Gluing of graphs and their Jacobians

The Jacobian of a graph is a discrete analogue of the Jacobian of a Riemann surface. In this paper, we explore how Jacobians of graphs change when we glue two graphs along a common subgraph focusing on the case of cycle graphs. Then, we link the computation of Jacobians of graphs with cycle matrices. Finally, we prove that Tutte's rotor construction with his original example produces two graphs with isomorphic Jacobians when all involved graphs are planar. This answers the question posed by Clancy, Leake, and Payne, stating it is affirmative in this case.Comment: v3; After we posted our first version on arXiv, we learned from Matt Baker the work of Chen and Ye by which one can obtain our Theorem B as a special case. Also, we added the work of Alfaro and Villagr{\'a}n which has the same definition in our matrix B_

Fault Detection and Diagnosis in Air Conditioners and Refrigerators

A fault detection and diagnosis (FDD) method was used to detect and diagnose faults on both a refrigerator and an air conditioner during normal cycling operation. The objective of the method is to identify a set of sensors that can detect faults reliably before they severely hinder system performance. Unlike other methods, this one depends on the accuracy of a number of small, on-line linear models, each of which is valid over a limited range of operating conditions. To detect N faults, N sensors are needed. Using M>N sensors can further reduce the risk of false positives. For both the refrigerator and air conditioner systems, about 1000 combinations of candidate sensor locations were examined. Through inspection of matrix condition numbers and each sensor's contribution to fault detection calculation, the highest quality sets of sensors were identified. The issue of detecting simultaneous multiple faults was also addressed, with varying success. Fault detection was verified using both model simulations and experimental data. The results were similar, although in practice only one of the two would probably be used. Both load-type faults (such as door gasket leaks) and system faults were simulated on the refrigerator. It was found that system faults were generally more easily detectable than load faults. Refrigerator experiments were performed on a typical household refrigerator because it was readily available in a laboratory, but the results of this project may be more immediately useful on larger commercial, industrial or transport refrigeration systems. Air conditioner experiments were performed on a 3-ton split system. Again, the economic benefits of this type of fault detection scheme may also be more feasible for larger field-assembled systems.Air Conditioning and Refrigeration Project 8

RacoonWW1.3: A Monte Carlo program for four-fermion production at e^+ e^- colliders

We present the Monte Carlo generator RacoonWW that computes cross sections to all processes e^+ e^- -> 4f and e^+ e^- -> 4f + gamma and calculates the complete O(alpha) electroweak radiative corrections to e^+ e^- -> W W -> 4f in the electroweak Standard Model in double-pole approximation. The calculation of the tree-level processes e^+ e^- -> 4f and e^+ e^- -> 4f + gamma is based on the full matrix elements for massless (polarized) fermions. When calculating radiative corrections to e^+ e^- -> W W -> 4f the complete virtual doubly-resonant electroweak corrections are included, i.e. the factorizable and non-factorizable virtual corrections in double-pole approximation, and the real corrections are based on the full matrix elements for e^+ e^- -> 4f + gamma. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method or by applying phase-space slicing. Higher-order initial-state photon radiation and naive QCD corrections are taken into account. RacoonWW also provides anomalous triple gauge-boson couplings for all processes e^+ e^- -> 4f and anomalous quartic gauge-boson couplings for all processes e^+ e^- -> 4f + gamma.Comment: 62 pages, LaTeX, elsart styl

Full State History Cooperative Localisation with Complete Information Sharing

This thesis presents a decentralised localisation method for multiple robots. We enable reduced bandwidth requirements whilst using local solutions that fuse information from other robots. This method does not specify a communication topology or require complex tracking of information. The methods for including shared data match standard elements of nonlinear optimisation algorithms. There are four contributions in this thesis. The first is a method to split the multiple vehicle problem into sections that can be iteratively transmitted in packets with bandwidth bounds. This is done through delayed elimination of external states, which are states involved in intervehicle observations. Observations are placed in subgraphs that accumulate between external states. Internal states, which are all states not involved in intervehicle observations, can then be eliminated from each subgraph and the joint probability of the start and end states is shared between vehicles and combined to yield the solution to the entire graph. The second contribution is usage of variable reordering within these packets to enable handling of delayed observations that target an existing state such as with visual loop closures. We identify the calculations required to give the conditional probability of the delayed historical state on the existing external states before and after. This reduces the recalculation to updating the factorisation of a single subgraph and is independent of the time since the observation was made. The third contribution is a method and conditions for insertion of states into existing packets that does not invalidate previously transmitted data. We derive the conditions that enable this method and our fourth contribution is two motion models that conform to the conditions. Together this permits handling of the general out of sequence case

Robust navigation for industrial service robots

Pla de Doctorats Industrials de la Generalitat de CatalunyaRobust, reliable and safe navigation is one of the fundamental problems of robotics. Throughout the present thesis, we tackle the problem of navigation for robotic industrial mobile-bases. We identify its components and analyze their respective challenges in order to address them. The research work presented here ultimately aims at improving the overall quality of the navigation stack of a commercially available industrial mobile-base. To introduce and survey the overall problem we first break down the navigation framework into clearly identified smaller problems. We examine the Simultaneous Localization and Mapping (SLAM) problem, recalling its mathematical grounding and exploring the state of the art. We then review the problem of planning the trajectory of a mobile-base toward a desired goal in the generated environment representation. Finally we investigate and clarify the use of the subset of the Lie theory that is useful in robotics. The first problem tackled is the recognition of place for closing loops in SLAM. Loop closure refers to the ability of a robot to recognize a previously visited location and infer geometrical information between its current and past locations. Using only a 2D laser range finder sensor, we address the problem using a technique borrowed from the field of Natural Language Processing (NLP) which has been successfully applied to image-based place recognition, namely the Bag-of-Words. We further improve the method with two proposals inspired from NLP. Firstly, the comparison of places is strengthened by considering the natural relative order of features in each individual sensor reading. Secondly, topological correspondences between places in a corpus of visited places are established in order to promote together instances that are ‘close’ to one another. We then tackle the problem of motion model calibration for odometry estimation. Given a mobile-base embedding an exteroceptive sensor able to observe ego-motion, we propose a novel formulation for estimating the intrinsic parameters of an odometry motion model. Resorting to an adaptation of the pre-integration theory initially developed for inertial motion sensors, we employ iterative nonlinear on-manifold optimization to estimate the wheel radii and wheel separation. The method is further extended to jointly estimate both the intrinsic parameters of the odometry model together with the extrinsic parameters of the embedded sensor. The method is shown to accommodate to variation in model parameters quickly when the vehicle is subject to physical changes during operation. Following the generation of a map in which the robot is localized, we address the problem of estimating trajectories for motion planning. We devise a new method for estimating a sequence of robot poses forming a smooth trajectory. Regardless of the Lie group considered, the trajectory is seen as a collection of states lying on a spline with non-vanishing n-th derivatives at each point. Formulated as a multi-objective nonlinear optimization problem, it allows for the addition of cost functions such as velocity and acceleration limits, collision avoidance and more. The proposed method is evaluated for two different motion planning tasks, the planning of trajectories for a mobile-base evolving in the SE(2) manifold, and the planning of the motion of a multi-link robotic arm whose end-effector evolves in the SE(3) manifold. From our study of Lie theory, we developed a new, ready to use, programming library called `manif’. The library is open source, publicly available and is developed following good software programming practices. It is designed so that it is easy to integrate and manipulate, and allows for flexible use while facilitating the possibility to extend it beyond the already implemented Lie groups.La navegación autónoma es uno de los problemas fundamentales de la robótica, y sus diferentes desafíos se han estudiado durante décadas. El desarrollo de métodos de navegación robusta, confiable y segura es un factor clave para la creación de funcionalidades de nivel superior en robots diseñados para operar en entornos con humanos. A lo largo de la presente tesis, abordamos el problema de navegación para bases robóticas móviles industriales; identificamos los elementos de un sistema de navegación; y analizamos y tratamos sus desafíos. El trabajo de investigación presentado aquí tiene como último objetivo mejorar la calidad general del sistema completo de navegación de una base móvil industrial disponible comercialmente. Para estudiar el problema de navegación, primero lo desglosamos en problemas menores claramente identificados. Examinamos el subproblema de mapeo del entorno y localización del robot simultáneamente (SLAM por sus siglas en ingles) y estudiamos el estado del arte del mismo. Al hacerlo, recordamos y detallamos la base matemática del problema de SLAM. Luego revisamos el subproblema de planificación de trayectorias hacia una meta deseada en la representación del entorno generada. Además, como una herramienta para las soluciones que se presentarán más adelante en el desarrollo de la tesis, investigamos y aclaramos el uso de teoría de Lie, centrándonos en el subconjunto de la teoría que es útil para la estimación de estados en robótica. Como primer elemento identificado para mejoras, abordamos el problema de reconocimiento de lugares para cerrar lazos en SLAM. El cierre de lazos se refiere a la capacidad de un robot para reconocer una ubicación visitada previamente e inferí información geométrica entre la ubicación actual del robot y aquellas reconocidas. Usando solo un sensor láser 2D, la tarea es desafiante ya que la percepción del entorno que proporciona el sensor es escasa y limitada. Abordamos el problema utilizando 'bolsas de palabras', una técnica prestada del campo de procesamiento del lenguaje natural (NLP) que se ha aplicado con éxito anteriormente al reconocimiento de lugares basado en imágenes. Nuestro método incluye dos nuevas propuestas inspiradas también en NLP. Primero, la comparación entre lugares candidatos se fortalece teniendo en cuenta el orden relativo natural de las características en cada lectura individual del sensor; y segundo, se establece un corpus de lugares visitados para promover juntos instancias que están "cerca" la una de la otra desde un punto de vista topológico. Evaluamos nuestras propuestas por separado y conjuntamente en varios conjuntos de datos, con y sin ruido, demostrando mejora en la detección de cierres de lazo para sensores láser 2D, con respecto al estado del arte. Luego abordamos el problema de la calibración del modelo de movimiento para la estimación de la edometría. Dado que nuestra base móvil incluye un sensor exteroceptivo capaz de observar el movimiento de la plataforma, proponemos una nueva formulación que permite estimar los parámetros intrínsecos del modelo cinemático de la plataforma durante el cómputo de la edometría del vehículo. Hemos recurrido a una adaptación de la teoría de reintegración inicialmente desarrollado para unidades inerciales de medida, y aplicado la técnica a nuestro modelo cinemático. El método nos permite, mediante optimización iterativa no lineal, la estimación del valor del radio de las ruedas de forma independiente y de la separación entre las mismas. El método se amplía posteriormente par idéntica de forma simultánea, estos parámetros intrínsecos junto con los parámetros extrínsecos que ubican el sensor láser con respecto al sistema de referencia de la base móvil. El método se valida en simulación y en un entorno real y se muestra que converge hacia los verdaderos valores de los parámetros. El método permite la adaptación de los parámetros intrínsecos del modelo cinemático de la plataforma derivados de cambios físicos durante la operación, tales como el impacto que el cambio de carga sobre la plataforma tiene sobre el diámetro de las ruedas. Como tercer subproblema de navegación, abordamos el reto de planificar trayectorias de movimiento de forma suave. Desarrollamos un método para planificar la trayectoria como una secuencia de configuraciones sobre una spline con n-ésimas derivadas en todos los puntos, independientemente del grupo de Lie considerado. Al ser formulado como un problema de optimización no lineal con múltiples objetivos, es posible agregar funciones de coste al problema de optimización que permitan añadir límites de velocidad o aceleración, evasión de colisiones, etc. El método propuesto es evaluado en dos tareas de planificación de movimiento diferentes, la planificación de trayectorias para una base móvil que evoluciona en la variedad SE(2), y la planificación del movimiento de un brazo robótico cuyo efector final evoluciona en la variedad SE(3). Además, cada tarea se evalúa en escenarios con complejidad de forma incremental, y se muestra un rendimiento comparable o mejor que el estado del arte mientras produce resultados más consistentes. Desde nuestro estudio de la teoría de Lie, desarrollamos una nueva biblioteca de programación llamada “manif”. La biblioteca es de código abierto, está disponible públicamente y se desarrolla siguiendo las buenas prácticas de programación de software. Esta diseñado para que sea fácil de integrar y manipular, y permite flexibilidad de uso mientras se facilita la posibilidad de extenderla más allá de los grupos de Lie inicialmente implementados. Además, la biblioteca se muestra eficiente en comparación con otras soluciones existentes. Por fin, llegamos a la conclusión del estudio de doctorado. Examinamos el trabajo de investigación y trazamos líneas para futuras investigaciones. También echamos un vistazo en los últimos años y compartimos una visión personal y experiencia del desarrollo de un doctorado industrial.Postprint (published version

Kodierungstheorie

[no abstract available

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Temporal accumulation of oriented visual features

In this paper we present a framework for accumulating on-line a model of a moving object (e.g., when manipulated by a robot). The proposed scheme is based on Bayesian filtering of local features, filtering jointly position, orientation and appearance information. The work presented here is novel in two aspects: first, we use an estimation mechanism that updates iteratively not only geometrical information, but also appearance information. Second, we propose a probabilistic version of the classical n-scan criterion that allows us to select which features are preserved and which are discarded, while making use of the available uncertainty model. The accumulated representations have been used in three different contexts: pose estimation, robotic grasping, and driver assistance scenario