Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Network and Algebraic Topology of Influenza Evolution

Evolution is a force that has molded human existence since its divergence from chimpanzees about 5.4 million years ago. In that same amount of time, an influenza virus, which replicates every six hours, would have undergone an equivalent number of generations over only a hundred years. The fast replication times of influenza, coupled with its high mutation rate, make the virus a perfect model to study real-time evolution at a mega-Darwin scale, more than a million times faster than human evolution. While recent developments in high-throughput sequencing provide an optimal opportunity to dissect their genetic evolution, a concurrent growth in computational tools is necessary to analyze the large influx of complex genomic data. In my thesis, I present novel computational methods to examine different aspects of influenza evolution. I first focus on seasonal influenza, particularly the problems that hamper public health initiatives to combat the virus. I introduce two new approaches: 1. The q2-coefficient, a method of quantifying pathogen surveillance, and 2. FluGraph, a technique that employs network topology to track the spread of seasonal influenza around the world. The second chapter of my thesis examines how mutations and reassortment combine to alter the course of influenza evolution towards pandemic formation. I highlight inherent deficiencies in the current phylogenetic paradigm for analyzing evolution and offer a novel methodology based on algebraic topology that comprehensively reconstructs both vertical and horizontal evolutionary events. I apply this method to viruses, with emphasis on influenza, but foresee broader application to cancer cells, bacteria, eukaryotes, and other taxa

Mathematics in Software Reliability and Quality Assurance

This monograph concerns the mathematical aspects of software reliability and quality assurance and consists of 11 technical papers in this emerging area. Included are the latest research results related to formal methods and design, automatic software testing, software verification and validation, coalgebra theory, automata theory, hybrid system and software reliability modeling and assessment

Impact of Symmetries in Graph Clustering

Diese Dissertation beschäftigt sich mit der durch die Automorphismusgruppe definierten Symmetrie von Graphen und wie sich diese auf eine Knotenpartition, als Ergebnis von Graphenclustering, auswirkt. Durch eine Analyse von nahezu 1700 Graphen aus verschiedenen Anwendungsbereichen kann gezeigt werden, dass mehr als 70 % dieser Graphen Symmetrien enthalten. Dies bildet einen Gegensatz zum kombinatorischen Beweis, der besagt, dass die Wahrscheinlichkeit eines zufälligen Graphen symmetrisch zu sein bei zunehmender Größe gegen Null geht. Das Ergebnis rechtfertigt damit die Wichtigkeit weiterer Untersuchungen, die auf mögliche Auswirkungen der Symmetrie eingehen. Bei der Analyse werden sowohl sehr kleine Graphen (10 000 000 Knoten/>25 000 000 Kanten) berücksichtigt. Weiterhin wird ein theoretisches Rahmenwerk geschaffen, das zum einen die detaillierte Quantifizierung von Graphensymmetrie erlaubt und zum anderen Stabilität von Knotenpartitionen hinsichtlich dieser Symmetrie formalisiert. Eine Partition der Knotenmenge, die durch die Aufteilung in disjunkte Teilmengen definiert ist, wird dann als stabil angesehen, wenn keine Knoten symmetriebedingt von der einen in die andere Teilmenge abgebildet werden und dadurch die Partition verändert wird. Zudem wird definiert, wie eine mögliche Zerlegbarkeit der Automorphismusgruppe in unabhängige Untergruppen als lokale Symmetrie interpretiert werden kann, die dann nur Auswirkungen auf einen bestimmten Bereich des Graphen hat. Um die Auswirkungen der Symmetrie auf den gesamten Graphen und auf Partitionen zu quantifizieren, wird außerdem eine Entropiedefinition präsentiert, die sich an der Analyse dynamischer Systeme orientiert. Alle Definitionen sind allgemein und können daher für beliebige Graphen angewandt werden. Teilweise ist sogar eine Anwendbarkeit für beliebige Clusteranalysen gegeben, solange deren Ergebnis in einer Partition resultiert und sich eine Symmetrierelation auf den Datenpunkten als Permutationsgruppe angeben lässt. Um nun die tatsächliche Auswirkung von Symmetrie auf Graphenclustering zu untersuchen wird eine zweite Analyse durchgeführt. Diese kommt zum Ergebnis, dass von 629 untersuchten symmetrischen Graphen 72 eine instabile Partition haben. Für die Analyse werden die Definitionen des theoretischen Rahmenwerks verwendet. Es wird außerdem festgestellt, dass die Lokalität der Symmetrie eines Graphen maßgeblich beeinflusst, ob dessen Partition stabil ist oder nicht. Eine hohe Lokalität resultiert meist in einer stabilen Partition und eine stabile Partition impliziert meist eine hohe Lokalität. Bevor die obigen Ergebnisse beschrieben und definiert werden, wird eine umfassende Einführung in die verschiedenen benötigten Grundlagen gegeben. Diese umfasst die formalen Definitionen von Graphen und statistischen Graphmodellen, Partitionen, endlichen Permutationsgruppen, Graphenclustering und Algorithmen dafür, sowie von Entropie. Ein separates Kapitel widmet sich ausführlich der Graphensymmetrie, die durch eine endliche Permutationsgruppe, der Automorphismusgruppe, beschrieben wird. Außerdem werden Algorithmen vorgestellt, die die Symmetrie von Graphen ermitteln können und, teilweise, auch das damit eng verwandte Graphisomorphie Problem lösen. Am Beispiel von Graphenclustering gibt die Dissertation damit Einblicke in mögliche Auswirkungen von Symmetrie in der Datenanalyse, die so in der Literatur bisher wenig bis keine Beachtung fanden

Development of Computer-aided Concepts for the Optimization of Single-Molecules and their Integration for High-Throughput Screenings

In the field of synthetic biology, highly interdisciplinary approaches for the design and modelling of functional molecules using computer-assisted methods have become established in recent decades. These computer-assisted methods are mainly used when experimental approaches reach their limits, as computer models are able to e.g., elucidate the temporal behaviour of nucleic acid polymers or proteins by single-molecule simulations, as well as to illustrate the functional relationship of amino acid residues or nucleotides to each other. The knowledge raised by computer modelling can be used continuously to influence the further experimental process (screening), and also shape or function (rational design) of the considered molecule. Such an optimization of the biomolecules carried out by humans is often necessary, since the observed substrates for the biocatalysts and enzymes are usually synthetic (``man-made materials'', such as PET) and the evolution had no time to provide efficient biocatalysts. With regard to the computer-aided design of single-molecules, two fundamental paradigms share the supremacy in the field of synthetic biology. On the one hand, probabilistic experimental methods (e.g., evolutionary design processes such as directed evolution) are used in combination with High-Throughput Screening (HTS), on the other hand, rational, computer-aided single-molecule design methods are applied. For both topics, computer models/concepts were developed, evaluated and published. The first contribution in this thesis describes a computer-aided design approach of the Fusarium Solanie Cutinase (FsC). The activity loss of the enzyme during a longer incubation period was investigated in detail (molecular) with PET. For this purpose, Molecular Dynamics (MD) simulations of the spatial structure of FsC and a water-soluble degradation product of the synthetic substrate PET (ethylene glycol) were computed. The existing model was extended by combining it with Reduced Models. This simulation study has identified certain areas of FsC which interact very strongly with PET (ethylene glycol) and thus have a significant influence on the flexibility and structure of the enzyme. The subsequent original publication establishes a new method for the selection of High-Throughput assays for the use in protein chemistry. The selection is made via a meta-optimization of the assays to be analyzed. For this purpose, control reactions are carried out for the respective assay. The distance of the control distributions is evaluated using classical static methods such as the Kolmogorov-Smirnov test. A performance is then assigned to each assay. The described control experiments are performed before the actual experiment (screening), and the assay with the highest performance is used for further screening. By applying this generic method, high success rates can be achieved. We were able to demonstrate this experimentally using lipases and esterases as an example. In the area of green chemistry, the above-mentioned processes can be useful for finding enzymes for the degradation of synthetic materials more quickly or modifying enzymes that occur naturally in such a way that these enzymes can efficiently convert synthetic substrates after successful optimization. For this purpose, the experimental effort (consumption of materials) is kept to a minimum during the practical implementation. Especially for large-scale screenings, a prior consideration or restriction of the possible sequence-space can contribute significantly to maximizing the success rate of screenings and minimizing the total time they require. In addition to classical methods such as MD simulations in combination with reduced models, new graph-based methods for the presentation and analysis of MD simulations have been developed. For this purpose, simulations were converted into distance-dependent dynamic graphs. Based on this reduced representation, efficient algorithms for analysis were developed and tested. In particular, network motifs were investigated to determine whether this type of semantics is more suitable for describing molecular structures and interactions within MD simulations than spatial coordinates. This concept was evaluated for various MD simulations of molecules, such as water, synthetic pores, proteins, peptides and RNA structures. It has been shown that this novel form of semantics is an excellent way to describe (bio)molecular structures and their dynamics. Furthermore, an algorithm (StreAM-Tg) has been developed for the creation of motif-based Markov models, especially for the analysis of single molecule simulations of nucleic acids. This algorithm is used for the design of RNAs. The insights obtained from the analysis with StreAM-Tg (Markov models) can provide useful design recommendations for the (re)design of functional RNA. In this context, a new method was developed to quantify the environment (i.e. water; solvent context) and its influence on biomolecules in MD simulations. For this purpose, three vertex motifs were used to describe the structure of the individual water molecules. This new method offers many advantages. With this method, the structure and dynamics of water can be accurately described. For example, we were able to reproduce the thermodynamic entropy of water in the liquid and vapor phase along the vapor-liquid equilibrium curve from the triple point to the critical point. Another major field covered in this thesis is the development of new computer-aided approaches for HTS for the design of functional RNA. For the production of functional RNA (e.g., aptamers and riboswitches), an experimental, round-based HTS (like SELEX) is typically used. By using Next Generation Sequencing (NGS) in combination with the SELEX process, this design process can be studied at the nucleotide and secondary structure levels for the first time. The special feature of small RNA molecules compared to proteins is that the secondary structure (topology), with a minimum free energy, can be determined directly from the nucleotide sequence, with a high degree of certainty. Using the combination of M. Zuker's algorithm, NGS and the SELEX method, it was possible to quantify the structural diversity of individual RNA molecules under consideration of the genetic context. This combination of methods allowed the prediction of rounds in which the first ciprofloxacin-riboswitch emerged. In this example, only a simple structural comparison was made for the quantification (Levenshtein distance) of the diversity of each round. To improve this, a new representation of the RNA structure as a directed graph was modeled, which was then compared with a probabilistic subgraph isomorphism. Finally, the NGS dataset (ciprofloxacin-riboswitch) was modeled as a dynamic graph and analyzed after the occurrence of defined seven-vertex motifs. For this purpose, motif-based semantics were integrated into HTS for RNA molecules for the first time. The identified motifs could be assigned to secondary structural elements that were identified experimentally in the ciprofloxacin aptamer R10k6. Finally, all the algorithms presented were integrated into an R library, published and made available to scientists from all over the world

Graphical Models and Symmetries : Loopy Belief Propagation Approaches

Whenever a person or an automated system has to reason in uncertain domains, probability theory is necessary. Probabilistic graphical models allow us to build statistical models that capture complex dependencies between random variables. Inference in these models, however, can easily become intractable. Typical ways to address this scaling issue are inference by approximate message-passing, stochastic gradients, and MapReduce, among others. Exploiting the symmetries of graphical models, however, has not yet been considered for scaling statistical machine learning applications. One instance of graphical models that are inherently symmetric are statistical relational models. These have recently gained attraction within the machine learning and AI communities and combine probability theory with first-order logic, thereby allowing for an efficient representation of structured relational domains. The provided formalisms to compactly represent complex real-world domains enable us to effectively describe large problem instances. Inference within and training of graphical models, however, have not been able to keep pace with the increased representational power. This thesis tackles two major aspects of graphical models and shows that both inference and training can indeed benefit from exploiting symmetries. It first deals with efficient inference exploiting symmetries in graphical models for various query types. We introduce lifted loopy belief propagation (lifted LBP), the first lifted parallel inference approach for relational as well as propositional graphical models. Lifted LBP can effectively speed up marginal inference, but cannot straightforwardly be applied to other types of queries. Thus we also demonstrate efficient lifted algorithms for MAP inference and higher order marginals, as well as the efficient handling of multiple inference tasks. Then we turn to the training of graphical models and introduce the first lifted online training for relational models. Our training procedure and the MapReduce lifting for loopy belief propagation combine lifting with the traditional statistical approaches to scaling, thereby bridging the gap between statistical relational learning and traditional statistical machine learning

