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Die dem Leben zugrundeliegenden Prozesse sind hochkomplex. Sie werden zu einem Großteil durch Proteine umgesetzt. Diese spielen eine tragende Rolle für die morphologische Struktur und Vielfalt sowie Spezifität der Fähigkeiten der verschiedenen Zelltypen. Jedoch wirken Proteine nicht isoliert für sich allein sondern indem sie miteinander oder mit anderen Molekülen in der Zelle (DNA, Metabolite, Signalstoffe etc.) wechselwirken. Gerät dieses Geflecht von aufeinander abgestimmten Wechselwirkungen aus dem Gleichgewicht, kann das eine Ursache für Erkrankungen sein. Die Kenntnis über fehlregulierte Interaktionen kann dabei helfen, die betreffende Krankheit besser zu verstehen und gegen sie zu intervenieren. Die vorliegende Dissertation beschäftigt sich mit der Identifizierung von solch differentiell regulierten Interaktionen. Im Rahmen der Arbeit wurde eine Methode mit dem Namen ExprEssence entwickelt, welche diejenigen Interaktionen in einem Protein-Protein-Interaktionsnetzwerk identifiziert, die sich zwischen zwei verglichenen Zuständen (z.B. krank versus gesund) am stärksten unterscheiden. Ziel ist es, das Netzwerk auf die wesentlichen Unterschiede zwischen den zwei untersuchten Zuständen zu reduzieren. Hierzu werden Genexpressions- oder Proteomdaten der beiden Zustände in das bereits bestehende Netzwerk integriert. Aus diesen Daten wird die Stärke/Häufigkeit des Auftretens der einzelnen Interaktionen des Netzwerks geschätzt. Die Interaktionen, deren Interaktionsstärken sich zwischen den betrachteten Zuständen am stärksten unterscheiden, werden beibehalten – die restlichen Interaktionen werden verworfen. Dies ergibt ein verkleinertes Subnetzwerk, das aus jenen Interaktionen besteht, die am stärksten differentiell reguliert sind. Diese Interaktionen und ihre Proteine sind Kandidaten für eine Erklärung der biologischen Unterschiede der betrachteten Zustände auf molekularem Niveau. Die Methode wurde auf verschiedene biologische Fragestellungen angewandt und mit anderen ähnlichen Methoden verglichen. Bei der Untersuchung der Unterschiede zwischen Erfolg und Misserfolg einer chemotherapeutischen Brustkrebstherapie konnte beispielsweise gezeigt werden, dass das mit ExprEssence erstellte Subnetzwerk einen stärkeren Bezug zu den bereits bekannten Therapieerfolg-relevanten Mechanismen aufweist als die Methoden, mit denen ExprEssence verglichen wurde. Weiterhin wurde im Subnetzwerk eine möglicherweise für den Therapieerfolg relevante Interaktion identifiziert, die in diesem Zusammenhang bisher nicht betrachtet wurde. Deren Bedeutung konnte in der experimentellen Nachverfolgung weiter untermauert werden. Einen weiteren Schwerpunkt der Arbeit bildete die Untersuchung des Interaktoms eines spezialisierten Zelltyps der Niere – des Podozyten. Dieser Zelltyp ist essentiell für die Filtrationskompetenz der Niere. Ein Interaktionsnetzwerk mit spezifisch für den Podozyten relevanten Interaktion gib es bisher nicht. Daher wurde ein Podozyten-spezifisches Protein-Protein-Interaktionsnetzwerk aus wissenschaftlichen Veröffentlichungen zusammengestellt und öffentlich verfügbar gemacht. Genexpressionsdaten vielfältiger Art, beispielsweise von Podozyten in verschiedenen Entwicklungsstadien oder in Zellkultur, wurden in das Netzwerk integriert und mit ExprEssence analysiert. So konnte beispielsweise gezeigt werden, dass die Dedifferenzierung von in Kultur gehaltenen Podozyten nicht dem Umkehrweg der zuvor durchlaufenen Differenzierung entspricht. Neben ExprEssence wurde weitere Software entwickelt, die die Anwendbarkeit von ExprEssence erweitert – MovieMaker und ExprEsSector. Mit MovieMaker werden die Übergänge zwischen den betrachteten Zuständen nachvollziehbarer visualisiert. ExprEsSector bildet die Vereinigungs- und Schnittmengen-Netzwerke von ExprEssence-Subnetzwerken. So können beispielsweise verschiedenen Krankheiten gemeinsame Veränderungen vom Normalzustand identifiziert werden. Ist für eine Krankheit bereits ein Therapieansatz vorhanden, der auf eine fehlregulierte Interaktion einwirkt, und ist diese Interaktion auch in der anderen Krankheit gleichartig differentiell reguliert, kann geprüft werden, ob diese Therapie auf die zweite Krankheit übertragen werden kann. Neben der Vorstellung und Diskussion der erzielten Ergebnisse, wird auch auf methodisch bedingte Nachteile eingegangen. Es werden Strategien aufgezeigt, wie die negativen Einflüsse möglichst minimiert werden können oder wie sie bei der Bewertung der Ergebnisse zu berücksichtigen sind. In Anbetracht der immer schneller ansteigenden Menge biologischer Daten ist es eine wesentliche Herausforderung geworden, aus diesen die essentiellen Informationen zu extrahieren. Der integrative Ansatz der Verknüpfung von Informationen verschiedener Quellen wurde mit ExprEssence und den Erweiterungen MovieMaker und ExprEsSector in einem Konzept zur Identifizierung zustandsrelevanter molekularer Mechanismen in intuitiv leicht erfassbarer Form umgesetzt.
We consider Walsh’s conformal map from the exterior of a compact set E ⊆ C onto a lemniscatic domain. If E is simply connected, the lemniscatic domain is the exterior of a circle, while if E has several components, the lemniscatic domain is the exterior of a generalized lemniscate and is determined by the logarithmic capacity of E and by the exponents and centers of the generalized lemniscate. For general E, we characterize the exponents in terms of the Green’s function of Ec. Under additional symmetry conditions on E, we also locate the centers of the lemniscatic domain. For polynomial pre-images E = P−1(Ω) of a simply-connected infinite compact set Ω, we explicitly determine the exponents in the lemniscatic domain and derive a set of equations to determine the centers of the lemniscatic domain. Finally, we present several examples where we explicitly obtain the exponents and centers of the lemniscatic domain, as well as the conformal map.
In dieser Arbeit wird ein Verfahren zur Bestimmung von Toleranzbereichen für 1H-NMR-Spektren von Neugeborenenurinen zur Detektion von angeborenen Stoffwechselerkrankungen vorgestellt. Diese Krankheiten werden durch genetische Defekte ausgelöst, die eine schwerwiegende Funktionsstörung im Stoffwechselkreislauf verursachen. Die dadurch entstehenden Krankheitsbilder führen in der Regel zu Behinderungen und oftmals zum Tod. Eine frühe Diagnose und Behandlung können in vielen Fällen ein Überleben ohne Symptome ermöglichen. Beim derzeitigen Neugeborenenscreening werden in Deutschland zwölf der häufigsten Stoffwechselerkrankungen routinemäßig abgetestet - weit über hundert sind aktuell bekannt. Basierend auf einem Referenzdatensatz von 695 Neugeborenenurinspektren, werden in dieser Arbeit mathematische Methoden zur Bestimmung von Toleranzbereichen entwickelt, die eine ungezielte Detektion von Abweichungen ermöglichen, um schwerwiegende Krankheiten wie angeborene Stoffwechselerkrankungen frühzeitig und routinemäßig diagnostizieren zu können. Das Verfahren basiert dabei auf der robusten Ermittlung von Verteilungsfunktionen, Toleranzbereichen und Identifikation von Ausreißern für eindimensionale Stichproben von unbekannten Verteilungen. Mithilfe einer von der Box-Cox-Transformation abgeleiteten Transformationsfamilie, werden die gemessenen Kenngrößen in normalverteilte Stichproben überführt. Für die Bestimmung der optimalen Transformationsparameter wird die Teststatistik des Shapiro-Wilk-Tests auf Normalverteilung der transformierten Stichprobe verwendet. Die Betrachtung verschiedener links- und rechtsseitiger Trimmungen sichert dabei eine robuste Bestimmung, die nicht von Ausreißern innerhalb des Referenzdatensatzes beeinflusst wird. Anhand von Simulationsstudien wird die Leistung dieses Verfahrens an Stichproben mit bekannten Verteilungen ermittelt und demonstriert. Die Anwendbarkeit an abgeleiteten Kenngrößen aus den realen Urinspektren wird zunächst anhand von Metabolitenkonzentrationen gezeigt. Hierfür wurden im Rahmen dieser Arbeit Methoden zur Identifikation und Quantifikation von 22 ausgewählten Metaboliten entwickelt. Für die ungezielte Analyse werden aus den NMR-Spektren abstrakte Kenngrößen abgeleitet, welche die Protonenkonzentrationen in verschiedenen chemischen Verschiebungsbereichen zusammenfassen (sogenannte Bucketierung). Dadurch wird jedes Signal, unabhängig von Molekül oder funktioneller Gruppe, erfasst und ausgewertet. Bei der in dieser Arbeit verwendeten Strategie entstehen dadurch 500 Messwerte pro Spektrum, von denen 479 (96%) in normalverteilte Variablen überführt werden können. Für diese werden schließlich Toleranzbereiche definiert, um Messungen von weiteren Urinproben abzugleichen. Zusätzlich wird ausgehend von den transformierten Variablen eine Möglichkeit dargestellt, auch multivariate Toleranzbereiche auf Basis der Mahalanobisdistanz zu ermitteln, welche die Sensitivität des Tests auf abweichende Signale signifikant erhöht. Anhand einer Spiking-Simulationsstudie mit ca. 500.000 Spektren, bei denen die Signale von elf Verbindungen, die in Zusammenhang mit angeborenen Stoffwechselerkrankungen stehen, numerisch zu den Referenzspektren addiert werden, können Detektionsraten in Abhängigkeit der Konzentrationen dieser Verbindungen ermittelt werden.
Given a manifold with a string structure, we construct a spinor bundle on its loop space. Our construction is in analogy with the usual construction of a spinor bundle on a spin manifold, but necessarily makes use of tools from infinite dimensional geometry. We equip this spinor bundle on loop space with an action of a bundle of Clifford algebras. Given two smooth loops in our string manifold that share a segment, we can construct a third loop by deleting this segment. If this third loop is smooth, then we say that the original pair of loops is a pair of compatible loops. It is well-known that this operation of fusing compatible loops is important if one wants to understand the geometry of a manifold through its loop space. In this work, we explain in detail how the spinor bundle on loop space behaves with respect to fusion of compatible loops. To wit, we construct a family of fusion isomorphisms indexed by pairs of compatible loops in our string manifold. Each of these fusion isomorphisms is an isomorphism from the relative tensor product of the fibres of the spinor bundle over its index pair of compatible loops to the fibre over the loop that is the result of fusing the index pair. The construction of a spinor bundle on loop space equipped with a fusion product as above was proposed by Stolz and Teichner with the goal of studying the Dirac operator on loop space". Our construction combines facets of the theory of bimodules for von Neumann algebras, infinite dimensional manifolds, and Lie groups and their representations. We moreover place our spinor bundle on loop space in the context of bundle gerbes and bundle gerbe modules.
As the tree of life is populated with sequenced genomes ever more densely, the new challenge is the accurate and consistent annotation of entire clades of genomes. In my dissertation, I address this problem with a new approach to comparative gene finding that takes a multiple genome alignment of closely related species and simultaneously predicts the location and structure of protein-coding genes in all input genomes, thereby exploiting negative selection and sequence conservation. The model prefers potential gene structures in the different genomes that are in agreement with each other, or—if not—where the exon gains and losses are plausible given the species tree. The multi-species gene finding problem is formulated as a binary labeling problem on a graph. The resulting optimization problem is NP hard, but can be efficiently approximated using a subgradient-based dual decomposition approach.
I tested the novel approach on whole-genome alignments of 12 vertebrate and 12 Drosophila species. The accuracy was evaluated for human, mouse and Drosophila melanogaster and compared to competing methods. Results suggest that the new method is well-suited for annotation of a large number of genomes of closely related species within a clade, in particular, when RNA-Seq data are available for many of the genomes. The transfer of existing annotations from one genome to another via the genome alignment is more accurate than previous approaches that are based on protein-spliced alignments, when the genomes are at close to medium distances. The method is implemented in C++ as part of the gene finder AUGUSTUS.
Abstract
The expected signature is an analogue of the Laplace transform for probability measures on rough paths. A key question in the area has been to identify a general condition to ensure that the expected signature uniquely determines the measures. A sufficient condition has recently been given by Chevyrev and Lyons and requires a strong upper bound on the expected signature. While the upper bound was verified for many well‐known processes up to a deterministic time, it was not known whether the required bound holds for random time. In fact, even the simplest case of Brownian motion up to the exit time of a planar disc was open. For this particular case we answer this question using a suitable hyperbolic projection of the expected signature. The projection satisfies a three‐dimensional system of linear PDEs, which (surprisingly) can be solved explicitly, and which allows us to show that the upper bound on the expected signature is not satisfied.
In dieser Arbeit beschäftigen wir uns mit symplektischen Lie-Algebren und metrischen, symplektischen Lie-Algebren. Wir erweitern ein bestehendes Klassifikationsschema mittels quadratischer Erweiterungen für metrische Lie-Algebren mit halbeinfachen, schiefsymmetrischen Derivationen so, dass damit sämtliche metrischen, symplektischen Lie-Algebren auf Isomorphie untersucht werden können. Damit bestimmen wir die Isomorphieklassen aller nichtabelschen, metrischen, symplektischen Lie-Algebren, der Dimension kleiner als zehn, sowie alle mit einem Index von kleiner oder gleich drei. Anschließend wird in Analogie zur Herangehensweise für metrische Lie-Algebren ein Klassifikationsschema für symplektische Lie-Algebren mit ausgeartetem Zentrum mittels quadratischer Erweiterungen aufgebaut, was uns zudem ein Klassifikationsschema für nilpotente, symplektische Lie-Algebren liefert. Abschließend berechnen wir konkret ein Repräsentantensystem der Isomorphieklassen aller sechsdimensionalen, nilpotenten, symplektischen Lie-Algebren.
Universal products provide an axiomatic framework to study noncommutative independences general enough to include, besides the well known "single-faced" case (i.e., tensor, free, Boolean, monotone and antimonotone independence), also more recent "multi-faced" examples like bifree independence. Questions concerning classification have been fully answered in the single-faced case, but are in general still open in the multi-faced case. In this thesis we discuss how one can use insights in the relation between universal products and their associated moment-cumulant formula as a starting point towards a combinatorial approach to (multi-faced) universal products. We define certain classes of partitions and discuss why the defining axioms are sufficient to associate to each of them a multi-faced universal product. For the two-faced case we present our result that every positive and symmetric universal product can be produced in this fashion and we outline how these results might contribute to a classification of positive and symmetric universal products.
Es wird ein neues Konzept für die Modellierung von (zeitlichen) Realisierungen komplexer und stark verrauschter Prozessabhängigkeiten ohne spezielle Vorkenntnisse vorgestellt. Als Grundlage dient das "Errors-in-Variables Model" (EVM) als ein "Total Least Square" (TLS)- Verfahren zur asymptotisch fehlerfreien Rekonstruktion einer linearen Prozessabhängigkeit. Die hierfür notwendigen Informationen zum Fehlerrauschen in den Variablen werden indirekt in den (zeitlichen) Realisierungen mit Hilfe eines neuen Vergleichsmaßes für Strukturen (EP- Maß) auf Basis des Ähnlichkeits- Koeffizienten nach Dice / Sørensen erhalten, d.h. solange der fehlerfreie Prozess sich nicht in Strukturen eines weißen Rauschens realisiert. Dies kann vorab mit Hilfe einer schrittweisen Gauß- Tiefpass- Filterung der Ausgangsdaten im jeweiligen EP- Vergleich zu den ungefilterten Daten entschieden werden. Durch ein unabhängiges Zusatz- Fehlerrauschen wird zwischen den modellierten und den abzubildenden Daten schrittweise eine maximale strukturelle Ähnlichkeit „künstlich“ hergestellt "Sequential Iterative NOise Matching Algorithm" (SINOMA), die dann mit Hilfe des Vergleichsmaßes unabhängig zum EVM- Verfahren erkannt werden kann. Unter diesen "Reduced Major Axis" (RMA-)Bedingungen des EVM- Verfahrens sind die Parameter der linearen Prozessabhängigkeit eindeutig bestimmbar, d.h. dann ohne Kenntnisse zum Fehlerrauschen in den Ausgangsdaten. Im Gegenteil, da hierbei das notwendige Zusatzrauschen für das Erreichen von RMA- Bedingungen „bekannt ist“, können auf diese Weise auch noch das Fehlerrauschen in den Ausgangsdaten und die entsprechenden Standardabweichungen der fehlerfreien Daten abgeschätzt werden. Hiermit sollte (erstmals) eine adäquate Lösung des Rekonstruktionsproblems prähistorischer Spannweiten klimatischer Schwankungen mit Hilfe von Proxy möglich sein.
The study of sow reproduction traits is important in livestock science and production to increase animal survival and economic efficiency. This work deals with the detection of different effects on within-litter variance of birth weight by applying different statistical models with different distributional assumptions. The piglets within one litter were separated by sex. The trait of sow was formed from the sample variances of birth weights within litter separated by sex to consider the sex effect on mean birth weight. A linear mixed model (LMM) approach was fitted to the logarithmized sample variance and the sample standard deviation. A generalized linear mixed model with gamma distributed residuals and log-link function was applied to the untransformed sample variance. Appropriate weights were constructed to account for individual litter sizes. Models were compared by analysing data from Landrace and Large White. The estimates of heritability for the different traits ranged from 6-14%. The LMM for the weighted standard deviation of birth weights was identified as most suitable in terms of residual normality. Furthermore, the impact of piglets´ sex on birth weight variability was tested, but it was only proved for one practical dataset. Additionally, we analysed the influence of including or not including birth weights of stillborn piglets on the estimates of variance components of birth weight variability. With omitted stillborns the estimates of heritability resulted in about 2% higher values than in investigations of total born piglets. We were interested in the presence of the random boar effect on birth weight variability. The corresponding variance component was tested via restricted likelihood ratio test. Among others, the null distribution of the test statistic was approximated by parametric bootstrap simulations which were computational intensive. We picked up a two-parametric approach from literature and proposed a three-parametric approach to approximate the null distribution of the test statistic. We have analysed correlated data in balanced (simulated data) and unbalanced (empirical data) designs. The two-parametric approach using a scaled mixture of chisquare-distributions as well as a three-parametric approach, that uses a mixture of the point mass at zero and a gamma distribution, behaved most solid in all investigations and were most powerful in the simulation study.
Statistical Methods and Applications for Biomarker Discovery Using Large Scale Omics Data Set
(2023)
This thesis focuses on identifying genetic factors associated with human kidney disease progression, with three articles presented. Article I describes the identification of loci associated with UACR through trans-ethnic, European-ancestry-specific, and diabetes-specific meta-analyses. An approximate conditional analysis was performed to identify additional independent UACR-associated variants within identified loci. The genome-wide significance level of 𝛼=5×10−8 is used for both primary GWAS association and conditional analyses. However, unlike primary association tests, conditional tests are limited to specific genomic regions surrounding primary GWAS index signals rather than being applied on a genome-wide scale.
In article II, we hypothesized that the application of 𝛼=5×10−8 is overly strict and results in a loss of power. To address this issue, we developed a quasi-adaptive method within a weighted hypothesis testing framework. This method exploits the type I error (𝛼=0.05) by providing less conservative SNP specific 𝛼-thresholds to select secondary signals in conditional analysis. Through simulation studies and power analyses, we demonstrate that the quasi-adaptive method outperforms the established criterion 𝛼=5×10−8 as well as the equal weighting scheme (the Sidak-correction). Furthermore, our method performs well when applied to real datasets and can potentially reveal previously undetected secondary signals in existing data.
In article III, we extended our quasi-adaptive method to identify plausible multiple independent signals at each locus (a secondary signal, a tertiary signal, a signal of 4th, and beyond) and applied it to the publically available GWAS meta-analysis to detect additional multiple independent eGFR-associated signals. The improved quasi-adaptive method successfully identified additional novel replicated independent SNPs that would have gone undetected by applying too conservative genome-wide significance level of 𝛼=5× 10−8. Colocalization analysis based on the novel independent signals identified potentially functional genes across the kidney and other tissues.
Overall, these articles contribute to the understanding of genetic factors associated with human kidney disease progression and provide novel methods for identifying secondary and multiple independent signals in conditional GWAS analyses.
Self-similar sets are a class of fractals which can be rigorously defined and treated by mathematical methods. Their theory has been developed in n-dimensional space, but we have just a few good examples of self-similar sets in three-dimensional space. This thesis has two different aims. First, to extend fractal constructions from two-dimensional space to three-dimensional space. Second, to study some of the properties of these fractals such as finite type, disk-likeness, ball-likeness, and the Hausdorff dimension of boundaries. We will use the neighbor graph tool for creating new fractals, and studying their properties.
Tafazzin is an acyltransferase with key functions in remodeling of the mitochondrial phospholipid cardiolipin (CL) by exchanging single fatty acids species in CL. Tafazzin-mediated CL remodeling determines the actual CL compositions and has been implicated in mitochondrial morphology and function. Thus, any deficiency of tafazzin leads to altered fatty acid composition of CL which is directly associated with impaired mitochondrial respiration and ATP production. Mutations in the tafazzin encoding gene TAZ, are the cause of the severe X-linked genetic disease, BARTH syndrome (BTHS).
Previous work provided first hints on a linkage of CL composition and subsequent limitations in the cellular ATP levels which may contribute to the restriction of growth. However, in C6 cells ATP levels remained unaltered due to compensatory activation of glycolysis. Moreover, it has been demonstrated that the substantial changes in CL composition are similarly resulting from knocking down either cardiolipin synthase (CRLS) or TAZ. This has also been shown in C6 glioma cells. Most notably only the knock down of TAZ, but not that of CRLS, compromised proliferation of C6 glioma cells. Therefore, a CL- independent role of TAZ in regulating cell proliferation is postulated.
In this study, any linkage of the lack of tafazzin to cellular proliferation should be investigated in more detail to allow first insight into underlying mechanisms.
The results of the current study demonstrate that the tafazzin knockout in C6 glioma cells show changes in global gene expression by applying transcriptome analysis using the- microarray Clarion S rat Affymetrix array. Out of 22,076 total number of genes detected, 1,099 genes were differentially expressed in C6 knockout cells which were either ≥2 and ≥4 fold up or down regulated genes. Furthermore, expression of selected target genes was validated using RT-qPCR. We have hypothesised that the changes in TAZ dependent gene expression is via PPAR transcription factor. According to eukaryotic promoter database (EPD) for selected target genes, exhibited at least one putative binding site for PPARG and PPARA transcription factors. However, pioglitazone and LG100268, synthetic ligands of PPARG and RXR, could not show any effect on changes in gene expression in C6 TAZ cells. Another class of cellular lipids, oxylipins were found to occur in significantly higher amounts in C6 TAZ cells compared to C6 cells which makes them candidates for mediating cellular effects and regulating gene expression via PPARs. A computational tool CiiiDER was used to for the prediction of transcription factor binding site. The transcription factors enriched in TAZ- regulated genes were found to be HOXA5 and PAX2, binding sites of which could be detected in 100 % of TAZ- regulated genes (>2-fold). By applying IPA to the differentially expressed genes we could identify lipid metabolism, and cholesterol superpathway in particular as the most affected pathway in C6 TAZ cells. This pathway consists of 20 genes, of which all (20/20) appeared to be differentially regulated in C6 TAZ cells. Of all the 20 genes, 4 of the differentially expressed genes were selected for further validation by RT-qPCR. By IPA it was possible to identify the upstream regulators that might be responsible for the differential expression of genes in C6 deficient cells. Some of the genes ACACA, HMGCR, FASN, ACSL1, 3 and, 5 identified was decreased by predicted activation and inhibition of the regulators. Further we have analysed the levels of cellular cholesterol content in C6 and C6 TAZ (w/o Δ5 and FL) cells. In C6 cells cholesterol is present more in its free form. C6 TAZ cells have increased amount of cholesterol compared to C6 cells. However, Δ5 and FL expressed C6 TAZ cells showed less amount of cholesterol.
Previous work established that knockout of tafazzin in C6 cells showed decreased cell proliferation in the absence of any changes in ATP content. To understand this phenomenon cellular senescence associated β-galactosidase in C6 and C6 TAZ cells was performed. C6 TAZ cells showed increased percentage of β-gal positive cells compared to C6 cells. Moreover, senescent associated secretory phenotype (SASP) represented by e.g. CXCL1, IL6, and IL1α was determined using RT-qPCR. Gene expression of these SASP factors was significantly upregulated in C6 TAZ cells.
Several human tafazzin isoforms exists due to alternate splicing. However, whether these isoforms differ in function and in CL remodelling activity or specificity, in particular, is unknown. The purpose of this work was to determine if specific isoforms, such as human isoform lacking exon 5 (Δ5), rat full length tafazzin (FL) and enzymatically dead full length tafazzin (H69L), can restore the wild type phenotype in terms of CL composition, cellular proliferation, and gene expression profile. Therefore, in the second part, it was demonstrated that expression of Δ5 to some extent and rat full length tafazzin can completely restore CL composition, in C6 TAZ cells which is naturally linked to the restoration of mitochondrial respiration. As expected, a comparable restoration of CL composition could not be seen after re-expressing an enzymatically dead full-length rat TAZ, (H69L; TAZ Mut). Furthermore, re-expression of the TAZ Mut largely failed to reverse the alterations in gene expression, in contrast re-expression of the TAZ FL and the Δ5 isoforms reversed gene expression to a larger extent. Moreover, only rat full length TAZ was able to reverse proliferation rate. Surprisingly, the expression of Δ5 in C6 TAZ cells did not promote proliferation of the wild type. Different effects of Δ5 and FL on CL composition and cell proliferation points to the specific and in part non-enzymatic functions of tafazzin isoforms, but this certainly requires further analysis.
Alternative splicing (AS) is a major mechanism for gene expression in eukaryotes, increasing proteome diversity but also regulating transcriptome abundance. High temperatures have a strong impact on the splicing profile of many genes and therefore AS is considered as an integral part of heat stress response. While many studies have established a detailed description of the diversity of the RNAome under heat stress in different plant species and stress regimes, little is known on the underlying mechanisms that control this temperature-sensitive process. AS is mainly regulated by the activity of splicing regulators. Changes in the abundance of these proteins through transcription and AS, post-translational modifications and interactions with exonic and intronic cis-elements and core elements of the spliceosomes modulate the outcome of pre-mRNA splicing. As a major part of pre-mRNAs are spliced co-transcriptionally, the chromatin environment along with the RNA polymerase II elongation play a major role in the regulation of pre-mRNA splicing under heat stress conditions. Despite its importance, our understanding on the regulation of heat stress sensitive AS in plants is scarce. In this review, we summarize the current status of knowledge on the regulation of AS in plants under heat stress conditions. We discuss possible implications of different pathways based on results from non-plant systems to provide a perspective for researchers who aim to elucidate the molecular basis of AS under high temperatures.
Im Rahmen des hier verwendeten abstrakten, nichtkommutativen Unabhängigkeitsbegriffs gibt es nach dem Klassifikationssatz von Muraki genau fünf konkrete Unabhängigkeitsbegriffe: Tensor, boolesch, frei, monoton und antimonoton. Hierbei umfasst der Tensor-Fall den Unabhängigkeitsbegriff aus der klassischen Wahrscheinlichkeitstheorie. Ein Quanten-Levy-Prozess (QLP) ist ein Prozess mit unabhängigen, stationären Zuwächsen, dessen Verteilung durch einen Generator g festgelegt ist. Die QLP und die Generatoren in dieser Arbeit sind auf den Voiculescuschen dualen Halbgruppen definiert. Ein Generator ist ein bedingt positives, lineares Funktional mit g(1)=0. Diese Arbeit untersucht das Problem, zu einem QLP mit gegebenem Generator einen QLP auf einen Fockraum mit demselben Generator anzugeben. Zur Problem wird in drei Teilen bearbeitet. Im ersten Teil wird für jede konkrete Unabhängigkeit die Existenz eines QLP zu gegebenem Generator g nachgewiesen. Hierbei wird die Schoenberg-Korrespondenz für duale Halbgruppen verwendet und ein Quanten-Kolomogoroff Satz für QLP gezeigt. Der zweite Teil, der zugleich den Hauptteil der Arbeit darstellt, besteht aus dem Transformationssatz für duale Halbgruppen. Dieser besagt in etwa, dass ein gegebener QLP mit Generator g unter einer Transformation genannten Abbildung k zwischen zwei dualen Gruppen zu einem QLP mit Generator k•g transformiert werden kann. Dabei operieren der transformierte QLP und der ursprüngliche QLP im Wesentlichen auf denselbem Raum. Der Beweis des Transformationssatzes wird ausschließlich auf dem abstrakten, nichtkommutativen Unabhängigkeitsbegriff aufgebaut. Dabei wird der Existenzsatz aus dem ersten Teil verwendet und die punktweise Konvergenz eines infinitesimalen Faltens des gegebenen QLP ausgewertet an einem normierten Vektor bewiesen. Somit sind alle fünf konkreten Unabhängigkeitsbegriffe in einem einheitlichen Rahmen enthalten. Zu jedem konkreten nichtkommutativen Unabhängigkeitsbegriff werden im dritten Teil die besonders einfachen, additven QLP auf Fockräumen betrachtet. Hierbei ist ein additiver QLP einfach die Summe aus einem Erzeugungs-, einem Erhaltungs- und einem Vernichtungsprozess auf einem Fockraum, sowie aus einem Generatoranteil. Die Realisierung von QLP auf Fockräumen, also das oben genannte Problem, wird durch Transformieren eines passenden, additiven QLP erreicht. Insbesondere erhalten wir somit erstmals eine Realisierung von QLP auf Fockräumen mithilfe der Transformationstheorie im freien Fall. In einer Anwendung wird das nichtkommutative Analogon der Unitären Gruppe als duale Gruppe betrachtet. Im freien Fall als konkreten, nichtkommutativen Unabhängigkeitsbegriff und aufgrund der Unitarität kann hier zusätzlich bewiesen werden, dass auch auf Operator-Ebene ein infinitesimales Falten der additiven QLP in der starken Operatortopologie existiert. Weiterhin gilt im Gauß-Fall, das heißt obiger Erhaltungsprozess-Anteil verschwindet, dass sogar Normkonvergenz vorliegt.
Abstract
With the advent of molecular genetic methods, an increasing number of morphologically cryptic taxa has been discovered. The majority of them, however, remains formally undescribed and without a proper name although their importance in ecology and evolution is increasingly being acknowledged. Despite suggestions to complement traditional descriptions with genetic characters, the taxonomic community appears to be reluctant to adopt this proposition. As an incentive, we introduce QUIDDICH, a tool for the QUick IDentification of DIgnostic CHaracters, which automatically scans a DNA or amino acid alignment for those columns that allow to distinguish taxa and classifies them into four different types of diagnostic characters. QUIDDICH is a system‐independent, fast and user‐friendly tool that requires few manual steps and provides a comprehensive output, which can be included in formal taxonomic descriptions. Thus, cryptic taxa do not have to remain in taxonomic crypsis and, bearing a proper name, can readily be included in biodiversity assessments and ecological and evolutionary analyses. QUIDDICH can be obtained from the comprehensive R archive network (CRAN, https://cran.r-project.org/package=quiddich).
Phytopathogenic Verticillia cause Verticillium wilt on numerous economically important crops. Plant infection begins at the roots, where the fungus is confronted with rhizosphere inhabiting bacteria. The effects of different fluorescent pseudomonads, including some known biocontrol agents of other plant pathogens, on fungal growth of the haploid Verticillium dahliae and/or the amphidiploid Verticillium longisporum were compared on pectin-rich medium, in microfluidic interaction channels, allowing visualization of single hyphae, or on Arabidopsis thaliana roots. We found that the potential for formation of bacterial lipopeptide syringomycin resulted in stronger growth reduction effects on saprophytic Aspergillus nidulans compared to Verticillium spp. A more detailed analyses on bacterial-fungal co-cultivation in narrow interaction channels of microfluidic devices revealed that the strongest inhibitory potential was found for Pseudomonas protegens CHA0, with its inhibitory potential depending on the presence of the GacS/GacA system controlling several bacterial metabolites. Hyphal tip polarity was altered when V. longisporum was confronted with pseudomonads in narrow interaction channels, resulting in a curly morphology instead of straight hyphal tip growth. These results support the hypothesis that the fungus attempts to evade the bacterial confrontation. Alterations due to co-cultivation with bacteria could not only be observed in fungal morphology but also in fungal transcriptome. P. protegens CHA0 alters transcriptional profiles of V. longisporum during 2 h liquid media co-cultivation in pectin-rich medium. Genes required for degradation of and growth on the carbon source pectin were down-regulated, whereas transcripts involved in redox processes were up-regulated. Thus, the secondary metabolite mediated effect of Pseudomonas isolates on Verticillium species results in a complex transcriptional response, leading to decreased growth with precautions for self-protection combined with the initiation of a change in fungal growth direction. This interplay of bacterial effects on the pathogen can be beneficial to protect plants from infection, as shown with A. thaliana root experiments. Treatment of the roots with bacteria prior to infection with V. dahliae resulted in a significant reduction of fungal root colonization. Taken together we demonstrate how pseudomonads interfere with the growth of Verticillium spp. and show that these bacteria could serve in plant protection.
Parsimonious Histograms
(2010)
The dissertation is concerned with the construction of data driven histograms. Histograms are the most elementary density estimators at all. However, they require the specification of the number and width of the bins. This thesis provides two new construction methods delivering adaptive histograms where the required parameters are determined automatically. Both methods follow the principle of parsimony, i.e. the histograms are solutions of predetermined optimization problems. In both cases, but under different aspects, the number of bins is minimized. The dissertation presents the algorithms that solve the optimization problems and illustrates them by a number of numerical experiments. Important properties of the estimators are shown. Finally, the new developed methods are compared with standard methods by an extensive simulation study. By means of synthetic samples of different size and distribution the histograms are evaluated by special performance criteria. As one main result, the proposed methods yield histograms with considerably fewer bins and with an excellent ability of peak detection.
Die vorliegende Arbeit ist im Bereich der parameterfreien Statistik anzusiedeln und beschäftigt sich mit der Anwendung von ordinalen Verfahren auf Zeitreihen und Bilddaten. Die Basis bilden dabei die sogenannten ordinalen Muster in ein bzw. zwei Dimensionen. Der erste Hauptteil der Arbeit gibt einen Überblick über die breiten Einsatzmöglichkeiten ordinaler Muster in der Zeitreihenanalyse. Mit ihrer Hilfe wird bei simulierten gebrochenen Brownschen Bewegungen der Hurst-Exponenten geschätzt und anhand von EEG-Daten eine Klassifikationsaufgabe gelöst. Des Weiteren wird die auf der Verteilung der ordinalen Muster beruhende Permutationsentropie eingesetzt, um in Magnetresonanztomographie (MRT)-Ruhedaten Kopfbewegungen der Probanden zu detektieren. Der zweite Hauptteil der Arbeit befasst sich mit der Erweiterung der ordinalen Muster auf zwei Dimensionen, um sie für Bilddaten nutzbar zu machen. Nach einigen Betrachtungen an fraktalen Oberflächen steht eine automatisierte und robuste Einschätzung der Qualität struktureller MRT-Daten im Vordergrund.
Today the process of improving technology and software allows to create, save and explore massive data sets in little time. "Big Data" are everywhere such as in social networks, meteorology, customers’ behaviour – and in biology. The Omics research field, standing for the organism-wide data exploration and analysis, is an example of biological research that has to deal with "Big Data" challenges. Possible challenges are for instance effcient storage and cataloguing of the data sets and finally the qualitative analysis and exploration of the information. In the last decade largescale genome-wide association studies and high-throughput techniques became more effcient, more profitable and less expensive. As a consequence of this rapid development, it is easier to gather massive amounts of genomic and proteomic data. However, these data need to get evaluated, analysed and explored. Typical questions that arise in this context include: which genes are active under sever al physical states, which proteins and metabolites are available, which organisms or cell types are similar or different in their enzymes’or genes’ behaviour. For this reason and because a scientist of any "Big Data" research field wants to see the data, there is an increasing need of clear, intuitively understandable and recognizable visualization to explore the data and confirm thesis. One way to get an overview of the data sets is to cluster it. Taxonomic trees and functional classification schemes are hierarchical structures used by biologists to organize the available biological knowledge in a systematic and computer readable way (such as KEGG, GO and FUNCAT). For example, proteins and genes could be clustered according to their function in an organism. These hierarchies tend to be rather complex, and many comprise thousands of biological entities. One approach for a space-filling visualization of these hierarchical structured data sets is a treemap. Existing algorithms for producing treemaps struggle with large data sets and have several other problems. This thesis addresses some of these problems and is structured as follows. After a short review of the basic concepts from graph theory some commonly used types of treemaps and a classification of treemaps according to information visualization aspects is presented in the first chapter of this thesis. The second chapter of this thesis provides several methods to improve treemap constructions. In certain applications the researcher wants to know, how the entities in a hierarchical structure are related to each other (such as enzymes in a metabolic pathway). Therefore in the 3 third chapter of this thesis, the focus is on the construction of a suitable layout overlaying an existing treemap. This gives rise to optimization problems on geometric graphs. In addition, from a practical point of view, options for enhancing the display of the computed layout are explored to help the user perform typical tasks in this context more effciently. One important aspect of the problems on geometric graphs considered in the third chapter of the thesis is that crossings of edges in a network structure are to be minimized while certain other properties such as connectedness are maintained. Motivated by this, in the fourth chapter of this thesis, related combinatorial and computational problems are explored from a more theoretical point of view. In particular some light is shed on properties of crossing-free spanning trees in geometric graphs.
