##
Modellierung und Simulation von Wellenbewegung in Pinguin-Kolonien

Christin Thole, 2015

Emperor penguins have to withstand the severe conditions during the Antarctic winter. Therefore it is essential for survival to preserve the warmth within their colony by forming dense huddles with a triangular lattice structure. Thus the penguins conserve their energy and are able to resist the harsh environment. Arbitrary movements enable penguins at colder edges of the colony to move into the huddle and hence into the warmth. Due to this position shifting a wave-like pattern is caused which has an effect on the whole colony as it travels trough the huddle.
The aim of this work is to model and simulate those wave movements with the aid of simple rules. For that reason the focus is on the microscopic and macroscopic observation of two different initial situations in terms of the movement sequences within the penguin huddle. Following the derivation and analysis of the current model the simulation results are presented. . [pdf-file]

##
Phasenseparation in
Teilchensystemen mit inter- und
intra-populären
Anziehungskräften

Meike Kinzel, 2015

To avoid the die-off of the whole population as a result of starvation, the free-living single
amoebae of the cellular slime mold Dictyostelium Discoideum organize themselves into
dense multicellular aggregates composed of cells which are able to germinate as well as of
cells which are going to die off. These initially random distributed cells undergo spatial
sorting resulting in the separation of the two subpopulations and subsequently evolve into
a fruiting body. In this thesis we will analyse the reasons of this separation by means of
population dynamic models. We will focus on the influences of self- and cross-population
attractive forces as well as on a chemotactic force to a chemoattractant and initially
provide an individual-based model of stochastic differential equations. Afterwards we
consider the limiting behaviour as the number of particles tends to infinity and obtain
a continuum model of partial differential equations, which is suited for the simulation
of the behaviour of very big populations. By the use of the numerical solution of the
individual-based model we then draw conclusions about the reasons of the separation in
the life cycle of Dictyostelium Discoideum. [pdf-file]

##
Mathematische Modelle für Phasenseparation bei aktiven Teilchen

Marie-Christin Tacke, 2015

The aim of this thesis is a qualitative description of the phase behaviour of a mixture of active and passive Brownian particles.
For this sake models based on stochastic differential equations are used. In a first step Langevin equations for describing the movement
are solved numerically and simulations of different starting configurations are carried out. In particular the behaviour of a random initial mixture of
active and passive particles is considered, which yields a clearly visible spatial phase separation. In a second step a macroscopic mean-field model is derived from
the Langevin equations.
[pdf-file]

##
Wandernde Wellen in makroskopischen Bewegungsmodellen

Leoni Hoffboll, 2015

Collective motion describes the movement of groups of various members in high density like cars in traffic jams. This is a great motivation to develop macroscopic models of such systems and study their remarkable behaviour. Traffic flow as well as colonial manner of emperor penguins in a huddle cause wavelike motions while the group tries to move.
Main topic of the following thesis are traveling waves, which represent a wavelike solution of non-linear partial differential equations. They have their origin in macroscopic models as mentioned above. This work tries to transfer the results of traffic flow models to the behaviour of emperor penguins in a huddle by emphasising the similarities and developing a proper model and the according traveling waves for travelling penguins.
[pdf-file]

##
Modelling Opinion Dynamics

Sei Ho Winsion Tang, 2015

We represent two mechanisms of opinion formation by kinetic equations involving both
the exchange of opinion between individuals and the diffusion of information. The first
one is a possible approach to the formation of choice in a society, following a linear
Boltzmann equation where the background density is nothing but a fixed distribution
of possible choices. In the second model we focus on the opinion formation in the pres-
ence of leaders, where the Boltzmann type equation based on a model predictive control
formulation, is introduced and discussed. Notably, according to the leaders strategy,
in order to achieve opinion consensus, a suitable functional is modified. Thanks to
the receding horizon strategy, the minimization of suitable cost functional is able to
embed into the binary interaction of the corresponding Boltzmann equation. Both
models start from microscopic interaction among individuals and we arrive at a macro-
scopic description of the opinion formation process which is described by a system of
Fokker-Planck type equation. The analytical results of this system give us an explicit
expression of a stationary solution. Several numerical results show various effects of
different model parameters in the first description and the robustness of the Boltzmann
type control approach to illustrate different variations in the leaders’ strategy.
[pdf-file]

##
Randomisiertes Kaczmarz -
Verfahren

Lena Neufeld, 2014

The Kaczmarz method is an iterative algorithm for solving systems of linear equations Ax=b and was the requirement for many applications like the computer tomography. Theoretical convergence rates for this algorithm were largely unknown until a randomized Kaczmarz method has been established. After a brief description of the standard Kaczmarz method the thesis deals with the randomized version which converges with exponential rate. Furthermore there is an analysis about the case where the system Ax=b is corrupted by noise (Ax=b+r). In this noisy version the randomized Kaczmarz method reaches an error threshold which depends on the matrix A with the same rate as in the error-free case. Moreover we describe numerical results for the improvement of the randomized Kaczmarz method compared with the standard version. Other numerical simulations demonstrate that the randomized Kaczmarz method can outperform the efficient conjugate gradient algorithm (CGLS method).
[pdf-file]

##
Non-Local-Means-Algorithm vs.
Expert Regularizers

Florian Schacht, 2014

In the field of mathematical image processing the problem of denoising images is a central component. For its solution various approaches have already been found and developed. In this work we deal with two advanced methods, namely on the one hand the Non-local means algorithm and on the other the Expert Regularizers. The goal of our consideration is the final comparison of these two image denoising methods. Therefore, in the first part of the work, we will provide a basic understanding by the look on the mathematical representation of images and treating the basic procedures before we make a detailed description of the two advanced approaches. [pdf-file]

##
Bildbasierte Algorithmen zur
Metall-Artefakt Reduktion in
der Computertomographie

Nils-Arne Dreier, 2014 (Supervision: Frank Wübbeling)

Metal-Artifacts are Errors in tomographic images, which are produced by metal pieces in the inspected object.
This thesis deals with image-based Methods for Metal-Artifact reduction. Various regularization techniques and
reconstruction methods are compiled and finally the results of each method are compared. The final outcome is that
Total-Variation-Regularization provides better results than conventional Metal-Artifact-Reduction techniques or
regularization methods.
[pdf-file]

##
Comparison of Topology-preserving
Segmentation Methods and Application
to Mitotic Cell Tracking

Jonas Geiping, 2014 (Supervision with Joana Grah, Hendrik Dirks)

This thesis compares two representative methods that constrain the topology of
an
active contours segmentation, the digital Simple-Points scheme and the
variational
Repelling-Snakes topology preservation. The comparison will be facilitated at
the
example of the MitosisAnalyser framework, a tool designed to find mitotic
cells in
phase contrast microcopy videos. It turns out that Repelling-Snakes is better
suited
for topology preservation for this framework than the Simple-Points scheme
that was
used before. Stable and effcient numerical implementations will also be
presented.
[pdf-file]

##
Diskreter optimaler Transport
und Anwendungen in der
Bildverarbeitung

Katja Krupp, 2014

The subject of this thesis is the optimal transport, which is used in picture processing among other
things. After formulating the theory of optimal transport it will exemplarily be used to transmit the
color histogram from one picture to another as optimally as possible. In the end, after introducing
different cluster algorithms, they will be compared to the optimal transport.
[pdf-file]

##
Algorithmen zur Berechnung von Democratic Representations

Alexander Rave, 2014

The present work deals with the computation of Democratic Representations. Therefore, we will compare three algorithms, which compute the minimum of the supremum norm in an underdetermined system of linear equations. Moreover we will describe the practical use, especially the vector quantization, the approximate nearest neighbor search and the reduction of the Peak-to-Average Power Ratio (PAPR). The latter will be shown by the three algorithms for some frames. [pdf-file]

##
Sparse PCA und Robust PCA -
PCA-Erweiterungen für die Bild-
und Videobearbeitung

Bastian Quebe, 2014

Principal component analysis (PCA) is a widely used method to structure data and reduce their
dimension. Also in the picture and video editing, it has some applications. However, PCA pushes in
terms of interpretability and robustness fast to its limits, especially in very large amounts of data.
Because of these problems extensions were developed, of which we will resolve two types here.
Sparse PCA is useful for an easier interpretability, robust PCA makes the algorithm more stable at
greatly differing values, called outliers. We will develop different approaches to these two
expansions. Finally we will check at appropriate examples from the image and video processing,
where each approach has advantages and which one is best suited for which case.
[pdf-file]

##
Methoden zur verbesserten TV-Regularisierung

Maren Irle, 2014

Diese Arbeit beschäftigt sich mit der Regularisierung, im Konkreten der Entrauschung,
von Bildern als Aufgabe der mathematischen Bildverarbeitung.
Nach der Einführung eines beliebten, da kantenerhaltenden Regularisierungsfunktionals,
der Totalvariation (kurz: TV), thematisieren wir die entstehenden
Stufenartefakte als ein großes Problem dieser Methode. Im Rahmen einer Lösung
dieses Problems stellen wir die verallgemeinerte Totalvariation und die
Infimale Konvolution von TV -typischen Funktionalen vor. Im nächsten Schritt
wird die numerische Umsetzung dieser Funktionale präsentiert und die Verbesserung
der Rekonstruktion durch diese Methoden an konkreten Bildern aufgezeigt.
[pdf-file]

##
Fußgängersimulation mit
entgegengesetzten
Bewegungsrichtungen

Matthias Walther, 2014

The social force model for pedestrian dynamics by Prof. Dirk Helbing is
a useful mathematical system to calculate the behavior and movement
pedestrians, especially in panic situations. In this bachelor thesis a
modified version of the Matlab code by Mrs. Schlake was used to run a
simulation in a room with two opposed doors and pedestrians crossing the
room from the one door to the other and the other way around. First the
impact of different entering rates to the average transit time of the
individuals is analyzed and secondly the kernel density estimation is
visualized tridimensionally
[pdf-file]

##
Regularisierter optimaler Transport in der Bildverarbeitung

Maximilian Geulen, 2014

The present thesis deals with the basics of the Optimal Transport theory and its application in image processing. It will be shown how a color transfer and an interpolation between two images can be computed. For both applications we will develop regularization terms in order to improve the visual results.
[pdf-file]

##
Spektralzerlegung von Bildern mit TV-Methoden

Lina Eckardt, 2014

Total variation is a popular tool in image processing due to its property of preserving edges but
producing nearly noise free images. Along with denoising, another task of image processing is the
decomposition of an image into components with certain properties. There one approach is the
Fourier transform, unfortunately corresponding filters yield some disadvantages as blurred images.
Therefore the aim of this work is a combination of both methods: a spectral decomposition of images
with TV methods. It allows us to decompose an image according to its texture scales and to filter
certain scales.
First we give an introduction to the needed basics of image processing, especially to total variation
and linked methods. Subsequently we derive a definition of spectral representatives for the TV flow.
In the second part the results are transferred to the ROF regularization and the inverse scale space
flow. Finally we deal with the application of spectral decomposition for texture processing and give
some numerical results.
[pdf-file]

##
Kinetische Modelle für Zellbewegung

Patricia Friele, 2013

This thesis refers to three kinetic-models for the movement of cells that
will be explained mathematically. The main part focuses on the
Velocity-Jump-Model for chemotactic cell movement and shows that
diffusion happens in the limit of this model.
In the second part of this paper two other models for the movement of
cells will be presented. They will also be explained mathematically on
the basis of the mentioned Velocity-Jump-Model. Important aspects like
cell-interaction and different specialized cells of one cell population
will also be taken into detail in this last part of the paper.
[pdf-file]

##
Mean Field Game Modelle am Beispiel von Herdenverhalten und Wohlstandsentwicklung

Tobias Trame, 2013

Mean field games are a synthesis of mean field theory from the realm of physics and the economically motivated game theory. They are used for the mathematical modeling of situations in
which many individuals or particles of the same kind are interacting and therefore can be treated as a crowd or an ensemble by looking at it from the outside. This thesis provides
microscopic and macroscopic models on the example of animal herding behavior and wealth development using mean field games and Nash equilibria. In addition it gives an implementation of
these examples and some numerical results which lead to an evaluation of the constructed frameworks.
[pdf-file]

##
Regularisierungen des
Keller-Segel Modells und
Blow-Up

Bernd Mekes, 2013

In biology, chemotaxis describes directed movement of cells due to attraction
by a chemical. The Keller-Segel model is a mathematical description of the
temporal evolution of a chemotactically moving population of cells. Solutions
of this models may become unbounded in finite time, which is an expression of
concentration of cells. This property is called blow-up and prevents global
existence of solutions. Therefore modified models, called regularizations, are
taken into consideration. They lead to introduce generalized solutions that
ensure global existence. With these regularizations and generalized solutions
it is possible to prove further results for the Keller-Segel model.
This thesis gives an overview of the procedure based on four examples taken
from various papers.
[pdf-file]

##
Persistent Turning Walker Modelle für
Fischverhalten

Niko Burschik, 2013

In biology, animal movements are often observed and analyzed. In this thesis a model of stochastic differential equations is used to describe the movement of a fish.
Our goal is to show, that, in large time and space scale, the model is of diffusive type. To prove this statement two methods are specified. In the first method we use
the variance of the position vector, the second one uses the Kolmogorov equation, which describes the dynamic of the fish as a time-dependent function.
The second part of this thesis introduces a way to add interactions between the fish
and its environment into the model, in terms of the tank walls. At last numerical simulations of
the fish movement are presented.
[pdf-file]

##
Improvement of PET-Images of
Freely-moving Mice by Registration of
Short-time Reconstructions

Julian Rasch, 2013 (Supervision: Frank Wübbeling)

Gathering 3-dimensional Positron Emission Tomography data of a non-anesthetized, freelymoving
mouse and computing a reasonable reconstruction image is tied to numerous problems.
The major problem is that the mouse is actually moving, since PET imaging usually requires
nearly motionless objects to be investigated. This work will present a framework consisting of
camera-based motion detection and expectation maximization image reconstruction in order to
obtain useful short-time reconstructions during motionless periods of a freely-moving mouse.
These are finally combined to one biologically and medically relevant and meaningful image
by means of registration.
[pdf-file]

##
Inkompressible Grenzwerte
kinetischer Gleichungen

Johannes Stamm, 2013

In this thesis we consider two different kinetic models. On the one hand we study the dynamics of gas, on the other hand the dynamics of animals, which move in flocks in a plain, two dimensional world.
The aim of the first part of this thesis is to derive a macroscopic model, the incompressible Navier-Stokes model, from the microscopic model, the Boltzmann model. To achieve this, we first deduce the Navier-Stokes equation from some basic physical conservation laws. Then we analyse some important properties of the Boltzmann-Equation and develope a velocity field by methods of mean field theory, which will satisfy the conservation equations.
In the second part we first make some presumptions about how a single animal would like to move and what is physically possible. This will lead us to a system of repulsiv and an attractiv forces depending on all the animals in the plain. This model is quite similar to the microscopic model in the first part, but not conservative. As next step we concider the limit of large numbers of animals, which will lead us to a macroscopic model, where we have flocks, regions with scattered animals and empty regions. We find that this is technicaly equivalent to a hydrodynamic system with a partly incompressible (for the region with the flocks) and partly compressible (for the scattered animals) fluid. As last step we figure out, how the dynamics of these different regions can be described. [pdf-file]

##
Transport auf Mikrotubuli - Modellierung der
dynamischen Länge und des Dichteprofils und
Berechnung stationärer Lösungen

Jonas Wanka, 2013

In biology, there are many dynamic structures that are difficult to analyze and model. In this thesis we will create models for microtubule, which are dynamic chain within a cell. For this purpose, two simplified modeling approaches are chosen to determine the length and the stationary states to detect the various operations of the microtubule leading to the lengthening and shortening. The second half of this thesis deals with the analysis of the density profile on the microtubule, which triggers the changes in length. First entropy solutions of time-dependent differential equations are developed in the first order, and then using the boundary layer theory, a solution to the stationary second-order differential equation. Finally, a brief numerical simulation of the differential equation is given to confirm the findings and to visualize.
[pdf-file]

##
Mathematische Modelle für
FRAP-Mikroskopie in
unterschiedlichen Anwendungen

Miriam Riedel, 2013

In this thesis, three different applications of Fluorescence Recovery after
Photobleaching are presented. These are supposed to demonstrate the variety of
uses of this method.
First an introduction into the functioning of Fluorescence Recovery after
Photobleaching as well as the mathematical background necessary for these
models are given. Next there will be the elaboration and evaluation of the
modelling of the three applications. Finally the sensitivity of the method and
the resulting high error potential are discussed.
[pdf-file]

##
Modellierung und Simulation von
FRAP bei Diffusionsprozessen

Janic Föcke, 2013

The determination of diffusion coefficients and flow velocity is subject
to some inaccuracies
and complications due to the microscopic size and the reactivity of a
cell with its
environment. Using Fluorescence Recovery After Photobleaching (FRAP)
these coefficients
are determined by the transport behavior of lipids at a precisely
defined reference
area. Molecules of the cell membrane are labeled with fluorophores and
bleached by
using a laser. Through the continuous process of transport, molecules
moving in and
out of the bleach region, cause an increasing intensity over time of
fluorophores in the
bleached spot. The characteristic curve of such a revovery process
allows conclusions
on the nature and strength of the active process.
First of all, we want to discuss the basic requirements for the
application of FRAP and
secondly work out a modeling of a recovery curve provided by Axelrod et
al. [3]. In
addition, our goal will be to examine the quality of modeling by data
simulations to
verify the applicability. [pdf-file]

##
Turing-Instabilitäten in
Reaktions-Diffusions-Modellen
für die Morphogenese und
numerische Löungen mit
Splitting-Verfahren

Carla Tameling, 2013

Theoretical biologists are very interested in the development of multicellular organisms. They would like to understand in which way the chemicals effect the development.
Morphogenesis is one part of this development. Today scientific researchers assume that this part can be described by Turing-Patterns.
The modeling of a reaction-diffusion-system with Turing-Patterns and the linear stability analysis are part of this thesis.
Furthermore numerical possibilities to solve a reaction-diffusion system are elaborated. In particular some time-splitting-methods are explained and compared.
[pdf-file]

##
Einfluss von Normierung auf die
Analyse von EKG-BSPM Daten

Jonas Kochinke, 2013

The analysis of Body Surface Potential Mapping (BSPM) data leads to a superior understanding of the human heart as an extension of the widely known ECG. In this thesis we discuss the analysis of real data measured by the
Münster University Hospital with the goal of being able to determine an occurring cardiac disease. Different kinds of
normalization of the BSPM data are performed and their effects on the real potential at the heart surface are examined.
[pdf-file]

##
Reconstruction Methods for
Positron Emission Tomography
with Short Scan Time

Sabrina Dill, 2013

Positron Emission Tomography is an important functional imaging technique in nuclear
medicine, where the measured data are corrupted by Poisson noise. Hence, this
thesis begins with an overview on PET and the introduction of a mathematical and
statistically motivated model in order to deal with the emerging inverse problem. At
this point numerical methods like regularization are required for image reconstruction
so we introduce iterative reconstruction algorithms. These methods are presented,
discussed and also combined to yield more accurate results. On the basis of two data
sets, which are taken from a computationally generated software phantom and a hardware
phantom resembling the human thorax, we present explicit error estimates and
reconstructed images as well as explain the effects that are theoretically expected and
evaluate the results critically.
[pdf-file]

##
Regularisierung der EEG/MEG Quellrekonstruktion und ihre Auswirkung auf Gruppenstudien

Miriam Hägele, 2012

In EEG and MEG research neuronal activity is measured outside the skull by capturing electrical potentials and the magnetic field. This leads to the inverse problem of reconstructing
the sources of neuronal activity from the collected data. Mathematically this problem is ill-posed. Therefore we need to use numerical methods such as regularization to solve this
inverse problem. Here we concentrate on singular value decomposition and classical Tikhonov regularization. The problem arising when doing group studies is to whether to treat the
equations separately or rather average them first before applying regularization methods. This is discussed on the basis of a generated set of MEG data in this thesis.
[pdf-file]

##
Dekonvolution in der Mikroskopie

Eva-Maria Brinkmann, 2012

Deblurring and denoising distorted images is one of the central problems in mathematical imaging science as these means provide us with the possibility of an improved image analysis resulting in more precise information about the displayed object. Considering
these problems image deconvolution is one important tool of image restoration, which, since the introduction of the first deconvolution algorithms in the early 1980s, has been of growing
importance in astronomy and optical microscopy. Nowadays the post production of digital photos or movies is another field of application increasing the interest in deconvolution even further.
This thesis gives an overview of the most popular methods of image decovolution focusing on the application in optical microscopy. After a short introduction the second chapter therefore
deals with the operating mode of the optical system that can be found in any light microscope and with its limitations. In the light of these observations a mathematical model of image
formation is presented. Starting from a deterministic or statistical viewpoint, different deconvolution algorithms, some of which include denoising techniques, are derived from this model.
The thesis concludes with the implementation of one relatively new deconvolution algorithm, namely the FB-EM-REG Algorithm, and with the presentation and discussion of results achieved by
applying the FB-EM-REG Algorithm to some microscopy images showing the gain in image quality.
[pdf-file]

