Contours in Visualization

This thesis studies the visualization of set collections either via or defines as the relations among contours. In the first part, dynamic Euler diagrams are used to communicate and improve semimanually the result of clustering methods which allow clusters to overlap arbitrarily. The contours of the Euler diagram are rendered as implicit surfaces called blobs in computer graphics. The interaction metaphor is the moving of items into or out of these blobs. The utility of the method is demonstrated on data arising from the analysis of gene expressions. The method works well for small datasets of up to one hundred items and few clusters. In the second part, these limitations are mitigated employing a GPU-based rendering of Euler diagrams and mixing textures and colors to resolve overlapping regions better. The GPU-based approach subdivides the screen into triangles on which it performs a contour interpolation, i.e. a fragment shader determines for each pixel which zones of an Euler diagram it belongs to. The rendering speed is thus increased to allow multiple hundred items. The method is applied to an example comparing different document clustering results. The contour tree compactly describes scalar field topology. From the viewpoint of graph drawing, it is a tree with attributes at vertices and optionally on edges. Standard tree drawing algorithms emphasize structural properties of the tree and neglect the attributes. Adapting popular graph drawing approaches to the problem of contour tree drawing it is found that they are unable to convey this information. Five aesthetic criteria for drawing contour trees are proposed and a novel algorithm for drawing contour trees in the plane that satisfies four of these criteria is presented. The implementation is fast and effective for contour tree sizes usually used in interactive systems and also produces readable pictures for larger trees. Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods to analyze these model\''s validity. The fourth part of the thesis focuses on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; they are huge and high dimensional. Their most salient features are described by their so-called barrier tree -- a contour tree for discrete observation spaces. The changing folding landscapes of a growing RNA chain are visualized as an animation of the corresponding barrier tree sequence. The animation is created as an adaption of the foresight layout with tolerance algorithm for dynamic graph layout. The adaptation requires changes to the concept of supergraph and it layout. The thesis finishes with some thoughts on how these approaches can be combined and how the task the application should support can help inform the choice of visualization modality

Towards Visualization of Discrete Optimization Problems and Search Algorithms

Diskrete Optimierung beschäftigt sich mit dem Identifizieren einer Kombination oder Permutation von Elementen, die im Hinblick auf ein gegebenes quantitatives Kriterium optimal ist. Anwendungen dafür entstehen aus Problemen in der Wirtschaft, der industriellen Fertigung, den Ingenieursdisziplinen, der Mathematik und Informatik. Dazu gehören unter anderem maschinelles Lernen, die Planung der Reihenfolge und Terminierung von Fertigungsprozessen oder das Layout von integrierten Schaltkreisen. Häufig sind diskrete Optimierungsprobleme NP-hart. Dadurch kommt der Erforschung effizienter, heuristischer Suchalgorithmen eine große Bedeutung zu, um für mittlere und große Probleminstanzen überhaupt gute Lösungen finden zu können. Dabei wird die Entwicklung von Algorithmen dadurch erschwert, dass Eigenschaften der Probleminstanzen aufgrund von deren Größe und Komplexität häufig schwer zu identifizieren sind. Ebenso herausfordernd ist die Analyse und Evaluierung von gegebenen Algorithmen, da das Suchverhalten häufig schwer zu charakterisieren ist. Das trifft besonders im Fall von emergentem Verhalten zu, wie es in der Forschung der Schwarmintelligenz vorkommt. Visualisierung zielt auf das Nutzen des menschlichen Sehens zur Datenverarbeitung ab. Das Gehirn hat enorme Fähigkeiten optische Reize von den Sehnerven zu analysieren, Formen und Muster darin zu erkennen, ihnen Bedeutung zu verleihen und dadurch ein intuitives Verstehen des Gesehenen zu ermöglichen. Diese Fähigkeit kann im Speziellen genutzt werden, um Hypothesen über komplexe Daten zu generieren, indem man sie in einem Bild repräsentiert und so dem visuellen System des Betrachters zugänglich macht. Bisher wurde Visualisierung kaum genutzt um speziell die Forschung in diskreter Optimierung zu unterstützen. Mit dieser Dissertation soll ein Ausgangspunkt geschaffen werden, um den vermehrten Einsatz von Visualisierung bei der Entwicklung von Suchheuristiken zu ermöglichen. Dazu werden zunächst die zentralen Fragen in der Algorithmenentwicklung diskutiert und daraus folgende Anforderungen an Visualisierungssysteme abgeleitet. Mögliche Forschungsrichtungen in der Visualisierung, die konkreten Nutzen für die Forschung in der Optimierung ergeben, werden vorgestellt. Darauf aufbauend werden drei Visualisierungssysteme und eine Analysemethode für die Erforschung diskreter Suche vorgestellt. Drei wichtige Aufgaben von Algorithmendesignern werden dabei adressiert. Zunächst wird ein System für den detaillierten Vergleich von Algorithmen vorgestellt. Auf der Basis von Zwischenergebnissen der Algorithmen auf einer Probleminstanz wird der Suchverlauf der Algorithmen dargestellt. Der Fokus liegt dabei dem Verlauf der Qualität der Lösungen über die Zeit, wobei die Darstellung durch den Experten mit zusätzlichem Wissen oder Klassifizierungen angereichert werden kann. Als zweites wird ein System für die Analyse von Suchlandschaften vorgestellt. Auf Basis von Pfaden und Abständen in der Landschaft wird eine Karte der Probleminstanz gezeichnet, die strukturelle Merkmale intuitiv erfassbar macht. Der zweite Teil der Dissertation beschäftigt sich mit der topologischen Analyse von Suchlandschaften, aufbauend auf einer Schwellwertanalyse. Ein Visualisierungssystem wird vorgestellt, dass ein topologisch equivalentes Höhenprofil der Suchlandschaft darstellt, um die topologische Struktur begreifbar zu machen. Dieses System ermöglicht zudem, den Suchverlauf eines Algorithmus direkt in der Suchlandschaft zu beobachten, was insbesondere bei der Untersuchung von Schwarmintelligenzalgorithmen interessant ist. Die Berechnung der topologischen Struktur setzt eine vollständige Aufzählung aller Lösungen voraus, was aufgrund der Größe der Suchlandschaften im allgemeinen nicht möglich ist. Um eine Anwendbarkeit der Analyse auf größere Probleminstanzen zu ermöglichen, wird eine Methode zur Abschätzung der Topologie vorgestellt. Die Methode erlaubt eine schrittweise Verfeinerung der topologischen Struktur und lässt sich heuristisch steuern. Dadurch können Wissen und Hypothesen des Experten einfließen um eine möglichst hohe Qualität der Annäherung zu erreichen bei gleichzeitig überschaubarem Berechnungsaufwand.Discrete optimization deals with the identification of combinations or permutations of elements that are optimal with regard to a specific, quantitative criterion. Applications arise from problems in economy, manufacturing, engineering, mathematics and computer sciences. Among them are machine learning, scheduling of production processes, and the layout of integrated electrical circuits. Typically, discrete optimization problems are NP hard. Thus, the investigation of efficient, heuristic search algorithms is of high relevance in order to find good solutions for medium- and large-sized problem instances, at all. The development of such algorithms is complicated, because the properties of problem instances are often hard to identify due to the size and complexity of the instances. Likewise, the analysis and evaluation of given algorithms is challenging, because the search behavior of an algorithm is hard to characterize, especially in case of emergent behavior as investigated in swarm intelligence research. Visualization targets taking advantage of human vision in order to do data processing. The visual brain possesses tremendous capabilities to analyse optical stimulation through the visual nerves, perceive shapes and patterns, assign meaning to them and thus facilitate an intuitive understanding of the seen. In particular, this can be used to generate hypotheses about complex data by representing them in a well-designed depiction and making it accessible to the visual system of the viewer. So far, there is only little use of visualization to support the discrete optimization research. This thesis is meant as a starting point to allow for an increased application of visualization throughout the process of developing discrete search heuristics. For this, we discuss the central questions that arise from the development of heuristics as well as the resulting requirements on visualization systems. Possible directions of research for visualization are described that yield a specific benefit for optimization research. Based on this, three visualization systems and one analysis method are presented. These address three important tasks of algorithm designers. First, a system for the fine-grained comparison of algorithms is introduced. Based on the intermediate results of algorithm runs on a given problem instance the search process is visualized. The focus is on the progress of the solution quality over time while allowing the algorithm expert to augment the depiction with additional domain knowledge and classification of individual solutions. Second, a system for the analysis of search landscapes is presented. Based on paths and distances in the landscape, a map of the problem instance is drawn that facilitates an intuitive cognition of structural properties. The second part of this thesis focuses on the topological analysis of search landscapes, based on barriers. A visualization system is presented that shows a topological equivalent height profile of the search landscape. Further, the system facilitates to observe the search process of an algorithm directly within the search landscape. This is of particular interest when researching swarm intelligence algorithms. The computation of topological structure requires a complete enumeration of all solutions which is not possible in the general case due to the size of the search landscapes. In order to enable an application to larger problem instances, we introduce a method to approximate the topological structure. The method allows for an incremental refinement of the topological approximation that can be controlled using a heuristic. Thus, the domain expert can introduce her knowledge and also hypotheses about the problem instance into the analysis so that an approximation of good quality is achieved with reasonable computational effort

The Role of Topological Constraints in RNA Tertiary Folding and Dynamics.

Functional RNA molecules must fold into highly complex three-dimensional (3D) structures and undergo precise structural dynamics in order to carry out their biological functions. However, the principles that govern RNA 3D folding and dynamics remain poorly understood. Recent studies have proposed that topological constraints arising from the basic connectivity and steric properties of RNA secondary structure strongly confine the 3D conformation of RNA junctions and thus may contribute to the specificity of RNA 3D folding and dynamics. Herein, this hypothesis is explored in quantitative detail using a combination of computational heuristic models and the specially developed coarse-grained molecular dynamics model TOPRNA. First, studies of two-way junctions provide new insight into the significance and mechanism of action of topological constraints. It is demonstrated that topological constraints explain the directionality and amplitude of bulge-induced bends, and that long-range tertiary interactions can modify topological constraints by disrupting non-canonical pairing in internal loops. Furthermore, topological constraints are shown to define free energy landscapes that coincide with the distribution of bulge conformations in structural databases and reproduce solution NMR measurements made on bulges. Next, TOPRNA is used to investigate the contributions of topological constraints to tRNA folding and dynamics. Topological constraints strongly constrain tRNA 3D conformation and notably discriminate against formation of non-native tertiary contacts, providing a sequence-independent source of folding specificity. Furthermore, topological constraints are observed to give rise to thermodynamic cooperativity between distinct tRNA tertiary interactions and encode functionally important 3D dynamics. Mutant tRNAs with unnatural secondary structures are shown to lack these favorable characteristics, suggesting that topological constraints underlie the evolutionary conservation of tRNA secondary structure. Additional studies of a non-canonical mitochondrial tRNA show that increased topological constraints can reduce the entropic cost of tertiary folding, and that disruptions of topological constraints explain the pathogenicity of a insertion mutation in this tRNA. UV melting experiments verify these findings. Finally, TOPRNA is used to study the topological constraints of the 197 nucleotide Azoarcus Group I ribozyme. It is shown that topological constraints strongly confine this RNA and provide a mechanism for encoding tertiary structure specificity and cooperative hierarchical folding behavior.PhDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110505/1/amustoe_1.pd

Modeling RNA, protein, and synthetic molecules using coarse-grained and all-atom representations

The aim of computational chemistry is to depict and understand the dynamics and interactions of molecular systems. In addition to increased comprehension in the physical and life sciences, this insight yields important applications to therapeutic design and materials science. In computational chemistry, molecules can be modeled in a number of representations depending on the molecular system and phenomena of interest. In this work, both simplified, coarse-grained representations and all-atom representations are used to model the interactions of RNA, cucurbituril host-guest chemistry, and cadmium selenide quantum dot binding to the Src homology 3 domain. For RNA, a coarse-grained model was developed termed RACER (RnA CoarsE-gRained) to accurately predict RNA structure and folding free energy. After optimization to statistical potentials, RACER accurately predicted the structures of 14 RNAs with an average 4.15Å root mean square deviation (RMSD) to the experimental structure. Further, RACER captured the sequence-specific variation in folding free energy for a set of 6 RNA hairpins and 5 RNA duplexes, with a R² correlation of 0.96 to experiment. The binding free energies of a cucurbituril host with 14 guests were computed using a polarizable force field and the free energy techniques of Bennett acceptance ratio and the orthogonal space random walk. The polarizable force field captured binding accurately, yet unexpectedly, the orthogonal space random walk method converged slowly, albeit at still reduced computational expense to the Bennett acceptance ratio. Lastly, the nanotoxicity effects of trioctylphosphine oxide coated cadmium selenide quantum dots are investigated with the model Src homology 3 protein domain in complex with its native proline rich motif ligand. With increasing quantum dot concentration, there is an increasing preference for the quantum dots to bind to the proline rich motif active site, inhibiting Src homology 3 function.Biomedical Engineerin

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Reliability-constrained design optimisation of extra-large offshore wind turbine support structures

The offshore wind industry has evolved significantly over the last decade, contributing considerably to Europe’s energy mix. For further penetration of this technology, it is essential to reduce its costs to make it competitive with conventional power generation technologies. To this end, optimising the design of components while simultaneously fulfilling design criteria is a crucial requirement for producing more cost-effective strategies. Traditional design optimisation techniques rely on the optimisation of design variables against constraints such as stresses or deformation in the form of limit states and to minimise an objective function such as the total mass of a component. Although this approach leads to more optimal designs, the presence of uncertainties, for instance, in material properties, manufacturing tolerances and environmental loads, requires more systematic consideration of these uncertainties. A combination of optimisation methods with concepts of structural reliability can be a suitable approach if challenges such as the approximation of the load effect concerning global input loads and computational requirements are addressed accordingly. In this study, a reliability-constrained optimisation framework for offshore wind turbine (OWT) support structures is developed, applied, and documented for the first time. First, a parametric finite element analysis (FEA) model of OWT support structures is developed, considering stochastic material properties and environmental loads. The parametric FEA model is then combined with response surface and Monte Carlo (MC) to create an assessment model in the Six Sigma module in ANSYS, which is then further integrated with an optimisation algorithm to develop a fully coupled reliability-constrained optimisation framework. The framework is applied to the NREL 5MW OWT and OC3 sub-structure. Results indicate that the proposed optimisation framework can effectively reduce the mass of OWT support structures meeting target reliability levels focusing on realistic limit states. At the end of the optimisation loop, an LCOE comparison is done to see the effect of mass reduction on the wind turbine cost. The study expanded with a scaling-up approach and investigated the technical feasibility of increasing the system’s power and size in deeper water depth for bottom-fixed support structures. Additionally, parametric equations have been developed to estimate the wind turbine rating and weight considering water depth in the conceptual design stage. Furthermore, the sensitivity analysis was performed on the latest reference support structure of the IEA 15MW turbine to see the effect of water depth between 30m to 60m. The results showed the influences of water depth on the current structural response of the monopile. It revealed that utilising the proposed support structure is not feasible for water-depth above 50m as the analysis did not fulfil design criteria.The offshore wind industry has evolved significantly over the last decade, contributing considerably to Europe’s energy mix. For further penetration of this technology, it is essential to reduce its costs to make it competitive with conventional power generation technologies. To this end, optimising the design of components while simultaneously fulfilling design criteria is a crucial requirement for producing more cost-effective strategies. Traditional design optimisation techniques rely on the optimisation of design variables against constraints such as stresses or deformation in the form of limit states and to minimise an objective function such as the total mass of a component. Although this approach leads to more optimal designs, the presence of uncertainties, for instance, in material properties, manufacturing tolerances and environmental loads, requires more systematic consideration of these uncertainties. A combination of optimisation methods with concepts of structural reliability can be a suitable approach if challenges such as the approximation of the load effect concerning global input loads and computational requirements are addressed accordingly. In this study, a reliability-constrained optimisation framework for offshore wind turbine (OWT) support structures is developed, applied, and documented for the first time. First, a parametric finite element analysis (FEA) model of OWT support structures is developed, considering stochastic material properties and environmental loads. The parametric FEA model is then combined with response surface and Monte Carlo (MC) to create an assessment model in the Six Sigma module in ANSYS, which is then further integrated with an optimisation algorithm to develop a fully coupled reliability-constrained optimisation framework. The framework is applied to the NREL 5MW OWT and OC3 sub-structure. Results indicate that the proposed optimisation framework can effectively reduce the mass of OWT support structures meeting target reliability levels focusing on realistic limit states. At the end of the optimisation loop, an LCOE comparison is done to see the effect of mass reduction on the wind turbine cost. The study expanded with a scaling-up approach and investigated the technical feasibility of increasing the system’s power and size in deeper water depth for bottom-fixed support structures. Additionally, parametric equations have been developed to estimate the wind turbine rating and weight considering water depth in the conceptual design stage. Furthermore, the sensitivity analysis was performed on the latest reference support structure of the IEA 15MW turbine to see the effect of water depth between 30m to 60m. The results showed the influences of water depth on the current structural response of the monopile. It revealed that utilising the proposed support structure is not feasible for water-depth above 50m as the analysis did not fulfil design criteria