In dieser Dissertation wird eine Problemstellung der Optimalen Steuerung aus dem Bereich der Linearen Elastizitätstheorie dargelegt und gelöst. Die Dissertation gliedert sich in die folgenden Schwerpunkte: Modellierung der Problemstellung, Formulierung der Optimalsteuerungsprobleme für den zeitunabhängigen (stationären) bzw. zeitabhängigen (instationären) Problem, die Herleitung der notwendigen Bedingungen für eine ermittelte optimale Lösung und die Berechnung von numerischen Lösungen des stationären bzw. instationären Problems sowie deren Überprüfung der Erfüllung der notwendigen Bedingungen. In der Modellierung werden Gleichungen zur Bestimmung der Deformation (Auslenkung) einer Zylinderschale unter rotations-symmetrischer Krafteinwirkung aus Grundgleichungen der Mechanik (Kräftegleichgewicht, Impulserhaltungssatz) hergeleitet. Bei dieser Herleitung werden die Hypothesen von Mindlin und Reissner verwendet und die spezielle Geometrie der Zylinderschale berücksichtigt. Die Dissertation erbringt den Nachweis der Existenz einer Lösung der modellierten Gleichungen im schwachen Sinne, d.h. für Lösungen in Sobolev-Räumen. Für die Formulierung der Optimalsteuerungsprobleme für den stationären und instationären Fall für Praxis relevante Problemstellungen setzen wir das Volumen des Zylinderrohres als konstant voraus (Volumenbedingung). Die Zielstellung der Optimalsteerungsprobleme besteht darin eine optimale Dicke zu bestimmen, welche die integrale Deformation (Auslenkung) der Zylinderschale (im instationären Fall zu einer ausgezeichneten Zeit) minimiert. Eine optimale Lösung (optimale Dicke) muss die notwendige Bedingung erster Ordnung (Variationsungleichung) für alle zulässigen Dicken, welche auch der Volumenbedingung genügen, erfüllen. Die Herleitung der konkreten Form dieser notwendigen Bedingungen für den stationären bzw. für die instationären Fälle wird in der Dissertation dargelegt. Durch die Verwendung der zugehörigen adjungierten Zustände können die notwendigen Bedingungen effizienter formuliert werden. Zur Berechnung einer Lösung der Gleichungen im stationären Fall bzw. in den instationären Fällen wurde die Finite Elemente Methode bzw. die Rothe-Methode im zeitabhängigen Fall verwendet, wobei die Lösungsräume exakt berücksichtigt werden. Das Optimierungsproblem wird diskretisiert und mit fmincon aus der Optimization-Toolbox von Matlab gelöst. Die damit berechneten diskreten optimalen Lösungen (optimale Dicke) für die einzelnen Problemstellungen werden auf die Erfüllung der notwendigen Bedingungen getestet. Die Dissertation wird durch viele Beispiel-Rechnungen abgerundet und deren Lösungen in grafischer Form präsentiert.
This thesis deals with thickness optimization of shells. The overall task is to find an optimal thickness distribution in order to minimize the deformation of a loaded shell with prescribed volume. In addition, lower and upper bounds for the thickness are given. The shell is made of elastic, isotropic, homogeneous material. The deformation is modeled using equations from Linear Elasticity. Here, a basic shell model based on the Reissner-Mindlin assumption is used. Both the stationary and the dynamic case are considered. The continuity and the Gâteaux-differentiability of the control-to-state operator is investigated. These results are applied to the reduced objective with help of adjoint theory. In addition, techniques from shape optimization are compared to the optimal control approach. In the following, the theoretical results are applied to cylindrical shells and an efficient numerical implementation is presented. Finally, numerical results are shown and analyzed for different examples.
The constructions of Lévy processes from convolution semigroups and of product systems from subproduct systems respectively, are formally quite similar. Since there are many more comparable situations in quantum stochastics, we formulate a general categorial concept (comonoidal systems), construct corresponding inductive systems and show under suitable assumptions general properties of the corresponding inductive limits. Comonoidal systems in different tensor categories play a role in all chapters of the thesis. Additive deformations are certain comonoidal systems of algebras. These are obtained by deformation of the algebra structure of a bialgebra. If the bialgebra is even a Hopf algebra, then compatibility with the antipode automatically follows. This remains true also in the case of braided Hopf algebras. Subproduct systems are comonoidal systems of Hilbert spaces. In the thesis we deal with the question, what are the possible dimensions of finite-dimensional subproduct systems. In discrete time, this can be reduced to the combinatorial problem of determining the complexities of factorial languages. We also discuss the rational and continuous time case. A further source for comonoidal systems are universal products, which are used in quantum probability to model independence. For the (r,s)-products, which were recently introduced by S. Lachs, we determine the corresponding product of representations by use of a generalized GNS-construction.
The geometric arena here is a smooth manifold of dimension n equipped with a Riemannian or pseudo-Riemannian metric and an affine connection. Field theories following from a variational principle are considered on this basis. In this context, all invariants which are quadratic in the curvature are determined. The work derives several manifestly covariant formulas for the Euler-Lagrange derivatives or the field equations. Some of these field theories can be interpreted as gravitational theories alternatively to Einstein´s general relativity theory. The work also touches the difficult problem to define and to calculate energy and momentum of a gravitational field.
Objektive Eingruppierung sequenzierter Tollwutisolate mithilfe des Affinity Propagation Clusterings.
(2018)
Das International Committee on Taxonomy of Viruses (ICTV) reguliert die Nomenklatur von Viren sowie die Entstehung neuer Taxa (dazu gehören: Ordnung, Familie, Unterfamilie, Gattung und Art/Spezies). Dank dieser Anstrengungen ist die Einteilung für verschiedenste Viren in diese Kategorien klar und transparent nachvollziehbar. In den vergangenen Jahrzehnten sind insgesamt mehr als 21.000 Datensätze der Spezies „rabies lyssavirus“ (RABV) sequenziert worden. Eine weiterführende Unterteilung der sequenzierten Virusisolate dieser Spezies ist bislang jedoch nicht einheitlich vorgeschlagen. Die große Anzahl an sequenzierten Isolaten führte auf Basis von phylogenetischen Bäumen zu uneindeutigen Ergebnissen bei der Einteilung in Cluster. Inhalt meiner Dissertation ist daher ein Vorschlag, diese Problematik mit der Anwendung einer partitionierenden Clusteringmethode zu lösen. Dazu habe ich erstmals die Methodik des affinity propagation clustering (AP) für solche Fragestellungen eingesetzt. Als Datensatz wurden alle verfügbaren sequenzierten Vollgenomisolate der Spezies RABV analysiert. Die Analysen des Datensatzes ergaben vier Hauptcluster, die sich geographisch separieren ließen und entsprechend als „Arctic“, „Cosmopolitain“, „Asian“ und „New World“ bezeichnet wurden. Weiterführende Analysen erlaubten auch eine weitere Aufteilung dieser Hauptcluster in 12-13 Untercluster. Zusätzlich konnte ich einen Workflow generieren, der die Möglichkeit bietet, die mittels AP definierten Cluster mit den Ergebnissen der phylogenetischen Auswertungen zu kombinieren. Somit lassen sich sowohl Verwandtschaftsverhältnisse erkennen als auch eine objektive Clustereinteilung vornehmen. Dies könnte auch ein möglicher Analyseweg für weitere Virusspezies oder andere vergleichende Sequenzanalysen sein.
Diese Dissertation untersucht Zusammenhänge der spieltheoretischen Begriffe des Nash- und Stackelberg-Gleichgewichts in Differenialspielen im N-Spieler-Fall. Weiterhin werden drei verschiedene Lösungskonzepte für das Finden von Gleichgewichten in 2-Spieler-Differentialspielen vorgestellt. Direkte Methoden aus der nichtlinearen Optimierung, der globalen Optimierung und der optimalen Steuerung werden verwendet, um Nash- und Stackelberg-Gleichgewichte in 2-Spieler-Differentialspielen zu finden. Anhand von Anwendungsbeispielen werden die Methoden getestet, analysiert und ausgewertet. Eine Erweiterung des Verfolgungsspiels von Isaacs auf Beschleunigungskomponenten wird betrachtet. Ein bisher unbekanntes Stackelberg-Gleichgewicht wird im Kapitalismusspiel nach Lancaster numerisch berechnet. Zuletzt wird ein Problem aus der Fischerei modelliert und anhand der eingeführten Methoden gelöst.
Numerische Lösung von Optimalsteuerungsaufgaben unter Nebenbedingungen mit biologischen Anwendungen
(2010)
In dieser Dissertation wird ein Verfahren zur Lösung von Optimalsteuerungsaufgaben mit Steuer-Zustandsbeschränkungen vorgestellt. Dazu werden die notwendigen Bedingungen an eine optimale Lösung benutzt, die ein System aus algebraischen Gleichungen, Ungleichungen und Differentialgleichungen erzeugen. Dieses System wird mit einem Newton-ähnlichen Ansatz gelöst. Außerdem wird die Erweiterung auf Problemen mit reinen Zustandsbeschränkungen vorgeführt. Eine deutliche Verbesserung der Konvergenzergebnisse kann durch die Anwendung der Fisher-Burmeister-Funktion auf die Komplementaritätsbedingungen erzielt werden. Die Iterationsverfahren werden auf eine Reihe von restringierten Optimalsteuerungsaufgaben (Aufgaben mit reinen Steuerbeschränkungen, gemischten Steuer-Zustandbeschränkungen und reinen Zustandsbeschränkungen für einzelne Zeitpunkte und für das gesamte Optimierungsintervall) angewendet, um ihr Verhalten bei verschiedenen Startwerten sowie unterschiedlichen Schrittweitenansätzen zu untersuchen. Dazu werden zum einen zwei aus der Literatur bekannte Aufgaben (das Rayleigh-Problem und das Minimum-Ernergy-Problem) gelöst und zum anderen werden zwei Probleme mit biologischem Hintergrund untersucht. So wird eine Optimalsteuerungsaufgabe aus der Fischerei um geeignete Einnahmenbedingungen erweitert, die absichern sollen, dass die Fischer keine längeren Phasen ohne Kapitalzuwachs haben. Dazu wird zwischen einer globalen Bedingung und einer Bedingung für endlich viele Zeitpunkte unterschieden. Desweiteren wird ein Modell einer HIV-Erkrankung untersucht, bei dem die numerischen Verfahren, die die notwendigen Bedingungen an eine optimale Lösung benutzen, nur für geringe Behandlungszeiten (bis zu 50 Tage) das Problem lösen. Es zeigt sich, dass die Stabilität dieser Verfahren deutlich verbessert werden kann, wenn das Modell um eine Obergrenze für die T-Zellen erweitert wird. Den Abschluss der Dissertation bildet ein Kapitel zur Konvergenzuntersuchung, in dem sich zeigt, dass die verwendeten Iterationsverfahren teilweise von sehr schlechter Konvergenzordnung sind, da die Bedingung für eine lineare Konvergenz nicht erfüllt wird.
Mathematical phylogenetics provides the theoretical framework for the reconstruction and analysis of phylogenetic trees and networks. The underlying theory is based on various mathematical disciplines, ranging from graph theory to probability theory.
In this thesis, we take a mostly combinatorial and graph-theoretical position and study different problems concerning phylogenetic trees and networks.
