Solving Connectivity Problems Parameterized by Treedepth in Single-Exponential Time and Polynomial Space

A breakthrough result of Cygan et al. (FOCS 2011) showed that connectivity problems parameterized by treewidth can be solved much faster than the previously best known time ?^*(2^{?(twlog tw)}). Using their inspired Cut&Count technique, they obtained ?^*(?^tw) time algorithms for many such problems. Moreover, they proved these running times to be optimal assuming the Strong Exponential-Time Hypothesis. Unfortunately, like other dynamic programming algorithms on tree decompositions, these algorithms also require exponential space, and this is widely believed to be unavoidable. In contrast, for the slightly larger parameter called treedepth, there are already several examples of matching the time bounds obtained for treewidth, but using only polynomial space. Nevertheless, this has remained open for connectivity problems. In the present work, we close this knowledge gap by applying the Cut&Count technique to graphs of small treedepth. While the general idea is unchanged, we have to design novel procedures for counting consistently cut solution candidates using only polynomial space. Concretely, we obtain time ?^*(3^d) and polynomial space for Connected Vertex Cover, Feedback Vertex Set, and Steiner Tree on graphs of treedepth d. Similarly, we obtain time ?^*(4^d) and polynomial space for Connected Dominating Set and Connected Odd Cycle Transversal

Multiscale Phenomenology of the Cosmic Web

We analyze the structure and connectivity of the distinct morphologies that define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF), we dissect the matter distribution of a cosmological $\Lambda$CDM N-body computer simulation into cluster, filaments and walls. The MMF is ideally suited to adress both the anisotropic morphological character of filaments and sheets, as well as the multiscale nature of the hierarchically evolved cosmic matter distribution. The results of our study may be summarized as follows: i).- While all morphologies occupy a roughly well defined range in density, this alone is not sufficient to differentiate between them given their overlap. Environment defined only in terms of density fails to incorporate the intrinsic dynamics of each morphology. This plays an important role in both linear and non linear interactions between haloes. ii).- Most of the mass in the Universe is concentrated in filaments, narrowly followed by clusters. In terms of volume, clusters only represent a minute fraction, and filaments not more than 9%. Walls are relatively inconspicous in terms of mass and volume. iii).- On average, massive clusters are connected to more filaments than low mass clusters. Clusters with $M \sim 10^{14}$ M$_{\odot}$ h$^{-1}$ have on average two connecting filaments, while clusters with $M \geq 10^{15}$ M$_{\odot}$ h$^{-1}$ have on average five connecting filaments. iv).- Density profiles indicate that the typical width of filaments is 2\Mpch. Walls have less well defined boundaries with widths between 5-8 Mpc h$^{-1}$. In their interior, filaments have a power-law density profile with slope ${\gamma}\approx -1$, corresponding to an isothermal density profile.Comment: 28 pages, 22 figures, accepted for publication in MNRAS. For a high-res version see http://www.astro.rug.nl/~weygaert/webmorph_mmf.pd

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

Ultrafast dynamics of small quantum systems studied using electron-ion coincidence spectroscopy

Studying how small quantum systems, like molecules and clusters, interact with X-rays is crucial to understanding the ultrafast processes that occur in nature on incredibly short timescales, ranging from femtoseconds to picoseconds. X-rays excite small quantum systems to unstable core hole states, leading to a cascade of phenomena, including Auger decay, nuclear rearrangement, and dissociation. The dissociation of molecules is influenced by the initial site of X-ray excitation, as well as the properties of the Auger populated states, such as charge localization and internal energy. In clusters, the dissociation process depends on intermolecular interactions, cluster size, and geometry. The interplay between electronic and nuclear dynamics in core-excited/ionized molecules and clusters is a critical factor that needs to be assessed. This thesis investigates X-ray-induced fragmentation of molecular adamantane and CO2 clusters using synchrotron radiation. The kinematics of molecular and cluster fragmentation is measured using advanced techniques, such as 3D momentum imaging of the ion fragments and multiparticle coincidence spectroscopy. Site-selective fragmentation of the carbon cage of the adamantane molecule is studied using Auger-electron Photoion coincidence spectroscopy, revealing the influence of the core-hole site on the Auger decay and dissociation process. Statistical data analysis treatment is developed and implemented to remove background contamination in the coincidence data using experimental random coincidences. The results highlight that the fragmentation of adamantane cation and dication is a complex dynamical process with competing relaxation pathways involving cage opening, hydrogen migration, and carbon-carbon bond breaking. Additionally, the thesis investigates the photoreactions of core-ionized CO2 clusters, reporting a significantly increased production of O2+ compared to isolated CO2 molecules. Through quantum chemistry calculations and multi-coincidence 3D momentum imaging, the study determined that the enhanced production of O2+ is due to a size-dependent structural transition of the clusters. The study also proposes two relevant photoreactions involving intermolecular interactions. This thesis highlights the complexity of core-hole dynamics in molecular and cluster chemistry and emphasizes the need for meticulous experimental and theoretical investigations of the underlying mechanisms. It also discusses the relevance of the results in the context of X-ray-induced astrochemistry. Indeed, the experiments presented are conducted in vacuum chambers in a controlled environment and can crudely replicate the conditions found in astrophysical environments. From the adamantane study, we conclude that X-ray absorption emphatically results in dissociation into smaller hydrocarbons and low photostability can play a part in the absence of diamondoids in the interstellar medium. From the CO2 clusters study, we found an enhancement in the O2+ yield, which can significantly influence the ion balance in CO2-rich atmospheres like Mars

Sensory processing and world modeling for an active ranging device

In this project, we studied world modeling and sensory processing for laser range data. World Model data representation and operation were defined. Sensory processing algorithms for point processing and linear feature detection were designed and implemented. The interface between world modeling and sensory processing in the Servo and Primitive levels was investigated and implemented. In the primitive level, linear features detectors for edges were also implemented, analyzed and compared. The existing world model representations is surveyed. Also presented is the design and implementation of the Y-frame model, a hierarchical world model. The interfaces between the world model module and the sensory processing module are discussed as well as the linear feature detectors that were designed and implemented

Do branch lengths help to locate a tree in a phylogenetic network?

Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental questions that arise in this context is whether the evolution of a gene with one copy in all species can be explained by a given network. In mathematical terms, this is often translated in the following way: is a given phylogenetic tree contained in a given phylogenetic network? Recently this tree containment problem has been widely investigated from a computational perspective, but most studies have only focused on the topology of the phylo- genies, ignoring a piece of information that, in the case of phylogenetic trees, is routinely inferred by evolutionary analyses: branch lengths. These measure the amount of change (e.g., nucleotide substitutions) that has occurred along each branch of the phylogeny. Here, we study a number of versions of the tree containment problem that explicitly account for branch lengths. We show that, although length information has the potential to locate more precisely a tree within a network, the problem is computationally hard in its most general form. On a positive note, for a number of special cases of biological relevance, we provide algorithms that solve this problem efficiently. This includes the case of networks of limited complexity, for which it is possible to recover, among the trees contained by the network with the same topology as the input tree, the closest one in terms of branch lengths

Improving Usability in Procedural Modeling

This work presents new approaches and algorithms for procedural modeling geared towards user convenience and improving usability, in order to increase artists’ productivity. Procedural models create geometry for 3D models from sets of rules. Existing approaches that allow to model trees, buildings, and terrain are reviewed and possible improvements are discussed. A new visual programming language for procedural modeling is discussed, where the user connects operators to visual programs called model graphs. These operators create geometry with textures, assign or evaluate variables or control the sequence of operations. When the user moves control points using the mouse in 3D space, the model graph is executed to change the geometry interactively. Thus, model graphs combine the creativity of freehand modeling with the power of programmed modeling while displaying the program structure more clearly than textbased approaches. Usability is increased as a result of these advantages. Also, an interactive editor for botanical trees is demonstrated. In contrast to previous tree modeling systems, we propose linking rules, parameters and geometry to semantic entities. This has the advantage that problems of associating parameters and instances are completely avoided. When an entity is clicked in the viewport, its parameters are displayed immediately, changes are applied to selected entities, and viewport editing operations are reflected in the parameter set. Furthermore, we store the entities in a hierarchical data structure and allow the user to activate recursive traversal via selection options for all editing operations. The user may choose to apply viewport or parameter changes to a single entity or many entities at once, and only the geometry for the affected entities needs to be updated. The proposed user interface simplifies the modeling process and increases productivity. Interactive editing approaches for 3D models often allow more precise control over a model than a global set of parameters that is used to generate a shape. However, usually scripted procedural modeling generates shapes directly from a fixed set of parameters, and interactive editing mostly uses a fixed set of tools. We propose to use scripts not only to generate models, but also for manipulating the models. A base script would set up the state of an object, and tool scripts would modify that state. The base script and the tool scripts generate geometry when necessary. Together, such a collection of scripts forms a template, and templates can be created for various types of objects. We examine how templates simplify the procedural modeling workflow by allowing for editing operations that are context-sensitive, flexible and powerful at the same time. Many algorithms have been published that produce geometry for fictional landscapes. There are algorithms which produce terrain with minimal setup time, allowing to adapt the level of detail as the user zooms into the landscape. However, these approaches lack plausible river networks, and algorithms that create eroded terrain with river networks require a user to supervise creation and minutes or hours of computation. In contrast to that, this work demonstrates an algorithm that creates terrain with plausible river networks and adaptive level of detail with no more than a few seconds of preprocessing. While the system can be configured using parameters, this text focuses on the algorithm that produces the rivers. However, integrating more tools for user-controlled editing of terrain would be possible.Verbesserung der Usability bei prozeduraler Modellierung Ziel der vorliegenden Arbeit ist es, prozedurale Modellierung durch neue neue Ansätze und Algorithmen einfacher, bequemer und anwendungsfreundlicher zu machen, und damit die Produktivität der Künstler zu erhöhen. Diese Anforderungen werden häufig unter dem Stichwort Usability zusammengefasst. Prozedurale Modelle spezifizieren 3D-Modelle über Regeln. Existierende Ansätze für Bäume, Gebäude und Terrain werden untersucht und es werden mögliche Verbesserungen diskutiert. Eine neue visuelle Programmiersprache für prozedurale Modelle wird vorgestellt, bei der Operatoren zu Modellgraphen verschaltet werden. Die Operatoren erzeugen texturierte Geometrie, weisen Variablen zu und werten sie aus, oder sie steuern den Ablauf der Operationen. Wenn der Benutzer Kontrollpunkte im Viewport mit der Maus verschiebt, wird der Modellgraph ausgeführt, um interaktiv neue Geometrie für das Modell zu erzeugen. Modellgraphen kombinieren die kreativen Möglichkeiten des freihändigen Editierens mit der Mächtigkeit der prozeduralen Modellierung. Darüber hinaus sind Modellgraphen eine visuelle Programmiersprache und stellen die Struktur der Algorithmen deutlicher dar als textbasierte Programmiersprachen. Als Resultat dieser Verbesserungen erhöht sich die Usability. Ein interaktiver Editor für botanische Bäume wird ebenfalls vorgestellt. Im Gegensatz zu früheren Ansätzen schlagen wir vor, Regeln, Parameter und Geometrie zu semantischen Entitäten zu verschmelzen. Auf diese Weise werden Zuordnungsprobleme zwischen Parametern und deren Instanzen komplett vermieden. Wenn im Viewport eine Instanz angeklickt wird, werden sofort ihre Parameter angezeigt, alle Änderungen wirken sich direkt auf die betroffenen Instanzen aus, und Änderungen im Viewport werden sofort in den Parametern reflektiert. Darüber hinaus werden die Entitäten in einer hierarchischen Datenstruktur gespeichert und alle Änderungen können rekursiv auf der Hierarchie ausgeführt werden. Dem Benutzer werden Selektionsoptionen zur Verfügung gestellt, über die er Änderungen an den Parametern oder Änderungen im Viewport an einzelnen oder vielen Instanzen gleichzeitig vornehmen kann. Anschließend muss das System nur die Geometrie der betroffenen Instanzen aktualisieren. Auch hier ist das Ziel, das User Interface möglichst an den Bedürfnissen des Benutzers auszurichten, um Vereinfachungen und eine Erhöhung der Produktivität zu erreichen. Interaktive Editieransätze für 3D-Modelle erlauben häufig eine präzisere Kontrolle über ein Modell als ein globaler Parametersatz, der für die Erzeugung des Modells genutzt wird. Trotzdem erzeugen prozedurale Modellierskripte ihre Modelle meist direkt aus einem festen Parametersatz, während interaktive Tools meist mit hartkodierten Operationen arbeiten. Wir schlagen vor, Skripte nicht nur zur Erzeugung der Modelle zu verwenden, sondern auch um die erzeugten Modelle zu editieren. Ein Basisskript soll die Statusinformationen eines Objekts anlegen, während weitere Skripte diesen Status verändern und passende Geometrie erzeugen. Diese Skripte bilden dann ein Template zum Erzeugen einer Klasse von Objekten. Verschiedene Objekttypen können jeweils ihr eigenes Template haben. Wir zeigen, wie Templates den Workflow mit prozeduralen Modellen vereinfachen können, indem Operationen geschaffen werden, die gleichzeitig kontext-sensitiv, mächtig und flexibel sind. Es existiert eine Reihe von Verfahren, um Geometrie für synthetische Landschaften zu erzeugen. Ein Teil der Algorithmen erzeugt Geometrie mit minimaler Vorberechnung und erlaubt es, den Detailgrad der Landschaft interaktiv an die Perspektive anzupassen. Leider fehlen den so erzeugten Landschaften plausible Flussnetze. Algorithmen, die erodiertes Terrain mit Flussnetzen erzeugen, müssen aufwendig vom Benutzer überwacht werden und brauchen Minuten oder Stunden Rechenzeit. Im Gegensatz dazu stellen wir einen Algorithmus vor, der plausible Flussnetze erzeugt, während sich der Betrachter interaktiv durch die Szene bewegt. Das System kann über Parameter gesteuert werden, aber der Fokus liegt auf dem Algorithmus zur Erzeugung der Flüsse. Dennoch wäre es möglich, Tools zum benutzergesteuerten Editieren von Terrain zu integrieren

Investigation of 3D electrical impedance mammography systems for breast cancer detection

Breast cancer is a major disease in women worldwide with a high rate of mortality, second only to lung cancer. Hence, there is considerable interest in developing non-invasive breast cancer detection methods with the aim of identifying breast cancer at an early stage, when it is most treatable. Electrical impedance mammography (EIM) is a relatively new medical imaging method for breast cancer detection. It is a safe, painless, non-invasive, non-ionizing imaging modality, which visualizes the internal conductivity distribution of the breast under investigation. Currently some EIM systems are in clinical trials but not commercialized, as there are still many challenges with sensitivity, spatial resolution and detectability. The research in this thesis aims to enhance and optimize EIM systems in order to address the current challenges. An enhanced image reconstruction algorithm using the duo-mesh method is developed. Both in simulations and real cases of phantoms and patients, the enhanced algorithm has proven more accurate and sensitive than the former algorithm and effective in improving vertical resolution for the EIM system with a planar electrode array. To evaluate the performance of the EIM system and the image reconstruction algorithms, an image processing based error analysis method is developed, which can provide an intuitive and accurate method to evaluate the reconstructed image and outline the shape of the object of interest. Two novel EIM systems are studied, which aim to improve the spatial resolution and the detectability of a tumour deep in the breast volume. These are: rotary planar-electrode-array EIM (RPEIM) system and combined electrode array EIM (CEIM) system. The RPEIM system permits the planar electrode array to rotate in the horizontal plane, which can dramatically increase the number of independent measurements, hence improving the spatial resolution. To support the rotation of the planner electrode array, a synchronous mesh method is developed. The CEIM system has a planar electrode array and a ring electrode array operated independently or together. It has three operational modes. This design provides enhanced detectability of a tumour deep within the tissue, as required for a large volume breast. The studies of the RPEIM system and the CEIM system are based on close-to-realistic digital breast phantoms, which comprise of skin, nipple, ducts, acini, fat and tumour. This approach makes simulations very close to a clinical trial of the technology