Abstracts of Ph.D. theses in mathematics

summary:Čihák, Michael: Teaching probability at secondary schools using computers. Pavlíková, Pavla: Life and work of Miloš Kössler. Bárta, Tomáš: Integrodifferential equations in Banach spaces Beneš, Michal: Asymptotic behavior of the regular orbits of strongly continuous semigroup Pavlica, David: On convex functions, dc-functions and boundary structure of convex sets. Henclová, Alena: Duality in multistage stochastic programming and its application to arbitrage theory. Polívka, Jan: Stochastic programming approach to asset-liability management. Rychtář, Jan: Some problems in rotund renormings of Banach spaces and in operator theory. Jeřábek, Emil: Weak pigeonehole principle and randomized computation. Kupčáková, Marie: Geometry as creation. Kundrátová, Karolína: Comparative analysis of geometric software packages based on solving selected problems. Bejček, Michal: Numerical methods for solving compressible flow problems. Ernestová, Martina: Systems of algebraic equations and their solution in antiquity and the middle ages. Příhoda, Pavel: Decompositions of modules. Jarolímková, Tereza: Valuation of life insurance using diffusion model of interest rate. Fajfrová, Lucie: Equilibrium behaviour of zero range processes on binary tree. Marek, Tomáš: Random coefficient moving average models

Piecewise Tensor Product Wavelet Bases by Extensions and Approximation Rates

Following [Studia Math., 76(2) (1983), pp. 1-58 and 95-136] by Z. Ciesielski and T. Figiel and [SIAM J. Math. Anal., 31 (1999), pp. 184-230] by W. Dahmen and R. Schneider, by the application of extension operators we construct a basis for a range of Sobolev spaces on a domain $\Omega$ from corresponding bases on subdomains that form a non-overlapping decomposition. As subdomains, we take hypercubes, or smooth parametric images of those, and equip them with tensor product wavelet bases. We prove approximation rates from the resulting piecewise tensor product basis that are independent of the spatial dimension of $\Omega$. For two- and three-dimensional polytopes we show that the solution of Poisson type problems satisfies the required regularity condition. The dimension independent rates will be realized numerically in linear complexity by the application of the adaptive wavelet-Galerkin scheme

Model-Based Multiple 3D Object Recognition in Range Data

Vision guided systems are relevant for many industrial application areas, including manufacturing, medicine, service robots etc. A task common to these applications consists of detecting and localizing known objects in cluttered scenes. This amounts to solve the "chicken and egg" problem consisting of data assignment and parameter estimation, that is to localize an object and to determine its pose. In this work, we consider computer vision techniques for the special scenario of industrial bin-picking applications where the goal is to accurately estimate the positions of multiple instances of arbitrary, known objects that are randomly assembled in a bin. Although a-priori knowledge of the objects simplifies the problem, model symmetries, mutual occlusion as well as noise, unstructured measurements and run-time constraints render the problem far from being trivial. A common strategy to cope with this problem is to apply a two-step approach that consists of rough initialization estimation for each objects' position followed by subsequent refinement steps. Established initialization procedures only take into account single objects, however. Hence, they cannot resolve contextual constraints caused by multiple object instances and thus yield poor estimates of the objects' pose in many settings. Inaccurate initial configurations, on the other hand, cause state-of-the-art refinement algorithms to be unable to identify the objects' pose, such that the entire two-step approach is likely to fail. In this thesis, we propose a novel approach for obtaining initial estimates of all object positions jointly. Additionally, we investigate a new local, individual refinement procedure that copes with the shortcomings of state-of-the-art approaches while yielding fast and accurate registration results as well as a large region of attraction. Both stages are designed using advanced numerical techniques such as large-scale convex programming and geometric optimization on the curved space of Euclidean transformations, respectively. They complement each other in that conflicting interpretations are resolved through non-local convex processing, followed by accurate non-convex local optimization based on sufficiently good initializations. Exhaustive numerical evaluation on artificial and real-world measurements experimentally confirms the proposed two-step approach and demonstrates the robustness to noise, unstructured measurements and occlusions as well as showing the potential to meet run-time constraints of real-world industrial applications

Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstracts

Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstract

Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstracts

Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstract

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Predictive Context-Based Adaptive Compliance for Interaction Control of Robot Manipulators

In classical industrial robotics, robots are concealed within structured and well-known environments performing highly-repetitive tasks. In contrast, current robotic applications require more direct interaction with humans, cooperating with them to achieve a common task and entering home scenarios. Above all, robots are leaving the world of certainty to work in dynamically-changing and unstructured environments that might be partially or completely unknown to them. In such environments, controlling the interaction forces that appear when a robot contacts a certain environment (be the environment an object or a person) is of utmost importance. Common sense suggests the need to leave the stiff industrial robots and move towards compliant and adaptive robot manipulators that resemble the properties of their biological counterpart, the human arm. This thesis focuses on creating a higher level of intelligence for active compliance control methods applied to robot manipulators. This work thus proposes an architecture for compliance regulation named Predictive Context-Based Adaptive Compliance (PCAC) which is composed of three main components operating around a 'classical' impedance controller. Inspired by biological systems, the highest-level component is a Bayesian-based context predictor that allows the robot to pre-regulate the arm compliance based on predictions about the context the robot is placed in. The robot can use the information obtained while contacting the environment to update its context predictions and, in case it is necessary, to correct in real time for wrongly predicted contexts. Thus, the predictions are used both for anticipating actions to be taken 'before' proceeding with a task as well as for applying real-time corrective measures 'during' the execution of a in order to ensure a successful performance. Additionally, this thesis investigates a second component to identify the current environment among a set of known environments. This in turn allows the robot to select the proper compliance controller. The third component of the architecture presents the use of neuroevolutionary techniques for selecting the optimal parameters of the interaction controller once a certain environment has been identified

Nonsmooth Convex Variational Approaches to Image Analysis

Variational models constitute a foundation for the formulation and understanding of models in many areas of image processing and analysis. In this work, we consider a generic variational framework for convex relaxations of multiclass labeling problems, formulated on continuous domains. We propose several relaxations for length-based regularizers, with varying expressiveness and computational cost. In contrast to graph-based, combinatorial approaches, we rely on a geometric measure theory-based formulation, which avoids artifacts caused by an early discretization in theory as well as in practice. We investigate and compare numerical first-order approaches for solving the associated nonsmooth discretized problem, based on controlled smoothing and operator splitting. In order to obtain integral solutions, we propose a randomized rounding technique formulated in the spatially continuous setting, and prove that it allows to obtain solutions with an a priori optimality bound. Furthermore, we present a method for introducing more advanced prior shape knowledge into labeling problems, based on the sparse representation framework