Numerical analysis of stochastic biochemical reaction networks

Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of the state space equals the number of molecular species involved in the reaction network and the size of the system of differential equations equals the number of states in the corresponding continuous-time Markov chain, which is usually enormously huge and often even infinite. Thus, efficient numerical solution approaches must be able to handle huge, possibly infinite and stiff systems of differential equations efficiently. In this thesis, we present efficient techniques for the numerical analysis of the biochemical reaction networks. We present an approximate numerical integration approach that combines a dynamical state space truncation procedure with efficient numerical integration schemes for systems of ordinary differential equations including adaptive step size selection based on local error estimates. We combine our dynamical state space truncation with the method of conditional moments, and present the implementation details and numerical results. We also incorporate ideas from importance sampling simulations into a non-simulative numerical method that approximates transient rare event probabilities based on a dynamical truncation of the state space. Finally, we present a maximum likelihood method for the estimation of the model parameters given noisy time series measurements of molecular counts. All approaches presented in this thesis are implemented as part of the tool STAR, which allows to model and simulate the biochemical reaction networks. The efficiency and accuracy is demonstrated by numerical examples.Numerische Lösungen der chemischen Master-Gleichung für stochastische Reaktionsnetzwerke leiden typischerweise an dem Zustandsraumexplosionsproblem aufgrund der hohen Dimensionalität und der Steifigkeit durch mehrfache Zeitskalen. Die Dimension des Zustandsraumes entspricht der Anzahl der molekularen Spezies von dem Reaktionsnetzwerk und die Größe des Systems von Differentialgleichungen entspricht der Anzahl der Zustände in der entsprechenden kontinuierlichen Markov-Kette, die in der Regel enorm gross und oft sogar unendlich gross ist. Daher müssen numerische Methoden in der Lage sein, riesige, eventuell unendlich grosse und steife Systeme von Differentialgleichungen effizient lösen zu können. In dieser Arbeit beschreiben wir effiziente Methoden für die numerische Analyse biochemischer Reaktionsnetzwerke. Wir betrachten einen inexakten numerischen Integrationsansatz, bei dem eine dynamische Zustandsraumbeschneidung und ein Verfahren mit einem effizienten numerischen Integrationsschema für Systeme von gewöhnlichen Differentialgleichungen benutzt werden. Wir kombinieren unsere dynamische Zustandsraumbeschneidungsmethode mit der Methode der bedingten Momente und beschreiben die Implementierungdetails und numerischen Ergebnisse. Wir benutzen auch Ideen des importance sampling für eine nicht-simulative numerische Methode, die basierend auf der Zustandsraumbeschneidung die Wahrscheinlichkeiten von seltenen Ereignissen berechnen kann. Schließlich beschreiben wir eine Maximum-Likelihood-Methode für die Schätzung der Modellparameter bei verrauschten Zeitreihenmessungen von molekularen Anzahlen. Alle in dieser Arbeit beschriebenen Ansätze sind in dem Software-Tool STAR implementiert, das erlaubt, biochemische Reaktionsnetzwerke zu modellieren und zu simulieren. Die Effizienz und die Genauigkeit werden durch numerische Beispiele gezeigt

Technology for Low Resolution Space Based RSO Detection and Characterisation

Space Situational Awareness (SSA) refers to all activities to detect, identify and track objects in Earth orbit. SSA is critical to all current and future space activities and protect space assets by providing access control, conjunction warnings, and monitoring status of active satellites. Currently SSA methods and infrastructure are not sufficient to account for the proliferations of space debris. In response to the need for better SSA there has been many different areas of research looking to improve SSA most of the requiring dedicated ground or space-based infrastructure. In this thesis, a novel approach for the characterisation of RSO’s (Resident Space Objects) from passive low-resolution space-based sensors is presented with all the background work performed to enable this novel method. Low resolution space-based sensors are common on current satellites, with many of these sensors being in space using them passively to detect RSO’s can greatly augment SSA with out expensive infrastructure or long lead times. One of the largest hurtles to overcome with research in the area has to do with the lack of publicly available labelled data to test and confirm results with. To overcome this hurtle a simulation software, ORBITALS, was created. To verify and validate the ORBITALS simulator it was compared with the Fast Auroral Imager images, which is one of the only publicly available low-resolution space-based images found with auxiliary data. During the development of the ORBITALS simulator it was found that the generation of these simulated images are computationally intensive when propagating the entire space catalog. To overcome this an upgrade of the currently used propagation method, Specialised General Perturbation Method 4th order (SGP4), was performed to allow the algorithm to run in parallel reducing the computational time required to propagate entire catalogs of RSO’s. From the results it was found that the standard facet model with a particle swarm optimisation performed the best estimating an RSO’s attitude with a 0.66 degree RMSE accuracy across a sequence, and ~1% MAPE accuracy for the optical properties. This accomplished this thesis goal of demonstrating the feasibility of low-resolution passive RSO characterisation from space-based platforms in a simulated environment

Toward guiding simulation experiments

To face the variety of simulation experiment methods, tools are needed that allow their seamless integration, guide the user through the steps of an experiment, and support him in selecting the most suitable method for the task at hand. This work presents techniques for facing such challenges. To guide users through the experiment process, six typical tasks have been identified for structuring the experiment workflow. The M&S framework JAMES II and its plug-in system is exploited to integrate various methods. Finally, an approach for automatic selection and use of such methods is realized

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

OPTIMIZATION OF ALGORITHMS WITH THE OPAL FRAMEWORK

RÉSUMÉ La question d'identifier de bons paramètres a été étudiée depuis longtemps et on peut compter un grand nombre de recherches qui se concentrent sur ce sujet. Certaines de ces recherches manquent de généralité et surtout de re-utilisabilité. Une première raison est que ces projets visent des systèmes spécifiques. En plus, la plupart de ces projets ne se concentrent pas sur les questions fondamentales de l'identification de bons paramètres. Et enfin, il n'y avait pas un outil puissant capable de surmonter des difficulté dans ce domaine. En conséquence, malgré un grand nombre de projets, les utilisateurs n'ont pas trop de possibilité à appliquer les résultats antérieurs à leurs problèmes. Cette thèse propose le cadre OPAL pour identifier de bons paramètres algorithmiques avec des éléments essentiels, indispensables. Les étapes de l'élaboration du cadre de travail ainsi que les résultats principaux sont présentés dans trois articles correspondant aux trois chapitres 4, 5 et 6 de la thèse. Le premier article introduit le cadre par l'intermédiaire d'exemples fondamentaux. En outre, dans ce cadre, la question d'identifier de bons paramètres est modélisée comme un problème d'optimisation non-lisse qui est ensuite résolu par un algorithme de recherche directe sur treillis adaptatifs. Cela réduit l'effort des utilisateurs pour accomplir la tâche d'identifier de bons paramètres. Le deuxième article décrit une extension visant à améliorer la performance du cadre OPAL. L'utilisation efficace de ressources informatiques dans ce cadre se fait par l'étude de plusieurs stratégies d'utilisation du parallélisme et par l'intermédiaire d'une fonctionnalité particulière appelée l'interruption des tâches inutiles. Le troisième article est une description complète du cadre et de son implémentation en Python. En plus de rappeler les caractéristiques principales présentées dans des travaux antérieurs, l'intégration est présentée comme une nouvelle fonctionnalité par une démonstration de la coopération avec un outil de classification. Plus précisément, le travail illustre une coopération de OPAL et un outil de classification pour résoudre un problème d'optimisation des paramètres dont l'ensemble de problèmes tests est trop grand et une seule évaluation peut prendre une journée.----------ABSTRACT The task of parameter tuning question has been around for a long time, spread over most domains and there have been many attempts to address it. Research on this question often lacks in generality and re-utilisability. A first reason is that these projects aim at specific systems. Moreover, some approaches do not concentrate on the fundamental questions of parameter tuning. And finally, there was not a powerful tool that is able to take over the difficulties in this domain. As a result, the number of projects continues to grow, while users are not able to apply the previous achievements to their own problem. The present work systematically approaches parameter tuning by figuring out the fundamental issues and identifying the basic elements for a general system. This provides the base for developing a general and flexible framework called OPAL, which stands for OPtimization of ALgorithms. The milestones in developing the framework as well as the main achievements are presented through three papers corresponding to the three chapters 4, 5 and 6 of this thesis. The first paper introduces the framework by describing the crucial basic elements through some very simple examples. To this end, the paper considers three questions in constructing an automated parameter tuning framework. By answering these questions, we propose OPAL, consisting of indispensable components of a parameter tuning framework. OPAL models the parameter tuning task as a blackbox optimization problem. This reduces the effort of users in launching a tuning session. The second paper shows one of the opportunities to extend the framework. To take advantage of the situations where multiple processors are available, we study various ways of embedding parallelism and develop a feature called ''interruption of unnecessary tasks'' in order to improve performance of the framework. The third paper is a full description of the framework and a release of its Python} implementation. In addition to the confirmations on the methodology and the main features presented in previous works, the integrability is introduced as a new feature of this release through an example of the cooperation with a classification tool. More specifically, the work illustrates a cooperation of OPAL and a classification tool to solve a parameter optimization problem of which the test problem set is too large and an assessment can take a day

Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-3)

Papers from the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES) are presented. The papers discuss current research in the general field of inverse, semi-inverse, and direct design and optimization in engineering sciences. The rapid growth of this relatively new field is due to the availability of faster and larger computing machines

Domänen parallele Maschinen

A computational model is introduced, which abstracts and idealizes computers with access to fragment shaders. While the set of functions computable by this model remains the same, the running times can be drastically reduced through parallelization compared to conventional models. Some of the algorithms designed for the model can be approximated using fragment shaders. With an automatic transcompilation scheme, fragment shader programs can be generated automatically from a description in a high-level language.In dieser Arbeit wird ein Rechenmodell, das Computer mit Zugriff zu Fragment Shader abstrahiert und idealisiert, eingeführt. Zwar bleibt der Umfang der durch dieses Modell berechenbarer Funktionen gleich, jedoch können die Laufzeiten durch Parallelisierung im Vergleich zu herkömmlichen Modellen drastisch verkürzt werden. Einige der für das Modell entworfenen Algorithmen lassen sich mithilfe von Fragment Shadern approximieren. In einer Hochsprache beschriebene Algorithmen werden automatisiert in Fragment Shader Programme übersetzt

Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft