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Territory design and districting may be viewed as the problem of grouping small geographic areas into larger geographic clusters called territories in such a way that the latter are acceptable according to relevant planning criteria. The availability of GIS on computers and the growing interest in Geo-Marketing leads to an increasing importance of this area. Despite the wide range of applications for territory design problems, when taking a closer look at the models proposed in the literature, a lot of similarities can be noticed. Indeed, the models are many times very similar and can often be, more or less directly, carried over to other applications. Therefore, our aim is to provide a generic application-independent model and present efficient solution techniques. We introduce a basic model that covers aspects common to most applications. Moreover, we present a method for solving the general model which is based on ideas from the field of computational geometry. Theoretical as well as computational results underlining the efficiency of the new approach will be given. Finally, we show how to extend the model and solution algorithm to make it applicable for a broader range of applications and how to integrate the presented techniques into a GIS.
In the literature, there are at least two equivalent two-factor Gaussian models for the instantaneous short rate. These are the original two-factor Hull White model (see [3]) and the G2++ one by Brigo and Mercurio (see [1]). Both these models first specify a time homogeneous two-factor short rate dynamics and then by adding a deterministic shift function '(·) fit exactly the initial term structure of interest rates. However, the obtained results are rather clumsy and not intuitive which means that a special care has to be taken for their correct numerical implementation.
In this paper, we study the inverse maximum flow problem under \(\ell_\infty\)-norm and show that this problem can be solved by finding a maximum capacity path on a modified graph. Moreover, we consider an extension of the problem where we minimize the number of perturbations among all the optimal solutions of Chebyshev norm. This bicriteria version of the inverse maximum flow problem can also be solved in strongly polynomial time by finding a minimum \(s - t\) cut on the modified graph with a new capacity function.
We present a parsimonious multi-asset Heston model. All single-asset submodels follow the well-known Heston dynamics and their parameters are typically calibrated on implied market volatilities. We focus on the calibration of the correlation structure between the single-asset marginals in the absence of sucient liquid cross-asset option price data. The presented model is parsimonious in the sense that d(d􀀀1)=2 asset-asset cross-correlations are required for a d-asset Heston model. In order to calibrate the model, we present two general setups corresponding to relevant practical situations: (1) when the empirical cross-asset correlations in the risk neutral world are given by the user and we need to calibrate the correlations between the driving Brownian motions or (2) when they have to be estimated from the historical time series. The theoretical background, including the ergodicity of the multidimensional CIR process, for the proposed estimators is also studied.
This work is concerned with dynamic flow problems, especially maximal dynamic flows and earliest arrival flows - also called universally maximal flows. First of all, a survey of known results about existence, computation and approximation of earliest arrival flows is given. For the special case of series-parallel graphs a polynomial algorithm for computing maximal dynamic flows is presented and this maximal dynamic flow is proven to be an earliest arrival flow.
In dieser Arbeit wurden für die Moleküle B3, B3- und C3+ mit dem MR-CI-Verfahren hochgenaue Potentialfächen für ein oder mehrere elektronische Zustände berechnet. Alle drei Moleküle besitzen elektronisch entartete Jahn-Teller-Zustände. Im Gegesatz zu den früher untersuchten Alkalitrimeren liegt hier die konische Durchschneidung so tief, dass sie bei der Schwingungsanalyse berücksichtigt werden muss und daher eine diabatische Behandlung erfordlich ist. Für den X<-1E'-Übergang im B3 konnte die Übereinstimmung des berechneten Spektrum mit dem gemessenen durch den Einsatz des größeren Basissatzes VQZ, im Vergleich zu den bereits veröffentlichten Ergebnissen, nochmals deutlich verbessert werden. Für den berechneten 00-Übergang ist im gemessen Spektrum kein Übergang zu beobachten. Neben der guten Übereinstimmung der anderen Peaks wird diese These auch die T00 Energie gestützt. Die einfache Progression des experimentellen X<-2E'-Übergangs im B3 konnte ebenfalls in gute Übereinstimmung berechnet werden. Die einfache und kurze Progression ergibt sich aus der Tatsache, dass praktisch keine Jahn-Teller-Verzerrung vorhanden ist, und beide Teilflächen fast deckungsgleich sind. Für den X<-1E'-Übergang des B3- wurde ebenfalls ein Spektrum simuliert, allerdings findet sich keine Übereinstimmung zu den gemessenen Übergängen. Da die beobachtete Elektronenablöseenergie nur unwesentlich oberhalb der Elektronenanregungsenergie liegt und im Hinblick auf die starken X<-2E'-Absorptionen des B3 in der gleichen Messung bleibt offen, welche Strukturn im Experiment zu sehen sind. Zum C3+ wurde eine Schwingungsanalyse für den E'-Grundzustand durchgeführt. Experimentelle Vergleichswerte fehlen in diesem Fall. Allerdings konnte die bereits seit mehr als einem Jahrzehnt diskutierte Höhe der Isomerisierungsenergie zwischen gewinkelter und linearer Geometrie sehr genau, auf nun 6.8 +- 0.5 kcal/mol festgelegt werden. Bei vibronischer Betrachtung unter Einbeziehung der Nullpunktsenergien reduziert sich diese auf bzw. 4.8 kcal/mol. Ausserdem wurde die Existenz eines linearen Minimums bestätigt. C3+ liefert auch ein sehr schönes Beispiel für die Verschränkung verschiedener lokaler und globaler Schwingungszustände, was zu einer irregulären Abfolge von Zuständen führt. Für die Reaktivität des C3+ wurde beobachtet, dass es unterhalb von 50 K die höchste Reaktivität besitzt und darüber deutlich abnimmt. Auf dieses Verhalten liefert die Schwingungsanalyse keine Antwort, da bis selbst zur Raumtemperatur keine thermische Schwingungsanregung statt finden kann.
Adaptive Extraction and Representation of Geometric Structures from Unorganized 3D Point Sets
(2009)
The primary emphasis of this thesis concerns the extraction and representation of intrinsic properties of three-dimensional (3D) unorganized point clouds. The points establishing a point cloud as it mainly emerges from LiDaR (Light Detection and Ranging) scan devices or by reconstruction from two-dimensional (2D) image series represent discrete samples of real world objects. Depending on the type of scenery the data is generated from the resulting point cloud may exhibit a variety of different structures. Especially, in the case of environmental LiDaR scans the complexity of the corresponding point clouds is relatively high. Hence, finding new techniques allowing the efficient extraction and representation of the underlying structural entities becomes an important research issue of recent interest. This thesis introduces new methods regarding the extraction and visualization of structural features like surfaces and curves (e.g. ridge-lines, creases) from 3D (environmental) point clouds. One main part concerns the extraction of curve-like features from environmental point data sets. It provides a new method supporting a stable feature extraction by incorporating a probability-based point classification scheme that characterizes individual points regarding their affiliation to surface-, curve- and volume-like structures. Another part is concerned with the surface reconstruction from (environmental) point clouds exhibiting objects that are more or less complex. A new method providing multi-resolutional surface representations from regular point clouds is discussed. Following the applied principles of this approach a volumetric surface reconstruction method based on the proposed classification scheme is introduced. It allows the reconstruction of surfaces from highly unstructured and noisy point data sets. Furthermore, contributions in the field of reconstructing 3D point clouds from 2D image series are provided. In addition, a discussion concerning the most important properties of (environmental) point clouds with respect to feature extraction is presented.
Radiotherapy is one of the major forms in cancer treatment. The patient is irradiated with high-energetic photons or charged particles with the primary goal of delivering sufficiently high doses to the tumor tissue while simultaneously sparing the surrounding healthy tissue. The inverse search for the treatment plan giving the desired dose distribution is done by means of numerical optimization [11, Chapters 3-5]. For this purpose, the aspects of dose quality in the tissue are modeled as criterion functions, whose mathematical properties also affect the type of the corresponding optimization problem. Clinical practice makes frequent use of criteria that incorporate volumetric and spatial information about the shape of the dose distribution. The resulting optimization problems are of global type by empirical knowledge and typically computed with generic global solver concepts, see for example [16]. The development of good global solvers to compute radiotherapy optimization problems is an important topic of research in this application, however, the structural properties of the underlying criterion functions are typically not taken into account in this context.
In this paper, the model of Köttgen, Barkey and Socie, which corrects the elastic stress and strain tensor histories at notches of a metallic specimen under non-proportional loading, is improved. It can be used in connection with any multiaxial s -e -law of incremental plasticity. For the correction model, we introduce a constraint for the strain components that goes back to the work of Hoffmann and Seeger. Parameter identification for the improved model is performed by Automatic Differentiation and an established least squares algorithm. The results agree accurately both with transient FE computations and notch strain measurements.