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We propose a multiscale model for tumor cell migration in a tissue network. The system of equations involves a structured population model for the tumor cell density, which besides time and
position depends on a further variable characterizing the cellular state with respect to the amount
of receptors bound to soluble and insoluble ligands. Moreover, this equation features pH-taxis and
adhesion, along with an integral term describing proliferation conditioned by receptor binding. The
interaction of tumor cells with their surroundings calls for two more equations for the evolution of
tissue fibers and acidity (expressed via concentration of extracellular protons), respectively. The
resulting ODE-PDE system is highly nonlinear. We prove the global existence of a solution and
perform numerical simulations to illustrate its behavior, paying particular attention to the influence
of the supplementary structure and of the adhesion.

This thesis investigates the electromechanic coupling of dielectric elastomers for the static and dynamic case by numerical simulations. To this end, the fundamental equations of the coupled field problem are introduced and the discretisation procedure for the numerical implementation is described. Furthermore, a three field formulation is proposed and implemented to treat the nearly incompressible behaviour of the elastomer. Because of the reduced electric permittivity of the material, very high electric fields are required for actuation purposes. To improve the electromechanic coupling a heterogeneous microstructure consisting of an elastomer matrix with barium titanate inclusions is proposed and studied.

Stochastic Network Calculus (SNC) emerged from two branches in the late 90s:
the theory of effective bandwidths and its predecessor the Deterministic Network
Calculus (DNC). As such SNC’s goal is to analyze queueing networks and support
their design and control.
In contrast to queueing theory, which strives for similar goals, SNC uses in-
equalities to circumvent complex situations, such as stochastic dependencies or
non-Poisson arrivals. Leaving the objective to compute exact distributions behind,
SNC derives stochastic performance bounds. Such a bound would, for example,
guarantee a system’s maximal queue length that is violated by a known small prob-
ability only.
This work includes several contributions towards the theory of SNC. They are
sorted into four main contributions:
(1) The first chapters give a self-contained introduction to deterministic net-
work calculus and its two branches of stochastic extensions. The focus lies on the
notion of network operations. They allow to derive the performance bounds and
simplifying complex scenarios.
(2) The author created the first open-source tool to automate the steps of cal-
culating and optimizing MGF-based performance bounds. The tool automatically
calculates end-to-end performance bounds, via a symbolic approach. In a second
step, this solution is numerically optimized. A modular design allows the user to
implement their own functions, like traffic models or analysis methods.
(3) The problem of the initial modeling step is addressed with the development
of a statistical network calculus. In many applications the properties of included
elements are mostly unknown. To that end, assumptions about the underlying
processes are made and backed by measurement-based statistical methods. This
thesis presents a way to integrate possible modeling errors into the bounds of SNC.
As a byproduct a dynamic view on the system is obtained that allows SNC to adapt
to non-stationarities.
(4) Probabilistic bounds are fundamentally different from deterministic bounds:
While deterministic bounds hold for all times of the analyzed system, this is not
true for probabilistic bounds. Stochastic bounds, although still valid for every time
t, only hold for one time instance at once. Sample path bounds are only achieved by
using Boole’s inequality. This thesis presents an alternative method, by adapting
the theory of extreme values.
(5) A long standing problem of SNC is the construction of stochastic bounds
for a window flow controller. The corresponding problem for DNC had been solved
over a decade ago, but remained an open problem for SNC. This thesis presents
two methods for a successful application of SNC to the window flow controller.

Buses not arriving on time and then arriving all at once - this phenomenon is known from
busy bus routes and is called bus bunching.
This thesis combines the well studied but so far separate areas of bus-bunching prediction
and dynamic holding strategies, which allow to modulate buses’ dwell times at stops to
eliminate bus bunching. We look at real data of the Dublin Bus route 46A and present
a headway-based predictive-control framework considering all components like data
acquisition, prediction and control strategies. We formulate time headways as time series
and compare several prediction methods for those. Furthermore we present an analytical
model of an artificial bus route and discuss stability properties and dynamic holding
strategies using both data available at the time and predicted headway data. In a numerical
simulation we illustrate the advantages of the presented predictive-control framework
compared to the classical approaches which only use directly available data.

This work introduces a promising concept for the preparation of new nano-sized receptors. Mixed monolayer protected gold nanoparticles (AuNPs) for low molecular weight compounds were prepared featuring functional groups on their surfaces. It has been shown that these AuNPs can engage in interactions with peptides in aqueous media. Quantitative binding information was obtained from DOSY-NMR titrations indicating that nanoparticles containing a combination of three orthogonal functional groups are more efficient in binding to dipeptides than mono or difunctionalised analogues. The strategy is highly modular and easily allows adapting the receptor selectivity to a
given substrate by varying the type, number, and ratio of binding sites on the nanoparticle
surface.

Advantage of Filtering for Portfolio Optimization in Financial Markets with Partial Information
(2016)

In a financial market we consider three types of investors trading with a finite
time horizon with access to a bank account as well as multliple stocks: the
fully informed investor, the partially informed investor whose only source of
information are the stock prices and an investor who does not use this infor-
mation. The drift is modeled either as following linear Gaussian dynamics
or as being a continuous time Markov chain with finite state space. The
optimization problem is to maximize expected utility of terminal wealth.
The case of partial information is based on the use of filtering techniques.
Conditions to ensure boundedness of the expected value of the filters are
developed, in the Markov case also for positivity. For the Markov modulated
drift, boundedness of the expected value of the filter relates strongly to port-
folio optimization: effects are studied and quantified. The derivation of an
equivalent, less dimensional market is presented next. It is a type of Mutual
Fund Theorem that is shown here.
Gains and losses eminating from the use of filtering are then discussed in
detail for different market parameters: For infrequent trading we find that
both filters need to comply with the boundedness conditions to be an advan-
tage for the investor. Losses are minimal in case the filters are advantageous.
At an increasing number of stocks, again boundedness conditions need to be
met. Losses in this case depend strongly on the added stocks. The relation
of boundedness and portfolio optimization in the Markov model leads here to
increasing losses for the investor if the boundedness condition is to hold for
all numbers of stocks. In the Markov case, the losses for different numbers
of states are negligible in case more states are assumed then were originally
present. Assuming less states leads to high losses. Again for the Markov
model, a simplification of the complex optimal trading strategy for power
utility in the partial information setting is shown to cause only minor losses.
If the market parameters are such that shortselling and borrowing constraints
are in effect, these constraints may lead to big losses depending on how much
effect the constraints have. They can though also be an advantage for the
investor in case the expected value of the filters does not meet the conditions
for boundedness.
All results are implemented and illustrated with the corresponding numerical
findings.

Urban quality of life is currently conceptualized in principally economic terms. As the decline in manufacturing activities, the rise of the service and knowledge economy, the growing importance of accessibility and globalizing processes continue to reconfigure the economic competition between cities, quality of life enters the discourse primarily as a means to attract high-skilled workers and improve the city’s economic prospects. Local governments increasingly seek partnerships with local and foreign capital, reorganizing institutions and tasks to attract capital, including the “selling of place”, strengthening place promotion and marketing efforts. The rhetoric clearly welcomes wealthy, creative, high-skilled people, disadvantaged and low skilled groups receive less attention in the making of places. Especially with respect to inner city areas, high quality of life is promoted as spaces for ‘clean’ and convenient consumption with positive atmospheres and shiny images.
Yet, a plethora of theoretical engagements with urban everyday live reminds us that, while on the one hand, variety of jobs, quality of public spaces, range of shops and services, cultural facilities and public transport are important place characteristics, more subjective aspects such as safe neighbourhoods, well-being, community prospects, social cohesion, happiness, satisfaction and social and spatial justice are equally crucial determinants of urban quality of life. These elements of urban quality of life – and how they are experienced by diverse formations of urban inhabitants – seem to be absent from, if not at odds with, the dominant discourse in rankings, policy and practice. Urban life, social cohesion and complexity are at risk in the dynamics of modernization and adaptation strategies of cities. Gentrification, the occupation of inner-city districts by hyper-rich people, segregation and displacement of lower and middle classes can be observed as a consequence of these long-lasting strategies.
Well-known sociologists and geographers from the UK and Germany have presented their insights on the matter and debate theoretical and empirical attempts to capture the dynamics of urban processes in shaping the quality of life.

Knowing the extent to which we rely on technology one may think that correct programs are nowadays the norm. Unfortunately, this is far from the truth. Luckily, possible reasons why program correctness is difficult often come hand in hand with some solutions. Consider concurrent program correctness under Sequential Consistency (SC). Under SC, instructions of each program's concurrent component are executed atomically and in order. By using logic to represent correctness specifications, model checking provides a successful solution to concurrent program verification under SC. Alas, SC’s atomicity assumptions do not reflect the reality of hardware architectures. Total Store Order (TSO) is a less common memory model implemented in SPARC and in Intel x86 multiprocessors that relaxes the SC constraints. While the architecturally de-atomized execution of stores under TSO speeds up program execution, it also complicates program verification. To be precise, due to TSO’s unbounded store buffers, a program’s semantics under TSO might be infinite. This, for example, turns reachability under SC (a PSPACE-complete task) into a non-primitive-recursive-complete problem under TSO. This thesis develops verification techniques targeting TSO-relaxed programs. To be precise, we present under- and over-approximating heuristics for checking reachability in TSO-relaxed programs as well as state-reducing methods for speeding up such heuristics. In a first contribution, we propose an algorithm to check reachability of TSO-relaxed programs lazily. The under-approximating refinement algorithm uses auxiliary variables to simulate TSO’s buffers along instruction sequences suggested by an oracle. The oracle’s deciding characteristic is that if it returns the empty sequence then the program’s SC- and TSO-reachable states are the same. Secondly, we propose several approaches to over-approximate TSO buffers. Combined in a refinement algorithm, these approaches can be used to determine safety with respect to TSO reachability for a large class of TSO-relaxed programs. On the more technical side, we prove that checking reachability is decidable when TSO buffers are approximated by multisets with tracked per address last-added-values. Finally, we analyze how the explored state space can be reduced when checking TSO and SC reachability. Intuitively, through the viewpoint of Shasha-and-Snir-like traces, we exploit the structure of program instructions to explain several state-space reducing methods including dynamic and cartesian partial order reduction.

Combining ultracold atomic gases with the peculiar properties of Rydberg excited atoms gained a lot of theoretical and experimental attention in recent years. Embedded in the ultracold gas, an interaction between the Rydberg atom and the surrounding ground state atoms arises through the scattering of the Rydberg electron from an intruding perturber atom. This peculiar interaction gives rise to a plenitude of previously unobserved effects. Within the framework of the present thesis, this interaction is studied in detail for Rydberg \(P\)-states in rubidium.
Due to their long lifetime, atoms in Rydberg states are subject to scattering with the surrounding ground state atoms in the ultracold cloud. By measuring their lifetime as a function of the ground state atom flux, we are able to obtain the total inelastic scattering cross section as well as the partial cross section for associative ionisation. The fact that the latter is three orders of magnitude larger than the size of the formed molecular
ion indicates the presence of an efficient mass transport mechanism that is mediated by the Rydberg–ground state interaction. The immense acceleration of the collisional process shows a close analogy to a catalytic process. The increase of the scattering cross section renders associative ionisation an important process that has to be considered for experiments in dense ultracold systems.
The interaction of the Rydberg atom with a ground state perturber gives rise to a highly oscillatory potential that supports molecular bound states. These so-called ultralong-range Rydberg molecules are studied with high resolution time-of-flight spectroscopy, where we are able to determine the binding energies and lifetimes of the molecular states between the two fine structure split \(25P\)-states. Inside an electric field, we observe a broadening of the
molecular lines that indicates the presence of a permanent electric dipole moment, induced by the mixing with high angular momentum states. Due to the mixing of the ground state atom’s hyperfine states by the molecular interaction, we are able to observe a spin-flip of the perturber upon creation of a Rydberg molecule. Furthermore, an incidental near-degeneracy in the underlying level scheme of the \(25P\)-state gives rise to highly entangled states between the Rydberg fine structure state and the perturber’s hyperfine structure. These mechanisms can be used to manipulate the quantum state of a remote particle over distances that exceed by far the typical contact interaction range.
Apart from the ultralong-range Rydberg molecules that predominantly consist of only one low angular momentum state, a class of Rydberg molecules is predicted to exist that strongly mixes the high angular momentum states of the degenerate hydrogenic manifolds. These states, the so-called trilobite- and butterfly Rydberg molecules, show very peculiar properties that cannot be observed for conventional molecules. Here we present the first experimental observation of butterfly Rydberg molecules. In addition to an extensive spectroscopy that reveals the binding energy, we are also able to observe the rotational structure of these exotic molecules. The arising pendular states inside an electric field allow us, in comparison to the model of a dipolar rotor, to extract the precise bond
length and dipole moment of the molecule. With the information obtained in the present study, it is possible to photoassociate butterfly molecules with a selectable bond length, vibrational state, rotational state, and orientation inside an electric field.
By shedding light on various previously unrevealed aspects, the experiments presented in this thesis significantly deepen our knowledge on the Rydberg–ground state interaction and the peculiar effects arising from it. The obtained spectroscopic information on Rydberg molecules and the changed reaction dynamics for molecular ion creation will surely provide valuable data for quantum chemical simulations and provide necessary data to plan future experiments. Beyond that, our study reveals that the hyperfine interaction in Rydberg molecules and the peculiar properties of butterfly states provide very promising new ways to alter the short- and long-range interactions in ultracold many-body systems. In this sense the investigated Rydberg–ground state interaction not only lies right at
the interface between quantum chemistry, quantum many-body systems, and Rydberg physics, but also creates many new and fascinating possibilities by combining these fields.