Operations research: from computational biology to sensor network

In this dissertation we discuss the deployment of combinatorial optimization methods for modeling and solve real life problemS, with a particular emphasis to two biological problems arising from a common scenario: the reconstruction of the three-dimensional shape of a biological molecule from Nuclear Magnetic Resonance (NMR) data. The fi rst topic is the 3D assignment pathway problem (APP) for a RNA molecule. We prove that APP is NP-hard, and show a formulation of it based on edge-colored graphs. Taking into account that interactions between consecutive nuclei in the NMR spectrum are diff erent according to the type of residue along the RNA chain, each color in the graph represents a type of interaction. Thus, we can represent the sequence of interactions as the problem of fi nding a longest (hamiltonian) path whose edges follow a given order of colors (i.e., the orderly colored longest path). We introduce three alternative IP formulations of APP obtained with a max flow problem on a directed graph with packing constraints over the partitions, which have been compared among themselves. Since the last two models work on cyclic graphs, for them we proposed an algorithm based on the solution of their relaxation combined with the separation of cycle inequalities in a Branch & Cut scheme. The second topic is the discretizable distance geometry problem (DDGP), which is a formulation on discrete search space of the well-known distance geometry problem (DGP). The DGP consists in seeking the embedding in the space of a undirected graph, given a set of Euclidean distances between certain pairs of vertices. DGP has two important applications: (i) fi nding the three dimensional conformation of a molecule from a subset of interatomic distances, called Molecular Distance Geometry Problem, and (ii) the Sensor Network Localization Problem. We describe a Branch & Prune (BP) algorithm tailored for this problem, and two versions of it solving the DDGP both in protein modeling and in sensor networks localization frameworks. BP is an exact and exhaustive combinatorial algorithm that examines all the valid embeddings of a given weighted graph G=(V,E,d), under the hypothesis of existence of a given order on V. By comparing the two version of BP to well-known algorithms we are able to prove the e fficiency of BP in both contexts, provided that the order imposed on V is maintained

Non-convex Optimization for Machine Learning

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-dimensional spaces or that train non-linear models such as tensor models and deep networks. The freedom to express the learning problem as a non-convex optimization problem gives immense modeling power to the algorithm designer, but often such problems are NP-hard to solve. A popular workaround to this has been to relax non-convex problems to convex ones and use traditional methods to solve the (convex) relaxed optimization problems. However this approach may be lossy and nevertheless presents significant challenges for large scale optimization. On the other hand, direct approaches to non-convex optimization have met with resounding success in several domains and remain the methods of choice for the practitioner, as they frequently outperform relaxation-based techniques - popular heuristics include projected gradient descent and alternating minimization. However, these are often poorly understood in terms of their convergence and other properties. This monograph presents a selection of recent advances that bridge a long-standing gap in our understanding of these heuristics. The monograph will lead the reader through several widely used non-convex optimization techniques, as well as applications thereof. The goal of this monograph is to both, introduce the rich literature in this area, as well as equip the reader with the tools and techniques needed to analyze these simple procedures for non-convex problems.Comment: The official publication is available from now publishers via http://dx.doi.org/10.1561/220000005

Physically Based Preconditioning Techniques Applied to the First Order Particle Transport and to Fluid Transport in Porous Media

Physically based preconditioning is applied to linear systems resulting from solving the first order formulation of the particle transport equation and from solving the homogenized form of the simple flow equation for porous media flows. The first order formulation of the particle transport equation is solved two ways. The first uses a least squares finite element method resulting in a symmetric positive definite linear system which is solved by a preconditioned conjugate gradient method. The second uses a discontinuous finite element method resulting in a non-symmetric linear system which is solved by a preconditioned biconjugate gradient stabilized method. The flow equation is solved using a mixed finite element method. Specifically four levels of improvement are applied: homogenization of the porous media domain, a projection method for the mixed finite element method which simplifies the linear system, physically based preconditioning, and implementation of the linear solver in parallel on graphic processing units. The conjugate gradient linear solver for the least squares finite element method is also applied in parallel on graphics processing units. The physically based preconditioner is shown to perform well in each case, in relation to speed-ups gained and as compared with several algebraic preconditioners