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005

Robust navigation for industrial service robots

Pla de Doctorats Industrials de la Generalitat de CatalunyaRobust, reliable and safe navigation is one of the fundamental problems of robotics. Throughout the present thesis, we tackle the problem of navigation for robotic industrial mobile-bases. We identify its components and analyze their respective challenges in order to address them. The research work presented here ultimately aims at improving the overall quality of the navigation stack of a commercially available industrial mobile-base. To introduce and survey the overall problem we first break down the navigation framework into clearly identified smaller problems. We examine the Simultaneous Localization and Mapping (SLAM) problem, recalling its mathematical grounding and exploring the state of the art. We then review the problem of planning the trajectory of a mobile-base toward a desired goal in the generated environment representation. Finally we investigate and clarify the use of the subset of the Lie theory that is useful in robotics. The first problem tackled is the recognition of place for closing loops in SLAM. Loop closure refers to the ability of a robot to recognize a previously visited location and infer geometrical information between its current and past locations. Using only a 2D laser range finder sensor, we address the problem using a technique borrowed from the field of Natural Language Processing (NLP) which has been successfully applied to image-based place recognition, namely the Bag-of-Words. We further improve the method with two proposals inspired from NLP. Firstly, the comparison of places is strengthened by considering the natural relative order of features in each individual sensor reading. Secondly, topological correspondences between places in a corpus of visited places are established in order to promote together instances that are ‘close’ to one another. We then tackle the problem of motion model calibration for odometry estimation. Given a mobile-base embedding an exteroceptive sensor able to observe ego-motion, we propose a novel formulation for estimating the intrinsic parameters of an odometry motion model. Resorting to an adaptation of the pre-integration theory initially developed for inertial motion sensors, we employ iterative nonlinear on-manifold optimization to estimate the wheel radii and wheel separation. The method is further extended to jointly estimate both the intrinsic parameters of the odometry model together with the extrinsic parameters of the embedded sensor. The method is shown to accommodate to variation in model parameters quickly when the vehicle is subject to physical changes during operation. Following the generation of a map in which the robot is localized, we address the problem of estimating trajectories for motion planning. We devise a new method for estimating a sequence of robot poses forming a smooth trajectory. Regardless of the Lie group considered, the trajectory is seen as a collection of states lying on a spline with non-vanishing n-th derivatives at each point. Formulated as a multi-objective nonlinear optimization problem, it allows for the addition of cost functions such as velocity and acceleration limits, collision avoidance and more. The proposed method is evaluated for two different motion planning tasks, the planning of trajectories for a mobile-base evolving in the SE(2) manifold, and the planning of the motion of a multi-link robotic arm whose end-effector evolves in the SE(3) manifold. From our study of Lie theory, we developed a new, ready to use, programming library called `manif’. The library is open source, publicly available and is developed following good software programming practices. It is designed so that it is easy to integrate and manipulate, and allows for flexible use while facilitating the possibility to extend it beyond the already implemented Lie groups.La navegación autónoma es uno de los problemas fundamentales de la robótica, y sus diferentes desafíos se han estudiado durante décadas. El desarrollo de métodos de navegación robusta, confiable y segura es un factor clave para la creación de funcionalidades de nivel superior en robots diseñados para operar en entornos con humanos. A lo largo de la presente tesis, abordamos el problema de navegación para bases robóticas móviles industriales; identificamos los elementos de un sistema de navegación; y analizamos y tratamos sus desafíos. El trabajo de investigación presentado aquí tiene como último objetivo mejorar la calidad general del sistema completo de navegación de una base móvil industrial disponible comercialmente. Para estudiar el problema de navegación, primero lo desglosamos en problemas menores claramente identificados. Examinamos el subproblema de mapeo del entorno y localización del robot simultáneamente (SLAM por sus siglas en ingles) y estudiamos el estado del arte del mismo. Al hacerlo, recordamos y detallamos la base matemática del problema de SLAM. Luego revisamos el subproblema de planificación de trayectorias hacia una meta deseada en la representación del entorno generada. Además, como una herramienta para las soluciones que se presentarán más adelante en el desarrollo de la tesis, investigamos y aclaramos el uso de teoría de Lie, centrándonos en el subconjunto de la teoría que es útil para la estimación de estados en robótica. Como primer elemento identificado para mejoras, abordamos el problema de reconocimiento de lugares para cerrar lazos en SLAM. El cierre de lazos se refiere a la capacidad de un robot para reconocer una ubicación