Institutes
Refine
Year of publication
Document Type
- Doctoral Thesis (91)
- Article (59)
- Bachelor Thesis (18)
- Book (13)
- Master's Thesis (10)
- Conference Proceeding (4)
- Contribution to a Periodical (4)
- Habilitation (2)
- Preprint (2)
- Diploma Thesis (1)
Has Fulltext
- yes (204)
Is part of the Bibliography
- no (204)
Keywords
- Machine Learning (5)
- NLP (5)
- ALICE (3)
- Annotation (3)
- Machine learning (3)
- Text2Scene (3)
- TextAnnotator (3)
- Virtual Reality (3)
- mathematics education (3)
- Artificial intelligence (2)
Institute
Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming
(2021)
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. The aim of this note is to point out a new connection between inverse coefficient problems and semidefinite programming that may help addressing these challenges. We show that an inverse elliptic Robin transmission problem with finitely many measurements can be equivalently rewritten as a uniquely solvable convex non-linear semidefinite optimization problem. This allows to explicitly estimate the number of measurements that is required to achieve a desired resolution, to derive an error estimate for noisy data, and to overcome the problem of local minima that usually appears in optimization-based approaches for inverse coefficient problems.
Die folgende Arbeit handelt von einer Text2Scene Anwendung, welche in der Virtual Reality (VR) umgesetzt wurde. Das System ermöglicht es den Usern aus einer Beschreibung einer Szene, diese virtuell nachzustellen. Dies bietet eine neue Art der Interaktion mit einem Text, die die visuelle Komponente hervorhebt und somit eine Geschichte auf neue Wege erfahrbar macht.
Dazu kann der User einen fertigen Text entweder vom Server zu laden oder einen eigenen erstellen, der dann automatisch verarbeitet wird. Dabei werden die vorhanden physischen Objekte im Text automatisch erkannt und dem User als 3D-Objekte in der virtuellen Umgebung zur Verfügung gestellt. Diese können dann manuell platziert werden und erzeugen dadurch die Szene, die im Ausgangstext beschrieben wurde. Das Ziel der Textverarbeitung ist eine möglichst genaue Beschreibung der Objekte, damit diese zielgerichtet in der Objektdatenbank gesucht werden können.
Bei der Textverarbeitung wird besonderer Wert auf das Erkennen von Teil-Ganz Beziehungen gelegt. Sodass Objekte, die im Text vorkommen und ein Holonym besitzen, automatisch mit diesem verknüpft werden. Gleichzeitig wird die Teil-Ganz Beziehung aber auch in die andere Richtung genauer betrachtet. Die Textverarbeitung soll ferner dazu in der Lage sein, Objekte genauer zu spezifizieren und an den Kontext des Textes anzupassen. Weiterhin wurde das Natural Language Processing (NLP) so ausgebaut, dass der Kontext des Textes erkannt wird und die Objekte entsprechend kategorisiert werden. Die Textverarbeitung wird mithilfe eines Neuronalen Netzes implementiert. Die verwendeten Tools zur Erkennung von Teil-Ganz Beziehungen, Kontext und Spezifikation von Objekten wurden anhand von Texteingaben nach der Genauigkeit der Ausgabe evaluiert.
Zur Nutzung der Textverarbeitung wurde eine virtuelle Szene entwickelt, die das Erstellen von eigenen Szenen aus vorher geladenen beziehungsweise eingegebenen Texten ermöglicht.
Dazu kann der Nutzer manuell oder automatisch Objekte laden lassen, die er dann platzieren kann.
Analysing survival or fixation probabilities for a beneficial allele is a prominent task in the field of theoretical population genetics. Haldane's asymptotics is an approximation for the fixation probability in the case of a single beneficial mutant with small selective advantage in a large population.
In this thesis we analyse the interplay between genetic drift and directional selection and prove Haldane's asymptotics in different settings: For the fixation probability in Cannings models with moderate selection and for the survival probability of a slightly supercritical branching processes in a random environment.
In Chapter 3 we introduce a class of Cannings models with selection that allow for a forward and backward construction. In particular, a Cannings ancestral selection process can be defined for this class of models, which counts the number of potential parents and is in sampling duality to the forward frequency process. By means of this duality the probability of fixation can be expressed through the expectation of the Cannings ancestral selection process in stationarity. A control of this expectation yields that the fixation probability fulfils Haldane's asymptotics in a regime of moderately weak selection (Thm. 8).
In Chapter 4 we study the fixation probability of Cannings models in a regime of moderately strong selection. Here couplings of the frequency process of beneficial individuals with slightly supercritical Galton-Watson processes imply that the fixation probability is given by Haldane's asymptotics (Thm. 9).
Lastly, in Chapter 5 we consider slightly supercritical branching processes in an independent and identically distributed random environment and study the probability of survival as the number of expected offspring tends from above to one. We show that only if variance and expectation of the random offspring mean are of the same order the random environment has a non-trivial influence on the probability of survival, which results in a modification of Haldane's asymptotics. Out of the critical parameter regime the population goes extinct or survives with a probability that fulfils Haldane's asymptotics (Thm. 10).
The proof establishes an expression for the survival probability in terms of the shape function of the random offspring generating functions. This expression exhibits similarities to perpetuities known from a financial context. Consequently, we prove a limiting theorem for perpetuities with vanishing interest rates (Thm. 11).
This work describes development of a comprehensive methodology for analyzing vibro-acoustic and wear mechanisms in transmission systems. The thesis addresses certain gaps present in the fields of structure dynamics and abrasion mechanism and opens new areas for further research.
The paper attempts to understand new and relatively unexplored challenges like influences of wear on the dynamics of drive train. It also focuses on developing new techniques for analyzing the vibration and acoustic behavior of the drive unit structures and surrounding fluids respectively.
The developed methodology meets the requirements of both the complete system and component level modeling by using specially identified combination of different simulation techniques. Based on the created template model, a three-stage spur plus helical gearbox is constructed and simulated as an application example. In addition to the internal mechanical excitation mechanisms, the transmission model also includes the rotational and translational dynamics of the gears, shafts and bearings. It is followed by illustration of wear among the rotating components.
Different kinds of static and dynamic analyses are performed and coupled at various levels depending on the mechanical complexities involved. Furthermore, the structure dynamic vibration of the housing and the associated sound particle radiations are mapped into the surrounding fluid. Additionally, the approach for selection of the potential parameters for optimization is depicted. Final part focuses on the measurements of different system states used for validation of the model. In the end, results obtained from both simulations and experiments are analyzed and assessed for there respective performances.
Machine Learning (ML) is so pervasive in our todays life that we don't even realise that, more often than expected, we are using systems based on it. It is also evolving faster than ever before. When deploying ML systems that make decisions on their own, we need to think about their ignorance of our uncertain world. The uncertainty might arise due to scarcity of the data, the bias of the data or even a mismatch between the real world and the ML-model. Given all these uncertainties, we need to think about how to build systems that are not totally ignorant thereof. Bayesian ML can to some extent deal with these problems. The specification of the model using probabilities provides a convenient way to quantify uncertainties, which can then be included in the decision making process.
In this thesis, we introduce the Bayesian ansatz to modeling and apply Bayesian ML models in finance and economics. Especially, we will dig deeper into Gaussian processes (GP) and Gaussian process latent variable model (GPLVM). Applied to the returns of several assets, GPLVM provides the covariance structure and also a latent space embedding thereof. Several financial applications can be build upon the output of the GPLVM. To demonstrate this, we build an automated asset allocation system, a predictor for missing asset prices and identify other structure in financial data.
It turns out that the GPLVM exhibits a rotational symmetry in the latent space, which makes it harder to fit. Our second publication reports, how to deal with that symmetry. We propose another parameterization of the model using Householder transformations, by which the symmetry is broken. Bayesian models are changed by reparameterization, if the prior is not changed accordingly. We provide the correct prior distribution of the new parameters, such that the model, i.e. the data density, is not changed under the reparameterization. After applying the reparametrization on Bayesian PCA, we show that the symmetry of nonlinear models can also be broken in the same way.
In our last project, we propose a new method for matching quantile observations, which uses order statistics. The use of order statistics as the likelihood, instead of a Gaussian likelihood, has several advantages. We compare these two models and highlight their advantages and disadvantages. To demonstrate our method, we fit quantiled salary data of several European countries. Given several candidate models for the fit, our method also provides a metric to choose the best option.
We hope that this thesis illustrates some benefits of Bayesian modeling (especially Gaussian processes) in finance and economics and its usage when uncertainties are to be quantified.
We show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to “true” under a uniformly random satisfying assignment.
Within the last thirty years, the contraction method has become an important tool for the distributional analysis of random recursive structures. While it was mainly developed to show weak convergence, the contraction approach can additionally be used to obtain bounds on the rate of convergence in an appropriate metric. Based on ideas of the contraction method, we develop a general framework to bound rates of convergence for sequences of random variables as they mainly arise in the analysis of random trees and divide-and-conquer algorithms. The rates of convergence are bounded in the Zolotarev distances. In essence, we present three different versions of convergence theorems: a general version, an improved version for normal limit laws (providing significantly better bounds in some examples with normal limits) and a third version with a relaxed independence condition. Moreover, concrete applications are given which include parameters of random trees, quantities of stochastic geometry as well as complexity measures of recursive algorithms under either a random input or some randomization within the algorithm.
Chatbots are a promising technology with the potential to enhance workplaces and everyday life. In terms of scalability and accessibility, they also offer unique possibilities as communication and information tools for digital learning. In this paper, we present a systematic literature review investigating the areas of education where chatbots have already been applied, explore the pedagogical roles of chatbots, the use of chatbots for mentoring purposes, and their potential to personalize education. We conducted a preliminary analysis of 2,678 publications to perform this literature review, which allowed us to identify 74 relevant publications for chatbots’ application in education. Through this, we address five research questions that, together, allow us to explore the current state-of-the-art of this educational technology. We conclude our systematic review by pointing to three main research challenges: 1) Aligning chatbot evaluations with implementation objectives, 2) Exploring the potential of chatbots for mentoring students, and 3) Exploring and leveraging adaptation capabilities of chatbots. For all three challenges, we discuss opportunities for future research.
The sketch map tool facilitates the assessment of OpenStreetMap data for participatory mapping
(2021)
A worldwide increase in the number of people and areas affected by disasters has led to more and more approaches that focus on the integration of local knowledge into disaster risk reduction processes. The research at hand shows a method for formalizing this local knowledge via sketch maps in the context of flooding. The Sketch Map Tool enables not only the visualization of this local knowledge and analyses of OpenStreetMap data quality but also the communication of the results of these analyses in an understandable way. Since the tool will be open-source and several analyses are made automatically, the tool also offers a method for local governments in areas where historic data or financial means for flood mitigation are limited. Example analyses for two cities in Brazil show the functionalities of the tool and allow the evaluation of its applicability. Results depict that the fitness-for-purpose analysis of the OpenStreetMap data reveals promising results to identify whether the sketch map approach can be used in a certain area or if citizens might have problems with marking their flood experiences. In this way, an intrinsic quality analysis is incorporated into a participatory mapping approach. Additionally, different paper formats offered for printing enable not only individual mapping but also group mapping. Future work will focus on advancing the automation of all steps of the tool to allow members of local governments without specific technical knowledge to apply the Sketch Map Tool for their own study areas.
This thesis presents research which spans three conference papers and one manuscript which has not yet been submitted for peer review.
The topic of 1 is the inherent complexity of maintaining perfect height in B-trees. We consider the setting in which a B-tree of optimal height contains n = (1−ϵ)N elements where N is the number of elements in full B-tree of the same height (the capacity of the tree). We show that the rebalancing cost when updating the tree—while maintaining optimal height—depends on ϵ. Specifically, our analysis gives a lower bound for the rebalancing cost of Ω(1/(ϵB)). We then describe a rebalancing algorithm which has an amortized rebalancing cost with an almost matching upper bound of O(1/(ϵB)⋅log²(min{1/ϵ,B})). We additionally describe a scheme utilizing this algorithm which, given a rebalancing budget f(n), maintains optimal height for decreasing ϵ until the cost exceeds the
budget at which time it maintains optimal height plus one. Given a rebalancing budget of Θ(logn), this scheme maintains optimal height for all but a vanishing fraction of sizes in the intervals between tree capacities.