##
Hauptkomponentenanalyse
und ihre Anwendung zur Klassifizierung
von Spermien aus Raman
Mikrospektroskopie-Daten

Julia Sietmann, 2012

In modern society the sperm quality of male is decreasing, which causes an increased demand for assisted reproduction.
For this sake it is important to classify the quality of sperm. In this thesis first attempts to evaluate data acquired
by Raman microspectroscopy using principal component analysis, and to subsequently classify sperm.
In order to provide a suitable background, the function and structure of human sperm was reviewed in this thesis, as well as the mathematical
background of principal component analysis.
[pdf-file]

##
Makroskopische Modelle für Kraftgesetze zwischen Zellen

Britte Agsten, 2012

To investigate the behavior of cellular tissues using discrete off-lattice-models, a lot of different aspects have to be considered.
This includes finding an appropriate model for passive physical forces acting between cells. These forces have a great influence on the reaction a
cellular tissue will show to active development (e.g cell-growth/-death, pressure). In this thesis different approaches to model such forces are presented and compared.
Therefore their influence on the behavior of cellular tissues was studied in one dimension, using a discrete model as well as a correspondent continuum model.
[pdf-file]

##
The inverse Problem of
Electrocardiography:
Explanation based on a simple Example

Mareike Hullerum, 2012 (Collaboration with SIMULA Research Labs, Oslo)

The basic idea of an inverse problem is to gather the cause from a given effect and is not always easy to solve. There are lot
of examples of inverse problems in reality. One of these is the inverse problem of electrocardiography, in which the elctrical
activity on the heart surface is computed with given potential on the body surface. In this thesis the medical and mathematical
background information are presented, needed to understand and solve the inverse problem of ecg. Moreover different
regularization techniques, used to obtain a stable solution, are explained based on a simple example. Finally, calculations with
real ecg data, measured by Münster University Hospital, can be found.
[pdf-file]

##
Kinetische Modelle für Schwarmverhalten

Steffen Keul, 2012

When we look into the sky and see a big cloud of birds circling or moving as one intelligence or into the ocean to see a group of fishes when they act like someone is controlling all of them at once its fascinating and we wounder: how do they communicate?
Some biological explenations described mathematicaly leads from the question about how could we discribe the behaviour of one single invididual in the swarm to the macroscopic behaviour of the whole swarm. Therefor we used partial differential equations to form a particle model and evolve it into a kinetic model of swarming.
This ideas are not just used in the description of processes which we can find in the nature but also in the communication technology or in programming.
[pdf-file]

##
Entmischung mit Sparsity-Regularisierung und Anwendungen

Claudia Averkamp, 2011

In this thesis l1-regularization with the split Bregman algorithm is presented to solve unmixing problems. After introducing the split Bregman algorithm two
applications are discussed. The first one is unmixing of hyperspectral images to get information of the structures contained in these images.
The second application is speech extraction. During speech extraction audio recordings of speech are separated from background interference.
Finally the split bregman algorithm is implemented for speech extraction with two audio sources and two mixtures.
[pdf-file]

##
Beschreibung und Vergleich der Form von Punktwolken durch Persistenzbarcodes

Christina Blanke, 2011

This thesis discusses a method to create persistence bar codes from a given point cloud. The barcode is used to
recognize shapes and compare them, which is tested in images of moving cells. Several difficulties and results are discussed.
[pdf-file]

##
SPECT Dämpfungskorrektur ohne zusätzliche Messungen

Carolin Rossmanith, 2011

SPECT imaging is an important aspect of modern nuclear medicine. In this context we are not only interested in adequate recontruction algorithms,
but also require methods for attenuation correction. In this thesis the main reconstruction techniques in SPECT imaging and two different ways to obtain the
attenuation field are presented. The first model makes use of an affine-lineare prototype for the attenuation and a consistency condition for the attenuated Radon transform,
which is proved in detail. The second model applies a non-linear attenuation prototype and improves it with regularization.
[pdf-file]

##
Erweiterungen des Helbing-Modells zur Fussgängerdynamik: Herding und Übergang zum Kontinuum

Karolina Weber, 2011

Pedestrian Motion is an important part in analysing panic situations. Therefore we use the Helbing Model in this thesis to
simulate crowd behaviour. This model is described in a general way and extended with the herding effect. Furthermore a
macroscopic equation is derived systematically from the given equations for continuum purposes. Results of evacuation time and
other phenomenons of a crowd are made on the basis of simulations and compared to previously published results and simulations by
the Helbing group.
[pdf-file]

##
Segmentierung von 2D-Graustufenbildern mit Hilfe homologischer Persistenz: Verschiedene Methoden

Joana Grah, 2011

Algebraic topology and applied mathematics are two basically different and separated directions of mathematical research.
The concept of persistent homology and its recent applications in image processing show the proof of the contrary. In this
thesis three methods for the segmentation of 2D gray scale images using persistent homology are presented. This term and the
required concepts of algebraic topology are explained in the beginning. After that the algorithms based on the theory and its
applications are depicted. Finally, both limitations and possible enhancements are discussed.
[pdf-file]

##
Methoden zur Hintergrunderkennung und Objektverfolgung in Bildfolgen

Jonas Hoppe, 2011

This thesis is about a few methods for recognition of the foreground by subtracting a background image from the image data in image sequences also
called background subtraction. These methods seperate in foreground and background. Furthermore tracking people in image sequences using background
subtraction is studied and an algorithm for tracking cells in microscope videos is introduced. Finally it is tried to get better results in cell tracking
by combining this algorithm and background subtraction techniques.
[pdf-file]

##
Kontinuumsmechanische Modelle der menschlichen Wirbelsäule

Florian Grüne, 2011

In this thesis a threedimensional continuum model for the mechanics of the human spine is developed. In order to provide the required understanding of the anatomy,
at first the composition of the spine is briefly considered. Thereafter the static standard model of structural mechanics is explained as a starting point for further modeling.
This model is a system of partial differential equations which describes the force equilibrium of a deformed body. Based on the mechanical properties of the individual components,
linear as well as nonlinear material models for the vertebrae, intervertabral discs and ligaments are discussed. Combined with the standard model they are adopted in a threedimensional
continuum model of the spine.
[pdf-file]

##
Gittergenerierungsmethoden zur Finite Elemente Simulation aus Bilddaten

Matthias Redecker, 2010

In this thesis we will appropriate some basics about grid generation. With grid we mean data points, which we connect in a specific manner. First we look at extraction of image data and in a next step we discuss how to generate grid structures which are able to represent the cross linked object as well as possible. As well as possible means: As fast as possible, as precise as possible, and in an as robust as possible algorithm. For this issue we take a look at different applications first in two and then in three dimensions.
[pdf-file]

##
Mathematische Modellierung des Ionenstroms durch Nanoporen

Katharina Wenzel, 2010

The understanding of ionic flux through nanopores in cells holds informations
about processes in biological systems. The modelling of such systems is an
important step for the investigation of mechanisms by computer simulations. This
thesis gives insight into the basics of modelling ionic flux through nanopores
by Poisson-Nernst-Planck equations with emphasis on the excess chemical
potential, one dimensional properties of the underlying equations and blocking
of the pore by sediments via the solubility product.
[pdf-file]

##
Mathematische Modelle für
Chemotaxis gemischter
Zellsysteme

Lena Frerking, 2010

This thesis discusses continuous models for chemotaxis. These models consist of partial differential equations which describe the directed movement of cells
based on a chemical gradient. Therefore the existence of a maximum cell density is included. The popular Keller-Segel model for chemotaxis is extended to a
model for two different cell populations which influence each other in the way of moving. It is shown that the entropy in this model decreases. This reflects
the capacity of cells to form specific patterns as a result of chemotaxis.
[pdf-file]

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Mathematische Bildregistrierung mit Anwendung in der Atlas-basierten Segmentierung

Sebastian Suhr, 2010

This thesis discusses two challenging tasks of medical imaging: Segmentation and Registration. In atlas-based segmentation both are combined.
In this thesis we outline the basics of Registration and Segmentation with the help of some examples. After presenting proofs for the existence of a
minimizer in some registration functionals, we take a short look at the numerical implementation . We complete this thesis with a numerical
experiments part with some medical registration problems and atlas-based segmentations.
[pdf-file]

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Parameteridentifikation in chemischen Reaktionsgleichungen

Ines Damerau, 2010

In this bachelor thesis, mathematical models of chemical reactions are developed based on the theory of physical
chemistry. The equations derived by these models contain various parameters which ought to be determined.
Data collected during actual chemical experiments is used to identify these parameters. Subsequently, this paper
focuses on the gaussian method of least square error to solve the equations, illustrated by the examples of coal
pyrolysis and the chlorite-iodide-reaction.
[pdf-file]