Techn. University, Diss., 2004--München.

Die Arbeit beschäftigt sich mit der Untersuchung der Beanspruchungen von Staurollenketten. Zunächst wurde in den Grundlagen der Aufbau von unterschiedlichen Staurollenkettenarten dargestellt, die Eigenschaften miteinander verglichen und kategorisiert. Aufbauend auf dem anschließend geschaffenen Verständnis der wirkenden Reibpaarungen bzw. -arten wurden FEM-Analysen durchgeführt, um dadurch auftretende Spannungen zu detektieren und das thermische Verhalten der unterschiedlichen Werkstoffpaarungen zu ermitteln. Innerhalb der praktischen Versuche der Arbeit kam es zur Ermittlung der Bruch- und Dauerfestigkeiten nach ISO15654 [DIN04]. Zur Untersuchung der Eigenschaften der Ketten unter praxisnahen Randbedingungen wurde ein Versuchsstand konzipiert, welcher die Ermittlung von Kennwerten zwei unterschiedlicher Kettengrößen unter härtesten Bedingungen ermöglicht. Durch diesen Versuchsstand wurden die Staukraft, die Kettenzugkraft durch das Drehmoment am Antrieb, die Kettengeschwindigkeit, die Kettenlängung und das Temperaturverhalten dauerhaft überwacht. Im letzten Kapitel der Arbeit wurde eine Überwachungsstation für unterschiedliche Baugrößen von Staurollenketten entwickelt und die Funktionsweise durch Versuche nachgewiesen. / This dissertation is dealing with the investigation of the load behaviour of accumulation roller chains. Initially, the structures of different types of accumulation roller chains are described, properties are compared and categorised. Based on the created understanding of acting tribological pairing and friction mechanisms, FEM analysis have been performed to evaluate occurring stresses and determine the thermal behaviour of the various material combinations. Within the testing procedures, breaking strength and fatigue strength have been investigated in accordance with DIN ISO 15654 [cf. DIN04]. A test bench has been developed for practically relevant testing of the chains, where determination of characteristic values can be done under hard testing conditions for two different chain types. The test bench ensures measurement and survey of accumulation forces, tensile chain forces (by torque moment at drive), chain speed, chain elongation and chain temperature during whole testing time. The last chapter of the dissertation deals with the development of a 'control and monitoring unit' for accumulation roller chains with various dimensions including proof of function by trials.

No description available.

No description available.

Objective: The aim of this study was to develop an immunomagnetic/real-time reverse transcriptase polymerase chain reaction (RT-PCR) assay and assess its clinical value for the molecular detection of circulating tumor cells (CTCs) in peripheral blood of pancreatic cancer patients. Methods: The presence of CTCs was evaluated in 34 pancreatic cancer patients before systemic therapy and in 40 healthy controls, through immunomagnetic enrichment, using the antibodies BM7 and VU1D9 [targeting mucin 1 and epithelial cell adhesion molecule (EpCAM), respectively], followed by real-time RT-PCR analysis of the genes KRT19, MUC1, EPCAM, CEACAM5 and BIRC5. Results: The developed assay showed high specificity, as none of the healthy controls were found to be positive for the multimarker gene panel. CTCs were detected in 47.1% of the pancreatic cancer patients before the beginning of systemic treatment. Shorter median progression-free survival (PFS) was observed for patients who had at least one detectable tumor-associated transcript, compared with patients who were CTC negative. Median PFS time was 66.0 days [95% confidence interval (CI) 44.8–87.2] for patients with baseline CTC positivity and 138.0 days (95% CI 124.1–151.9) for CTC-negative patients (p = 0.01, log-rank test). Conclusion: Our results suggest that in addition to the current prognostic methods, CTC analysis represents a potential complementary tool for prediction of outcome in pancreatic cancer patients. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

Hierarchical Markovian Models (HMMs) are composed of multiple low level models (LLMs) and high level model (HLM) that defines the interaction among LLMs. The essence of the HMM approach is to model the system at hand in the form of interacting components so that its (larger) underlying continous-time Markov chain (CTMC) is not generated but implicitly represented as a sum of Kronecker products of (smaller) component matrices. The Kronecker structure of an HMM induces nested block partitionings in its underlying CTMC. These partitionings may be used in block versions of classical iterative methods based on splittings, such as block SOR (BSOR), to solve the underlying CTMC for its stationary vector. Therein the problem becomes that of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of a particular partitioning. This paper shows that in each HLM state there may be diagonal blocks with identical off-diagonal parts and diagonals differing from each other by a multiple of the identity matrix. Such diagonal blocks are named candidate blocks. The paper explains how candidate blocks can be detected and how the can mutually benefit from a single real Schur factorization. It gives sufficient conditions for the existence of diagonal blocks with real eigenvalues and shows how these conditions can be checked using component matrices. It describes how the sparse real Schur factors of candidate blocks satisfying these conditions can be constructed from component matrices and their real Schur factors. It also demonstrates how fill in- of LU factorized (non-candidate) diagonal blocks can be reduced by using the column approximate minimum degree algorithm (COLAMD). Then it presents a three-level BSOR solver in which the diagonal blocks at the first level are solved using block Gauss-Seidel (BGS) at the second and the methods of real Schur and LU factorizations at the third level. Finally, on a set of numerical experiments it shows how these ideas can be used to reduce the storage required by the factors of the diagonal blocks at the third level and to improve the solution time compared to an all LU factorization implementation of the three-level BSOR solver.

Kronecker structured representations are used to cope with the state space explosion problem in Markovian modeling and analysis. Currently an open research problem is that of devising strong preconditioners to be used with projection methods for the computation of the stationary vector of Markov chains (MCs) underlying such representations. This paper proposes a block SOR (BSOR) preconditioner for hierarchical Markovian Models (HMMs) that are composed of multiple low level models and a high level model that defines the interaction among low level models. The Kronecker structure of an HMM yields nested block partitionings in its underlying continuous-time MC which may be used in the BSOR preconditioner. The computation of the BSOR preconditioned residual in each iteration of a preconditioned projection method becoms the problem of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of the chosen partitioning. The proposed BSOR preconditioner solvers these systems using sparse LU or real Schur factors of diagonal blocks. The fill-in of sparse LU factorized diagonal blocks is reduced using the column approximate minimum degree algorithm (COLAMD). A set of numerical experiments are presented to show the merits of the proposed BSOR preconditioner.

A Markov chain is introduced to the major steps of the process of learning a subject matter by a group of students in the classroom, in order to obtain a mathematical representation of the above process. A classroom experiment for learning mathematics is also presented illustrating the applicability of our results in practice.

No description available.

Cancer as a disease causes about 8.8 million deaths worldwide per year, a number that will largely increase in the next decades. Although the cellular processes involved in tumor emergence are more and more understood, the implications of specific changes at the cellular scale on tumor emergence at the tissue scale remain elusive. Main reasons for this lack of understanding are that the cellular processes are often hardly observable especially in the early phase of tumor development and that the interplay between cellular and tissue scale is difficult to deduce. Cell-based mathematical models provide a valuable tool to investigate in which way observable phenomena on the tissue scale develop by cellular processes. The implications of these models can elucidate underlying mechanisms and generate quantitative predictions that can be experimentally validated. In this thesis, we infer the role of genetic and phenotypic cell changes on tumor development with the help of cell-based Markov chain models which are calibrated by tissue-scale data. In the first part, we utilize data on the diagnosed fractions of benign and malignant tumor subtypes to unravel the consequences of genetic cell changes on tumor development. We introduce extensions of Moran models to investigate two specific biological questions. First, we evaluate the tumor regression behavior of pilocytic astrocytoma which represents the most common brain tumor in children and young adults. We formulate a Moran model with two absorbing states representing different subtypes of this tumor, derive the absorption probabilities in these states and calculate the tumor regression probability within the model. This analysis allows to predict the chance for tumor regression in dependency of the remaining tumor size and implies a different clinical resection strategy for pilocytic astrocytoma compared to other brain tumors. Second, we shed light on the hardly observable early cellular dynamics of tumor development and its consequences on the emergence of different tumor subtypes on the tissue scale. For this purpose, we utilize spatial and non-spatial Moran models with two absorbing states which describe both benign and malignant tumor subtypes and estimate lower and upper bounds for the range of cellular competition in different tissues. Our results suggest the existence of small and tissue-specific tumor-originating niches in which the fate of tumor development is decided long before a tumor manifests. These findings might help to identify the tumor-originating cell types for different cancer types. From a theoretical point of view, the novel analytical results regarding the absorption behavior of our extended Moran models contribute to a better understanding of this model class and have several applications also beyond the scope of this thesis. The second part is devoted to the investigation of the role of phenotypic plasticity of cancer cells in tumor development. In order to understand how phenotypic heterogeneity in tumors arises we describe cell state changes by a Markov chain model. This model allows to quantify the cell state transitions leading to the observed heterogeneity from experimental tissue-scale data on the evolution of cell state proportions. In order to bridge the gap between mathematical modeling and the analysis of such data, we developed an R package called CellTrans which is freely available. This package automatizes the whole process of mathematical modeling and can be utilized to (i) infer the transition probabilities between different cell states, (ii) predict cell line compositions at a certain time, (iii) predict equilibrium cell state compositions and (iv) estimate the time needed to reach this equilibrium. We utilize publicly available data on the evolution of cell compositions to demonstrate the applicability of CellTrans. Moreover, we apply CellTrans to investigate the observed cellular phenotypic heterogeneity in glioblastoma. For this purpose, we use data on the evolution of glioblastoma cell line compositions to infer to which extent the heterogeneity in these tumors can be explained by hierarchical phenotypic transitions. We also demonstrate in which way our newly developed R package can be utilized to analyze the influence of different micro-environmental conditions on cell state proportions. Summarized, this thesis contributes to gain a better understanding of the consequences of both genetic and phenotypic cell changes on tumor development with the help of Markov chain models which are motivated by the specific underlying biological questions. Moreover, the analysis of the novel Moran models provides new theoretical results, in particular regarding the absorption behavior of the underlying stochastic processes.