Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen

Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von großer Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen präsentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer Lösungen von q-holonomen Rekursionen beschrieben. Das fünfte Kapitel beschäftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung für die Koeffizienten ermittelt. Ferner können wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung für die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der nützlich ist, um q-holonome Rekursionen für bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schließlich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden können. ________________________________________________________________________________________________________________

Strategische Erfolgsfaktoren für ein kosten-risiko-optimales Public Debt Management - Organisatorische und inhaltliche Parameter im internationalen Vergleich

Aus den im Rahmen dieser Forschungsarbeit empirisch gewonnenen Erkenntnissen werden Gestaltungsempfehlungen für das Public Debt Management abgeleitet. Diese zeigen, dass ein wirtschaftliches Public Debt Management nicht ein ausschließlich kostenminimierendes (sparsames), sondern ein kosten-risiko-optimales Public Debt Management mit effektiven internen und externen Überwachungsinstrumenten und wirksamer externer Finanzkontrolle sein muss.

Surface Reflectance Recognition and Real-World Illumination Statistics

Humans distinguish materials such as metal, plastic, and paper effortlessly at a glance. Traditional computer vision systems cannot solve this problem at all. Recognizing surface reflectance properties from a single photograph is difficult because the observed image depends heavily on the amount of light incident from every direction. A mirrored sphere, for example, produces a different image in every environment. To make matters worse, two surfaces with different reflectance properties could produce identical images. The mirrored sphere simply reflects its surroundings, so in the right artificial setting, it could mimic the appearance of a matte ping-pong ball. Yet, humans possess an intuitive sense of what materials typically "look like" in the real world. This thesis develops computational algorithms with a similar ability to recognize reflectance properties from photographs under unknown, real-world illumination conditions. Real-world illumination is complex, with light typically incident on a surface from every direction. We find, however, that real-world illumination patterns are not arbitrary. They exhibit highly predictable spatial structure, which we describe largely in the wavelet domain. Although they differ in several respects from the typical photographs, illumination patterns share much of the regularity described in the natural image statistics literature. These properties of real-world illumination lead to predictable image statistics for a surface with given reflectance properties. We construct a system that classifies a surface according to its reflectance from a single photograph under unknown illuminination. Our algorithm learns relationships between surface reflectance and certain statistics computed from the observed image. Like the human visual system, we solve the otherwise underconstrained inverse problem of reflectance estimation by taking advantage of the statistical regularity of illumination. For surfaces with homogeneous reflectance properties and known geometry, our system rivals human performance.

Cooperative Physics of Fly Swarms: An Emergent Behavior

We have simulated the behavior of several artificial flies, interacting visually with each other. Each fly is described by a simple tracking system (Poggio and Reichardt, 1973; Land and Collett, 1974) which summarizes behavioral experiments in which individual flies fixate a target. Our main finding is that the interaction of theses implemodules gives rise to a variety of relatively complex behaviors. In particular, we observe a swarm-like behavior of a group of many artificial flies for certain reasonable ranges of our tracking system parameters.

The Japanese Business System: Key Features and Prospects for Change

This paper argues that the Japanese business system cannot be adequately understood without extending the focus of analysis beyond the individual firm to the vertical keiretsu, or business group. The vertical group or keiretsu structure was first identified and studied in the auto and electronics industries, where it is most strongly marked, but it characterizes virtually all sectors, service industries as well as manufacturing. Large industrial vertical keiretsu are composed of subsidiaries engaged in three distinct types of activities (manufacturing, marketing, and quasirelated business). The coordination and control systems are built on the flows of products, financial resources, information and technology, and people across formal company boundaries, with the parent firm controlling the key flows. The paper examines the prevailing explanations first for the emergence and then for the persistence of the vertical group structure, and looks at the current pressures for change and adaptation in the system.

Integració d’ una unitat inercial i d’ un giroscopi de fibra òptica en un robot submarí i desenvolupament d’ un sistema de posicionament dins una piscina

El Grup de Visió per Computador i Robòtica (VICOROB) del departament d'Electrònica, Informàtica i Automàtica de la Universitat de Girona investiga en el camp de la robòtica submarina. Al CIRS (Centre d’Investigació en Robòtica Submarina), laboratori que forma part del grup VICOROB, el robot submarí Ictineu és la principal eina utilitzada per a desenvolupar els projectes de recerca. Recentment, el CIRS ha adquirit un nou sistema de sensors d' orientació basat en una unitat inercial i un giroscopi de fibra òptica. Aquest projecte pretén realitzar un estudi d' aquests dispositius i integrar-los al robot Ictineu. D' altra banda, aprofitant les característiques d’aquests sensors giroscopics i les mesures d' un sonar ja integrat al robot, es vol desenvolupar un sistema de localització capaç de determinar la posició del robot en el pla horitzontal de la piscina en temps real

Eina de mobilitat pel sistema de la producció d’Ormetal

L’objectiu principal d’aquest projecte consisteix en realitzar l’estudi, l' anàlisi, el disseny, i el desenvolupament d’una aplicació que millori i faciliti la tasca d’un empleat que treballi fora de l’empresa. Es fa una anàlisi dels requeriments de l’aplicació, es fa el model d’anàlisi i tot seguit el model de disseny, i s’implementarà mitjançant les eines que utilitza la nostra empresa o les que millor s’adaptin a ella. S’analitza també el tipus i el volum d’informació que haurà de manejar. Durant el procés de cada una de les etapes de desenvolupament s’aniran realitzant les corresponents proves per, finalment, realitzar una posada en marxa sobre un empleat a mode de proves en un entorn real. Degut a la necessitat de mobilitat dels comercials s’utilitzen dispositius PDA (Personal Digital Assistant) per al desenvolupament de l’aplicació que els permetrà realitzar les seves tasques. En canvi, l’aplicació corporativa de gestió de l’empresa està situada en un servidor Windows, i per centralitzar i gestionar la informació de les PDA s’utilitzarà una aplicació sota el sistema Windows. L’aplicació s’haurà de confeccionar en funció de les dades que es vulgui que el comercial pugui consultar sobre un client, obra, ... Per millorar-ne la seva funcionalitat, es permetrà l’opció de multi-llenguatge. L’aplicació de la PDA tindrà a grans trets les següents funcionalitats: gestió de clients, gestió de contactes, consultar gestions comercials, consultar obres dels clients, consultar el planning i l’estat dels muntadors. Altres processos que haurà de permetre l’aplicació son: la configuració i instal·lació de l’aplicació en els dispositius PDA i la càrrega i el traspàs de les dades entre l’aplicació del PDA i l’aplicació corporativa de l’empresa

Learning and adaptation in physical heterogeneous teams of robots

In this paper we present a novel approach to assigning roles to robots in a team of physical heterogeneous robots. Its members compete for these roles and get rewards for them. The rewards are used to determine each agent’s preferences and which agents are better adapted to the environment. These aspects are included in the decision making process. Agent interactions are modelled using the concept of an ecosystem in which each robot is a species, resulting in emergent behaviour of the whole set of agents. One of the most important features of this approach is its high adaptability. Unlike some other learning techniques, this approach does not need to start a whole exploitation process when the environment changes. All this is exemplified by means of experiments run on a simulator. In addition, the algorithm developed was applied as applied to several teams of robots in order to analyse the impact of heterogeneity in these systems

Programació del robot e-puck amb Microsoft Robotics Studio

Microsoft Robotics Studio (MRS) és un entorn per a crear aplicacions per a robots utilitzant una gran varietat de plataformes hardware. Conté un entorn de simulació en el que es pot modelar i simular el moviment del robot. Permet també programar el robot, i executar-lo en l’entorn simulat o bé en el real. MRS resol la comunicació entre els diferents processos asíncrons que solen estar presents en el software de control d’un robot: processos per atendre sensors, actuadors, sistemes de control, comunicacions amb l’exterior,... MRS es pot utilitzar per modelar nous robots utilitzant components que ja estiguin disponibles en les seves llibreries, o també permet crear component nous. Per tal de conèixer en detall aquesta eina, seria interessant utilitzar-la per programa els robots e-pucks, uns robots mòbils autònoms de petites dimensions que disposen de dos motors i un complet conjunt de sensors. El que es vol és simular-los, realitzar un programa de control, realitzar la interfície amb el robot i comprovar el funcionament amb el robot real

An hybrid methodology for RL-based behavior coordination in a target following mission with an AUV

Proposes a behavior-based scheme for high-level control of autonomous underwater vehicles (AUVs). Two main characteristics can be highlighted in the control scheme. Behavior coordination is done through a hybrid methodology, which takes in advantages of the robustness and modularity in competitive approaches, as well as optimized trajectories

Vision-based localization of an underwater robot in a structured environment

This paper presents a vision-based localization approach for an underwater robot in a structured environment. The system is based on a coded pattern placed on the bottom of a water tank and an onboard down looking camera. Main features are, absolute and map-based localization, landmark detection and tracking, and real-time computation (12.5 Hz). The proposed system provides three-dimensional position and orientation of the vehicle along with its velocity. Accuracy of the drift-free estimates is very high, allowing them to be used as feedback measures of a velocity-based low-level controller. The paper details the localization algorithm, by showing some graphical results, and the accuracy of the system

Dam wall detection and tracking using a Mechanically Scanned Imaging Sonar

In dam inspection tasks, an underwater robot has to grab images while surveying the wall meanwhile maintaining a certain distance and relative orientation. This paper proposes the use of an MSIS (mechanically scanned imaging sonar) for relative positioning of a robot with respect to the wall. An imaging sonar gathers polar image scans from which depth images (range & bearing) are generated. Depth scans are first processed to extract a line corresponding to the wall (with the Hough transform), which is then tracked by means of an EKF (Extended Kalman Filter) using a static motion model and an implicit measurement equation associating the sensed points to the candidate line. The line estimate is referenced to the robot fixed frame and represented in polar coordinates (rho&thetas) which directly corresponds to the actual distance and relative orientation of the robot with respect to the wall. The proposed system has been tested in simulation as well as in water tank conditions

Pose-based SLAM with probabilistic scan matching algorithm using a mechanical scanned imaging sonar

This paper proposes a pose-based algorithm to solve the full SLAM problem for an autonomous underwater vehicle (AUV), navigating in an unknown and possibly unstructured environment. The technique incorporate probabilistic scan matching with range scans gathered from a mechanical scanning imaging sonar (MSIS) and the robot dead-reckoning displacements estimated from a Doppler velocity log (DVL) and a motion reference unit (MRU). The proposed method utilizes two extended Kalman filters (EKF). The first, estimates the local path travelled by the robot while grabbing the scan as well as its uncertainty and provides position estimates for correcting the distortions that the vehicle motion produces in the acoustic images. The second is an augment state EKF that estimates and keeps the registered scans poses. The raw data from the sensors are processed and fused in-line. No priory structural information or initial pose are considered. The algorithm has been tested on an AUV guided along a 600 m path within a marina environment, showing the viability of the proposed approach

WMR navigation using local potential field corridors and narrow local occupancy grid perception

Path planning and control strategies applied to autonomous mobile robots should fulfil safety rules as well as achieve final goals. Trajectory planning applications should be fast and flexible to allow real time implementations as well as environment interactions. The methodology presented uses the on robot information as the meaningful data necessary to plan a narrow passage by using a corridor based on attraction potential fields that approaches the mobile robot to the final desired configuration. It employs local and dense occupancy grid perception to avoid collisions. The key goals of this research project are computational simplicity as well as the possibility of integrating this method with other methods reported by the research community. Another important aspect of this work consist in testing the proposed method by using a mobile robot with a perception system composed of a monocular camera and odometers placed on the two wheels of the differential driven motion system. Hence, visual data are used as a local horizon of perception in which trajectories without collisions are computed by satisfying final goal approaches and safety criteria

Local WMR navigation with monocular data

This article presents recent WMR (wheeled mobile robot) navigation experiences using local perception knowledge provided by monocular and odometer systems. A local narrow perception horizon is used to plan safety trajectories towards the objective. Therefore, monocular data are proposed as a way to obtain real time local information by building two dimensional occupancy grids through a time integration of the frames. The path planning is accomplished by using attraction potential fields, while the trajectory tracking is performed by using model predictive control techniques. The results are faced to indoor situations by using the lab available platform consisting in a differential driven mobile robot