
@phdthesis{Polyvyanyy2012,
  author    = {Polyvyanyy, Artem},
  title     = {Structuring process models},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59024},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {One can fairly adopt the ideas of Donald E. Knuth to conclude that process modeling is both a science and an art. Process modeling does have an aesthetic sense. Similar to composing an opera or writing a novel, process modeling is carried out by humans who undergo creative practices when engineering a process model. Therefore, the very same process can be modeled in a myriad number of ways. Once modeled, processes can be analyzed by employing scientific methods. Usually, process models are formalized as directed graphs, with nodes representing tasks and decisions, and directed arcs describing temporal constraints between the nodes. Common process definition languages, such as Business Process Model and Notation (BPMN) and Event-driven Process Chain (EPC) allow process analysts to define models with arbitrary complex topologies. The absence of structural constraints supports creativity and productivity, as there is no need to force ideas into a limited amount of available structural patterns. Nevertheless, it is often preferable that models follow certain structural rules. A well-known structural property of process models is (well-)structuredness. A process model is (well-)structured if and only if every node with multiple outgoing arcs (a split) has a corresponding node with multiple incoming arcs (a join), and vice versa, such that the set of nodes between the split and the join induces a single-entry-single-exit (SESE) region; otherwise the process model is unstructured. The motivations for well-structured process models are manifold: (i) Well-structured process models are easier to layout for visual representation as their formalizations are planar graphs. (ii) Well-structured process models are easier to comprehend by humans. (iii) Well-structured process models tend to have fewer errors than unstructured ones and it is less probable to introduce new errors when modifying a well-structured process model. (iv) Well-structured process models are better suited for analysis with many existing formal techniques applicable only for well-structured process models. (v) Well-structured process models are better suited for efficient execution and optimization, e.g., when discovering independent regions of a process model that can be executed concurrently. Consequently, there are process modeling languages that encourage well-structured modeling, e.g., Business Process Execution Language (BPEL) and ADEPT. However, the well-structured process modeling implies some limitations: (i) There exist processes that cannot be formalized as well-structured process models. (ii) There exist processes that when formalized as well-structured process models require a considerable duplication of modeling constructs. Rather than expecting well-structured modeling from start, we advocate for the absence of structural constraints when modeling. Afterwards, automated methods can suggest, upon request and whenever possible, alternative formalizations that are "better" structured, preferably well-structured. In this thesis, we study the problem of automatically transforming process models into equivalent well-structured models. The developed transformations are performed under a strong notion of behavioral equivalence which preserves concurrency. The findings are implemented in a tool, which is publicly available.},
  language  = {en}
}