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An entropy-based approach to the optimum design of reliable water distribution networksTanyimboh, Tiku Tanyienow January 1993 (has links)
No description available.
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Biological Inference using Flow NetworksWestbrooks, Kelly Anthony 18 May 2009 (has links)
Many bioinformatics problems are inference problems: Given partial or incomplete information about something, use that information to infer the missing or unknown data. This work addresses two inference problems in bioinformatics. The rst problem is inferring viral quasispecies sequences and their frequencies from 454 pyrosequencing reads. The second problem is inferring the structure of signal transduction networks from observations of interactions between cellular components. At first glance, these problems appear to be unrelated to each other. However, this work successfully penetrates both problems using the machinery of ow networks and transitive reduction, tools from classical computer science that prove useful in a wide array of application domains.
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Interactive Design and Debugging of GPU-based Volume VisualizationsMeyer-Spradow, Jennis, Ropinski, Timo, Mensmann, Jörg, Hinrichs, Klaus January 2010 (has links)
There is a growing need for custom visualization applications to deal with the rising amounts of volume data to be analyzed in fields like medicine, seismology, and meteorology. Visual programming techniques have been used in visualization and other fields to analyze and visualize data in an intuitive manner. However, this additional step of abstraction often results in a performance penalty during the actual rendering. In order to prevent this impact, a careful modularization of the required processing steps is necessary, which provides flexibility and good performance at the same time. In this paper, we will describe the technical foundations as well as the possible applications of such a modularization for GPU-based volume raycasting, which can be considered the state-of-the-art technique for interactive volume rendering. Based on the proposed modularization on a functional level, we will show how to integrate GPU-based volume ray-casting in a visual programming environment in such a way that a high degree of flexibility is achieved without any performance impact.
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Flows, morphology, and memory: study of a living networkKramar, Mirna Elizabeta 10 June 2021 (has links)
No description available.
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Visual Analytics of Cascaded Bottlenecks in Planar Flow NetworksPost, Tobias, Gillmann, Christina, Wischgoll, Thomas, Hamann, Bernd, Hagen, Hans 25 January 2019 (has links)
Finding bottlenecks and eliminating them to increase the overall flow of a network often appears in real world applications, such as production planning, factory layout, flow related physical approaches, and even cyber security. In many cases, several edges can form a bottleneck (cascaded bottlenecks). This work presents a visual analytics methodology to analyze these cascaded bottlenecks. The methodology consists of multiple steps: identification of bottlenecks, identification of potential improvements, communication of bottlenecks, interactive adaption of bottlenecks, and a feedback loop that allows users to adapt flow networks and their resulting bottlenecks until they are satisfied with the flow network configuration. To achieve this, the definition of a minimal cut is extended to identify network edges that form a (cascaded) bottleneck. To show the effectiveness of the presented approach, we applied the methodology to two flow network setups and show how the overall flow of these networks can be improved.
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Temporal and spatial aspects of correlation networks and dynamical network modelsTupikina, Liubov 30 March 2017 (has links)
In der vorliegenden Arbeit untersuchte ich die komplexen Strukturen von Netzwerken, deren zeitliche Entwicklung, die Interpretationen von verschieden Netzwerk-Massen und die Klassen der Prozesse darauf. Als Erstes leitete ich Masse für die Charakterisierung der zeitlichen Entwicklung der Netzwerke her, um räumlich Veränderungsmuster zu erkennen. Als Nächstes führe ich eine neue Methode zur Konstruktion komplexer Netzwerke von Flussfeldern ein, bei welcher man das Set-up auch rein unter Berufung Berufung auf das Geschwindigkeitsfeld ändern kann. Diese Verfahren wurden für die Korrelationen skalarer Grössen, z. B. Temperatur, entwickelt, welche eine Advektions-Diffusions-Dynamik in der Gegenwart von Zwingen und Dissipation. Die Flussnetzwerk-Methode zur Zeitreihenanalyse konstruiert die Korrelationsmatrizen und komplexen Netzwerke. Dies ermöglicht die Charakterisierung von Transport in Flüssigkeiten, die Identifikation verschiedene Misch-Regimes in dem Fluss und die Anwendung auf die Advektions-DiffusionsDynamik, Klimadaten und anderen Systemen, in denen Teilchentransport eine entscheidende Rolle spielen. Als Letztes, entwickelte ich ein neuartiges Heterogener Opinion Status Modell (HOpS) und Analysetechnik basiert auf Random Walks und Netzwerktopologie Theorien, um dynamischen Prozesse in Netzwerken zu studieren, wie die Verbreitung von Meinungen in sozialen Netzwerken oder Krankheiten in der Gesellschaft. Ein neues Modell heterogener Verbreitung auf einem Netzwerk wird als Beispielssystem für HOpS verwendent, um die vergleichsweise Einfachheit zu nutzen. Die Analyse eines diskreten Phasenraums des HOPS-Modells hat überraschende Eigenschaften, welches sensibel auf die Netzwerktopologie reagieren. Sie können verallgemeinert werden, um verschiedene Klassen von komplexen Netzwerken zu quantifizieren, Transportphänomene zu charakterisieren und verschiedene Zeitreihen zu analysieren. / In the thesis I studied the complex architectures of networks, the network evolution in time, the interpretation of the networks measures and a particular class of processes taking place on complex networks. Firstly, I derived the measures to characterize temporal networks evolution in order to detect spatial variability patterns in evolving systems. Secondly, I introduced a novel flow-network method to construct networks from flows, that also allows to modify the set-up from purely relying on the velocity field. The flow-network method is developed for correlations of a scalar quantity (temperature, for example), which satisfies advection-diffusion dynamics in the presence of forcing and dissipation. This allows to characterize transport in the fluids, to identify various mixing regimes in the flow and to apply this method to advection-diffusion dynamics, data from climate and other systems, where particles transport plays a crucial role. Thirdly, I developed a novel Heterogeneous Opinion-Status model (HOpS) and analytical technique to study dynamical processes on networks. All in all, methods, derived in the thesis, allow to quantify evolution of various classes of complex systems, to get insight into physical meaning of correlation networks and analytically to analyze processes, taking place on networks.
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Advances in uncertainty modelling : from epistemic uncertainty estimation to generalized generative flow networksLahlou, Salem 08 1900 (has links)
Les problèmes de prise de décision se produisent souvent dans des situations d'incertitude, englobant à la fois l'incertitude aléatoire due à la présence de processus inhérents aléatoires et l'incertitude épistémique liée aux connaissances limitées. Cette thèse explore le concept d'incertitude, un aspect crucial de l'apprentissage automatique et un facteur clé pour que les agents rationnels puissent déterminer où allouer leurs ressources afin d'obtenir les meilleurs résultats.
Traditionnellement, l'incertitude est encodée à travers une probabilité postérieure, obtenue par des techniques d'inférence Bayésienne approximatives. Le premier ensemble de contributions de cette thèse tourne autour des propriétés mathématiques des réseaux de flot génératifs, qui sont des modèles probabilistes de séquences discrètes et des échantillonneurs amortis de distributions de probabilités non normalisées. Les réseaux de flot génératifs trouvent des applications dans l'inférence Bayésienne et peuvent être utilisés pour l'estimation de l'incertitude. De plus, ils sont utiles pour les problèmes de recherche dans de vastes espaces compositionnels. Au-delà du renforcement du cadre mathématique sous-jacent, une étude comparative avec les méthodes variationnelles hiérarchiques est fournie, mettant en lumière les importants avantages des réseaux de flot génératifs, tant d'un point de vue théorique que par le biais d'expériences diverses. Ces contributions incluent une théorie étendant les réseaux de flot génératifs à des espaces continus ou plus généraux, ce qui permet de modéliser la probabilité postérieure et l'incertitude dans de nombreux contextes intéressants. La théorie est validée expérimentalement dans divers domaines.
Le deuxième axe de travail de cette thèse concerne les mesures alternatives de l'incertitude épistémique au-delà de la modélisation de la probabilité postérieure. La méthode présentée, appelée Estimation Directe de l'Incertitude Épistémique (DEUP), surmonte une faiblesse majeure des techniques d'inférence Bayésienne approximatives due à la mauvaise spécification du modèle. DEUP repose sur le maintien d'un prédicteur secondaire des erreurs du prédicteur principal, à partir duquel des mesures d'incertitude épistémique peuvent être déduites. / Decision-making problems often occur under uncertainty, encompassing both aleatoric uncertainty arising from inherent randomness in processes and epistemic uncertainty due to limited knowledge. This thesis explores the concept of uncertainty, a crucial aspect of machine learning and a key factor for rational agents to determine where to allocate their resources for achieving the best possible results.
Traditionally, uncertainty is encoded in a posterior distribution, obtained by approximate \textit{Bayesian} inference techniques. This thesis's first set of contributions revolves around the mathematical properties of generative flow networks, which are probabilistic models over discrete sequences and amortized samplers of unnormalized probability distributions. Generative flow networks find applications in Bayesian inference and can be used for uncertainty estimation. Additionally, they are helpful for search problems in large compositional spaces. Beyond deepening the mathematical framework underlying them, a comparative study with hierarchical variational methods is provided, shedding light on the significant advantages of generative flow networks, both from a theoretical point of view and via diverse experiments. These contributions include a theory extending generative flow networks to continuous or more general spaces, which allows modelling the Bayesian posterior and uncertainty in many interesting settings. The theory is experimentally validated in various domains.
This thesis's second line of work is about alternative measures of epistemic uncertainty beyond posterior modelling. The presented method, called Direct Epistemic Uncertainty Estimation (DEUP), overcomes a major shortcoming of approximate Bayesian inference techniques caused by model misspecification. DEUP relies on maintaining a secondary predictor of the errors of the main predictor, from which measures of epistemic uncertainty can be deduced.
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Towards an extension of causal discovery with generative flow networks to latent variables modelsManta, Dragos Cristian 12 1900 (has links)
Le raisonnement causal est au centre des facultés intellectuelles humaines qui nous permettent de transférer nos connaissances acquises dans des situations très différentes de l'expérience vécue à partir de peu de nouvelles observations.
En fait, notre science en entier se base sur l'hypothèse qu'on puisse expliquer tous les phénomènes de l'univers à partir d'un nombre relativement petit de principes simples et constants à travers le temps qui donnent naissance au monde complexe qui nous entoure grâce au très grand nombre de conditions expérimentales possibles, qui correspondent à des interventions dans un modèle causal graphique.
La découverte algorithmique de ces mécanismes semble donc être un pilier important, non seulement afin de produire des agents artificiels dotés de capacités cognitives humaines, mais également en vue d'automatiser la découverte scientifique.
Nous nous penchons sur une variante du problème de la découverte causale dans laquelle les données observées ne correspondent pas directement aux variables d'intérêt, que l'on considère latentes.
Nous utilisons les réseaux de flot génératifs pour apprendre une distribution bayésienne a posteriori définie sur la structure des réseaux bayésiens latents et sur les valeurs des variables latentes. / Causal reasoning is at the center of the human intellectual abilities that allow us to transfer our acquired knowledge in situations that are very different from our past experience from few new observations.
In fact, our whole science is based on the assumption that we can explain all the phenomena of the universe from a relatively small set of simple principles that are constant through time and that give rise to the complex world surrounding us due to the very large number of possible experimental conditions that correspond to interventions in a causal graphical model.
The algorithmic discovery of these mechanisms thus seems to be an important pillar, not only to create artificial agents endowed with human cognitive abilities, but also to automate scientific discovery.
We are looking into a variant of the causal discovery problem in which the observed data does not directly correspond to the variables of interest, which we consider to be latent.
We use Generative Flow Networks to learn a Bayesian posterior distribution defined over latent Bayesian networks and over the values of the latent variables.
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Perturbation analysis and numerical discretisation of hyperbolic partial differential algebraic equations describing flow networksHuck, Christoph 05 December 2018 (has links)
Diese Arbeit beschäftigt sich mit verschiedenen mathematischen Fragestellungen hinsichtlich der Modellierung, Analysis und numerischen Simulation von Gasnetzen. Hierbei liegt der Fokus auf der mathematischen Handhabung von partiellen differential-algebraischen Gleichungen, die mit algebraischen Gleichungen gekoppelt sind. Diese bieten einen einfachen Zugang hinsichtlich der Modellierung von dynamischen Strukturen auf Netzen Somit sind sie insbesondere für Gasnetze geeignet, denen im Zuge der steigenden Bedeutung von erneuerbaren Energien ein gestiegenes Interesse seitens der Öffentlichkeit, Politik und Wissenschaft entgegen gebracht wird.
Wir führen zunächst die gängigsten Elemente, die in Gasnetzen benötigt werden ein und formulieren zwei PDAE-Klassen für solche Netze: Eine für reine Rohrnetze, und eine, die zusätzliche Elemente wie Verdichter und Widerstände beinhaltet. Des Weiteren untersuchen wir die Sensitivität der Lösung der Rohrnetz-PDAE hinsichtlich Störungen. Dabei berücksichtigen wir Störungen, die nicht nur den dynamischen Teil der PDAE beeinflussen, sondern auch Störungen in den algebraischen Gleichungen und weisen Stabilitätseigenschaften für die Lösung der PDAE nach.
Darüber hinaus beschäftigen wir uns mit einer neu entwickelten, an die Netztopologie angepassten Ortsdiskretisierung, welche die Stabilitätseigenschaften der PDAE auf DAE Systeme überträgt. Des Weiteren zeigen wir, wie sich die Gasnetz-DAE zu einer gewöhnlichen Differentialgleichung, welche die inhärente Dynamik der DAE widerspiegelt entkoppeln lässt. Dieses entkoppelte System kann darüber hinaus direkt aus den Topologie- und Elementinformationen des Netzes aufgestellt werden. Abschließend demonstrieren wir die Ergebnisse an Benchmark-Gasnetzen. Dabei vergleichen wir sowohl die entkoppelte Differentialgleichung mit dem ursprünglichen DAE System, zeigen aber auch, welche Vorteile die an die Netztopologie angepasste Ortsdiskretisierung gegenüber existierenden Verfahren besitzt. / This thesis addresses several aspects regarding modelling, analysis and numerical simulation of gas networks. Hereby, our focus lies on (partial) differential-algebraic equations, thus systems of partial and ordinary differential equations which are coupled by algebraic equations. These coupled systems allow an easy approach towards the modelling of dynamic structures on networks. Therefore, they are well suited for gas networks, which have gained a rise of attention in society, politics and science due to the focus towards renewable energies.
We give an introduction towards gas network modelling that includes the most common elements that also appear in real gas networks and present two PDAE systems: One for pipe networks and one that includes additional elements like resistors and compressors. Furthermore, we investigate the impact of perturbations onto the pipe network PDAE, where we explicitly allow perturbations to affect the system in the differential as well as in the algebraic components. We conclude that the solution of the PDAE possesses stability properties.
In addition, this thesis introduces a new spatial discretisation that is adapted to the net- work topology. This topology-adapted semi-discretisation results in a DAE which possesses the same perturbation behaviour as the space continuous PDAE. Furthermore, we present a topology based decoupling procedure that allows to reformulate the DAE as an ordinary differential equation (ODE), which represents the inherent dynamics of the DAE system. This ODE, together with a decoupled set of algebraic equations, can be derived from the topology and element information directly. We conclude by demonstrating the established results for several benchmark networks. This includes a comparison of numerical solutions for the decoupled ODE and the DAE system. In addition we present the advantages of the topology-adapted spatial discretisation over existing well established methods.
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