Refine
Year of publication
- 2022 (15) (remove)
Document Type
- Doctoral Thesis (15) (remove)
Language
- English (15)
Has Fulltext
- yes (15)
Is part of the Bibliography
- no (15)
Keywords
- Algebraic number theory (1)
- Anabelian Geometry (1)
- Bifurcation Theory (1)
- CBM (1)
- CBM experiment (1)
- Cellular Automaton (1)
- Demuškin groups (1)
- HPC (1)
- Heavy Ion experiments (1)
- Kalman Filter (1)
Institute
- Informatik und Mathematik (15) (remove)
This thesis presents a first-of-its-kind phenomenological framework that formally describes the development of acquired epilepsy and the role of the neuro-immune axis in this development. Formulated as a system of nonlinear differential equations, the model describes the interaction of processes such as neuroinflammation, blood- brain barrier disruption, neuronal death, circuit remodeling, and epileptic seizures. The model allows for the simulation of epilepsy development courses caused by a variety of neurological injuries. The simulation results are in agreement with ex- perimental findings from three distinct animal models of epileptogenesis. Simula- tions capture injury-specific temporal patterns of seizure occurrence, neuroinflam- mation, blood-brain barrier leakage, and progression of neuronal death. In addition, the model provides insights into phenomena related to epileptogenesis such as the emergence of paradoxically long time scales of disease development after injury, the dose-dependence of epileptogenesis features on injury severity, and the variability of clinical outcomes in subjects exposed to identical injury. Moreover, the developed framework allows for the simulation of therapeutic interventions, which provides insights into the injury-specificity of prominent intervention strategies. Thus, the model can be used as an in silico tool for the generation of testable predictions, which may aid pre-clinical research for the development of epilepsy treatments.
Die Emergenz digitaler Netzwerke ist auf die ständige Entwicklung und Transformation neuer Informationstechnologien zurückzuführen.
Dieser Strukturwandel führt zu äußerst komplexen Systemen in vielen verschiedenen Lebensbereichen.
Es besteht daher verstärkt die Notwendigkeit, die zugrunde liegenden wesentlichen Eigenschaften von realen Netzwerken zu untersuchen und zu verstehen.
In diesem Zusammenhang wird die Netzwerkanalyse als Mittel für die Untersuchung von Netzwerken herangezogen und stellt beobachtete Strukturen mithilfe mathematischer Modelle dar.
Hierbei, werden in der Regel parametrisierbare Zufallsgraphen verwendet, um eine systematische experimentelle Evaluation von Algorithmen und Datenstrukturen zu ermöglichen.
Angesichts der zunehmenden Menge an Informationen, sind viele Aspekte der Netzwerkanalyse datengesteuert und zur Interpretation auf effiziente Algorithmen angewiesen.
Algorithmische Lösungen müssen daher sowohl die strukturellen Eigenschaften der Eingabe als auch die Besonderheiten der zugrunde liegenden Maschinen, die sie ausführen, sorgfältig berücksichtigen.
Die Generierung und Analyse massiver Netzwerke ist dementsprechend eine anspruchsvolle Aufgabe für sich.
Die vorliegende Arbeit bietet daher algorithmische Lösungen für die Generierung und Analyse massiver Graphen.
Zu diesem Zweck entwickeln wir Algorithmen für das Generieren von Graphen mit vorgegebenen Knotengraden, die Berechnung von Zusammenhangskomponenten massiver Graphen und zertifizierende Grapherkennung für Instanzen, die die Größe des Hauptspeichers überschreiten.
Unsere Algorithmen und Implementierungen sind praktisch effizient für verschiedene Maschinenmodelle und bieten sequentielle, Shared-Memory parallele und/oder I/O-effiziente Lösungen.
Antimicrobial resistant infections arise as a consequential response to evolutionary mechanisms within microbes which cause them to be protected from the effects of antimicrobials. The frequent occurrence of resistant infections poses a global public health threat as their control has become challenging despite many efforts. The dynamics of such infections are driven by processes at multiple levels. For a long time, mathematical models have proved valuable for unravelling complex mechanisms in the dynamics of infections. In this thesis, we focus on mathematical approaches to modelling the development and spread of resistant infections at between-host (population-wide) and within-host (individual) levels.
Within an individual host, switching between treatments has been identified as one of the methods that can be employed for the gradual eradication of resistant strains on the long term. With this as motivation, we study the problem using dynamical systems and notions from control theory. We present a model based on deterministic logistic differential equations which capture the general dynamics of microbial resistance inside an individual host. Fundamentally, this model describes the spread of resistant infections whilst accounting for evolutionary mutations observed in resistant pathogens and capturing them in mutation matrices. We extend this model to explore the implications of therapy switching from a control theoretic perspective by using switched systems and developing control strategies with the goal of reducing the appearance of drug resistant pathogens within the host.
At the between-host level, we use compartmental models to describe the transmission of infection between multiple individuals in a population. In particular, we make a case study of the evolution and spread of the novel coronavirus (SARS-CoV-2) pandemic. So far, vaccination remains a critical component in the eventual solution to this public health crisis. However, as with many other pathogens, vaccine resistant variants of the virus have been a major concern in control efforts by governments and all stakeholders. Using network theory, we investigate the spread and transmission of the disease on social networks by compartmentalising and studying the progression of the disease in each compartment, considering both the original virus strain and one of its highly transmissible vaccine-resistant mutant strains. We investigate these dynamics in the presence of vaccinations and other interventions. Although vaccinations are of absolute importance during viral outbreaks, resistant variants coupled with population hesitancy towards vaccination can lead to further spread of the virus.
We thoroughly study the properties of conically stable polynomials and imaginary projections. A multivariate complex polynomial is called stable if its nonzero whenever all coordinates of the respective argument have a positive imaginary part. In this dissertation we consider the generalized notion of K-stability. A multivariate complex polynomial is called K-stable if its non-zero whenever the imaginary part of the respective argument lies in the relative interior of the cone K. We study connections to various other objects, including imaginary projections as well as preservers and combinatorial criteria for conically stable polynomials.
People can describe spatial scenes with language and, vice versa, create images based on linguistic descriptions. However, current systems do not even come close to matching the complexity of humans when it comes to reconstructing a scene from a given text. Even the ever-advancing development of better and better Transformer-based models has not been able to achieve this so far. This task, the automatic generation of a 3D scene based on an input text, is called text-to-3D scene generation. The key challenge, and focus of this dissertation, now relate to the following topics:
(a) Analyses of how well current language models understand spatial information, how static embeddings compare, and whether they can be improved by anaphora resolution.
(b) Automated resource generation for context expansion and grounding that can help in the creation of realistic scenes.
(c) Creation of a VR-based text-to-3D scene system that can be used as an annotation and active-learning environment, but can also be easily extended in a modular way with additional features to solve more contexts in the future.
(d) Analyze existing practices and tools for digital and virtual teaching, learning, and collaboration, as well as the conditions and strategies in the context of VR.
In the first part of this work, we could show that static word embeddings do not benefit significantly from pronoun substitution. We explain this result by the loss of contextual information, the reduction in the relative occurrence of rare words, and the absence of pronouns to be substituted. But we were able to we have shown that both static and contextualizing language models appear to encode object knowledge, but require a sophisticated apparatus to retrieve it. The models themselves in combination with the measures differ greatly in terms of the amount of knowledge they allow to extract.
Classifier-based variants perform significantly better than the unsupervised methods from bias research, but this is also due to overfitting. The resources generated for this evaluation are later also an important component of point three.
In the second part, we present AffordanceUPT, a modularization of UPT trained on the HICO-DET dataset, which we have extended with Gibsonien/telic annotations. We then show that AffordanceUPT can effectively make the Gibsonian/telic distinction and that the model learns other correlations in the data to make such distinctions (e.g., the presence of hands in the image) that have important implications for grounding images to language.
The third part first presents a VR project to support spatial annotation respectively IsoSpace. The direct spatial visualization and the immediate interaction with the 3D objects should make the labeling more intuitive and thus easier. The project will later be incorporated as part of the Semantic Scene Builder (SeSB). The project itself in turn relies on the Text2SceneVR presented here for generating spatial hypertext, which in turn is based on the VAnnotatoR. Finally, we introduce Semantic Scene Builder (SeSB), a VR-based text-to-3D scene framework using Semantic Annotation Framework (SemAF) as a scheme for annotating semantic relations. It integrates a wide range of tools and resources by utilizing SemAF and UIMA as a unified data structure to generate 3D scenes from textual descriptions and also supports annotations. When evaluating SeSB against another state-of-the-art tool, it was found that our approach not only performed better, but also allowed us to model a wider variety of scenes. The final part reviews existing practices and tools for digital and virtual teaching, learning, and collaboration, as well as the conditions and strategies needed to make the most of technological opportunities in the future.
In the human brain, the incoming light to the retina is transformed into meaningful representations that allow us to interact with the world. In a similar vein, the RGB pixel values are transformed by a deep neural network (DNN) into meaningful representations relevant to solving a computer vision task it was trained for. Therefore, in my research, I aim to reveal insights into the visual representations in the human visual cortex and DNNs solving vision tasks.
In the previous decade, DNNs have emerged as the state-of-the-art models for predicting neural responses in the human and monkey visual cortex. Research has shown that training on a task related to a brain region’s function leads to better predictivity than a randomly initialized network. Based on this observation, we proposed that we can use DNNs trained on different computer vision tasks to identify functional mapping of the human visual cortex.
To validate our proposed idea, we first investigate a brain region occipital place area (OPA) using DNNs trained on scene parsing task and scene classification task. From the previous investigations about OPA’s functions, we knew that it encodes navigational affordances that require spatial information about the scene. Therefore, we hypothesized that OPA’s representation should be closer to a scene parsing model than a scene classification model as the scene parsing task explicitly requires spatial information about the scene. Our results showed that scene parsing models had representation closer to OPA than scene classification models thus validating our approach.
We then selected multiple DNNs performing a wide range of computer vision tasks ranging from low-level tasks such as edge detection, 3D tasks such as surface normals, and semantic tasks such as semantic segmentation. We compared the representations of these DNNs with all the regions in the visual cortex, thus revealing the functional representations of different regions of the visual cortex. Our results highly converged with previous investigations of these brain regions validating the feasibility of the proposed approach in finding functional representations of the human brain. Our results also provided new insights into underinvestigated brain regions that can serve as starting hypotheses and promote further investigation into those brain regions.
We applied the same approach to find representational insights about the DNNs. A DNN usually consists of multiple layers with each layer performing a computation leading to the final layer that performs prediction for a given task. Training on different tasks could lead to very different representations. Therefore, we first investigate at which stage does the representation in DNNs trained on different tasks starts to differ. We further investigate if the DNNs trained on similar tasks lead to similar representations and on dissimilar tasks lead to more dissimilar representations. We selected the same set of DNNs used in the previous work that were trained on the Taskonomy dataset on a diverse range of 2D, 3D and semantic tasks. Then, given a DNN trained on a particular task, we compared the representation of multiple layers to corresponding layers in other DNNs. From this analysis, we aimed to reveal where in the network architecture task-specific representation is prominent. We found that task specificity increases as we go deeper into the DNN architecture and similar tasks start to cluster in groups. We found that the grouping we found using representational similarity was highly correlated with grouping based on transfer learning thus creating an interesting application of the approach to model selection in transfer learning.
During previous works, several new measures were introduced to compare DNN representations. So, we identified the commonalities in different measures and unified different measures into a single framework referred to as duality diagram similarity. This work opens up new possibilities for similarity measures to understand DNN representations. While demonstrating a much higher correlation with transfer learning than previous state-of-the-art measures we extend it to understanding layer-wise representations of models trained on the Imagenet and Places dataset using different tasks and demonstrate its applicability to layer selection for transfer learning.
In all the previous works, we used the task-specific DNN representations to understand the representations in the human visual cortex and other DNNs. We were able to interpret our findings in terms of computer vision tasks such as edge detection, semantic segmentation, depth estimation, etc. however we were not able to map the representations to human interpretable concepts. Therefore in our most recent work, we developed a new method that associates individual artificial neurons with human interpretable concepts.
Overall, the works in this thesis revealed new insights into the representation of the visual cortex and DNNs...
In this thesis, we cover two intimately related objects in combinatorics, namely random constraint satisfaction problems and random matrices. First we solve a classic constraint satisfaction problem, 2-SAT using the graph structure and a message passing algorithm called Belief Propagation. We also explore another message passing algorithm called Warning Propagation and prove a useful result that can be employed to analyze various type of random graphs. In particular, we use this Warning Propagation to study a Bernoulli sparse parity matrix and reveal a unique phase transition regarding replica symmetry. Lastly, we use variational methods and a version of local limit theorem to prove a sufficient condition for a general random matrix to be of full rank.
The main task of modern large experiments with heavy ions, such as CBM (FAIR), STAR (BNL) and ALICE (CERN) is a detailed study of the phase diagram of quantum chromodynamics (QCD) in the quark-gluon plasma (QGP), the equation of state of matter at extremely high baryonic densities, and the transition from the hadronic phase of matter to the quark-gluon phase.
In the thesis, the missing mass method is developed for the reconstruction of short-lived particles with neutral particles in their decay products, as well as its implementation in the form of fast algorithms and a set of software for prac- tical application in heavy ion physics experiments. Mathematical procedures implementing the method were developed and implemented within the KF Par- ticle Finder package for the future CBM (FAIR) experiment and subsequently adapted and applied for processing and analysis of real data in the STAR (BNL) experiment.
The KF Particle Finder package is designed to reconstruct most signal particles from the physics program of the CBM experiment, including strange particles, strange resonances, hypernuclei, light vector mesons, charm particles and char- monium. The package includes searches for over a hundred decays of short-lived particles. This makes the KF Particle Finder a universal platform for short-lived particle reconstruction and physics analysis both online and offline.
The missing mass method has been proposed to reconstruct decays of short-lived charged particles when one of the daughter particles is neutral and is not regis- tered in the detector system. The implementation of the missing mass method was integrated into the KF Particle Finder package to search for 18 decays with a neutral daughter particle.
Like all other algorithms of the KF Particle Finder package, the missing mass method is implemented with extensive use of vector (SIMD) instructions and is optimized for parallel operation on modern many-core high performance com- puter clusters, which can include both processors and coprocessors. A set of algorithms implementing the method was tested on computers with tens of cores and showed high speed and practically linear scalability with respect to the num- ber of cores involved.
It is extremely important, especially for the initial stage of the CBM experiment, which is planned for 2025, to demonstrate already now on real data the reliability of the developed approach, as well as the high efficiency of the current implemen- tation of both the entire KF Particle Finder package, and its integral part, the missing mass method. Such an opportunity was provided by the FAIR Phase-0 program, motivating the use in the STAR experiment of software packages orig- inally developed for the CBM experiment.
Application of the method to real data of the STAR experiment shows very good results with a high signal-to-background ratio and a large significance value. The results demonstrate the reliability and high efficiency of the missing mass method in the reconstruction of both charged mother particles and their neutral daughter particles. Being an integral part of the KF Particle Finder package, now the main approach for reconstruction and analysis of short-lived particles in the STAR experiment, the missing mass method will continue to be used for the physics analysis in online and offline modes.
The high quality of the results of the express data analysis has led to their status as preliminary physics results with the right to present them at international physics conferences and meetings on behalf of the STAR Collaboration.
In this thesis we discuss the group Out(Gal_K) of outer automorphism of the absolute Galois group Gal_K of a p-adic number field K. Using results about the mapping class group of a surface S, as well as a result by Jannsen--Wingberg on the structure of the absolute Galois group Gal_K, we construct a large subgroup of Out(Gal_K) arising as images of certain Dehn twists on S.
This thesis is concerned with the study of symmetry breaking phenomena for several different semilinear partial differential equations. Roughly speaking, this encompasses equations whose symmetries are not necessarily inherited by their solutions, which is particularly interesting for ground state solutions.