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In this paper we develop a data-driven mixture of vector autoregressive models with exogenous components. The process is assumed to change regimes according to an underlying Markov process. In contrast to the hidden Markov setup, we allow the transition probabilities of the underlying Markov process to depend on past time series values and exogenous variables. Such processes have potential applications to modeling brain signals. For example, brain activity at time t (measured by electroencephalograms) will can be modeled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). Furthermore, we establish stationarity, geometric ergodicity and the existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as deriving the asymptotic behavior of various statistics and model parameter estimators.
We propose a constraint-based approach for the two-dimensional rectangular packing problem with orthogonal orientations. This problem is to arrange a set of rectangles that can be rotated by 90 degrees into a rectangle of minimal size such that no two rectangles overlap. It arises in the placement of electronic devices during the layout of 2.5D System-in-Package integrated electronic systems. Moffitt et al. [8] solve the packing without orientations with a branch and bound approach and use constraint propagation. We generalize their propagation techniques to allow orientations. Our approach is compared to a mixed-integer program and we provide results that outperform it.
Abstract. An efficient approach to the numerical upscaling of thermal conductivities of fibrous media, e.g. insulation materials, is considered. First, standard cell problems for a second order elliptic equation are formulated for a proper piece of random fibrous structure, following homogenization theory. Next, a graph formed by the fibers is considered, and a second order elliptic equation with suitable boundary conditions is solved on this graph only. Replacing the boundary value problem for the full cell with an auxiliary problem with special boundary conditions on a connected subdomain of highly conductive material is justified in a previous work of the authors. A discretization on the graph is presented here, and error estimates are provided. The efficient implementation of the algorithm is discussed. A number of numerical experiments is presented in order to illustrate the performance of the proposed method.
JSR 170 spezifiziert die Java Content Repository (JCR) Schnittstelle. Diese Schnittstelle wird als Standard im Bereich Web-Anwendungen und Content Management akzeptiert. Sie gliedert sich in Level 1 (lesender Zugriff) and Level 2 (Lese- und Schreibzugriffe) und beschreibt darüber hinaus vier weitere optionale Funktionen. Das in JSR 170 beschriebene hierarchische Datenmodell weist starke Analogie zu XML auf. Jedoch verwenden die meisten JCR-Implementierungen relationale Datenbanken. Durch native XML Datenbanken, wie XTC, können XML-Daten effizient verwaltet werden. Diese Arbeit beschreibt das Design und die Implementierung eines Level 2 JCRs, welches alle Anforderungen an die Persistenz mit Hilfe von DOM und XQuery Operationen auf XML-Dokumenten in XTC erfüllt. Die optionalen FuJSR 170 spezifiziert die Java Content Repository (JCR) Schnittstelle. Diese Schnittstelle wird als Standard im Bereich Web-Anwendungen und Content Management akzeptiert. Sie gliedert sich in Level 1 (lesender Zugriff) und Level 2 (Lese- und Schreibzugriffe) und beschreibt darüber hinaus vier weitere optionale Funktionen. Das in JSR 170 beschriebene hierarchische Datenmodell weist starke Analogie zu XML auf. Jedoch verwenden die meisten JCR-Implementierungen relationale Datenbanken. Durch native XML Datenbanken, wie XTC, können XML-Daten effizient verwaltet werden. Diese Arbeit beschreibt das Design und die Implementierung eines Level 2 JCRs, welches alle Anforderungen an die Persistenz mit Hilfe von DOM und XQuery Operationen auf XML-Dokumenten in XTC erfüllt. Die optionalen Funktionen “Versionierung” und “Transaktionen” werden ebenfalls unterstützt. Um die Implementierung zu testen werden zwei Demo-Anwendungen (Blog & Wiki) entwickelt und Vergleichstests gegen die Referenzimplementierung angestellt.
A Lattice Boltzmann Method for immiscible multiphase flow simulations using the Level Set Method
(2008)
We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young-Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.
Finding a delivery plan for cancer radiation treatment using multileaf collimators operating in ''step-and-shoot mode'' can be formulated mathematically as a problem of decomposing an integer matrix into a weighted sum of binary matrices having the consecutive-ones property - and sometimes other properties related to the collimator technology. The efficiency of the delivery plan is measured by both the sum of weights in the decomposition, known as the total beam-on time, and the number of different binary matrices appearing in it, referred to as the cardinality, the latter being closely related to the set-up time of the treatment. In practice, the total beam-on time is usually restricted to its minimum possible value, (which is easy to find), and a decomposition that minimises cardinality (subject to this restriction) is sought.
The problem discussed in this paper is motivated by the new recycling directiveWEEE of the EC. The core of this law is, that each company which sells electrical or electronic equipment in a European country has the obligation to recollect and recycle an amount of returned items which is proportional to its market share. To assign collection stations to companies, in Germany for one product type a territory design approach is planned. However, in contrast to classical territory design, the territories should be geographically as dispersed as possible to avoid that a company, resp. its logistics provider responsible for the recollection, gains a monopoly in some region. First, we identify an appropriate measure for the dispersion of a territory. Afterwards, we present a first mathematical programming model for this new problem as well as a solution method based on the GRASP methodology. Extensive computational results illustrate the suitability of the model and assess the effectiveness of the heuristic.
In this thesis, we investigate a statistical model for precipitation time series recorded at a single site. The sequence of observations consists of rainfall amounts aggregated over time periods of fixed duration. As the properties of this sequence depend strongly on the length of the observation intervals, we follow the approach of Rodriguez-Iturbe et. al. [1] and use an underlying model for rainfall intensity in continuous time. In this idealized representation, rainfall occurs in clusters of rectangular cells, and each observations is treated as the sum of cell contributions during a given time period. Unlike the previous work, we use a multivariate lognormal distribution for the temporal structure of the cells and clusters. After formulating the model, we develop a Markov-Chain Monte-Carlo algorithm for fitting it to a given data set. A particular problem we have to deal with is the need to estimate the unobserved intensity process alongside the parameter of interest. The performance of the algorithm is tested on artificial data sets generated from the model. [1] I. Rodriguez-Iturbe, D. R. Cox, and Valerie Isham. Some models for rainfall based on stochastic point processes. Proc. R. Soc. Lond. A, 410:269-288, 1987.
The main goal of this work is to model size effects, as they occur in materials with an intrinsic microstructure at the consideration of specimens that are not by orders larger than this microstructure. The micromorphic continuum theory as a generalized continuum theory is well suited to account for the occuring size effects. Thereby additional degrees of freedoms capture the independent deformations of these microstructures, while they provide additional balance equation. In this thesis, the deformational and configurational mechanics of the micromorphic continuum is exploited in a finite-deformation setting. A constitutive and numerical framework is developed, in which also the material-force method is advanced. Furthermore the multiscale modelling of thin material layers with a heterogeneous substructure is of interest. To this end, a computational homogenization framework is developed, which allows to obtain the constitutive relation between traction and separation based on the properties of the underlying micromorphic mesostructure numerically in a nested solution scheme. Within the context of micromorphic continuum mechanics, concepts of both gradient and micromorphic plasticity are developed by systematically varying key ingredients of the respective formulations.
Computer-based simulation and visualization of acoustics of a virtual scene can aid during the design process of concert halls, lecture rooms, theaters, or living rooms. Because, not only the visual aspect of the room is important, but also its acoustics. In factory floors noise reduction is important since noise is hazardous to health. Despite the obvious dissimilarity between our aural and visual senses, many techniques required for the visualization of photo-realistic images and for the auralization of acoustic environments are quite similar. Both applications can be served by geometric methods such as particle- and ray tracing if we neglect a number of less important effects. By means of the simulation of room acoustics we want to predict the acoustic properties of a virtual model. For auralization, a pulse response filter needs to be assembled for each pair of source and listener positions. The convolution of this filter with an anechoic source signal provides the signal received at the listener position. Hence, the pulse response filter must contain all reverberations (echos) of a unit pulse, including their frequency decompositions due to absorption at different surface materials. For the room acoustic simulation a method named phonon tracing, since it is based on particles, is developed. The approach computes the energy or pressure decomposition for each particle (phonon) sent out from a sound source and uses this in a second pass (phonon collection) to construct the response filters for different listeners. This step can be performed in different precision levels. During the tracing step particle paths and additional information are stored in a so called phonon map. Using this map several sound visualization approaches were developed. From the visualization, the effect of different materials on the spectral energy / pressure distribution can be observed. The first few reflections already show whether certain frequency bands are rapidly absorbed. The absorbing materials can be identified and replaced in the virtual model, improving the overall acoustic quality of the simulated room. Furthermore an insight into the pressure / energy received at the listener position is possible. The phonon tracing algorithm as well as several sound visualization approaches are integrated into a common system utilizing Virtual Reality technologies in order to facilitate the immersion into the virtual scene. The system is a prototype developed within a project at the University of Kaiserslautern and is still a subject of further improvements. It consists of a stereoscopic back-projection system for visual rendering as well as professional audio equipment for auralization purposes.