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Description: All-optical telecommunication networks allow for switching connections by lightpaths which can pass several network links without any opto-electronic conversion. Upon arrival of a connection request, it must be decided online, i.e., without knowledge of future requests, if it is accepted and in that case on which lightpaths the connection is routed. This online problem with the goal of maximizing the total profit gained by accepted requests is called Dynamic Singleclass Call Admission Problem (DSCA). We present existing and new algorithms for the DSCA as well as their theoretical and practical evaluation.

Description: The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.

Description: In this paper, a new shared protection mechanism for meshed optical networks is presented. Significant network design cost reductions can be achieved in comparison to the well-known 1+1 protection scheme. Demand-wise Shared Protection (DSP) bases on the diversification of demand routings and exploits the network connectivity to restrict the number of backup lightpaths needed to provide the desired level of prorection. Computational experiments approve the benefits of the concept DSP for cost efficient optical network designs.

Description: The correlation of the inner architecture of bone and its functional loading was already stated by Wolff in 1892. Our objective is to demonstrate this interdependence in the case of the human mandible. For this purpose, stress/strain profiles occuring at a human lateral bite were simulated. Additionally, by a combination of computer graphics modules, a three--dimensional volumetric visualization of bone mineral density could be given. Qualitative correspondences between the density profile of the jaw and the simulated stress/strain profiles could be pointed out. In the long run, this might enable the use of the simulation for diagnosis and prognosis. The solution of the underlying partial differential equations describing linear elastic material behaviour was provided by an adaptive finite element method. Estimates of the discretization errors, local grid refinement, and multilevel techniques guaranteed the reliability and efficiency of the method.

Description: UMTS is a 3rd generation mobile telecommunication system which enables multi-service and multi-bit rate communication going beyond the possibilities of previous systems. The simulator MoDySim models UMTS in great detail. Characteristics of UMTS such as soft hand-over and the interdependency of load and capacity among neighbouring cells are challenges for the parallelisation of such a system. In this paper we explain how the software was parallelised and present performance results of a UMTS simulation for the city of Berlin.

Description: We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose the Hybrid Monte Carlo algorithm was used and an explicit symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the Wilson fermion action. The order parameter $\langle\bar{\psi}i\gamma_{5}\tau^{3}\psi\rangle$ was studied at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$. Our largest lattices can be considered as infintely large allowing to extrapolate to $h=0$. The existence of a parity-flavor-breaking phase can be confirmed at $\beta=4.0$ and $\beta=4.3$ while we find no sign of parity-flavor-breaking at $\beta=4.6$ and $\beta=5.0$.

Description: In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplicial struture this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplicial structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this kind of approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs.

Description: This diploma thesis deals with the restoration problem in telecommunication networks. The goal is to find a cost minimal capacity capacity assignment on the edges and nodes of a network such that given demands can be satisfied even in case of the failure of an edge or node in the network. Moreover, restrictions on the routing paths (like length restrictions) and hardware constraints have to be satisfied. A Mixed Integer Programming model is presented which takes into account restoration requirements as well as hardware constraints and which abstracts from a particular restoration protocol and failure situation. This abstraction provides new insight into the structure of the network restoration problem and shows that from a mathematical point of view, the commonly used restoration techniques Link Restoration, Path Restoration and Reservation are not as different as they seem to be from a practical point of view. In addition, our model allows (but is not limited to) optimizing working capacity, intended for normal use, and spare capacity, intended for rerouting purposes in case of a failure, in one step. Furthermore, our formulation of capacity cost allows taking into account the effects of discrete, non-linear cost structures which are common in practice. Up to our knowledge, no publication in the existing literature covers all these aspects, let alone in one model, although they are of major practical interest. The model has been implemented in a Branch and Cut framework. The theoretical background of the algorithmic procedure is presented in detail, including computational complexity investigations on the pricing problem. The abstraction from a particular restoration protocol turns out to be useful both from a theoretical and computational point of view. In fact, our investigations suggest a distinction into Local Restoration and Global Restoration rather than into Link Restoration,Path Restoration, Reservation and mixtures of these concepts. In addition to the theoretical aspects of the algorithmic procedure, some implementational details are briefly discussed. Our implementation has been tested on 14 real world instances, which is described in detail. One part of the computational results consists of a comparison of optimal network cost values using diffeent restoration mechanisms, applied to securing either all single node failures, all single edge failures or both. In addition, the effects of a discrete cost structure are investigated, which has rarely been considered yet in literature. Furthermore, the cost ifference between joint and successive working and spare capacity optimization is investigated. In the second part of the computational results, several heuristics for the network restoration problem are compared with respect to both solution quality and time. This diploma thesis deals with the restoration problem in telecommunication networks. The goal is to find a cost minimal capacity capacity assignment on the edges and nodes of a network such that given demands can be satisfied even in case of the failure of an edge or node in the network. Moreover, restrictions on the routing paths (like length restrictions) and hardware constraints have to be satisfied. A Mixed Integer Programming model is presented which takes into account restoration requirements as well as hardware constraints and which abstracts from a particular restoration protocol and failure situation. This abstraction provides new insight into the structure of the network restoration problem and shows that from a mathematical point of view, the commonly used restoration techniques Link Restoration, Path Restoration and Reservation are not as different as they seem to be from a practical point of view. In addition, our model allows (but is not limited to) optimizing working capacity, intended for normal use, and spare capacity, intended for rerouting purposes in case of a failure, in one step. Furthermore, our formulation of capacity cost allows taking into account the effects of discrete, non-linear cost structures which are common in practice. Up to our knowledge, no publication in the existing literature covers all these aspects, let alone in one model, although they are of major practical interest. The model has been implemented in a Branch and Cut framework. The theoretical background of the algorithmic procedure is presented in detail, including computational complexity investigations on the pricing problem. The abstraction from a particular restoration protocol turns out to be useful both from a theoretical and computational point of view. In fact, our investigations suggest a distinction into Local Restoration and Global Restoration rather than into Link Restoration, Path Restoration, Reservation and mixtures of these concepts. In addition to the theoretical aspects of the algorithmic procedure, some implementational details are briefly discussed. Our implementation has been tested on 14 real world instances, which is described in detail. One part of the computational results consists of a comparison of optimal network cost values using different restoration mechanisms, applied to securing either all single node failures, all single edge failures or both. In addition, the effects of a discrete cost structure are investigated, which has rarely been considered yet in literature. Furthermore, the cost difference between joint and successive working and spare capacity optimization is investigated. In the second part of the computational results, several heuristics for the network restoration problem are compared with respect to both solution quality and time.

Description: The Web of the future will provide a huge amount of information. We need better ways for dealing with and managing the information. A qualified semantic annotation of the information plays a key role for the Web of the future. This article gives an overview about the efforts of the mathematical community to build up a distributed and open information and communication system for mathematics: the Math-Net. The Math-Net Initiative has developed metadata schemas for some classes of Web resources which are relevant in mathematics. Math-Net Services process this information and enable the user to efficiently search and access the information.

Description: In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.