Manuscript 2 presents empirical analysis of practical randomized external-memory algorithms for computing the connected components of graphs. The best known theoretical results for this problem are essentially all derived from results for minimum spanning tree algorithms. In the realm of randomized external-memory MST algorithms, the best asymptotic result has I/O-complexity O(sort(|E|)) in expectation while an empirically studied practical algorithm has a bound of O(sort(|E|)⋅log(|V|/M)). We implement and evaluate an algorithm for connected components with expected I/O-complexity O(sort(|E|))—a simplification of the MST
algorithm with this asymptotic cost, we show that this approach may also yield good results in practice.
In paper 3, we present a novel approach to simulating large-scale population protocol models. Naive simulation of N interactions of a population protocol with n agents and m states requires Θ(nlogm) bits of memory and Θ(N) time. For
very large n, this is prohibitive both in memory consumption and time, as interesting protocols will typically require N > n interactions for convergence. We describe a histogram-based simulation framework which requires Θ(mlogn) bits of memory instead—an improvement as it is typically the case that
n ≫ m. We analyze, implement, and compare a number of different data structures to perform correct agent sampling in this regime. For this purpose, we develop dynamic alias tables which allow sampling an interaction in expected amortized
constant time. We then show how to use sampling techniques to process agent interactions in batches, giving a simulation approach which uses subconstant time per interaction under reasonable assumptions.
With paper 4, we introduce the new model of fragile complexity for comparison-based algorithms. Within this model, we analyze classical comparison-based problems such as finding the minimum value of a set, selection (or finding the median), and sorting. We prove a number of lower and upper bounds and in particular, we give a number of randomized results which describe trade-offs not achievable by deterministic algorithms.
Um Wissen in einer Form abzulegen, in der es automatisiert verarbeitet werden kann, werden unter anderem Ontologien verwendet. Ontologien erlauben über einen als Inferenz bezeichneten Prozess die Ableitung neuen Wissens. Bei inhaltlichen Überschneidungen werden Ontologien über Ontologie-Alignments miteinander verbunden, die Entitäten aus den verschiedenen Ontologien in Beziehung zueinander setzen. Üblicherweise werden diese Alignments als Mengen von Äquivalenzen formuliert, die beschreiben, welche Konzepte aus einer Ontologie Konzepten aus einer anderen Ontologie entsprechen. Ebenfalls verbreitet sind Ober- und Unterklassenbeziehungen in Alignments.
Diese Ontologie-Alignments werden zum Beispiel in der Biomedizin in Forschungsdatenbanken verwendet, da durch Alignments Informationen aus verschiedenen Bereichen zusammengeführt werden können. Der manuelle Aufwand, um große Ontologien und Alignments zu erstellen, ist sehr hoch. Dementsprechend wäre es wünschenswert, bei einer Veränderung von Ontologien nicht wieder von vorne beginnen und eine neue Ontologie erstellen zu müssen und möglichst viel aus der veränderten Ontologie und den die Ontologie betreffenden Alignments wiederverwenden zu können. Daher sollten möglichst automatisierte Verfahren verwendet werden. Diese Arbeit untersucht vier Ansätze, um die Anpassung von Alignments an Veränderungen in Ontologien zu automatisieren.
Der erste Ansatz bezieht Inferenzen in den Prozess zur Vorhersage von Alignment-Änderungen mit ein. Dazu werden die Inferenzen vor und nach der Änderung der Ontologien berechnet und auf Basis der Unterschiede mit einem regelbasierten Algorithmus bestimmt, wie sich das Alignment ändern soll. Der zweite Ansatz, wie auch die weiteren Ansätze, hat nicht zum Ziel das Alignment direkt anzupassen. Stattdessen soll vorhergesagt werden, welche Teile des Alignments angepasst werden müssen. Dazu werden die Ontologien und das Alignment als Wissensgraph-Embeddings repräsentiert. Diese Embeddings bilden Knoten aus den Ontologien in einen Raum mit 300-1000 Dimensionen so ab, dass in dem Raum auch die Beziehungen zwischen den Entitäten der Ontologien repräsentiert werden können. Diese Embeddings werden dann verwendet, um verschiedene Klassifikationsalgorithmen zu trainieren. Auf diese Weise wird vorhergesagt, welche Teile des Alignments sich verändern werden. Der dritte Ansatz verbindet Embeddings mit einem Veränderungsmodell. Das Veränderungsmodell kategorisiert die an den Ontologien vorgenommenen Veränderungen. Auf diese Kategorisierung und das Embedding werden dann Klassifikationsalgorithmen angewandt. Der vierte Ansatz verwendet eine speziell auf Wissensgraphen ausgerichtete Architektur für neuronale Netze, sogenannte Graph Convolutional Networks, um Veränderungen an Alignments vorher zu sagen.
Diese Ansätze werden auf ihre jeweiligen Vor- und Nachteile untersucht. Dazu werden die Verfahren an zwei Anwendungsfällen untersucht. Der Ansatz zur regelbasierten Einbeziehung von Inferenzen wird anhand eines Anwendungsbeispiels aus dem Bereich der Interweaving Systems betrachtet. In dem Beispiel wird eine allgemeine Methode für Interweaving Systems angewandt um das Selbstmanagement von Ampelsteuerungen zu ermöglichen. Die auf maschinellem Lernen aufbauenden Ansätze werden auf einem Auszug aus der biomedizinischen Forschungsdatenbank UMLS evaluiert.
Dabei konnte festgestellt werden, dass die betrachteten Ansätze grundsätzlich zur Anpassung von Alignments an Ontologie-Veränderungen eingesetzt werden können. Der Ansatz zur regelbasierten Einbeziehung von Inferenzen kann dabei vor allem auf sehr kleinen Datensätzen eingesetzt werden, bei denen alle Gesetzmäßigkeiten der Veränderungen grundsätzlich bekannt sind. Diese Anwendbarkeit ergibt sich aus dem Entwurf der Problemstellung für den ersten Ansatz. Die auf maschinellem Lernen aufbauenden Ansätze eignen sich besonders für große Datensätze und bieten den Vorteil, dass auch ohne ein vollständiges Verständnis des Veränderungsprozesses Vorhersagen getroffen werden können.
Unter den Ansätzen, die maschinelles Lernen einsetzen, zeigte die Einbeziehung von Veränderungsmodellen keine Vorteile gegenüber den anderen Ansätzen. Auf einem etwas
kleineren Datensatz waren die Ergebnisse des Embedding-basierten Ansatzes und der Relational Graph Convolutional Networks vergleichbar, während auf einem größeren Datensatz
die Graph Convolutional Networks etwas bessere Ergebnisse erreichen konnten.
Weitere Ergebnisse dieser Arbeit stellen eine Formalisierung der Problemstellung der Anpassung von Ontologie-Alignments an Veränderungen sowie eine formale Darstellung der Ansätze dar. Ein weiterer Beitrag der Arbeit ist die Vorstellung eines Anwendungsfalls aus dem Bereich der Interweaving Systems für Ontologie-Alignments. Außerdem wurde das Problem der Anpassung von Alignments an Veränderungen so formuliert, dass es mithilfe von
maschinellem Lernen betrachtet werden kann.
Principles of cognitive maps
(2021)
This thesis analyses the concept of a cognitive map in the research fields of geography. Cognitive mapping research is essential as it investigates the relations between cognitive maps and external representations of space that people regularly use by acquiring spatial knowledge, such as maps in geographic information systems. Moreover, cognitive maps, when expanded on semantic maps, explain the relations between people and things in a non-physically environment, where the considered space is not spanned by distance but with other non-spatially variables. Nevertheless, cognitive maps are often distorted. Although a good formation of a cognitive map is vital in navigation processes, cognitive distortions are barely investigated in the field of geography. By analyzing the relevant work, especially Tobler’s first law of geography, a new lexical variant of Tobler’s first law could be stated that could presumably describe a specific distortion in the processing of landmarks in cognitive maps.
In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children’s homes. Therefore, teachers had to set rules, implement procedures and make didactical–methodical decisions regarding how to handle this new situation. In this paper, we focus on the roles of mathematics teachers in Germany and Spain. The article first describes how mathematics lessons were conducted using distance learning. Second, problems encountered throughout this process were examined. Third, teachers drew conclusions from their mathematics teaching experiences during distance learning. To address these research interests, a questionnaire was answered by N = 248 teachers (N1 = 171 German teachers; N2 = 77 Spanish teachers). Resulting from a mixed methods approach, differences between the countries can be observed, e.g., German teachers conducted more lessons asynchronously. In contrast, Spanish teachers used synchronous teaching more frequently, but still regard the lack of personal contact as a main challenge. Finally, for both countries, the digitization of mathematics lessons seems to have been normalized by the pandemic.
Deep learning with neural networks seems to have largely replaced traditional design of computer vision systems. Automated methods to learn a plethora of parameters are now used in favor of previously practiced selection of explicit mathematical operators for a specific task. The entailed promise is that practitioners no longer need to take care of every individual step, but rather focus on gathering big amounts of data for neural network training. As a consequence, both a shift in mindset towards a focus on big datasets, as well as a wave of conceivable applications based exclusively on deep learning can be observed.
This PhD dissertation aims to uncover some of the only implicitly mentioned or overlooked deep learning aspects, highlight unmentioned assumptions, and finally introduce methods to address respective immediate weaknesses. In the author’s humble opinion, these prevalent shortcomings can be tied to the fact that the involved steps in the machine learning workflow are frequently decoupled. Success is predominantly measured based on accuracy measures designed for evaluation with static benchmark test sets. Individual machine learning workflow components are assessed in isolation with respect to available data, choice of neural network architecture, and a particular learning algorithm, rather than viewing the machine learning system as a whole in context of a particular application. Correspondingly, in this dissertation, three key challenges have been identified: 1. Choice and flexibility of a neural network architecture. 2. Identification and rejection of unseen unknown data to avoid false predictions. 3. Continual learning without forgetting of already learned information. These latter challenges have already been crucial topics in older literature, alas, seem to require a renaissance in modern deep learning literature. Initially, it may appear that they pose independent research questions, however, the thesis posits that the aspects are intertwined and require a joint perspective in machine learning based systems. In summary, the essential question is thus how to pick a suitable neural network architecture for a specific task, how to recognize which data inputs belong to this context, which ones originate from potential other tasks, and ultimately how to continuously include such identified novel data in neural network training over time without overwriting existing knowledge.
Thus, the central emphasis of this dissertation is to build on top of existing deep learning strengths, yet also acknowledge mentioned weaknesses, in an effort to establish a deeper understanding of interdependencies and synergies towards the development of unified solution mechanisms. For this purpose, the main portion of the thesis is in cumulative form. The respective publications can be grouped according to the three challenges outlined above. Correspondingly, chapter 1 is focused on choice and extendability of neural network architectures, analyzed in context of popular image classification tasks. An algorithm to automatically determine neural network layer width is introduced and is first contrasted with static architectures found in the literature. The importance of neural architecture design is then further showcased on a real-world application of defect detection in concrete bridges. Chapter 2 is comprised of the complementary ensuing questions of how to identify unknown concepts and subsequently incorporate them into continual learning. A joint central mechanism to distinguish unseen concepts from what is known in classification tasks, while enabling consecutive training without forgetting or revisiting older classes, is proposed. Once more, the role of the chosen neural network architecture is quantitatively reassessed. Finally, chapter 3 culminates in an overarching view, where developed parts are connected. Here, an extensive survey further serves the purpose to embed the gained insights in the broader literature landscape and emphasizes the importance of a common frame of thought. The ultimately presented approach thus reflects the overall thesis’ contribution to advance neural network based machine learning towards a unified solution that ties together choice of neural architecture with the ability to learn continually and the capability to automatically separate known from unknown data.
We show the existence of additive kinematic formulas for general flag area measures, which generalizes a recent result by Wannerer. Building on previous work by the second named author, we introduce an algebraic framework to compute these formulas explicitly. This is carried out in detail in the case of the incomplete flag manifold consisting of all (p+1)-planes containing a unit vector.
We calculate the Masur–Veech volume of the gothic locus G in the stratum H(23) of genus 4. Our method is based on the use of the formulae for the Euler characteristics of gothic Teichmu ̈ller curves to determine the number of lattice points of given area. We also use this method to recal- culate the Masur–Veech volumes of the Prym loci P3 ⊂ H(4) and P4 ⊂ H(6) in genus 3 and 4.
