This thesis is on the numerical computation of eigenvalues of symmetric hierarchical matrices. The numerical algorithms used for this computation are derivations of the LR Cholesky algorithm, the preconditioned inverse iteration, and a bisection method based on LDLT factorizations. The investigation of QR decompositions for H-matrices leads to a new QR decomposition. It has some properties that are superior to the existing ones, which is shown by experiments using the HQR decompositions to build a QR (eigenvalue) algorithm for H-matrices does not progress to a more efficient algorithm than the LR Cholesky algorithm. The implementation of the LR Cholesky algorithm for hierarchical matrices together with deflation and shift strategies yields an algorithm that require O(n) iterations to find all eigenvalues. Unfortunately, the local ranks of the iterates show a strong growth in the first steps. These H-fill-ins makes the computation expensive, so that O(n³) flops and O(n²) storage are required. Theorem 4.3.1 explains this behavior and shows that the LR Cholesky algorithm is efficient for the simple structured Hl-matrices. There is an exact LDLT factorization for Hl-matrices and an approximate LDLT factorization for H-matrices in linear-polylogarithmic complexity. This factorizations can be used to compute the inertia of an H-matrix. With the knowledge of the inertia for arbitrary shifts, one can compute an eigenvalue by bisectioning. The slicing the spectrum algorithm can compute all eigenvalues of an Hl-matrix in linear-polylogarithmic complexity. A single eigenvalue can be computed in O(k²n log^4 n). Since the LDLT factorization for general H-matrices is only approximative, the accuracy of the LDLT slicing algorithm is limited. The local ranks of the LDLT factorization for indefinite matrices are generally unknown, so that there is no statement on the complexity of the algorithm besides the numerical results in Table 5.7. The preconditioned inverse iteration computes the smallest eigenvalue and the corresponding eigenvector. This method is efficient, since the number of iterations is independent of the matrix dimension. If other eigenvalues than the smallest are searched, then preconditioned inverse iteration can not be simply applied to the shifted matrix, since positive definiteness is necessary. The squared and shifted matrix (M-mu I)² is positive definite. Inner eigenvalues can be computed by the combination of folded spectrum method and PINVIT. Numerical experiments show that the approximate inversion of (M-mu I)² is more expensive than the approximate inversion of M, so that the computation of the inner eigenvalues is more expensive. We compare the different eigenvalue algorithms. The preconditioned inverse iteration for hierarchical matrices is better than the LDLT slicing algorithm for the computation of the smallest eigenvalues, especially if the inverse is already available. The computation of inner eigenvalues with the folded spectrum method and preconditioned inverse iteration is more expensive. The LDLT slicing algorithm is competitive to H-PINVIT for the computation of inner eigenvalues. In the case of large, sparse matrices, specially tailored algorithms for sparse matrices, like the MATLAB function eigs, are more efficient. If one wants to compute all eigenvalues, then the LDLT slicing algorithm seems to be better than the LR Cholesky algorithm. If the matrix is small enough to be handled in dense arithmetic (and is not an Hl(1)-matrix), then dense eigensolvers, like the LAPACK function dsyev, are superior. The H-PINVIT and the LDLT slicing algorithm require only an almost linear amount of storage. They can handle larger matrices than eigenvalue algorithms for dense matrices. For Hl-matrices of local rank 1, the LDLT slicing algorithm and the LR Cholesky algorithm need almost the same time for the computation of all eigenvalues. For large matrices, both algorithms are faster than the dense LAPACK function dsyev.

Enhancing the quality of services in the distribution system is an important topic for power system research. It is imperative to employ precise network modeling and effective simulation tools, and a good system model is the key. This dissertation starts with modifying the building algorithms of Y-admittance and Z-impedance matrices. The Y-matrix will be built according to phase sequences. With the facts that the line self-impedance is significantly greater than the mutual-coupling terms and the existence of a high r/x ratio in distribution, two decoupled load flow methods (Phase-Decoupled¡BPD and Sub-Phase-Decoupled¡BSPD) with Current Injection Model(CIM) were developed. A new Z-matrix building algorithm was also developed in this dissertation. It decomposed the traditional Z into two sub-matrices, the upper and lower triangular matrices respectively. The matrices represent the relationships between the branch current and the bus injection current, and between the bus voltage and the branch current. Enhancing the quality of services will be effectively achieved by a proper capacitor placement technique. This dissertation develops a linear relationships of voltage changes versus the capacitor compensation, the branch current changes versus the capacitor compensation, and loss reductions versus the capacitor compensation. For loss reduction, a linear optimization function was defined to solve the capacitor placement problem. Tests have shown that the proposed methods were suitable for applications to an unbalance distribution system.

Epithelial to mesenchymal transition (EMT), the transdifferentation of an epithelial cell into a mesenchymal fibroblast, is a cellular process necessary for embryonic development and wound healing. However, uncontrolled EMT can result in accumulation of myofibroblasts and excessive deposition of ECM, contributing to the pathological progression of fibrotic diseases such as pulmonary fibrosis. The ability to control EMT is important for development of novel therapeutics for fibrotic pathologies and for designing novel biomaterials for tissue engineering applications seeking to promote EMT for development of complex tissues. EMT is a highly orchestrated process involving the integration of biochemical signals from specific integrin-mediated interactions with extracellular matrix (ECM) proteins and soluble growth factors such as TGFβ. TGFβ, a potent inducer of EMT, is activated via cell contraction-mediated mechanical release of the growth factor from a macromolecular latency complex. Thus TGFβ activity and subsequent EMT may be influenced by the biochemical and biophysical state of the surrounding ECM. Based on these knowns, it was hypothesized that both changes in integrin engagement and increases in substrate rigidity would modulate EMT due to changes in epithelial cell contraction and TGFβ activation. Here we show that integrin-specific interactions with fibronectin (Fn) fragments displaying both the RGD and PHSRN binding sites facilitate cell binding through α5β1 and α3β1 integrins, and lead to maintenance of epithelial phenotype, while Fn fragments displaying only the RGD site facilitate cell binding through αv integrins and lead to EMT. An in depth investigation into α3β1 binding to Fn fragments indicates that binding is dependent on both the presence and orientation of the PHSRN site. Studies investigating the contribution of ECM stiffening on EMT responses show that increasingly rigid Fn substrates are sufficient to induce spontaneous EMT. Analysis of TGFβ-responsive genes implicate TGFβ-expression, activation or signaling as a mechanism for the observed EMT responses. Together these results suggest that the ECM micromechanical environment is a significant contributor to the onset of EMT responses and provide insights into the design of biomaterial-based microenvironments for the control of epithelial cell phenotype.

<p>Husqvarna is a Swedish company producing products for forestry, park and gardens. Due to harder competition they wish to increase efficacy in production. This can be achieved by shorter lead-times in the complex process of making casting molds. Activities within this process have certain relations and dependencies between each other that can be analyzed by using a Dependence Structure Matrix. The Dependence Structure Matrix is a tool that can improve efficiency by rearranging activities according to how they are dependent of each other.</p><p>The purpose is to make a Dependence Structure Matrix of activities that Husqvarna can use to analyze dependencies within the process of cast molding. The DSM Matrix will propose restructured activities of the process which can be evaluated to determine if greater efficacy can be reached.</p><p>To determine the activities within the process of making cast molds a workshop at Husqvarna for the people involved was conducted. A matrix has been constructed based on the information of activities and their dependencies. This information has then been analyzed by the software Multiplan.</p><p>The process of making casting molds could be analyzed by the DSM/DMM approach. A new order of how to carry out activities is the outcome of the analysis. The result can be analyzed by Husqvarna in order to determine if greater efficacy can be reached.</p>

<p>Navigation with unmanned aerial vehicles (UAVs) requires good knowledge of the current position and other states. A UAV navigation system often uses GPS and inertial sensors in a state estimation solution. If the GPS signal is lost or corrupted state estimation must still be possible and this is where simultaneous localization and mapping (SLAM) provides a solution. SLAM considers the problem of incrementally building a consistent map of a previously unknown environment and simultaneously localize itself within this map, thus a solution does not require position from the GPS receiver.</p><p>This thesis presents a visual feature based SLAM solution using a low resolution video camera, a low-cost inertial measurement unit (IMU) and a barometric pressure sensor. State estimation in made with a extended information filter (EIF) where sparseness in the information matrix is enforced with an approximation.</p><p>An implementation is evaluated on real flight data and compared to a EKF-SLAM solution. Results show that both solutions provide similar estimates but the EIF is over-confident. The sparse structure is exploited, possibly not fully, making the solution nearly linear in time and storage requirements are linear in the number of features which enables evaluation for a longer period of time.</p>

Die Mikrosystemtechnik entwickelt sehr kleine Sensoren und Aktuatoren, deren Größe wie der Name schon sagt in Mikrometern gemessen werden kann. Die meist aus Silizium gefertigten Bauteile werden durch Dotierung elektrisch leitfähig. Die so erzeugten Elektroden können nun mittels elektrostatischer Kräfte bewegt werden. Für die numerische Simulation dieser System ist die Kenntnis der Kapazität dieser Elektrodenanordnungen notwendig. In den folgenden Kapiteln wird eine Möglichkeit der Bestimmung der Kapazitätsmatrix für solche Elektrodenanordnungen aufgezeigt. Dazu werden wir zunächst im Kapitel 2 einige Begriffe der Elektrostatik definieren und ihre Zusammenhänge erläutern. Danach werden wir im Kapitel 3 eine Randintegralgleichung herleiten mit deren Hilfe eine Bestimmung der Kapazitätsmatrix möglich ist. Um diese Gleichung zu Lösen werden wir sie im Kapitel 4 diskretisieren. Diese Diskretisierung wird zu einem vollbesetzten Gleichungssystem führen. Das Lösen dieses Gleichungssystems ist relativ teuer, daher wird in den Kapiteln 5 und 6 eine Approximation erläutert, die den Speicherbedarf und Rechenaufwand reduziert. Im Kapitel 7 werden wir die Fehler, welche durch die Diskretisierung und die Approximation entstehen, näher untersuchen. Abschließend werden wir im Kapitel 8 die Kapazitätsmatrizen einiger Beispiele berechnen und mit früheren Berechnungsergebnissen vergleichen.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 73-82).

Dissertation (Ph.D.)--University of South Florida, 2008. / Includes vita. Includes bibliographical references. Also available online.

Complex products are comprised of a large number of tightly integrated components, assemblies and systems resulting in extensive logical and physical interdependences between the constituent parts. Thus a change to one item of a system is highly likely to lead to a change to another item, which in turn can propagate further. The aim of this research therefore is to investigate dependency models that can be used to identify the impact and trace thepropagation of changes in different information domains, such as requirements, physical product architecture or organisation. Cont/d.

The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and LU decomposition can be implemented efficiently using the <i>H</i>-matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of <i>H</i>-matrices. In the past, two different approaches for this task have been suggested. We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an <i>H</i>-matrix. Like other <i>H</i>-arithmetic operations the <i>H</i>QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach.