Der Beitrag beschäftigt sich mit der Frage, ob Schildkröten alleine anhand der Musterung bzw. Struktur ihres Bauch- Rückenpanzers eindeutig identifiziert werden können. Dabei sollen sinnvolle Identifizierungsmerkmale entwickelt werden, die auf der Basis von Fotos ausgewertet werden. Das Besondere an diesem Problem ist, dass es mit Lernenden ganz unterschiedlicher Altersstufen bearbeitet werden kann und dass es eine unheimliche Vielfalt an mathematischen Methoden gibt, die auf dem Weg zu einer Lösung hilfreich sind: Dies reicht von einfachen geometrischen Überlegungen über Analysis (Integration, Kurvendiskussion) bis hin zu mathematischer Bildverarbeitung und Fragen der Robustheit. Genauso breit wie das Spektrum der einsetzbaren mathematischen Werkzeuge ist die Altergruppe, mit der ein derartiges Projekt durchführbar ist: Vom Grundschulalter bis hin zur Masterarbeit ist eine Bearbeitung möglich, und die benötigte Zeitspanne reicht von wenigen Stunden bis hin zu mehreren Monaten. Im Beitrag wird die angesprochene Vielfalt exemplarisch gezeigt, so dass die Leser im Idealfall das Projekt genau an die Bedürfnisse ihrer Lerngruppe anpassen können.
Um Spielkarten zu mischen gibt es unterschiedliche Techniken, die sich sowohl in ihrem Zeitaufwand, als auch in der Güte der Durchmischung unterscheiden. Der folgende Artikel vermittelt, wie man die Frage nach einer besonders guten Mischtechnik nutzen kann, um mathematische Modellierung anhand einer alltagsnahen Fragestellung in den Unterricht einzubinden. Dabei können verschiedene Aspekte der Stochastik angesprochen werden, und es bietet sich ein breites Potential, auf unterschiedlichen Niveaus Computer zum Generieren von Zufallsexperimenten zu verwenden.
Die Planung von Bushaltestellen in Innenstädten ist ein authentisches Thema, welches sich für den Einsatz in einem realitätsbezogenen Unterricht in unterschiedlichen Klassenstufen eignet. Verschiedene Interessen und Gegebenheiten müssen in einem Modell und in einer Lösungsstrategie vereint werden. Durch eine sehr offen gewählte Fragestellung sind verschiedene Ansätze und Modelle möglich. Somit wird mathematisches Modellieren trainiert und das Durchlaufen eines Modellierungsprozesses in einem interessanten Projekt ermöglicht. Die mathematischen Hintergründe sowie das vielseitige Lösungsspektrum von Schülerinnen und Schülern unterschiedlicher Jahrgangsstufen zu derselben Fragestellung werden im Folgenden vorgestellt.
Die Autoren befassen sich mit der Ableitung und Bearbeitung eines Modellierungsprojektes aus der populären Sportart Fußball: Ein Freistoß wird unter Beachtung der gegebenen physikalischen Effekte mathematisch modelliert und simuliert. Der Fokus liegt auf der möglichen Durchführung dieses Modellierungsprojekts mit Schülerinnen und Schülern der Sekundarstufe II.
Typically software engineers implement their software according to the design of the software
structure. Relations between classes and interfaces such as method-call relations and inheritance
relations are essential parts of a software structure. Accordingly, analyzing several types of
relations will benefit the static analysis process of the software structure. The tasks of this
analysis include but not limited to: understanding of (legacy) software, checking guidelines,
improving product lines, finding structure, or re-engineering of existing software. Graphs with
multi-type edges are possible representation for these relations considering them as edges, while
nodes represent classes and interfaces of software. Then, this multiple type edges graph can
be mapped to visualizations. However, the visualizations should deal with the multiplicity of
relations types and scalability, and they should enable the software engineers to recognize visual
patterns at the same time.
To advance the usage of visualizations for analyzing the static structure of software systems,
I tracked difierent development phases of the interactive multi-matrix visualization (IMMV)
showing an extended user study at the end. Visual structures were determined and classified
systematically using IMMV compared to PNLV in the extended user study as four categories:
High degree, Within-package edges, Cross-package edges, No edges. In addition to these structures
that were found in these handy tools, other structures that look interesting for software
engineers such as cycles and hierarchical structures need additional visualizations to display
them and to investigate them. Therefore, an extended approach for graph layout was presented
that improves the quality of the decomposition and the drawing of directed graphs
according to their topology based on rigorous definitions. The extension involves describing
and analyzing the algorithms for decomposition and drawing in detail giving polynomial time
complexity and space complexity. Finally, I handled visualizing graphs with multi-type edges
using small-multiples, where each tile is dedicated to one edge-type utilizing the topological
graph layout to highlight non-trivial cycles, trees, and DAGs for showing and analyzing the
static structure of software. Finally, I applied this approach to four software systems to show
The goal of this work is to develop statistical natural language models and processing techniques
based on Recurrent Neural Networks (RNN), especially the recently introduced Long Short-
Term Memory (LSTM). Due to their adapting and predicting abilities, these methods are more
robust, and easier to train than traditional methods, i.e., words list and rule-based models. They
improve the output of recognition systems and make them more accessible to users for browsing
and reading. These techniques are required, especially for historical books which might take
years of effort and huge costs to manually transcribe them.
The contributions of this thesis are several new methods which have high-performance computing and accuracy. First, an error model for improving recognition results is designed. As
a second contribution, a hyphenation model for difficult transcription for alignment purposes
is suggested. Third, a dehyphenation model is used to classify the hyphens in noisy transcription. The fourth contribution is using LSTM networks for normalizing historical orthography.
A size normalization alignment is implemented to equal the size of strings, before the training
phase. Using the LSTM networks as a language model to improve the recognition results is
the fifth contribution. Finally, the sixth contribution is a combination of Weighted Finite-State
Transducers (WFSTs), and LSTM applied on multiple recognition systems. These contributions
will be elaborated in more detail.
Context-dependent confusion rules is a new technique to build an error model for Optical
Character Recognition (OCR) corrections. The rules are extracted from the OCR confusions
which appear in the recognition outputs and are translated into edit operations, e.g., insertions,
deletions, and substitutions using the Levenshtein edit distance algorithm. The edit operations
are extracted in a form of rules with respect to the context of the incorrect string to build an
error model using WFSTs. The context-dependent rules assist the language model to find the
best candidate corrections. They avoid the calculations that occur in searching the language
model and they also make the language model able to correct incorrect words by using context-
dependent confusion rules. The context-dependent error model is applied on the university of
Washington (UWIII) dataset and the Nastaleeq script in Urdu dataset. It improves the OCR
results from an error rate of 1.14% to an error rate of 0.68%. It performs better than the
state-of-the-art single rule-based which returns an error rate of 1.0%.
This thesis describes a new, simple, fast, and accurate system for generating correspondences
between real scanned historical books and their transcriptions. The alignment has many challenges, first, the transcriptions might have different modifications, and layout variations than the
original book. Second, the recognition of the historical books have misrecognition, and segmentation errors, which make the alignment more difficult especially the line breaks, and pages will
not have the same correspondences. Adapted WFSTs are designed to represent the transcription. The WFSTs process Fraktur ligatures and adapt the transcription with a hyphenations
model that allows the alignment with respect to the varieties of the hyphenated words in the line
breaks of the OCR documents. In this work, several approaches are implemented to be used for
the alignment such as: text-segments, page-wise, and book-wise approaches. The approaches
are evaluated on German calligraphic (Fraktur) script historical documents dataset from “Wan-
derungen durch die Mark Brandenburg” volumes (1862-1889). The text-segmentation approach
returns an error rate of 2.33% without using a hyphenation model and an error rate of 2.0%
using a hyphenation model. Dehyphenation methods are presented to remove the hyphen from
the transcription. They provide the transcription in a readable and reflowable format to be used
for alignment purposes. We consider the task as classification problem and classify the hyphens
from the given patterns as hyphens for line breaks, combined words, or noise. The methods are
applied on clean and noisy transcription for different languages. The Decision Trees classifier
returns better performance on UWIII dataset and returns an accuracy of 98%. It returns 97%
on Fraktur script.
A new method for normalizing historical OCRed text using LSTM is implemented for different texts, ranging from Early New High German 14th - 16th centuries to modern forms in New
High German applied on the Luther bible. It performed better than the rule-based word-list
approaches. It provides a transcription for various purposes such as part-of-speech tagging and
n-grams. Also two new techniques are presented for aligning the OCR results and normalize the
size by using adding Character-Epsilons or Appending-Epsilons. They allow deletion and insertion in the appropriate position in the string. In normalizing historical wordforms to modern
wordforms, the accuracy of LSTM on seen data is around 94%, while the state-of-the-art combined rule-based method returns 93%. On unseen data, LSTM returns 88% and the combined
rule-based method returns 76%. In normalizing modern wordforms to historical wordforms, the
LSTM delivers the best performance and returns 93.4% on seen data and 89.17% on unknown
In this thesis, a deep investigation has been done on constructing high-performance language
modeling for improving the recognition systems. A new method to construct a language model
using LSTM is designed to correct OCR results. The method is applied on UWIII and Urdu
script. The LSTM approach outperforms the state-of-the-art, especially for unseen tokens
during training. On the UWIII dataset, the LSTM returns reduction in OCR error rates from
1.14% to 0.48%. On the Nastaleeq script in Urdu dataset, the LSTM reduces the error rate
from 6.9% to 1.58%.
Finally, the integration of multiple recognition outputs can give higher performance than a
single recognition system. Therefore, a new method for combining the results of OCR systems is
explored using WFSTs and LSTM. It uses multiple OCR outputs and votes for the best output
to improve the OCR results. It performs better than the ISRI tool, Pairwise of Multiple Sequence and it helps to improve the OCR results. The purpose is to provide correct transcription
so that it can be used for digitizing books, linguistics purposes, N-grams, and part-of-speech
tagging. The method consists of two alignment steps. First, two recognition systems are aligned
using WFSTs. The transducers are designed to be more flexible and compatible with the different symbols in line and page breaks to avoid the segmentation and misrecognition errors.
The LSTM model then is used to vote the best candidate correction of the two systems and
improve the incorrect tokens which are produced during the first alignment. The approaches
are evaluated on OCRs output from the English UWIII and historical German Fraktur dataset
which are obtained from state-of-the-art OCR systems. The Experiments show that the error
rate of ISRI-Voting is 1.45%, the error rate of the Pairwise of Multiple Sequence is 1.32%, the
error rate of the Line-to-Page alignment is 1.26% and the error rate of the LSTM approach has
the best performance with 0.40%.
The purpose of this thesis is to contribute methods providing correct transcriptions corresponding to the original book. This is considered to be the first step towards an accurate and
more effective use of the documents in digital libraries.
In this paper we introduce a binary autoregressive model. In contrast to the typical autoregression framework, we allow the conditional distribution of the observed process to depend on past values of the time series and some exogenous variables. Such processes have
potential applications in econometrics, medicine and environmental sciences. In this
paper, we establish stationarity and geometric ergodicity of these
processes under suitable conditions on the parameters of the model. Such properties are
important for understanding the stability properties of the model as well as for deriving the
asymptotic behavior of the parameter estimators.
In this paper we consider a multivariate switching model, with constant states means
and covariances. In this model, the switching mechanism between the basic states of
the observed time series is controlled by a hidden Markov chain. As illustration, under
Gaussian assumption on the innovations and some rather simple conditions, we prove
the consistency and asymptotic normality of the maximum likelihood estimates of the model parameters.
An efficient mathematical model to virtually generate woven metal wire meshes is
presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional
images of real meshes, which are produced via computer tomography. Virtual structures
are generated for three types of metal wire meshes using only easy to measure parameters. For these
geometries the velocity-dependent pressure drop is simulated and compared with measurements
performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of
the measurements. The generation of the structures and the numerical simulations were done at
GKD using the Fraunhofer GeoDict software.
Continuously improving imaging technologies allow to capture the complex spatial
geometry of particles. Consequently, methods to characterize their three
dimensional shapes must become more sophisticated, too. Our contribution to
the geometric analysis of particles based on 3d image data is to unambiguously
generalize size and shape descriptors used in 2d particle analysis to the spatial
While being defined and meaningful for arbitrary particles, the characteristics
were actually selected motivated by the application to technical cleanliness. Residual
dirt particles can seriously harm mechanical components in vehicles, machines,
or medical instruments. 3d geometric characterization based on micro-computed
tomography allows to detect dangerous particles reliably and with
high throughput. It thus enables intervention within the production line. Analogously
to the commonly agreed standards for the two dimensional case, we
show how to classify 3d particles as granules, chips and fibers on the basis of
the chosen characteristics. The application to 3d image data of dirt particles is