We study development of mortality tables from 1950 to present in Czech Republic. Our aim is to look at the 6 basic models, which can be potentially used to describe behavior of dying for people over 60 years. Models that are being investigated vary from generally accepted Gompertz-Makeham model to logistic models of Thatcher and Kannisto. We also introduce Coale-Kisker and Heligman- Pollard model. Our analysis is concentrated mostly on projecting abilities of given models to the highest ages. Especially for women, where data do not show such dispersion as in the case of men, there is a visible trend that can be described better by using logistic models instead of Gompertz-Makeham model, which has a tendency to overestimate the probabilities of dying in higher ages. Keywords: projection of mortality tables, Gompertz-Makeham, logistic models 1

The graph-based formulation of the navigation problem is establishing itself as one of the standard ways to formulate the navigation problem within the sensor fusion community. It enables a convenient way to access information from previous positions which can be used to enhance the estimate of the current position.To restrict working memory usage, map partitioning can be used to store older parts of the map on a hard drive, in the form of submaps. This limits the number of previous positions within the active map. This thesis examines the effect that map partitioning information loss has on the state of the art positioning algorithm iSAM2, both in open routes and when loop closure is achieved. It finds that larger submaps appear to cause a smaller positional error than smaller submaps for open routes. The smaller submaps seem to give smaller positional error than larger submaps when loop closure is achieved. The thesis also examines how the density of landmarks at the partition point affects the positional error, but the obtained result is mixed and no clear conclusions can be made. Finally it reviews some loop closure detection algorithms that can be convenient to pair with the iSAM2 algorithm.

The master thesis is looking into the estimation of yield curve using two ap- proaches. The first one is searching for parametric model which is able to describe the behavior of yield curve well and estimate its parameters. The parametric mo- dels used in the thesis are derived from the class of models introduced by Nelson and Siegel. The second approach is nonparametric estimation of yield curves using spline smoothing and kernel smoothing. All used methods are then compared on real observed data and their suitability for various tasks and concrete available observations is considered. 1

This thesis presents an analysis of several smoothness energies (also called smoothing energies) in geometry processing, and introduces new methods as well as a mathematical proof of correctness and convergence for a well-established method. Geometry processing deals with the acquisition, modification, and output (be it on a screen, in virtual reality, or via fabrication and manufacturing) of complex geometric objects and data. It is closely related to computer graphics, but is also used by many other fields that employ applied mathematics in the context of geometry. The popular Laplacian energy is a smoothness energy that quantifies smoothness and that is closely related to the biharmonic equation (which gives it desirable properties). Minimizers of the Laplacian energy solve the biharmonic equation. This thesis provides a proof of correctness and convergence for a very popular discretization method for the biharmonic equation with zero Dirichlet and Neumann boundary conditions, the piecewise linear Lagrangian mixed finite element method. The same approach also discretizes the Laplacian energy. Such a proof has existed for flat surfaces for a long time, but there exists no such proof for the curved surfaces that are needed to represent the complicated geometries used in geometry processing. This proof will improve the usefulness of this discretization for the Laplacian energy. In this thesis, the novel Hessian energy for curved surfaces is introduced, which also quantifies the smoothness of a functions, and whose minimizers solve the biharmonic equation. This Hessian energy has natural boundary conditions that allow the construction of functions that are not significantly biased by the geometry and presence of boundaries in the domain (unlike the Laplacian energy with zero Neumann boundary conditions), while still conforming to constraints informed by the application. This is useful in any situation where the boundary of the domain is not an integral part of the problem itself, but just an artifact of data representation---be it, because of artifacts created by an imprecise scan of the surface, because information is missing outside of a certain region, or because the application simply demands a result that should not depend on the geometry of the boundary. Novel discretizations of this energy are also introduced and analyzed. This thesis also presents the new developability energy, which quantifies a different kind of smoothness than the Laplacian and Hessian energies: how easy is it to unfold a surface so that it lies flat on the plane without any distortion (surfaces for which this is possible are called developable surfaces). Developable surfaces are interesting, as they can be easily constructed from cheap material such as paper and plywood, or manufactured with methods such as 5-axis CNC milling. A novel definition of developability for discrete triangle meshes, as well as a variety of discrete developability energies are also introduced and applied to problems such as approximation of a surface by a piecewise developable surface, and the design and fabrication of piecewise developable surfaces. This will enable users to more easily take advantages of these cheap and quick fabrication methods. The novel methods, algorithms and the mathematical proof introduced in this thesis will be useful in many applications and fields, including numerical analysis of elliptic partial differential equations, geometry processing of triangle meshes, character animation, data denoising, data smoothing, scattered data interpolation, fabrication from simple materials, computer-controlled fabrication, and more.

Functional data analysis, commonly known as FDA", refers to the analysis of information on curves of functions. Key aspects of FDA include the choice of smoothing techniques, data reduction, model evaluation, functional linear modeling and forecasting methods. FDA is applicable in numerous applications such as Bioscience, Geology, Psychology, Sports Science, Econometrics, Meteorology, etc. This dissertation main objective is to focus more specifically on Functional Linear Regression Modelling (FLRM), which is an extension of Multivariate Linear Regression Modeling. The problem of constructing a Functional Linear Regression modelling with functional predictors and functional response variable is considered in great details. Discretely observed data for each variable involved in the modelling are expressed as smooth functions using: Fourier Basis, B-Splines Basis and Gaussian Basis. The Functional Linear Regression Model is estimated by the Least Square method, Maximum Likelihood method and more thoroughly by Penalized Maximum Likelihood method. A central issue when modelling Functional Regression models is the choice of a suitable model criterion as well as the number of basis functions and an appropriate smoothing parameter. Four different types of model criteria are reviewed: the Generalized Cross-Validation, the Generalized Information Criterion, the modified Akaike Information Criterion and Generalized Bayesian Information Criterion. Each of these aforementioned methods are applied to a dataset and contrasted based on their respective results.

The objective of this paper is to retrospectively evaluate forecast models for polling data, to be used prospectively for the Swedish general election in 2022. One of the simplest ways of forecasting an election result is through opinion polls, and using the latest observation as the forecast. This paper considers five different forecasting models on polling data which are evaluated based on different error measures and the results are compared to previous research done on the same topic. The data in this paper consists of time series data of party-preference polls from Statistics Sweden. When forecasting polling data, the naive forecasting model was the most accurate, but forecasting the election in 2018 resulted in the forecast combinations model being the most accurate. Finally, the models are used to make forecasts on the Swedish general election taking place in September of 2022.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17869号 / 工博第3778号 / 新制||工||1578(附属図書館) / 30689 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 寶 馨, 教授 細田 尚, 准教授 立川 康人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18286号 / 工博第3878号 / 新制||工||1595(附属図書館) / 31144 / 京都大学大学院工学研究科電子工学専攻 / (主査)教授 木本 恒暢, 教授 白石 誠司, 准教授 浅野 卓 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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Die Sensordatenfusion ist eine allgegenwärtige Aufgabe im Bereich der mobilen Robotik und darüber hinaus. In der vorliegenden Arbeit wird das typischerweise verwendete Verfahren zur Sensordatenfusion in der Robotik in Frage gestellt und anhand von neuartigen Algorithmen, basierend auf einem Faktorgraphen, gelöst sowie mit einer korrespondierenden Extended-Kalman-Filter-Implementierung verglichen. Im Mittelpunkt steht dabei das technische sowie algorithmische Sensorkonzept für die Navigation eines Flugroboters im Innenbereich. Ausführliche Experimente zeigen die Qualitätssteigerung unter Verwendung der neuen Variante der Sensordatenfusion, aber auch Einschränkungen und Beispiele mit nahezu identischen Ergebnissen beider Varianten der Sensordatenfusion. Neben Experimenten anhand einer hardwarenahen Simulation wird die Funktionsweise auch anhand von realen Hardwaredaten evaluiert.