We start by considering phylogenetic diversity indices that rank species for conservation. Two such indices for rooted trees are the Fair Proportion index and the Equal Splits index, and we analyze how different they can be from each other and under which circumstances they coincide. Moreover, we define and investigate analogues of these indices for unrooted trees.
Subsequently, we study the Shapley value of unrooted trees, another popular phylogenetic diversity index. We show that it may fail as a prioritization criterion in biodiversity conservation and is outcompeted by an existing greedy approach. Afterwards, we leave the biodiversity setting and consider the Shapley value as a tree reconstruction tool. Here, we show that non-isomorphic trees may have permutation-equivalent Shapley transformation matrices and identical Shapley values, implying that the Shapley value cannot reliably be employed in tree reconstruction.
In addition to phylogenetic diversity indices, another class of indices frequently discussed in mathematical phylogenetics, is the class of balance indices. In this thesis, we study one of the oldest and most popular of them, namely the Colless index for rooted binary trees. We focus on its extremal values and analyze both its maximum and minimum values as well as the trees that achieve them.
Having analyzed various questions regarding phylogenetic trees, we finally turn to phylogenetic networks. We focus on a certain class of phylogenetic networks, namely tree-based networks, and consider this class both in a rooted and in an unrooted setting.
First, we prove the existence of a rooted non-binary universal tree-based network with n leaves for all positive integers n, that is, we show that there exists a rooted non-binary tree-based network with $n$ leaves that has every non-binary phylogenetic tree on the same leaf set as a base tree.
Finally, we study unrooted tree-based networks and introduce a class of networks that are necessarily tree-based, namely edge-based networks. We show that edge-based networks are closely related to a family of graphs in classical graph theory, so-called generalized series-parallel graphs, and explore this relationship in full detail.
In summary, we add new insights into existing concepts in mathematical phylogenetics, answer open questions in the literature, and introduce new concepts and approaches. In doing so, we make a small but relevant contribution to current research in mathematical phylogenetics.
The innate immune system relies on families of pattern recognition receptors (PRRs)
that detect distinct conserved molecular motifs from microbes to initiate antimicrobial responses.
Activation of PRRs triggers a series of signaling cascades, leading to the release of pro-inflammatory
cytokines, chemokines and antimicrobials, thereby contributing to the early host defense against
microbes and regulating adaptive immunity. Additionally, PRRs can detect perturbation of cellular
homeostasis caused by pathogens and fine-tune the immune responses. Among PRRs, nucleotide
binding oligomerization domain (NOD)-like receptors (NLRs) have attracted particular interest in the
context of cellular stress-induced inflammation during infection. Recently, mechanistic insights into
the monitoring of cellular homeostasis perturbation by NLRs have been provided. We summarize
the current knowledge about the disruption of cellular homeostasis by pathogens and focus on NLRs
as innate immune sensors for its detection. We highlight the mechanisms employed by various
pathogens to elicit cytoskeleton disruption, organelle stress as well as protein translation block, point
out exemplary NLRs that guard cellular homeostasis during infection and introduce the concept of
stress-associated molecular patterns (SAMPs). We postulate that integration of information about
microbial patterns, danger signals, and SAMPs enables the innate immune system with adequate
plasticity and precision in elaborating responses to microbes of variable virulence.
Neutrophils in Tuberculosis: Cell Biology, Cellular Networking and Multitasking in Host Defense
(2021)
Neutrophils readily infiltrate infection foci, phagocytose and usually destroy microbes. In
tuberculosis (TB), a chronic pulmonary infection caused by Mycobacterium tuberculosis (Mtb),
neutrophils harbor bacilli, are abundant in tissue lesions, and their abundances in blood correlate
with poor disease outcomes in patients. The biology of these innate immune cells in TB is complex.
Neutrophils have been assigned host-beneficial as well as deleterious roles. The short lifespan of
neutrophils purified from blood poses challenges to cell biology studies, leaving intracellular
biological processes and the precise consequences of Mtb–neutrophil interactions ill-defined. The
phenotypic heterogeneity of neutrophils, and their propensity to engage in cellular cross-talk and
to exert various functions during homeostasis and disease, have recently been reported, and such
observations are newly emerging in TB. Here, we review the interactions of neutrophils with Mtb,
including subcellular events and cell fate upon infection, and summarize the cross-talks between
neutrophils and lung-residing and -recruited cells. We highlight the roles of neutrophils in TB
pathophysiology, discussing recent findings from distinct models of pulmonary TB, and emphasize
technical advances that could facilitate the discovery of novel neutrophil-related disease
mechanisms and enrich our knowledge of TB pathogenesis
Neue robuste Methoden zur Herzschlagerkennung und zur Quantifizierung der Herzfrequenzvariabilität
(2016)
Für die Analyse der Herzfrequenz ist eine genaue Detektion des Herzschlags aus Rohdaten unerlässlich. Standardmethoden der Herzschlagerkennung sind für elektrische Biosignale konfiguriert worden, die in einem standardisierten klinischen Umfeld erhoben wurden, insbesondere für das Elektrokardiogramm. Im Zuge neuer Möglichkeiten zur Erfassung der Vitalparameter (über Smartphone, drahtlose Möglichkeiten) und zur Reduktion von Falschalarmen im Krankenhaus werden zunehmend robuste Methoden benötigt. Im ersten Kapitel haben wir einen neuen Algorithmus eingeführt, welcher in der Lage ist, unterschiedliche Wellenformen zu verarbeiten und die Informationen aus mehreren gleichzeitig erhobenen Biosignalen zu bündeln. Die Leistungsfähigkeit wurde im Vergleich mit anderen Methoden an freien Datensätzen überprüft und wir konnten uns von der vielfältigen Anwendbarkeit und der Störungsresistenz überzeugen. Im zweiten Kapitel haben wir uns mit der Quantifizierung der Herzfrequenzvariabilität (HRV) beschäftigt und ein neues leicht verständliches Maß eingeführt. Das dafür notwendige Konzept von relativen RR-Abständen wurde diskutiert und die Nutzung zur Artefaktfilterung und zur Klassifikation von Arrhythmiearten aufgezeigt. Vor- und Nachteile klassischer Methoden der HRV haben wir durch einige mathematische Eigenschaften begründet. Im dritten Kapitel der Dissertation haben wir das neue Maß an realen Daten angewendet und die Abhängigkeit der HRV vom Alter der Probanden und von der Herzfrequenz untersucht. Zudem haben wir periodische Strukturen des Streudiagramms von relativen RR-Abständen betrachtet, für die die Atmung ursächlich ist. Als wissenschaftliche Transferleistung wurde abschließend ein freies Programm geschaffen, welches die neuen robusten Methoden umsetzt.
Die Arbeit untersucht die Geometrie selbstähnlicher Mengen endlichen Typs, indem die möglichen Nachbarschaften kleiner Teile klassifiziert und ihr Zusammenhang untersucht werden. Anwendungen sind die Dimension von selbstähnlichen Maßen und überlappenden Konstruktionen sowie die Bestimmung von Zusammenhangseigenschaften.
We introduce a multi-step machine learning approach and use it to classify data from EEG-based brain computer interfaces. This approach works very well for high-dimensional EEG data. First all features are divided into subgroups and linear discriminant analysis is used to obtain a score for each subgroup. Then it is applied to subgroups of the resulting scores. This procedure is iterated until there is only one score remaining and this one is used for classification. In this way we avoid estimation of the high-dimensional covariance matrix of all features. We investigate the classifification performance with special attention to the small sample size case. For the normal model, we study the asymptotic error rate when dimension p and sample size n tend to infinity. This indicates how to defifine the sizes of subgroups at each step. In addition we present a theoretical error bound for the spatio-temporal normal model with separable covariance matrix, which results in a recommendation on how subgroups should be formed for this kind of data. Finally some techniques, for example wavelets and independent component analysis, are used to extract features of some kind of EEG-based brain computer interface data.
Spatial variation in survival has individual fitness consequences and influences population dynamics. It proximately and ultimately impacts space use including migratory connectivity. Therefore, knowing spatial patterns of survival is crucial to understand demography of migrating animals. Extracting information on survival and space use from observation data, in particular dead recovery data, requires explicitly identifying the observation process. The main aim of this work is to establish a modeling framework which allows estimating spatial variation in survival, migratory connectivity and observation probability using dead recovery data. We provide some biological background on survival and migration and a short methodological overview of how similar situations are modeled in literature.
Afterwards, we provide REML-like estimators for discrete space and show identifiability of all three parameters using the characteristics of the multinomial distribution. Moreover, we formulate a model in continuous space using mixed binomial point processes. The continuous model assumes a constant recovery probability over space. To drop this strict assumption, we develop an optimization procedure combining the discrete and continuous space model. Therefore, we use penalized M-splines. In simulation studies we demonstrate the performance of the estimators for all three model approaches. Furthermore, we apply the models to real-world data sets of European robins \textit{Erithacus rubecula} and ospreys \textit{Pandion haliaetus}.
We discuss how this study can be embedded in the framework of animal movement and the capture mark recapture/recovery methodology. It can be seen as a contribution and an extension to distance sampling, local stationary everyday movement and dispersal. We emphasize the importance of having a mathematically clearly formulated modeling framework for applied methods. Moreover, we comment on model assumptions and their limits. In the future, it would be appealing to extend this framework to the full annual cycle and carry-over effects.
Die Arbeit befasst sich mit der Parameterbestimmung in gewöhnlichen Differentialgleichungssystemen aus gegebenen Messdaten. Als Zielfunktion wird die quadratische Abweichungen betrachtet, ebenso wie die Betragssummen- und Tschebyschev-Norm der Differenz von der Lösung der gewöhnlichen Differentialgleichung und des Messwert-Vektors. Zur Anwendung kommen dabei sowohl iterative Optimierungsverfahren als auch direkte Methoden der optimalen Steuerung.
Jedes Metagenom umfasst die gesamte genomische Information eines kompletten Ökosystems. Die Analyse eines solchen Systems bedarf der Bestimmung aller darin enthaltenen Nukleinsäuren, stellvertretend für den Bauplan eines jeden Organismus, um Kenntnis über die in diesem Ökosystem nachweisbaren Organismen zu erlangen. Ferner bietet die diagnostische Metagenomanalyse eine Möglichkeit zur Identifizierung von sowohl bekannten als auch unbekannten Pathogenen. Zu diesem Zweck wird dem Metagenom eine Probe entnommen, welche einen repräsentativen Ausschnitt aller darin vorliegenden Organismen enthält. Da a priori keine Informationen zu den in der Probe enthaltenen Organismen vorliegen, bedarf es einer ungerichteten Methode zur Bestimmung aller enthaltenen Nukleinsäuren. Eine geeignete Lösung bietet die Sequenzierung. Darin werden alle Moleküle der Ausgangsprobe mit ungefähr gleicher Wahrscheinlichkeit bestimmt und der erzeugte Datensatz, bestehend aus Millionen kleiner Sequenzabschnitte, entspricht einem repräsentativen Querschnitt der in der Probe nachweisbaren Organismen. Die Herausforderung besteht in der Zuordnung einer jeden Sequenz zu ihren Ursprungsorganismen und die Sequenzen zu identifizieren, die mit einem potentiellen Erreger assoziiert werden können. Aktuell herrscht ein Defizit an Werkzeugen, die diese Zuordnung sowohl schnell als auch präzise vornehmen und speziell für die diagnostische Metagenomanalyse konzipiert sind. Zu diesem Zweck wurde im Rahmen dieser Arbeit eine Software-Pipeline mit Namen RIEMS (164) (Reliable Information Extraction from Metagenomic Sequence datasets) entwickelt, die bestehende Software zur Analyse von Sequenzdaten auf eine Weise verknüpft, die deren Stärken ausnutzt und Schwächen eliminiert. RIEMS ist in der Lage mit Hilfe bekannter Alignierungsalgorithmen und dem Abgleich der Sequenzen mit einschlägigen Datenbanken umfangreiche Datensätze schnell zu analysieren und Nukleinsäuresequenzen präzise ihren putativen Ursprungstaxa zuzuordnen (164). Die vorliegende Arbeit verdeutlicht die Effizienz dieses Computerprogramms im Vergleich zu bestehenden Software-Pipelines. Des Weiteren illustriert sie dessen möglichen Einsatz in der Diagnostik zur Pathogenidentifizierung anhand einiger Beispiele. Dabei können nicht nur bekannte Organismen identifiziert werden, sondern auch unbekannte, noch nicht näher beschriebene Organismen detektiert werden.
Gram-negative bacteria secrete lipopolysaccharides (LPS), leading to a host immune
response of proinflammatory cytokine secretion. Those proinflammatory cytokines are
TNF-α and IFN-γ, which induce the production of indoleamine 2,3-dioxygenase (IDO). IDO production is increased during severe sepsis, and septic shock. High IDO
levels are associated with increased mortality. This enzyme catalyzes the degradation of tryptophan (TRP) to kynurenine (KYN) along the kynurenine pathway (KP).
KYN is further degraded to kynurenic acid (KYNA). Increased IDO levels accompany
with increased levels of KYNA, which is associated with immunoparalysis.
Due to its central role, the KP is a potential target of therapeutic intervention.
The degradation of TRP to KYN by IDO was intervened by 1-Methyltryptophan (1-
MT), which is assumed to inhibit IDO. By administering 1-MT, the survival of
1-MT-treated mice suffering from sepsis increased compared to mice not treated with
1-MT. The levels of downstream metabolites such as KYN and KYNA were
expected to be decreased. Surprisingly, in healthy mice and pigs, an increase in KYNA
after 1-MT administration was reported. Those unexpected metabolite alterations after 1-MT administration, and the mode of action, were not the focus of recent
research. Hence, there is no explanation for KYNA increase, while KYN did not change.
This thesis aims to postulate a possible degradation pathway of 1-MT along the KP
with the help of ordinary differential equation (ODE) systems.
Moreover, the developed ODE models were used to determine the ability of 1-MT to
inhibit IDO in vivo. Therefore, a multiplicity of ODE models were developed, including
a model of the KP, an extension by lipopolysaccharide (LPS) administration, and 1-MT
administration.
Moreover, seven ODE models were developed, all considering possible degradation pathways of 1-MT. The most likely degradation pathway was combined with the ODE model
of LPS administration, including the inhibitory effects of 1-MT.
Those models consist of several dependent equations describing the dynamics of the KP.
For each component of the KP, one equation describes the alterations over time. Equations for TRP, KYN, KYNA, and quinolinic acid (QUIN) were developed.
Moreover, the alterations of serotonin (SER) were also included. All together belong
to the TRP metabolism. They include the degradation of TRP to SER and to KYN,
which is further degraded to KYNA and QUIN. Every degradation is catalyzed by an enzyme. Therefore, Michaelis-Menten (MM) equations were used employing the substrate
constant Km and the maximal degradation velocity Vmax. To reduce the complexity of
parameter calculation, Km values of the different enzymes were fixed to literature values.
The remaining parameters of the equations were determined so that the trajectories of
the calculated metabolite levels correspond to data. The parameters of different models were determined. To propose a degradation pathway of 1-MT leading to increased
KYNA levels, seven models were developed and compared. The most likely model was
extended to test whether the inhibitory effects of 1-MT on IDO can be determined.
Three different approaches determined the ODE model parameters of the different hypothesis of 1-MT degradation. In the first approach, ODE model parameters were fixed
to values fitted to an independent data set. In the second approach, parameters were
fitted to a subset of the data set, which was used for simulations of the different hypotheses. The third approach calculated ODE model parameters 100 times without
fixed parameters. The parameter set ending up in trajectories of the TRP metabolites,
which have the smallest distance to the data, was assumed to be the most likely. The
ODE model parameters were fitted to data measured in pigs. Two different
experimental models delivered data used in this thesis. The first experimental model
activates IDO by LPS administration in pigs. The second one combines the IDO
activation by LPS with the administration of 1-MT in pigs.
The most likely hypothesis, according to approach 1 was the degradation of 1-MT to
KYNA and TRP. For the second data set the most likely one was the direct degradation of 1-MT to KYNA. With approach 2 the most likely degradation pathways were
the combination of all degradation pathways and the degradation of 1-MT to TRP and
TRP to KYNA. With approach 3 the most likely way of KYNA increase was given by
the direct degradation of 1-MT to KYNA. In summary, the three approaches revealed
hypothesis 2, the direct degradation of 1-MT to KYNA most frequently. A cell-free
assay validated this result. This experiment combined 1-MT or TRP with or without
the enzyme kynurenine aminotransferase (KAT). KAT was already shown to degrade
TRP directly to KYNA. The levels of TRP, KYN and KYNA were measured. The
highest KYNA levels were yielded with an assay adding KAT to 1-MT, corresponding
to hypothesis 2. The models describing the inhibitory effects of 1-MT revealed that
the model without inhibitory effects of 1-MT on IDO was more likely for all three approaches.
The correctness of hypothesis 2 has to be confirmed by further in vitro experiments. It
also has to be investigated which reactions promote the degradation of 1-MT to KYNA.
The missing inhibitory properties of 1-MT on IDO, determined by the in silico ODE
models, align with previous research. It was shown that the saturation of 1-MT was too
low, e.g. in pigs, to inhibit IDO efficiently.
In this study, the first possible degradation pathway of 1-MT along the KP is proposed.
The reliability of the results depends on the quality of the experimental data, and the
season, when data were measured. Moreover, the results vary between the different
approaches of parameter fitting. Different approaches of parameter fitting have to be
included in the analysis to get more evidence for the correctness of the results.
Diese Arbeit beschäftigt sich mit der Analyse und Modellierung des Microarrayexperiments. Hierfür wird das gesamte Experiment in fünf Teilprozesse zerlegt, die Reverse Transkription, die Hybridisierung, das Waschen, die Fluoreszenz und die Detektion. Jeder Teilprozess wurde separat modelliert und analysiert. Anschließend wurde die Teilprozesse im Gesamtmodell vereint und dieses für verschiedene Parametersituationen simuliert. Diese Arbeit ermöglicht eine mathematische Handhabung des Microarrayexperiments und deckt seine Abhängigkeit von den einzelnen Schritten des Experiments auf. Dies kann benutzt werden, um Normalisierung und Analyse zu verbessern.
Background
The alignment of large numbers of protein sequences is a challenging task and its importance grows rapidly along with the size of biological datasets. State-of-the-art algorithms have a tendency to produce less accurate alignments with an increasing number of sequences. This is a fundamental problem since many downstream tasks rely on accurate alignments.
Results
We present learnMSA, a novel statistical learning approach of profile hidden Markov models (pHMMs) based on batch gradient descent. Fundamentally different from popular aligners, we fit a custom recurrent neural network architecture for (p)HMMs to potentially millions of sequences with respect to a maximum a posteriori objective and decode an alignment. We rely on automatic differentiation of the log-likelihood, and thus, our approach is different from existing HMM training algorithms like Baum–Welch. Our method does not involve progressive, regressive, or divide-and-conquer heuristics. We use uniform batch sampling to adapt to large datasets in linear time without the requirement of a tree. When tested on ultra-large protein families with up to 3.5 million sequences, learnMSA is both more accurate and faster than state-of-the-art tools. On the established benchmarks HomFam and BaliFam with smaller sequence sets, it matches state-of-the-art performance. All experiments were done on a standard workstation with a GPU.
Conclusions
Our results show that learnMSA does not share the counterintuitive drawback of many popular heuristic aligners, which can substantially lose accuracy when many additional homologs are input. LearnMSA is a future-proof framework for large alignments with many opportunities for further improvements.
Jump penalized L1-Regression
(2012)
Die vorgelegte Arbeit beschäftigt sich mit Kurvenschätzung in einem Regressionsmodell für eindimensionale verrauschte Daten, welche die Ausreißer enthalten können. Dabei ist die Regression Funktion, also Funktion welche a priori unbekannt ist und welche geschätzt werden soll, eine beliebige absolut-integrierbare Funktion auf dem Intervall [0, 1) und Regression Schätzer eine Stückweise-konstante Funktion auf dem Intervall [0, 1). Die von uns betrachtende Schätzer sind stückweise-konstante Funktionen, welche die L1-Version den sogenannten Potts Funktional minimieren (s. [8]). Das L1 Potts Funktional ist so gewählt, dass einerseits die Komplexität des Schätzers in Form der Anzahl ihrer Sprünge beachtet wird und anderseits die absolute Abweichungen von den Daten betrachtet werden. Die Stufen des Minimierers vom L1 Potts Funktional entsprechen den lokalen Medianen von verrauschten Daten, im Gegensatz dazu entsprechen die Stufen des Minimierers von dem klassischen Potts Funktional (L2-Fall) den lokalen Mittelwerten von den Daten. Der Vorteil der L1-Version gegenüber L2-Version des Potts Funktionals kann dadurch erklärt werden, dass die Mediane bekannterweise viel robuster gegen Ausreißer als Mittelwerte sind. In der vorgelegten Arbeit wurden die asymptotischen Eigenschaften sowohl von der L1 Potts Funktionals als auch von seinen Minimierer studiert. Unter anderem, es konnte die Konsistenz des Schätzers für den Fall, dass die Originalfunktion f selbst eine Stufenfunktion ist, gezeigt werden. Dies stellt das Hauptergebnis der Arbeit dar. Konsistenz heißt hier, dass unter bestimmten Bedingungen die Minimierer vom L1 Potts Funktional gegen die Originalfunktion f konvergieren.
The history of Mathematics has been lead in part by the desire for generalization: once an object was given and had been understood, there was the desire to find a more general version of it, to fit it into a broader framework. Noncommutative Mathematics fits into this description, as its interests are objects analoguous to vector spaces, or probability spaces, etc., but without the commonsense interpretation that those latter objects possess. Indeed, a space can be described by its points, but also and equivalently, by the set of functions on this space. This set is actually a commutative algebra, sometimes equipped with some more structure: *-algebra, C*-algebra, von Neumann algebras, Hopf algebras, etc. The idea that lies at the basis of noncommutative Mathematics is to replace such algebras by algebras that are not necessarily commutative any more and to interpret them as "algebras of functions on noncommutative spaces". Of course, these spaces do not exist independently from their defining algebras, but facts show that a lot of the results holding in (classical) probability or (classical) group theory can be extended to their noncommutative counterparts, or find therein powerful analogues. The extensions of group theory into the realm of noncommutative Mathematics has long been studied and has yielded the various quantum groups. The easiest version of them, the compact quantum groups, consist of C*-algebras equipped with a *-homomorphism &Delta with values in the tensor product of the algebra with itself and verifying some coassociativity condition. It is also required that the compact quantum group verifies what is known as quantum cancellation property. It can be shown that (classical) compact groups are indeed a particular case of compact quantum groups. The area of compact quantum groups, and of quantum groups at large, is a fruitful area of research. Nevertheless, another generalization of group theory could be envisioned, namely by taking a comultiplication &Delta taking values not in the tensor product but rather in the free product (in the category of unital *-algebras). This leads to the theory of dual groups in the sense of Voiculescu, also called H-algebras by Zhang. These objects have not been so thoroughly studied as their quantum counterparts. It is true that they are not so flexible and that we therefore do not know many examples of them and showing that some relations cannot exist in the dual group case because they do not pass the coproduct. Nevertheless, I have been interested during a great part of my PhD work by these objects and I have made some progress towards their understanding, especially regarding quantum Lévy processes defined on them and Haar states.
Interactive Visualization for the Exploration of Aligned Biological Networks and Their Evolution
(2011)
Network Visualization is a widely used tool in biology. The biological networks, as protein-interaction-networks are important for many aspects in life. Today biologists use the comparison of networks of different species (network alignment) to understand the networks in more detail and to understand the underlying evolution. The goal of this work is to develop a visualization software that is able to visualize network alignments and also their evolution. The presented software is the first software for such visualization tasks. It uses 3D graphics and also animations for the dynamic visualization of evolution. This work consists of a review of the Related Work, a chapter about our Graph-based Approach for Interactive Visualization of Evolving Network Alignments, an explanation of the Graph Layout Algorithm and some hints for the Software System.
High-throughput expression data have become the norm in molecular biology research. However, the analysis of expression data is statistically and computationally challenging and has not kept up with their generation. This has resulted in large amounts of unexplored data in public repositories. After pre-processing and quality control, the typical gene expression analysis workflow follows two main steps. First, the complexity of the data is reduced by removing the genes that are redundant or irrelevant for the biological question that motivated the experiment, using a feature selection method. Second, relevant genes are investigated to extract biological information that could aid in the interpretation of the results. Different methods, such as functional annotation, clustering, network analysis, and/or combinations thereof are useful for the latter purpose. Here, I investigated and presented solutions to three problems encountered in the expression data analysis workflow. First, I worked on reducing complexity of high-throughput expression data by selecting relevant genes in the context of the sample classification problem. The sample classification problem aims to assign unknown samples into one of the known classes, such as healthy and diseased. For this purpose, I developed the relative signal-to-noise ratio (rSNR), a novel feature selection method which was shown to perform significantly better than other methods with similar objectives. Second, to better understand complex phenotypes using high-throughput expression data, I developed a pipeline to identify the underlying biological units, as well as their interactions. These biological units were assumed to be represented by groups of genes working in synchronization to perform a given function or participate in common biological processes or pathways. Thus, to identify biological units, those genes that had been identified as relevant to the phenotype under consideration through feature selection methods were clustered based on both their functional annotations and expression profiles. Relationships between the associated biological functions, processes, and/or pathways were investigated by means of a co-expression network. The developed pipeline provides a new perspective to the analysis of high-throughput expression data by investigating interactions between biological units. Finally, I contributed to a project where a network describing pluripotency in mouse was used to infer the corresponding network in human. Biological networks are context-specific. Combining network information with high-throughput expression data can explain the control mechanisms underlying changes and maintenance of complex phenotypes. The human network was constructed on the basis of orthology between mouse and human genes and proteins. It was validated with available data in the literature. The methods and strategies proposed here were mainly trained and tested on microarray expression data. However, they can be easily adapted to next-generation sequencing and proteomics data.
Independence is a basic concept of probability theory and statistics. In a lot of fields of sciences, dependency of different variables is gained lots of attention from scientists. A measure, named information dependency, is proposed to express the dependency of a group of random variables. This measure is defined as the Kullback-Leibler divergence of a joint distribution with respect to a product-marginal distribution of these random variables. In the bivariate case, this measure is known as mutual information of two random variables. Thus, the measure information dependency has a strong relationship with the Information Theory. The thesis aims to give a thorough study of the information dependency from both mathematical and practical viewpoints. Concretely, we would like to research three following problems: 1. Proving that the information dependency is a useful tool to express the dependency of a group of random variables by comparing it with other measures of dependency. 2. Studying the methods to estimate the information dependency based on the samples of a group of random variables. 3. Investigating how the Independent Component Analysis problem, an interesting problem in statistics, can be solved using information dependency.
Convolutional Neural Network-based image classification models are the current state-of-the-art for solving image classification problems. However, obtaining and using such a model to solve a specific image classification problem presents several challenges in practice. To train the model, we need to find good hyperparameter values for training, such as initial model weights or learning rate. However, finding these values is usually a non-trivial process. Another problem is that the training data used for model training is often class-imbalanced in practice. This usually has a negative impact on model training. However, not only is it challenging to obtain a Convolutional Neural Network-based model, but also to use the model after model training. After training, the model might be applied to images that were drawn from a data distribution that is different from the data distribution the training data was drawn from. These images are typically referred to as out-of-distribution samples. Unfortunately, Convolutional Neural Network-based image classification models typically fail to predict the correct class for out-of-distribution samples without warning, which is problematic when such a model is used for safety-critical applications. In my work, I examined whether information from the layers of a Convolutional Neural Network-based image classification model (pixels and activations) can be used to address all of these issues. As a result, I suggest a method for initializing the model weights based on image patches, a method for balancing a class-imbalanced dataset based on layer activations, and a method for detecting out-of-distribution samples, which is also based on layer activations. To test the proposed methods, I conducted extensive experiments using different datasets. My experiments showed that layer information (pixels and activations) can indeed be used to address all of the aforementioned challenges when training and using Convolutional Neural Network-based image classification models.
Liver diseases are important causes of morbidity and mortality worldwide. The aim of
this study was to identify differentially expressed microRNAs (miRNAs), target genes, and key
pathways as innovative diagnostic biomarkers in liver patients with different pathology and functional
state. We determined, using RT-qPCR, the expression of 472 miRNAs in 125 explanted livers from
subjects with six different liver pathologies and from control livers. ANOVA was employed to
obtain differentially expressed miRNAs (DEMs), and miRDB (MicroRNA target prediction database)
was used to predict target genes. A miRNA–gene differential regulatory (MGDR) network was
constructed for each condition. Key miRNAs were detected using topological analysis. Enrichment
analysis for DEMs was performed using the Database for Annotation, Visualization, and Integrated
Discovery (DAVID). We identified important DEMs common and specific to the different patient
groups and disease progression stages. hsa-miR-1275 was universally downregulated regardless
the disease etiology and stage, while hsa-let-7a*, hsa-miR-195, hsa-miR-374, and hsa-miR-378 were
deregulated. The most significantly enriched pathways of target genes controlled by these miRNAs
comprise p53 tumor suppressor protein (TP53)-regulated metabolic genes, and those involved in
regulation of methyl-CpG-binding protein 2 (MECP2) expression, phosphatase and tensin homolog
(PTEN) messenger RNA (mRNA) translation and copper homeostasis. Our findings show a novel
panel of deregulated miRNAs in the liver tissue from patients with different liver pathologies. These
miRNAs hold potential as biomarkers for diagnosis and staging of liver diseases.