visitada previamente e inferí información geométrica entre la ubicación actual del robot y aquellas reconocidas. Usando solo un sensor láser 2D, la tarea es desafiante ya que la percepción del entorno que proporciona el sensor es escasa y limitada. Abordamos el problema utilizando 'bolsas de palabras', una técnica prestada del campo de procesamiento del lenguaje natural (NLP) que se ha aplicado con éxito anteriormente al reconocimiento de lugares basado en imágenes. Nuestro método incluye dos nuevas propuestas inspiradas también en NLP. Primero, la comparación entre lugares candidatos se fortalece teniendo en cuenta el orden relativo natural de las características en cada lectura individual del sensor; y segundo, se establece un corpus de lugares visitados para promover juntos instancias que están "cerca" la una de la otra desde un punto de vista topológico. Evaluamos nuestras propuestas por separado y conjuntamente en varios conjuntos de datos, con y sin ruido, demostrando mejora en la detección de cierres de lazo para sensores láser 2D, con respecto al estado del arte. Luego abordamos el problema de la calibración del modelo de movimiento para la estimación de la edometría. Dado que nuestra base móvil incluye un sensor exteroceptivo capaz de observar el movimiento de la plataforma, proponemos una nueva formulación que permite estimar los parámetros intrínsecos del modelo cinemático de la plataforma durante el cómputo de la edometría del vehículo. Hemos recurrido a una adaptación de la teoría de reintegración inicialmente desarrollado para unidades inerciales de medida, y aplicado la técnica a nuestro modelo cinemático. El método nos permite, mediante optimización iterativa no lineal, la estimación del valor del radio de las ruedas de forma independiente y de la separación entre las mismas. El método se amplía posteriormente par idéntica de forma simultánea, estos parámetros intrínsecos junto con los parámetros extrínsecos que ubican el sensor láser con respecto al sistema de referencia de la base móvil. El método se valida en simulación y en un entorno real y se muestra que converge hacia los verdaderos valores de los parámetros. El método permite la adaptación de los parámetros intrínsecos del modelo cinemático de la plataforma derivados de cambios físicos durante la operación, tales como el impacto que el cambio de carga sobre la plataforma tiene sobre el diámetro de las ruedas. Como tercer subproblema de navegación, abordamos el reto de planificar trayectorias de movimiento de forma suave. Desarrollamos un método para planificar la trayectoria como una secuencia de configuraciones sobre una spline con n-ésimas derivadas en todos los puntos, independientemente del grupo de Lie considerado. Al ser formulado como un problema de optimización no lineal con múltiples objetivos, es posible agregar funciones de coste al problema de optimización que permitan añadir límites de velocidad o aceleración, evasión de colisiones, etc. El método propuesto es evaluado en dos tareas de planificación de movimiento diferentes, la planificación de trayectorias para una base móvil que evoluciona en la variedad SE(2), y la planificación del movimiento de un brazo robótico cuyo efector final evoluciona en la variedad SE(3). Además, cada tarea se evalúa en escenarios con complejidad de forma incremental, y se muestra un rendimiento comparable o mejor que el estado del arte mientras produce resultados más consistentes. Desde nuestro estudio de la teoría de Lie, desarrollamos una nueva biblioteca de programación llamada “manif”. La biblioteca es de código abierto, está disponible públicamente y se desarrolla siguiendo las buenas prácticas de programación de software. Esta diseñado para que sea fácil de integrar y manipular, y permite flexibilidad de uso mientras se facilita la posibilidad de extenderla más allá de los grupos de Lie inicialmente implementados. Además, la biblioteca se muestra eficiente en comparación con otras soluciones existentes. Por fin, llegamos a la conclusión del estudio de doctorado. Examinamos el trabajo de investigación y trazamos líneas para futuras investigaciones. También echamos un vistazo en los últimos años y compartimos una visión personal y experiencia del desarrollo de un doctorado industrial.Postprint (published version

A survey of algorithmic methods in IC reverse engineering

The discipline of reverse engineering integrated circuits (ICs) is as old as the technology itself. It grew out of the need to analyze competitor’s products and detect possible IP infringements. In recent years, the growing hardware Trojan threat motivated a fresh research interest in the topic. The process of IC reverse engineering comprises two steps: netlist extraction and specification discovery. While the process of netlist extraction is rather well understood and established techniques exist throughout the industry, specification discovery still presents researchers with a plurality of open questions. It therefore remains of particular interest to the scientific community. In this paper, we present a survey of the state of the art in IC reverse engineering while focusing on the specification discovery phase. Furthermore, we list noteworthy existing works on methods and algorithms in the area and discuss open challenges as well as unanswered questions. Therefore, we observe that the state of research on algorithmic methods for specification discovery suffers from the lack of a uniform evaluation approach. We point out the urgent need to develop common research infrastructure, benchmarks, and evaluation metrics

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports