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In this report, we focus on Biofluids problems, specifically the Stokes Equation. The method of regularized Stokeslets can be derived from bound- ary integral equations derived from the Lorentz reciprocal identity. When body forces are known, this is a direct numerical approximation of an in- tegral, resulting in a summation to determine the fluid velocity. In certain cases, which this report is focused on, we know the velocity and want to determine the forces on a structure immersed in a fluid. This results in a lin- ear system Af = u, where A is a square dense matrix. We study different methods to solve this system of equations to determine the force f on the structure. For solving a linear system with a dense coefficient matrix, the backslash command in MATLAB can be used. This will use an efficient and robust direct method for solving a smaller matrix, but this is not an efficient method for a large, dense coefficient matrix. For a large, dense coefficient ma- trix, we will explore other direct methods as well as several iterative methods to determine computation time and error on a test case with an exact solu- tion. For direct methods, we will study backslash, LU factorization and QR factorization methods. For iterative methods, we stuied Jacobi, Gauss-Seidel, SOR, GMRES, CG, CGS, BICGSTAB and Schulz CG methods for these bioflu- ids applications. All of these methods have different requirements. For our coefficient matrix A, we identified specific properties and then used proper methods, both direct and iterative. Result showed that iterative methods are more efficient then direct method for large size A. Schulz CG was slower but had a smaller error for the test case where there was an exact solution.

We construct some new spaces determined by SN functions based on the classical SN theory.Also we have some new result in the densness of algebraic elements in a C* algebra.

No description available.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 66-67).

In this dissertation we consider the problem of mining cohesive (dense) subgraphs in probabilistic graphs, where each edge has a probability of existence. Mining probabilistic graphs has become the focus of interest in analyzing many real-world datasets, such as social, trust, communication, and biological networks due to the intrinsic uncertainty present in them. Studying cohesive subgraphs can reveal important information about connectivity, centrality, and robustness of the network, with applications in areas such as bioinformatics and social networks. In deterministic graphs, there exists various definitions of cohesive substructures, including cliques, quasi-cliques, k-cores and k-trusses. In this regard, k-core and k-truss decompositions are popular tools for finding cohesive subgraphs. In deterministic graphs, a k-core is the largest subgraph in which each vertex has at least k neighbors, and a k-truss is the largest subgraph whose edges are contained in at least k triangles (or k-2 triangles depending on the definition). The k-core and k-truss decomposition in deterministic graphs have been thoroughly studied in the literature. However, in the probabilistic context, the computation is challenging and state-of-art approaches are not scalable to large graphs. The main challenge is efficient computation of the tail probabilities of vertex degrees and triangle count of edges in probabilistic graphs. We employ a special version of central limit theorem (CLT) to obtain the tail probabilities efficiently. Based on our CLT approach we propose peeling algorithms for core and truss decomposition of a probabilistic graph that scales to very large graphs and offers significant improvement over state-of-the-art approaches. Moreover, we propose a second algorithm for probabilistic core decomposition that can handle graphs not fitting in memory by processing them sequentially one vertex at a time. In terms of truss decomposition, we design a second method which is based on progressive tightening of the estimate of the truss value of each edge based on h-index computation and novel use of dynamic programming. We provide extensive experimental results to show the efficiency of the proposed algorithms. Another contribution of this thesis is mining cohesive subgraphs using the recent notion of nucleus decomposition introduced by Sariyuce et al. Nucleus decomposition is based on higher order structures such as cliques nested in other cliques. Nucleus decomposition can reveal interesting subgraphs that can be missed by core and truss decompositions. In this dissertation, we present nucleus decomposition for probabilistic graphs. The major questions we address are: How to define meaningfully nucleus decomposition in probabilistic graphs? How hard is computing nucleus decomposition in probabilistic graphs? Can we devise efficient algorithms for exact or approximate nucleus decomposition in large graphs? We present three natural definitions of nucleus decomposition in probabilistic graphs: local, global, and weakly-global. We show that the local version is in PTIME, whereas global and weakly-global are #P-hard and NP-hard, respectively. We present an efficient and exact dynamic programming approach for the local case. Further, we present statistical approximations that can scale to bigger datasets without much loss of accuracy. For global and weakly-global decompositions we complement our intractability results by proposing efficient algorithms that give approximate solutions based on search space pruning and Monte-Carlo sampling. Extensive experiments show the scalability and efficiency of our algorithms. Compared to probabilistic core and truss decompositions, nucleus decomposition significantly outperforms in terms of density and clustering metrics. / Graduate

L’une des applications du développement durable se trouve incarnée par des opérations urbaines, considérées comme exemplaires : les éco-quartiers nord-européens qui, depuis 1990, expérimentent l’urbanisme durable au point d’inspirer leur application dans d’autres pays et d’autres sociétés. Le phénomène semble se retrouver partout dans le monde, tendant vers une universalité de la notion, tant dans sa philosophie que dans les différentes formes urbaines. Cette diversité formelle se retrouve dans l’histoire de l’architecture et de l’urbanisme depuis le siècle dernier : une recherche de lien avec la nature et la prospection d’une densité idéale pour les habitants, que l’on retrouve dans les utopies fondatrices d’Ebenezer Howard, de Franck Lloyd Wright et du Corbusier. Cette recherche de modèles permet de mieux comprendre et de définir une identité universelle des éco-quartiers dont le succès ne cesse de grandir en France : 160 projets ont candidaté au Concours EcoQuartier en 2009, 394 en 2011. L’éco-quartier du Raquet, aménagé en régie directe par la Communauté d’Agglomération du Douaisis sur les communes de Douai et de Sin-le-Noble, s’établit dans un contexte particulier, enserré par des opérations d’aménagement successives. Le projet de construire dans cette dent creuse urbaine un véritable morceau de ville de 4 000 à 4 500 logements nécessite une méthodologie d’approche tenant compte des spécificités du contexte tout en promouvant la performance environnementale. Basé sur des indicateurs thématiques de la « ville verte » et de la « ville compacte », il apparaît que la méthodologie s’approche d’un système, fractal aux interactions complexes. / One application of sustainable development could be found in different urban operations, considered exemplary: the northern European eco-neighborhoods since 1990, experimenting sustainable urbanism and inspire their application in other countries and other societies. The phenomenon seems to be found anywhere in the world, tending towards universality of the concept, both in its philosophy and in different urban forms. This formal diversity is found in the history of architecture and urbanism in the last century: a search for connections with nature and exploration of an ideal density for the inhabitants, which can be found in Ebenezer Howard’s, Franck Lloyd Wright’s and Le Corbusier’s utopias. This research of models leads us to better understand and define a universal identity eco-neighborhoods whose success continues to grow in France: 160 projects were candidate in EcoQuartier competition in 2009, 394 in 2011. Ecodistrict “Le Raquet”, built directly by the Agglomeration Community of Douai (CAD) in the towns of Douai and Sin-le-Noble, settled in a particular context, contained by successive development operations. The project to build a real piece of town of 4 000 to 4 500 units requires a methodological approach, taking into account the specific context while promoting environmental performance. Based on thematic indicators of "green city" and "compact city", it appears that the methodology seems to be a system, fractal with complex interactions.

Dans cette thèse, je propose plusieurs modèles et outils numériques afin de mieux comprendre et prédire le comportement et le développement de cultures et dispositifs neuronaux.Les cultures de neurones ont en effet été un outil précieux durant les 20 dernières années : elles ont permis de mieux comprendre la manière dont le cerveau traite les différentes informations qui lui parviennent en donnant aux scientifiques la possibilité de tester les effets de médicaments sur les neurones, ainsi que d'obtenir leurs réponses détaillées à diverses perturbations et stimuli.De plus, de récentes avancées en microfluidiques ont ouvert la voie à la conception de dispositifs neuronaux plus élaborés, rapprochant encore un peu plus la perspective du traitement de signaux complexes via des neurones in vitro.Dans une première partie, je propose un mécanisme pour expliquer les bouffées d'activité épileptiformes présentes dans les cultures, mécanisme que je formule via un modèle théorique concis. J'effectue ensuite une vérification expérimentale des prédictions du modèle sur des cultures et montre que celles-ci sont effectivement compatibles avec le comportement observé in vitro.Dans une seconde partie, je décris plus en détail la description de la dynamique spatio-temporelle du phénomène, notamment le fait que les bursts nucléent en des zones bien précises du réseau neuronal.Comme les prédictions et analyses effectuées dépendent fortement de la structure de ce réseau, je présente ensuite la réalisation d'une plateforme de simulation afin de permettre de modéliser efficacement le développement des réseaux neuronaux. Ce logiciel prend en compte les interactions entre les neurones et leur environnement et constitue la première plateforme à fournir des modèles polyvalents et complets pour décrire l'intégralité du processus de croissance neuronal. Je montre ensuite que ce simulateur est capable de générer des morphologies valides et l'utilise pour proposer des nouvelles topologies de réseaux afin de décrire les cultures de neurones. Je reproduis également des dispositifs neuronaux existants et montre que les activités entretenues par ces structures sont compatibles avec les observations expérimentales. Enfin, je discute plusieurs directions de recherche possibles, pour lesquelles l'utilisation de dispositifs neuronaux spécifiques permettrait de contourner les limitations des cultures neuronales et fournirait ainsi de nouvelles informations sur les processus sous-tendant le développement et la plasticité cérébrale / In this thesis, I provide models and numerical tools to better understand and predict the behavior and development of neuronal cultures and devices.Neuronal cultures have proven invaluable in improving our understanding of how the brain processes information, by enabling researchers to investigate neuronal and network response functions to various perturbations and stimuli.Furthermore, recent progress in microfluidics have opened the gate towards more elaborated neuronal devices, bringing us one step closer to complex signal processing with living in vitro neurons.In a first part, I propose a mechanism to explain the epileptiform bursts of activity present in cultures, mechanism which I formulate as a concise theoretical model. I subsequently test the predictions of this model on cultures and show that they are indeed compatible with the behavior observed in vitro.I further develop this description in the second part of the thesis, where I analyze its spatiotemporal dynamics and the fact that burst nucleate in specific areas in the network.Since predictions and analysis of these nucleation centers strongly depends on the network structure, I develop a simulation platform to enable efficient modeling of the network development. This software takes into account the interactions between the neurons and their environment and is the first platform to provide versatile and complete models to simulate the entire growth process of neurons. I demonstrate that this simulator is able to generate valid neuronal morphologies, then use it to propose new network topologies to describe neuronal cultures, as well as to reproduce existing neuronal devices. I then show that the activities sustained by these structures are compatible with the experimental recordings.Eventually, I discuss several future directions for which the use of neuronal devices would enable to circumvent current limitations of neuronal cultures, thus providing new information on the processes which underlie brain development and plasticity.

Dense medium cyclones (DMCs) have become the workhorse of the coal preparation industry due to their high efficiency, large capacity, small footprint and low maintenance requirements. Although the advantages of DMCs make them highly desirable, size-by-size partitioning data collected from industrial operations suggest that DMC performance can suffer in response to fluctuations in feed coal quality. In light of this problem, a multi-stream monitoring system that simultaneously measures the densities of the feed, overflow and underflow medium around a DMC circuit was designed, installed and evaluated at an industrial plant site. The data obtained from this real-time data acquisition system indicated that serious shortcomings exist in the methods commonly used by industry to monitor and control DMC circuits. This insight, together with size-by-size partition data obtained from in-plant sampling campaigns, was used to develop an improved control algorithm that optimizes DMC performance over a wide range of feed coal types and operating conditions. This document describes the key features of the multi-stream monitoring system and demonstrates how this approach may be used to potentially improve DMC performance. / Master of Science

ix, 134 leaves : tables, graphs (part fold.) ; 30 cm / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.), University of Adelaide, Dept. of Botany, 1979