@phdthesis{Wangorsch2013, author = {Wangorsch, Gaby}, title = {Mathematical modeling of cellular signal transduction}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-87746}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2013}, abstract = {A subtly regulated and controlled course of cellular processes is essential for the healthy functioning not only of single cells, but also of organs being constituted thereof. In return, this entails the proper functioning of the whole organism. This implies a complex intra- and inter-cellular communication and signal processing that require equally multi-faceted methods to describe and investigate the underlying processes. Within the scope of this thesis, mathematical modeling of cellular signaling finds its application in the analysis of cellular processes and signaling cascades in different organisms. ...}, subject = {Mathematische Modellierung}, language = {en} } @phdthesis{Schardt2023, author = {Schardt, Simon}, title = {Agent-based modeling of cell differentiation in mouse ICM organoids}, doi = {10.25972/OPUS-30194}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-301940}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2023}, abstract = {Mammalian embryonic development is subject to complex biological relationships that need to be understood. However, before the whole structure of development can be put together, the individual building blocks must first be understood in more detail. One of these building blocks is the second cell fate decision and describes the differentiation of cells of the inner cell mass of the embryo into epiblast and primitive endoderm cells. These cells then spatially segregate and form the subsequent bases for the embryo and yolk sac, respectively. In organoids of the inner cell mass, these two types of progenitor cells are also observed to form, and to some extent to spatially separate. This work has been devoted to these phenomena over the past three years. Plenty of studies already provide some insights into the basic mechanics of this cell differentiation, such that the first signs of epiblast and primitive endoderm differentiation, are the expression levels of transcription factors NANOG and GATA6. Here, cells with low expression of GATA6 and high expression of NANOG adopt the epiblast fate. If the expressions are reversed, a primitive endoderm cell is formed. Regarding the spatial segregation of the two cell types, it is not yet clear what mechanism leads to this. A common hypothesis suggests the differential adhesion of cell as the cause for the spatial rearrangement of cells. In this thesis however, the possibility of a global cell-cell communication is investigated. The approach chosen to study these phenomena follows the motto "mathematics is biology's next microscope". Mathematical modeling is used to transform the central gene regulatory network at the heart of this work into a system of equations that allows us to describe the temporal evolution of NANOG and GATA6 under the influence of an external signal. Special attention is paid to the derivation of new models using methods of statistical mechanics, as well as the comparison with existing models. After a detailed stability analysis the advantages of the derived model become clear by the fact that an exact relationship of the model parameters and the formation of heterogeneous mixtures of two cell types was found. Thus, the model can be easily controlled and the proportions of the resulting cell types can be estimated in advance. This mathematical model is also combined with a mechanism for global cell-cell communication, as well as a model for the growth of an organoid. It is shown that the global cell-cell communication is able to unify the formation of checkerboard patterns as well as engulfing patterns based on differently propagating signals. In addition, the influence of cell division and thus organoid growth on pattern formation is studied in detail. It is shown that this is able to contribute to the formation of clusters and, as a consequence, to breathe some randomness into otherwise perfectly sorted patterns.}, subject = {Mathematische Modellierung}, language = {en} } @phdthesis{Hossfeld2009, author = {Hoßfeld, Tobias}, title = {Performance Evaluation of Future Internet Applications and Emerging User Behavior}, doi = {10.25972/OPUS-3067}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-37570}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2009}, abstract = {In future telecommunication systems, we observe an increasing diversity of access networks. The separation of transport services and applications or services leads to multi-network services, i.e., a future service has to work transparently to the underlying network infrastructure. Multi-network services with edge-based intelligence, like P2P file sharing or the Skype VoIP service, impose new traffic control paradigms on the future Internet. Such services adapt the amount of consumed bandwidth to reach different goals. A selfish behavior tries to keep the QoE of a single user above a certain level. Skype, for instance, repeats voice samples depending on the perceived end-to-end loss. From the viewpoint of a single user, the replication of voice data overcomes the degradation caused by packet loss and enables to maintain a certain QoE. The cost for this achievement is a higher amount of consumed bandwidth. However, if the packet loss is caused by congestion in the network, this additionally required bandwidth even worsens the network situation. Altruistic behavior, on the other side, would reduce the bandwidth consumption in such a way that the pressure on the network is released and thus the overall network performance is improved. In this monograph, we analyzed the impact of the overlay, P2P, and QoE paradigms in future Internet applications and the interactions from the observing user behavior. The shift of intelligence toward the edge is accompanied by a change in the emerging user behavior and traffic profile, as well as a change from multi-service networks to multi-networks services. In addition, edge-based