<p>A technique to detect deviations in sets of systems in a self-organized way is described in this work. System features are extracted to allow compact representation of the system. Distances between systems are calculated by computing distances between the features. The distances are then stored in an affinity matrix. Deviating systems are detected by assuming a statistical model for the affinities. The key idea is to extract features and and identify deviating systems in a self-organized way, using nonlinear techniques for the feature extraction. The results are compared with those achieved with linear techniques, (principal component analysis).</p><p>The features are computed with principal curves and an isometric feature mapping. In the case of principal curves the feature is the curve itself. In the case of isometric feature mapping is the feature a set of curves in the embedding space. The similarity measure between two representations is either the Hausdorff distance, or the Frechet distance. The deviation detection is performed by computing the probability of each system to be observed given all the other systems. To perform reliable inference the Bootstrapping technique was used.</p><p>The technique is demonstrated on simulated and on-road vehicle cooling system data. The results show the applicability and comparison with linear techniques.</p>

<p>In this thesis we consider two models for the computation of option prices. The first one is a generalization of the Black-Scholes model. In this generalization the volatility Sigma is not a constant. In the simplest case it changes at once at a certain time moment Tau. In some sense this is the conditionally Levy model. For this generalized Black-Scholes model have been theoretically obtained formulas for vanilla Call/Put option prices. Under the assumption of a good prediction of the parameter Sigma the obtained numerical results fit the real dara better than standard Black-Scholes model.</p><p>Second model is an exponential Levy model, where a Levy process is the CGMY process. We use the finite-difference scheme for computations of option prices. As example we consider vanilla Call/Put, Double-Barrier and Up-and-out options. After the estimation of the parameters of the CGMY process by the method of moments we obtain options prices and calculate fitting error. This fitting error for the CGMY model is smaller than for the Black-Scholes model.</p>

<p>Our main objective of this thesis is to measure the conflict risk and then on the basis of this risk allocate the slots for future communication.</p>

The modern theory of condition measures for convex optimization problems was initially developed for convex problems in conic format, and several aspects of the theory have now been extended to handle non-conic formats as well. In this theory, the (Renegar-) condition measure C(d) for a problem instance with data d=(A,b,c) has been shown to be connected to bounds on a wide variety of behavioral and computational characteristics of the problem instance, from sizes of optimal solutions to the complexity of algorithms. Herein we test the practical relevance of the condition measure theory, as applied to linear optimization problems that one might typically encounter in practice. Using the NETLIB suite of linear optimization problems as a test bed, we found that 71% of the NETLIB suite problem instances have infinite condition measure. In order to examine condition measures of the problems that are the actual input to a modern IPM solver, we also computed condition measures for the NETLIB suite problems after pre-preprocessing by CPLEX 7.1. Here we found that 19% of the post-processed problem instances in the NETLIB suite have infinite condition measure, and that log C(d) of the post-processed problems is fairly nicely distributed. Furthermore, there is a positive linear relationship between IPM iterations and log C(d) of the post-processed problem instances (significant at the 95% confidence level), and 42% of the variation in IPM iterations among the NETLIB suite problem instances is accounted for by log C(d) of the post-processed problem instances. / Singapore-MIT Alliance (SMA)

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We study the (strong-)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion / when the initial distribution is Gibbsian.

The majority of computers around us are embedded in productsand dedicated to perform certain tasks. A specific task is thecontrol of a dynamic system. The computers are ofteninterconnected by communication networks forming a distributedsystem. Vehicles and manufacturing equipment are two types ofmechatronic machines which often host dedicated computercontrol systems. A research problem is how the real-timebehaviour of the computer system affects the application,especially the control of the dynamic system. If the internal or external conditions varies over time, itbecomes difficult to assign a fixed resource reservation thatwill work well in all situations. In general, the more time anapplication gets of a resource, the better its gauged orperceived quality will be. A strategy is to alter the resourcereservation when the condition changes. This can be constructedas a negotiation between competing applications, a method forwhich the termquality of control, QoC, has been coined. Scalability isthe ability to change the structure and configuration of asystem. It promotes evolving systems and a can help manage acomplex product family. An architecture for a QoC middleware ontop of a scalable computer system, has been proposed. As aquality measureof a control application, the well-knownweighted quadratic loss function used in optimal control, hasbeen revised to encompass a subset of the so called timingproperties. The timing properties are the periods and thedelays in the control loop, including time-varying period anddelay. They are the interface between control and computerengineering, from a control engineering viewpoint. The qualitymeasure can be used both offline and on-line given a model ofthe sampled-data system and an appropriate description of thetiming properties. In order to use a computer system efficiently and toguarantee its responsiveness, real-time scheduling is a must.In fixed priority scheduling each task arrives periodically andhas a fixed priority. A task with a high priority can preempt alow priority task and gain access to the resource. Thebest-case response time characterizes the delays in the system,which is useful from a control viewpoint. A new algorithm tocalculate thebest-caseresponsetime has been derived. It is based on ascheduling scenario which yields a recurrence equation. Themodel is dual to the well-known worst-case response timeanalysis. Besides the dynamic fixed priority scheduling algorithm,optimal control usingstatic schedulinghas been studied, assuming a limitedcommunication. In the static schedule, which is constructedpre-runtime, each task is assigned a time window within aschedule repeated in eternity. The optimal scheduling sequenceis sought by optimizing the overall control performance. Aninteresting aspect is that the non-specified control periodfalls out as a result of theoptimal schedule. The time-varying delay is accountedfor in the control design. Keywords:Real-time scheduling, sampled-data control,performance measure, quality of control, limited communication,time-varying delay, jitter.

In this thesis we consider two models for the computation of option prices. The first one is a generalization of the Black-Scholes model. In this generalization the volatility Sigma is not a constant. In the simplest case it changes at once at a certain time moment Tau. In some sense this is the conditionally Levy model. For this generalized Black-Scholes model have been theoretically obtained formulas for vanilla Call/Put option prices. Under the assumption of a good prediction of the parameter Sigma the obtained numerical results fit the real dara better than standard Black-Scholes model. Second model is an exponential Levy model, where a Levy process is the CGMY process. We use the finite-difference scheme for computations of option prices. As example we consider vanilla Call/Put, Double-Barrier and Up-and-out options. After the estimation of the parameters of the CGMY process by the method of moments we obtain options prices and calculate fitting error. This fitting error for the CGMY model is smaller than for the Black-Scholes model.

By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.

The Laplace equation and the related p-Laplace equation are closely associated with Sobolev spaces. During the last 15 years people have been exploring the possibility of solving partial differential equations in general metric spaces by generalizing the concept of Sobolev spaces. One such generalization is the Newtonian space where one uses upper gradients to compensate for the lack of a derivative. All papers on this topic are written for an audience of fellow researchers and people with graduate level mathematical skills. In this thesis we give an introduction to the Newtonian spaces accessible also for senior undergraduate students with only basic knowledge of functional analysis. We also give an introduction to the tools needed to deal with the Newtonian spaces. This includes measure theory and curves in general metric spaces. Many of the properties of ordinary Sobolev spaces also apply in the generalized setting of the Newtonian spaces. This thesis includes proofs of the fact that the Newtonian spaces are Banach spaces and that under mild additional assumptions Lipschitz functions are dense there. To make them more accessible, the proofs have been extended with comments and details previously omitted. Examples are given to illustrate new concepts. This thesis also includes my own result on the capacity associated with Newtonian spaces. This is the theorem that if a set has p-capacity zero, then the capacity of that set is zero for all smaller values of p.