Refine
Year of publication
Document Type
- Doctoral Thesis (36)
- Article (30)
- Final Thesis (1)
Language
- English (67) (remove)
Has Fulltext
- yes (67)
Is part of the Bibliography
- no (67)
Keywords
- - (21)
- Statistik (4)
- fractal (4)
- permutation entropy (3)
- Algebra (2)
- Bioinformatik (2)
- Bundle Gerbes (2)
- Fraktal (2)
- Funktionalanalysis (2)
- Hierarchie (2)
- Kategorientheorie (2)
- Logarithmic capacity (2)
- Mathematical Physics (2)
- NOD1/2 (2)
- Selbstähnlichkeit (2)
- YOLOv4 (2)
- animal activity (2)
- animal monitoring (2)
- autocorrelation (2)
- cellular homeostasis (2)
- computer vision (2)
- order pattern (2)
- self-similarity (2)
- signal processing (2)
- time series (2)
- tuberculosis (2)
- (generalized) linear mixed model (1)
- (verallgemeinertes) lineares gemischtes Modell (1)
- 16S rRNA gene sequencing (1)
- 33C10 (1)
- 60B15 (1)
- 60H05 (primary) (1)
- <i>A. thaliana</i> (1)
- <i>Mycobacterium avium</i> ssp. <i>paratuberculosis</i> (MAP) (1)
- <i>Mycobacterium tuberculosis</i> (1)
- AUGUSTUS (1)
- Algebra Bundles (1)
- Algebra, Funktionalanalysis (1)
- Algorithmic Cheminformatics (1)
- Algorithmus (1)
- Alignment (1)
- Alignment <Biochemie> (1)
- Alignment anchor (1)
- BAYES (1)
- Barth syndrome, Cardiolipin, tafazzin, cellular proliferation, gene expression (1)
- Bayes-Netz (1)
- Beobachtungsprozess (1)
- Bernoulli convolution (1)
- Bernoulli convolutions (1)
- Bernoulli-Faltungen (1)
- Bialgebra (1)
- Bildklassifikation (1)
- Bioinformatics (1)
- Biomathematik , Bioinformatik (1)
- Bundle gerbe (1)
- Buneman theorem (1)
- Buscher rules (1)
- Bündelgerbe (1)
- CRF (1)
- Cantor dust (1)
- Cantor set (1)
- Characteristic Attribute Organization System (1)
- Charge simulation method (1)
- Clade Annotation (1)
- Class-imbalanced Data (1)
- Classification (1)
- Cluster (1)
- Comparative Gene Finding (1)
- Comparative Genomics (1)
- Conformal map (1)
- Convergence of Markov chains (1)
- Convolutional Neural Networks (1)
- Covid-19 (1)
- DNA taxonomy (1)
- Darbellay-Vajda Partitionsregel (1)
- Darstellung (1)
- Data Science (1)
- Dichteschätzung (1)
- Differentialgeometrie (1)
- Differentialgleichung (1)
- Dimensionsreduktion (1)
- Dual Decomposition (1)
- Dualität (1)
- Dynamical System (1)
- Dynamische Systeme (1)
- ELISA (1)
- Elastizitätstheorie (1)
- Enzym (1)
- Eulerian numbers (1)
- Evolution (1)
- Evolution der Genregulation (1)
- Evolution of Gene Regulation (1)
- Expressionsdaten (1)
- Fast multipole method (1)
- Fettleber (1)
- Fock-Raum (1)
- GMRES method (1)
- GNS-Konstruktion (1)
- Gammaverteilung (1)
- Gene Structure Prediction (1)
- Gene prediction (1)
- Genetic Evolution (1)
- Genetische Netzwerke (1)
- Genome Annotation (1)
- Genome alignment (1)
- Genregulation (1)
- Geometric hashing (1)
- Geometrie (1)
- Geometry (1)
- Germany (1)
- Graph (1)
- Graph Theory (1)
- Graphentheorie (1)
- Graphenzeichnen (1)
- Green’s function (1)
- Grenzwertsatz (1)
- Hausdorff-Dimension (1)
- High-Dimensional Data (1)
- Highest density regions (1)
- Histogramm (1)
- Histogramm-Konstruktion (1)
- Histogramme (1)
- Hoch-dimensionale Daten (1)
- Hochdurchsatz (1)
- Hopf bundle (1)
- Hopf-Algebra (1)
- Hopfbündel (1)
- Hutchinson Operator (1)
- Hutchinson-Operator (1)
- Hybride stochastische Modelle (1)
- IL-10 (1)
- Image Classification (1)
- Imbalancierte Daten (1)
- In-Host Modeling (1)
- Infinite Dimensional Geometry (1)
- Informationsabhängigkeit (1)
- Informationsvisualisierung (1)
- Innerwurfvarianz (1)
- Integer Linear Program (1)
- Interaktionsfläche (1)
- Interpretability (1)
- Interpretable Machine Learning (1)
- Iterated Function System (1)
- Iteriertes Funktionensystem (1)
- Kotensorfunktor (1)
- Labelingproblem (1)
- Lagrangian Relaxation (1)
- Latent Structure (1)
- Lemniscatic domain (1)
- Level-Set-Methode (1)
- Likelihood-Quotienten-Test (1)
- Linear Elasticity (1)
- Lévy processes (1)
- Lévy-Prozess (1)
- Lévy-prozess (1)
- MCMC (1)
- Markierungswiederherstellung (1)
- Markov-Kette (1)
- Maschinelles Lernen (1)
- Mathematical Phylogenetic (1)
- Mathematical Phylogenetics (1)
- Mathematik (1)
- Mathematische Modellierung (1)
- Mathematische Phylogenetik (1)
- Maßanalyse (1)
- Metabolismus (1)
- Miniprot (1)
- Minkowski-Metrik (1)
- Model selection (1)
- Modeling Infection (1)
- Modeling Tryptophan-Metabolism (1)
- Modeling in Pigs (1)
- Modeling of Infectious Diseases (1)
- Modellierung (1)
- Monoidale Kategorie (1)
- Multiply connected domain (1)
- NGS (1)
- NLRP1 (1)
- NLRP3 (1)
- NOD-like receptors (1)
- NOD‐like receptors (1)
- NP-completeness (1)
- Network (1)
- Netzwerk (1)
- Nichtlineares dynamisches System (1)
- One Health (1)
- Optimal Control (1)
- Optimale Kontrolle (1)
- Outlier Detection (1)
- Outlier-Erkennung (1)
- PD-L1 (1)
- PDE (1)
- Perron-Frobenius theorem (1)
- Phylogenetic tree (1)
- Phylogenetics (1)
- Pisot-Zahl (1)
- Polynomial pre-image (1)
- Position Specific Scoring Matrix (1)
- Protein (1)
- Protein coding gene (1)
- Proteinwechselwirkungsstelle (1)
- Quanten-Lévy-Prozess (1)
- Quantengruppe (1)
- Quantenwahrscheinlichkeitstheorie (1)
- Quasi-Pseudo-Metrik (1)
- Random matrices (1)
- Randomisierung (1)
- Rechenmethoden (1)
- SNP-specific alpha-level, colocalization (1)
- SPecies IDentity and Evolution in R (1)
- Schale (1)
- Schwein (1)
- Segmentierung (1)
- Self-assembling protein design (1)
- Shells (1)
- Simulation (1)
- Slice (1)
- Spaced seeds (1)
- Spannender Baum (1)
- Spektrum (1)
- Spike and Slab (1)
- Statistics (1)
- Stetiger Markov-Prozess (1)
- Stoffwechselweg (1)
- String Geometry (1)
- Stückweise deterministischer Markov Prozess (1)
- T-Duality (1)
- T-Dualität (1)
- Taxonomie (1)
- Test von zufälligen Effekten (1)
- Transcription Factor Binding Site (1)
- Transfer Operator (1)
- Transfer-Operator (1)
- Transkriptionsfaktorbindestellen (1)
- Treemap (1)
- Tryptophan (1)
- Tryptophan-Metabolism (1)
- Twisted K-Theory (1)
- Unabhängigkeitanalyse (1)
- Ungewissheit (1)
- Urinary albumin to creatinine ratio (UACR) (1)
- Variationsrechnung (1)
- Visualisierung (1)
- Visualization (1)
- Vorhersage (1)
- X-splits (1)
- Zufallsmatrizen (1)
- Zylinderschale (1)
- aging (1)
- alternative splicing (1)
- animal behavior (1)
- animal welfare (1)
- aperiodic tile (1)
- bacterial-fungal interaction (1)
- beta-representation (1)
- bioinformatics (1)
- biologischer Quellen (1)
- body posture (1)
- cattle trade (1)
- cell biology (1)
- cell fractionation (1)
- classification models (1)
- co-transcriptional regulation (1)
- community detection (1)
- concentration coefficient (1)
- conditional association analysis (1)
- conditional random field (1)
- dairy cows (1)
- diagnostic (genetic) characters (1)
- drug (1)
- duale Halbgruppe (1)
- emerging diseases (1)
- environmental samples (1)
- epidemic model (1)
- estimated glomerular filtration rate (eGFR) (1)
- exhaled breath (1)
- expression quantitative trait loci (eQTL) (1)
- fecal culture (1)
- fecal headspace (1)
- fluorescent pseudomonads (1)
- free probability (1)
- fungal growth inhibition (1)
- gamma distribution (1)
- gene expression (1)
- genome-wide association studies (GWAS) (1)
- granuloma (1)
- high temperature (1)
- histogram construction (1)
- histograms (1)
- immunology (1)
- infectious diseases (1)
- inflammation (1)
- influenza A virus infection (1)
- innate immunity (1)
- integrative taxonomy (1)
- invariant measure (1)
- invariantes Maß (1)
- konsistente Schätzung (1)