intelligence may lead to a higher dynamics in the network topology, since the applications are often controlled by an overlay network, which can rapidly change in size and structure as new nodes can leave or join the overlay network in an entirely distributed manner. As a result, we found that the performance evaluation of such services provides new challenges, since novel key performance factors have to be first identified, like pollution of P2P systems, and appropriate models of the emerging user behavior are required, e.g. taking into account user impatience. As common denominator of the presented studies in this work, we focus on a user-centric view when evaluating the performance of future Internet applications. For a subscriber of a certain application or service, the perceived quality expressed as QoE will be the major criterion of the user's satisfaction with the network and service providers. We selected three different case studies and characterized the application's performance from the end user's point of view. Those are (1) cooperation in mobile P2P file sharing networks, (2) modeling of online TV recording services, and (3) QoE of edge-based VoIP applications. The user-centric approach facilitates the development of new mechanisms to overcome problems arising from the changing user behavior. An example is the proposed CycPriM cooperation strategy, which copes with selfish user behavior in mobile P2P file sharing system. An adequate mechanism has also been shown to be efficient in a heterogeneous B3G network with mobile users conducting vertical handovers between different wireless access technologies. The consideration of the user behavior and the user perceived quality guides to an appropriate modeling of future Internet applications. In the case of the online TV recording service, this enables the comparison between different technical realizations of the system, e.g. using server clusters or P2P technology, to properly dimension the installed network elements and to assess the costs for service providers. Technologies like P2P help to overcome phenomena like flash crowds and improve scalability compared to server clusters, which may get overloaded in such situations. Nevertheless, P2P technology invokes additional challenges and different user behavior to that seen in traditional client/server systems. Beside the willingness to share files and the churn of users, peers may be malicious and offer fake contents to disturb the data dissemination. Finally, the understanding and the quantification of QoE with respect to QoS degradations permits designing sophisticated edge-based applications. To this end, we identified and formulated the IQX hypothesis as an exponential interdependency between QoE and QoS parameters, which we validated for different examples. The appropriate modeling of the emerging user behavior taking into account the user's perceived quality and its interactions with the overlay and P2P paradigm will finally help to design future Internet applications.}, subject = {Leistungsbewertung}, language = {en} } @phdthesis{Forster2016, author = {Forster, Johannes}, title = {Variational Approach to the Modeling and Analysis of Magnetoelastic Materials}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-147226}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2016}, abstract = {This doctoral thesis is concerned with the mathematical modeling of magnetoelastic materials and the analysis of PDE systems describing these materials and obtained from a variational approach. The purpose is to capture the behavior of elastic particles that are not only magnetic but exhibit a magnetic domain structure which is well described by the micromagnetic energy and the Landau-Lifshitz-Gilbert equation of the magnetization. The equation of motion for the material's velocity is derived in a continuum mechanical setting from an energy ansatz. In the modeling process, the focus is on the interplay between Lagrangian and Eulerian coordinate systems to combine elasticity and magnetism in one model without the assumption of small deformations. The resulting general PDE system is simplified using special assumptions. Existence of weak solutions is proved for two variants of the PDE system, one including gradient flow dynamics on the magnetization, and the other featuring the Landau-Lifshitz-Gilbert equation. The proof is based on a Galerkin method and a fixed point argument. The analysis of the PDE system with the Landau-Lifshitz-Gilbert equation uses a more involved approach to obtain weak solutions based on G. Carbou and P. Fabrie 2001.}, subject = {Magnetoelastizit{\"a}t}, language = {en} } @misc{Forster2013, type = {Master Thesis}, author = {Forster, Johannes}, title = {Mathematical Modeling of Complex Fluids}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-83533}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2013}, abstract = {This thesis gives an overview over mathematical modeling of complex fluids with the discussion of underlying mechanical principles, the introduction of the energetic variational framework, and examples and applications. The purpose is to present a formal energetic variational treatment of energies corresponding to the models of physical phenomena and to derive PDEs for the complex fluid systems. The advantages of this approach over force-based modeling are, e.g., that for complex systems energy terms can be established in a relatively easy way, that force components within a system are not counted twice, and that this approach can naturally combine effects on different scales. We follow a lecture of Professor Dr. Chun Liu from Penn State University, USA, on complex fluids which he gave at the University of Wuerzburg during his Giovanni Prodi professorship in summer 2012. We elaborate on this lecture and consider also parts of his work and publications, and substantially extend the lecture by own calculations and arguments (for papers including an overview over the energetic variational treatment see [HKL10], [Liu11] and references therein).}, subject = {Variationsrechnung}, language = {en} }