Collaboration is an important 21st Century skill. Co-located (or face-to-face) collaboration (CC) analytics gained momentum with the advent of sensor technology. Most of these works have used the audio modality to detect the quality of CC. The CC quality can be detected from simple indicators of collaboration such as total speaking time or complex indicators like synchrony in the rise and fall of the average pitch. Most studies in the past focused on “how group members talk” (i.e., spectral, temporal features of audio like pitch) and not “what they talk”. The “what” of the conversations is more overt contrary to the “how” of the conversations. Very few studies studied “what” group members talk about, and these studies were lab based showing a representative overview of specific words as topic clusters instead of analysing the richness of the content of the conversations by understanding the linkage between these words. To overcome this, we made a starting step in this technical paper based on field trials to prototype a tool to move towards automatic collaboration analytics. We designed a technical setup to collect, process and visualize audio data automatically. The data collection took place while a board game was played among the university staff with pre-assigned roles to create awareness of the connection between learning analytics and learning design. We not only did a word-level analysis of the conversations, but also analysed the richness of these conversations by visualizing the strength of the linkage between these words and phrases interactively. In this visualization, we used a network graph to visualize turn taking exchange between different roles along with the word-level and phrase-level analysis. We also used centrality measures to understand the network graph further based on how much words have hold over the network of words and how influential are certain words. Finally, we found that this approach had certain limitations in terms of automation in speaker diarization (i.e., who spoke when) and text data pre-processing. Therefore, we concluded that even though the technical setup was partially automated, it is a way forward to understand the richness of the conversations between different roles and makes a significant step towards automatic collaboration analytics.
Studying large discrete systems is of central interest in, non-exclusively, discrete mathematics, computer sciences and statistical physics. The study of phase transitions, e.g. points in the evolution of a large random system in which the behaviour of the system changes drastically, became of interest in the classical field of random graphs, the theory of spin glasses as well as in the analysis of algorithms [78,82, 121].
It turns out that ideas from the statistical physics’ point of view on spin glass systems can be used to study inherently combinatorial problems in discrete mathematics and theoretical computer sciences(for instance, satisfiability) or to analyse phase transitions occurring in inference problems (like the group testing problem) [68, 135, 168]. A mathematical flaw of this approach is that the physical methods only render mathematical conjectures as they are not known to be rigorous.
In this thesis, we will discuss the results of six contributions. For instance, we will explore how the
theory of diluted mean-field models for spin glasses helps studying random constraint satisfaction problems through the example of the random 2−SAT problem. We will derive a formula for the number of satisfying assignments that a random 2−SAT formula typically possesses [2].
Furthermore, we will discuss how ideas from spin glass models (more precisely, from their planted versions) can be used to facilitate inference in the group testing problem. We will answer all major open questions with respect to non-adaptive group testing if the number of infected individuals scales sublinearly in the population size and draw a complete picture of phase transitions with respect to the
complexity and solubility of this inference problem [41, 46].
Subsequently, we study the group testing problem under sparsity constrains and obtain a (not fully understood) phase diagram in which only small regions stay unexplored [88].
In all those cases, we will discover that important results can be achieved if one combines the rich theory of the statistical physics’ approach towards spin glasses and inherent combinatorial properties of the underlying random graph.
Furthermore, based on partial results of Coja-Oghlan, Perkins and Skubch [42] and Coja-Oghlan et al. [49], we introduce a consistent limit theory for discrete probability measures akin to the graph limit theory [31, 32, 128] in [47]. This limit theory involves the extensive study of a special variant of the cut-distance and we obtain a continuous version of a very simple algorithm, the pinning operation, which allows to decompose the phase space of an underlying system into parts such that a probability
measure, restricted to this decomposition, is close to a product measure under the cut-distance. We will see that this pinning lemma can be used to rigorise predictions, at least in some special cases, based on the physical idea of a Bethe state decomposition when applied to the Boltzmann distribution.
Finally, we study sufficient conditions for the existence of perfect matchings, Hamilton cycles and bounded degree trees in randomly perturbed graph models if the underlying deterministic graph is sparse [93].