- kw: Graph Theory (1)
- latent class model (1)
- liver disease (1)
- mRNA (1)
- machine learning (1)
- mathematical modeling (1)
- mathematical statistics (1)
- mathematische Statistik (1)
- maximum parsimony (1)
- metaproteome (1)
- microRNA (1)
- microarray (1)
- microbiome (1)
- microfluidic device (1)
- migratory connectivity (1)
- milk pools (1)
- mixed binomial point process (1)
- mixture proposals (1)
- modularity (1)
- multinomial distribution (1)
- multiple sequence alignment (1)
- myeloid-derived suppressor cells (1)
- neighbor map (1)
- network analysis (1)
- neutrophils (1)
- nichtparametrische Dichteschätzung (1)
- non-commutative independences (1)
- nonparametric density estimation (1)
- observation process (1)
- oocyte (1)
- ordinal time series (1)
- ovine anaplasmosis (1)
- parametric bootstrap (1)
- parametrisches Bootstrap (1)
- paratuberculosis (1)
- pathogens (1)
- pathology (1)
- plant pathogen (1)
- pn: Nikolai Nøjgaard (1)
- pre-mRNA (1)
- probabilistic interface labeling problem (1)
- profile hidden Markov model (1)
- protein (1)
- proteome (1)
- quadratic number field (1)
- quantum groups (1)
- quantum probability (1)
- random forest (1)
- randomization (1)
- real-time PCR (1)
- red foxes (1)
- regulatory networks (1)
- relative entropy (1)
- reprogramming (1)
- restricted M-splines (1)
- räumliches Überleben (1)
- self-similar (1)
- sheep (1)
- sleep stages (1)
- small molecule (1)
- snoRNAs (1)
- sparsame Darstellung von Daten (1)
- sparse representation of data (1)
- spatial survival (1)
- spectrum (1)
- sphingolipid metabolism (1)
- splicing regulation (1)
- stable air (1)
- statistics (1)
- stichprobenabhängige Partitionsregel (1)
- stochastic block model (1)
- subsp. (1)
- systems biology (1)
- test of random effects (1)
- tick-borne fever (1)
- tiling, self-similarity, fractal, aperiodic, iterated function system (1)
- tissue specificity (1)
- trans dimensional sampling (1)
- universelles Produkt (1)
- virology (1)
- volatile organic compound (VOC) (1)
- within-litter variation (1)
Institute
- Institut für Mathematik und Informatik (67) (remove)
Publisher
- MDPI (14)
- Frontiers Media S.A. (6)
- Springer Nature (4)
- BioMed Central (BMC) (2)
- Oxford University Press (1)
- Wiley (1)
A lot of research data has become available since the outbreak of the COVID-19
pandemic in 2019. Connecting this data is essential for the understanding of the
SARS-CoV-2 virus and the fight against the pandemic.
Amongst biological and biomedical research data, computational models targeting
COVID-19 have been emerging and their number is growing constantly. They are a
central part of the field of Systems Biology, which aims to understand the mechanisms
and behaviour of biological systems. Model predictions help to understand the
mechanisms of the novel coronavirus and the life-threatening disease it is causing.
Both biomedical research data and modelling data regarding COVID-19 have
previously been stored in separated domain-specific graph databases. MaSyMoS,
short for Management System for Models and Simulations, is a graph database for
storing simulation studies of biological and biochemical systems. The CovidGraph
project integrates research data regarding COVID-19 and the coronavirus family
from various data resources in a knowledge graph.
In this thesis, we integrate simulation models from MaSyMoS, including models
targeting COVID-19, into the CovidGraph. Therefore, we present a concept for
the integration of simulation studies and the linkage through ontology terms and
reference publications in the CovidGraph. Ultimately, we connect data from the field
of systems biology and biomedical research data in a graph database.
This thesis revolves around a new concept of independence of algebras. The independence nicely fits into the framework of universal products, which have been introduced to classify independence relations in quantum probability theory; the associated product is called (r,s)-product and depends on two complex parameters r and s. Based on this product, we develop a theory which works without using involutive algebras or states. The following aspects are considered: 1. Classification: Universal products are defined on the free product of algebras (the coproduct in the category of algebras) and model notions of independence in quantum probability theory. We distinguish universal products according to their behaviour on elements of length two, calling them (r,s)-universal products with complex parameters r and s respectively. In case r and s equal 1, Muraki was able to show that there exist exactly five universal products (Muraki’s five). For r equals s nonzero we get five one parameter families (q-Muraki’s five). We prove that in the case r not equal to s the (r,s)-product, a two parameter deformation of the Boolean product, is the only universal product satisfying our set of axioms. The corresponding independence is called (r,s)-independence. 2. Dual pairs and GNS construction: By use of the GNS construction, one can associate a product of representations with every positive universal product. Since the (r,s)-product does not preserve positivity, we need a substitute for the usual GNS construction for states on involutive algebras. In joint work with M. Gerhold, the product of representations associated with the (r,s)-product was determined, whereby we considered representations on dual pairs instead of Hilbert spaces. This product of representations is - as we could show - essentially different from the Boolean product. 3. Reduction and quantum Lévy processes: U. Franz introduced a category theoretical concept which allows a reduction of the Boolean, monotone and antimonotone independence to the tensor independence. This existing reduction could be modified in order to apply to the (r,s)-independence. Quantum Lévy processes with (r,s)-independent increments can, in analogy with the tensor case, be realized as solutions of quantum stochastic differential equations. To prove this theorem, the previously mentioned reduction principle in the sense of U. Franz and a generalization of M. Schürmann’s theory for symmetric Fock spaces over dual pairs are used. As the main result, we obtain the realization of every (r,s)-Lévy process as solution of a quantum stochastic differential equation. When one, more generally, defines Lévy processes in a categorial way using U. Franz’s definition of independence for tensor categories with inclusions, compatibility of the inclusions with the tensor category structure plays an important role. For this thesis such a compatibility condition was formulated and proved to be equivalent to the characterization proposed by M. Gerhold. 4. Limit distributions: We work with so-called dual semigroups in the sense of D. V. Voiculescu (comonoids in the tensor category of algebras with free product). The polynomial algebra with primitive comultiplication is an example for such a dual semigroup. We use a "weakened" reduction which we call reduction of convolution and which essentially consists of a cotensor functor constructed from the symmetric tensor algebra. It turns dual semigroups into commutative bialgebras and also translates the convolution exponentials. This method, which can be nicely described in the categorial language, allows us to formulate central limit theorems for the (r,s)-independence and to calculate the correponding limit distributions (convergence in moments). We calculate the moments appearing in the central limit theorem for the (r,s)-product: The even moments are homogeneous polynomials in r and s with the Eulerian numbers as coefficients; the odd moments vanish. The moment sequence that we get from the central limit theorem for an arbitrary universal product is the moment sequence of a probability measure on the real line if and only if r equals s greater or equal to 1. In this case we present an explicit formula for the probability measure.
A New Kind of Permutation Entropy Used to Classify Sleep Stages from Invisible EEG Microstructure
(2017)
We consider Iterated Function Systems (IFS) on the real line and on the complex plane. Every IFS defines a self-similar measure supported on a self-similar set. We study the transfer operator (which acts on the space of continuous functions on the self-similar set) and the Hutchinson operator (which acts on the space of Borel regular measures on the self-similar set). We show that the transfer operator has an infinitely countable set of polynomial eigenfunctions. These eigenfunctions can be regarded as generalized Bernoulli polynomials. The polynomial eigenfuctions define a polynomial approximation of the self-similar measure. We also study the moments of the self-similar measure and give recursions for computing them. Further, we develop a numerical method based on Markov chains to study the spectrum of the Hutchinson and transfer operators. This method provides numerical approximations of the invariant measure for which we give error bounds in terms of the Wasserstein-distance. The standard example in this thesis is the parametric family of Bernoulli convolutions.
Self-affine tiles and fractals are known as examples in analysis and topology, as models of quasicrystals and biological growth, as unit intervals of generalized number systems, and as attractors of dynamical systems. The author has implemented a software which can find new examples and handle big databases of self-affine fractals. This thesis establishes the algebraic foundation of the algorithms of the IFStile package. Lifting and projection of algebraic and rational iterated function systems and many properties of the resulting attractors are discussed.
Anaplasma phagocytophilum and Anaplasma ovis–Emerging Pathogens in the German Sheep Population
(2021)
Knowledge on the occurrence of pathogenic tick-borne bacteria Anaplasma phagocytophilum and Anaplasma ovis is scarce in sheep from Germany. In 2020, owners from five flocks reported ill thrift lambs and ewes with tick infestation. Out of 67 affected sheep, 55 animals were clinically examined and hematological values, blood chemistry and fecal examinations were performed to investigate the underlying disease causes. Serological tests (cELISA, IFAT) and qPCR were applied to all affected sheep to rule out A. phagocytophilum and A. ovis as a differential diagnosis. Ticks were collected from selected pastures and tested by qPCR. Most animals (n = 43) suffered from selenium deficiency and endoparasites were detected in each flock. Anaplasma spp. antibodies were determined in 59% of examined sheep. Seventeen animals tested positive for A. phagocytophilum by qPCR from all flocks and A. phagocytophilum was also detected in eight pools of Ixodes ricinus. Anaplasma phagocytophilum isolates from sheep and ticks were genotyped using three genes (16S rRNA, msp4 and groEL). Anaplasma ovis DNA was identified in six animals from one flock. Clinical, hematological and biochemical changes were not significantly associated with Anaplasma spp. infection. The 16S rRNA analysis revealed known variants of A. phagocytophilum, whereas the msp4 and groEL showed new genotypes. Further investigations are necessary to evaluate the dissemination and health impact of both pathogens in the German sheep population particularly in case of comorbidities.
In phylogenetics, evolutionary relationships of different species are represented by phylogenetic trees.
In this thesis, we are mainly concerned with the reconstruction of ancestral sequences and the accuracy of this reconstruction given a rooted binary phylogenetic tree.
For example, we wish to estimate the DNA sequences of the ancestors given the observed DNA sequences of today living species.
In particular, we are interested in reconstructing the DNA sequence of the last common ancestor of all species under consideration. Note that this last common ancestor corresponds to the root of the tree.
There exist various methods for the reconstruction of ancestral sequences.
A widely used principle for ancestral sequence reconstruction is the principle of parsimony (Maximum Parsimony).
This principle means that the simplest explanation it the best.
Applied to the reconstruction of ancestral sequences this means that a sequence which requires the fewest evolutionary changes along the tree is reconstructed.
Thus, the number of changes is minimized, which explains the name of Maximum Parsimony.
Instead of estimating a whole DNA sequence, Maximum Parsimony considers each position in the sequence separately. Thus in the following, each sequence position is regarded separately, and we call a single position in a sequence state.
It can happen that the state of the last common ancestor is reconstructed unambiguously, for example as A. On the other hand, Maximum Parsimony might be indecisive between two DNA nucleotides, say for example A and C.
In this case, the last common ancestor will be reconstructed as {A,C}.
Therefore we consider, after an introduction and some preliminary definitions, the following question in Section 3: how many present-day species need to be in a certain state, for example A, such that the Maximum Parsimony estimate of the last common ancestor is also {A}?
The answer of this question depends on the tree topology as well as on the number of different states.
In Section 4, we provide a sufficient condition for Maximum Parsimony to recover the ancestral state at the root correctly from the observed states at the leaves.
The so-called reconstruction accuracy for the reconstruction of ancestral states is introduced in Section 5. The reconstruction accuracy is the probability that the true root state is indeed reconstructed and always takes two processes into account: on the one hand the approach to reconstruct ancestral states, and on the other hand the way how the states evolve along the edges of the tree. The latter is given by an evolutionary model.
In the present thesis, we focus on a simple symmetric model, the Neyman model.
The symmetry of the model means for example that a change from A to C is equally likely than a change from C to A.
Intuitively, one could expect that the reconstruction accuracy it the highest when all present-day species are taken into account. However, it has long been known that the reconstruction accuracy improves when some taxa are disregarded for the estimation.
Therefore, the question if there exits at least a lower bound for the reconstruction accuracy arises, i.e. if it is best to consider all today living species instead of just one for the reconstruction.
This is bad news for Maximum Parsimony as a criterion for ancestral state reconstruction, and therefore the question if there exists at least a lower bound for the reconstruction accuracy arises.
In Section 5, we start with considering ultrametric trees, which are trees where the expected number of substitutions from the root to each leaf is the same.
For such trees, we investigate a lower bound for the reconstruction accuracy, when the number of different states at the leaves of the tree is 3 or 4.
Subsequently in Section 6, in order to generalize this result, we introduce a new method for ancestral state reconstruction: the coin-toss method.
We obtain new results for the reconstruction accuracy of Maximum Parsimony by relating Maximum Parsimony to the coin-toss method.
Some of these results do not require the underlying tree to be ultrametric.
Then, in Section 7 we investigate the influence of specific tree topologies on the reconstruction accuracy of Maximum Parsimony. In particular, we consider balanced and imbalanced trees as the balance of a tree may have an influence on the reconstruction accuracy.
We end by introducing the Colless index in Section 8, an index which measures the degree of balance a rooted binary tree can have, and analyze its extremal properties.
Influenza A Virus (IAV) infection followed by bacterial pneumonia often leads to hospitalization and death in individuals from high risk groups. Following infection, IAV triggers the process of viral RNA replication which in turn disrupts healthy gut microbial community, while the gut microbiota plays an instrumental role in protecting the host by evolving colonization resistance. Although the underlying mechanisms of IAV infection have been unraveled, the underlying complex mechanisms evolved by gut microbiota in order to induce host immune response following IAV infection remain evasive. In this work, we developed a novel Maximal-Clique based Community Detection algorithm for Weighted undirected Networks (MCCD-WN) and compared its performance with other existing algorithms using three sets of benchmark networks. Moreover, we applied our algorithm to gut microbiome data derived from fecal samples of both healthy and IAV-infected pigs over a sequence of time-points. The results we obtained from the real-life IAV dataset unveil the role of the microbial families Ruminococcaceae, Lachnospiraceae, Spirochaetaceae and Prevotellaceae in the gut microbiome of the IAV-infected cohort. Furthermore, the additional integration of metaproteomic data enabled not only the identification of microbial biomarkers, but also the elucidation of their functional roles in protecting the host following IAV infection. Our network analysis reveals a fast recovery of the infected cohort after the second IAV infection and provides insights into crucial roles of Desulfovibrionaceae and Lactobacillaceae families in combating Influenza A Virus infection. Source code of the community detection algorithm can be downloaded from https://github.com/AniBhar84/MCCD-WN.
Approaches to the Analysis of Proteomics and Transcriptomics Data based on Statistical Methodology
(2014)
Recent developments in genomics and molecular biology led to the generation of an enormous amount of complex data of different origin. This is demonstrated by a number of published results from microarray experiments in Gene Expression Omnibus. The number was growing in exponential pace over the last decade. The challenge of interpreting these vast amounts of data from different technologies led to the development of new methods in the fields of computational biology and bioinformatics. Researchers often want to represent biological phenomena in the most detailed and comprehensive way. However, due to the technological limitations and other factors like limited resources this is not always possible. On one hand, more detailed and comprehensive research generates data of high complexity that is very often difficult to approach analytically, however, giving bioinformatics a chance to draw more precise and deeper conclusions. On the other hand, for low-complexity tasks the data distribution is known and we can fit a mathematical model. Then, to infer from this mathematical model, researchers can use well-known and standard methodologies. In return for using standard methodologies, the biological questions we are answering might not be unveiling the whole complexity of the biological meaning. Nowadays it is a standard that a biological study involves generation of large amounts of data that needs to be analyzed with a statistical inference. Sometimes data challenge researchers with low complexity task that can be performed with standard and popular methodologies as in Proteomic analysis of mouse oocytes reveals 28 candidate factors of the "reprogrammome". There, we established a protocol for proteomics data that involves preprocessing of the raw data and conducting Gene Ontology overrepresentation analysis utilizing hypergeometric distribution. In cases, where the data complexity is high and there are no published frameworks a researcher could follow, randomization can be an approach to exploit. In two studies by The mouse oocyte proteome escapes maternal aging and CellFateScout - a bioinformatics tool for elucidating small molecule signaling pathways that drive cells in a specific direction we showed how randomization can be performed for distinct complex tasks. In The mouse oocyte proteome escapes maternal aging we constructed a random sample of semantic similarity score between oocyte transcriptome and random transcriptome subset of oocyte proteome size. Therefore, we could calculate whether the proteome is representative of the trancriptome. Further, we established a novel framework for Gene Ontology overrepresentation that involves randomization testing. Every Gene Ontology term is tested whether randomly reassigning all gene labels of belonging to or not belonging to this term will decrease the overall expression level in this term. In CellFateScout - a bioinformatics tool for elucidating small molecule signaling pathways that drive cells in a specific direction we validated CellFateScout against other well-known bioinformatics tools. We stated the question whether our plugin is able to predict small molecule effects better in terms of expression signatures. For this, we constructed a protocol that uses randomization testing. We assess here if the small molecule effect described as a (set of) active signaling pathways, as detected by our plugin or other bioinformatics tools, is significantly closer to known small molecule targets than a random path.
In this thesis, we elaborate upon Bayesian changepoint analysis, whereby our focus is on three big topics: approximate sampling via MCMC, exact inference and uncertainty quantification. Besides, modeling matters are discussed in an ongoing fashion. Our findings are underpinned through several changepoint examples with a focus on a well-log drilling data.
A slice is an intersection of a hyperplane and a self-similar set. The main purpose of this work is the mathematical description of slices. A suitable tool to describe slices are branching dynamical systems. Such systems are a generalisation of ordinary discrete dynamical systems for multivalued maps. Simple examples are systems arising from Bernoulli convolutions and beta-representations. The connection between orbits of branching dynamical systems and slices is demsonstrated and conditions are derived under which the geometry of a slice can be computed. A number of interesting 2-d and 3-d slices through 3-d and 4-d fractals is discussed.
Abstract
Cellular stress has been associated with inflammation, yet precise underlying mechanisms remain elusive. In this study, various unrelated stress inducers were employed to screen for sensors linking altered cellular homeostasis and inflammation. We identified the intracellular pattern recognition receptors NOD1/2, which sense bacterial peptidoglycans, as general stress sensors detecting perturbations of cellular homeostasis. NOD1/2 activation upon such perturbations required generation of the endogenous metabolite sphingosine‐1‐phosphate (S1P). Unlike peptidoglycan sensing via the leucine‐rich repeats domain, cytosolic S1P directly bound to the nucleotide binding domains of NOD1/2, triggering NF‐κB activation and inflammatory responses. In sum, we unveiled a hitherto unknown role of NOD1/2 in surveillance of cellular homeostasis through sensing of the cytosolic metabolite S1P. We propose S1P, an endogenous metabolite, as a novel NOD1/2 activator and NOD1/2 as molecular hubs integrating bacterial and metabolic cues.
We present classical and hybrid modeling approaches for genetic regulatory networks focusing on promoter analysis for negatively and positively autoregulated networks. The main aim of this thesis is to introduce an alternative mathematical approach to model gene regulatory networks based on piecewise deterministic Markov processes (PDMP). During somitogenesis, a process describing the early segmentation in vertebrates, molecular oscillators play a crucial role as part of a segmentation clock. In mice, these oscillators are called Hes1 and Hes7 and are commonly modeled by a system of two delay differential equations including a Hill function, which describes gene repression by their own gene products. The Hill coefficient, which is a measure of nonlinearity of the binding processes in the promoter, is assumed to be equal to two, based on the fact that Hes1 and Hes7 form dimers.However, by standard arguments applied to binding analysis, we show that a higher Hill coefficient is reasonable. This leads to results different from those in literature which requires a more sophisticated model. For the Hes7 oscillator we present a system of ordinary differential equations including a Michaelis-Menten term describing a nonlinear degradation of the proteins by the ubiquitinpathway. As demonstrated by the Hes1 and Hes7 oscillator, promoter behavior can have strong influence on the dynamical behavior of genetic networks. Since purely deterministic systems cannot reveal phenomenons caused by the inherent random fluctuations, we propose a novel approach based on PDMPs. Such models allow to model binding processes of transcription factors to binding sites in a promoter as random processes, where all other processes like synthesis, degradation or dimerization of the gene products are modeled in deterministic manner. We present and discuss a simulation algorithm for PDMPs and apply it to three types of genetic networks: an unregulated gene, a toggle switch, and a positively autoregulated network. The different regulation characteristics are analyzed and compared by numerical means. Furthermore, we determine analytical solutions of the stationary distributions of one negatively, and three positively autoregulated networks. Based on these results, we analyze attenuation of noise in a negative feedback loop, and the question of graded or binary response in autocatalytic networks.
The goal of this doctoral thesis is to create and to implement methods for fully automatic segmentation applications in magnetic resonance images and datasets. The work introduces into technical and physical backgrounds of magnetic resonance imaging (MRI) and summarizes essential segmentation challenges in MRI data including technical malfunctions and ill-posedness of inverse segmentation problems. Theoretical background knowledge of all the used methods that are adapted and extended to combine them for problem-specific segmentation applications are explained in more detail. The first application for the implemented solutions in this work deals with two-dimensional tissue segmentation of atherosclerotic plaques in cardiological MRI data. The main part of segmentation solutions is designed for fully automatic liver and kidney parenchyma segmentation in three-dimensional MRI datasets to ensure computer-assisted organ volumetry in epidemiological studies. The results for every application are listed, described and discussed before important conclusions are drawn. Among several applied methods, the level set method is the main focus of this work and is used as central segmentation concept in the most applications. Thus, its possibilities and limitations for MRI data segmentation are analyzed. The level set method is extended by several new ideas to overcome possible limitations and it is combined as important part of modularized frameworks. Additionally, a new approach for probability map generation is presented in this thesis, which reduces data dimensionality of multiple MR-weightings and incorporates organ position probabilities in a probabilistic framework. It is shown, that essential organ features (i.e. MR-intensity distributions, locations) can be well represented in the calculated probability maps. Since MRI data are produced by using multiple MR- weightings, the used dimensionality reduction technique is very helpful to generate a single probability map, which can be used for further segmentation steps in a modularized framework.
Simple Summary
Monitoring animal behavior provides an indicator of their health and welfare. For this purpose, video surveillance is an important method to get an unbiased insight into behavior, as animals often show different behavior in the presence of humans. However, manual analysis of video data is costly and time-consuming. For this reason, we present a method for automated analysis using computer vision—a method for teaching the computer to see like a human. In this study, we use computer vision to detect red foxes and their body posture (lying, sitting, or standing). With this data we are able to monitor the animals, determine their activity, and identify their behavior.
Abstract
The behavior of animals is related to their health and welfare status. The latter plays a particular role in animal experiments, where continuous monitoring is essential for animal welfare. In this study, we focus on red foxes in an experimental setting and study their behavior. Although animal behavior is a complex concept, it can be described as a combination of body posture and activity. To measure body posture and activity, video monitoring can be used as a non-invasive and cost-efficient tool. While it is possible to analyze the video data resulting from the experiment manually, this method is time consuming and costly. We therefore use computer vision to detect and track the animals over several days. The detector is based on a neural network architecture. It is trained to detect red foxes and their body postures, i.e., ‘lying’, ‘sitting’, and ‘standing’. The trained algorithm has a mean average precision of 99.91%. The combination of activity and posture results in nearly continuous monitoring of animal behavior. Furthermore, the detector is suitable for real-time evaluation. In conclusion, evaluating the behavior of foxes in an experimental setting using computer vision is a powerful tool for cost-efficient real-time monitoring.
We apply the charge simulation method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many “small” components. This application allows to use just a single charge point for each component. The resulting method therefore is significantly more efficient than methods based on discretizations of the boundaries (for example, our own method presented in Liesen et al. (Comput. Methods Funct. Theory 17, 689–713, 2017)), while maintaining a very high level of accuracy. We study properties of the linear algebraic systems that arise in the CSM, and show how these systems can be solved efficiently using preconditioned iterative methods, where the matrix-vector products are computed using the fast multipole method. We illustrate the use of the method on generalized Cantor sets and the Cantor dust.
Phylogenetic (i.e., leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple optimization criterion for such reconstructions is maximum parsimony. It is generally assumed that this criterion works well for data in which state changes are rare. In the present manuscript, we prove that each binary phylogenetic tree T with n ≥ 20k leaves is uniquely defined by the set Ak (T), which consists of all characters with parsimony score k on T. This can be considered as a promising first step toward showing that maximum parsimony as a tree reconstruction criterion is justified when the number of changes in the data is relatively small.
Simple Summary
Paratuberculosis is a disease which affects ruminants worldwide. Many countries have implemented certification and monitoring systems to control the disease, particularly in dairy herds. Monitoring herds certified as paratuberculosis non-suspect is an important component of paratuberculosis herd certification programs. The challenge is to detect the introduction or reintroduction of the infectious agent as early as possible with reasonable efforts but high certainty. In our study, we evaluated different low-cost testing schemes in herds where the share of infected animals was low, resulting in a low within-herd prevalence of animals shedding the bacteria that causes paratuberculosis in their feces. The test methods used were repeated pooled milk samples and fecal samples from the barn environment. Our study showed that numerous repetitions of different samples are necessary to monitor such herds with sufficiently high certainty. In the case of herds with a very low prevalence, our study showed that a combination of different sampling approaches is required.
Abstract
An easy-to-use and affordable surveillance system is crucial for paratuberculosis control. The use of environmental samples and milk pools has been proven to be effective for the detection of Mycobacterium avium subsp. paratuberculosis (MAP)-infected herds, but not for monitoring dairy herds certified as MAP non-suspect. We aimed to evaluate methods for the repeated testing of large dairy herds with a very low prevalence of MAP shedders, using different sets of environmental samples or pooled milk samples, collected monthly over a period of one year in 36 herds with known MAP shedder prevalence. Environmental samples were analyzed by bacterial culture and fecal PCR, and pools of 25 and 50 individual milk samples were analyzed by ELISA for MAP-specific antibodies. We estimated the cumulative sensitivity and specificity for up to twelve sampling events by adapting a Bayesian latent class model and taking into account the between- and within-test correlation. Our study revealed that at least seven repeated samplings of feces from the barn environment are necessary to achieve a sensitivity of 95% in herds with a within-herd shedder prevalence of at least 2%. The detection of herds with a prevalence of less than 2% is more challenging and, in addition to numerous repetitions, requires a combination of different samples.