Density-Aware Linear Algebra in a Column-Oriented In-Memory Database System

Linear algebra operations appear in nearly every application in advanced analytics, machine learning, and of various science domains. Until today, many data analysts and scientists tend to use statistics software packages or hand-crafted solutions for their analysis. In the era of data deluge, however, the external statistics packages and custom analysis programs that often run on single-workstations are incapable to keep up with the vast increase in data volume and size. In particular, there is an increasing demand of scientists for large scale data manipulation, orchestration, and advanced data management capabilities. These are among the key features of a mature relational database management system (DBMS). With the rise of main memory database systems, it now has become feasible to also consider applications that built up on linear algebra. This thesis presents a deep integration of linear algebra functionality into an in-memory column-oriented database system. In particular, this work shows that it has become feasible to execute linear algebra queries on large data sets directly in a DBMS-integrated engine (LAPEG), without the need of transferring data and being restricted by hard disc latencies. From various application examples that are cited in this work, we deduce a number of requirements that are relevant for a database system that includes linear algebra functionality. Beside the deep integration of matrices and numerical algorithms, these include optimization of expressions, transparent matrix handling, scalability and data-parallelism, and data manipulation capabilities. These requirements are addressed by our linear algebra engine. In particular, the core contributions of this thesis are: firstly, we show that the columnar storage layer of an in-memory DBMS yields an easy adoption of efficient sparse matrix data types and algorithms. Furthermore, we show that the execution of linear algebra expressions significantly benefits from different techniques that are inspired from database technology. In a novel way, we implemented several of these optimization strategies in LAPEG’s optimizer (SpMachO), which uses an advanced density estimation method (SpProdest) to predict the matrix density of intermediate results. Moreover, we present an adaptive matrix data type AT Matrix to obviate the need of scientists for selecting appropriate matrix representations. The tiled substructure of AT Matrix is exploited by our matrix multiplication to saturate the different sockets of a multicore main-memory platform, reaching up to a speed-up of 6x compared to alternative approaches. Finally, a major part of this thesis is devoted to the topic of data manipulation; where we propose a matrix manipulation API and present different mutable matrix types to enable fast insertions and deletes. We finally conclude that our linear algebra engine is well-suited to process dynamic, large matrix workloads in an optimized way. In particular, the DBMS-integrated LAPEG is filling the linear algebra gap, and makes columnar in-memory DBMS attractive as efficient, scalable ad-hoc analysis platform for scientists

Realtime Face Tracking and Animation

Capturing and processing human geometry, appearance, and motion is at the core of computer graphics, computer vision, and human-computer interaction. The high complexity of human geometry and motion dynamics, and the high sensitivity of the human visual system to variations and subtleties in faces and bodies make the 3D acquisition and reconstruction of humans in motion a challenging task. Digital humans are often created through a combination of 3D scanning, appearance acquisition, and motion capture, leading to stunning results in recent feature films. However, these methods typically require complex acquisition systems and substantial manual post-processing. As a result, creating and animating high-quality digital avatars entails long turn-around times and substantial production costs. Recent technological advances in RGB-D devices, such as Microsoft Kinect, brought new hopes for realtime, portable, and affordable systems allowing to capture facial expressions as well as hand and body motions. RGB-D devices typically capture an image and a depth map. This permits to formulate the motion tracking problem as a 2D/3D non-rigid registration of a deformable model to the input data. We introduce a novel face tracking algorithm that combines geometry and texture registration with pre-recorded animation priors in a single optimization. This led to unprecedented face tracking quality on a low cost consumer level device. The main drawback of this approach in the context of consumer applications is the need for an offline user-specific training. Robust and efficient tracking is achieved by building an accurate 3D expression model of the user's face who is scanned in a predefined set of facial expressions. We extended this approach removing the need of a user-specific training or calibration, or any other form of manual assistance, by modeling online a 3D user-specific dynamic face model. In complement of a realtime face tracking and modeling algorithm, we developed a novel system for animation retargeting that allows learning a high-quality mapping between motion capture data and arbitrary target characters. We addressed one of the main challenges of existing example-based retargeting methods, the need for a large number of accurate training examples to define the correspondence between source and target expression spaces. We showed that this number can be significantly reduced by leveraging the information contained in unlabeled data, i.e. facial expressions in the source or target space without corresponding poses. Finally, we present a novel realtime physics-based animation technique allowing to simulate a large range of deformable materials such as fat, flesh, hair, or muscles. This approach could be used to produce more lifelike animations by enhancing the animated avatars with secondary effects. We believe that the realtime face tracking and animation pipeline presented in this thesis has the potential to inspire numerous future research in the area of computer-generated animation. Already, several ideas presented in thesis have been successfully used in industry and this work gave birth to the startup company faceshift AG

Elevation changes of mountain glaciers in the Antarctic Peninsula using ASTER-controlled archival aerial photography

PhD ThesisOver the last 50 years a significant increase in the atmospheric and upper ocean temperatures in the Antarctic Peninsula (AP) region has been observed. As a result major ice-shelves have retreated during the 20th century. In connection, glaciers have accelerated and an increased dynamic ice mass loss is observed, especially over the last decade. Despite these major changes, an exact quantification of ice mass changes of the AP, with its roughly 1000 glaciers, is not available. Almost no long-term (multi-decadal) glacier mass balance records for the AP exist and in-situ measurements are rare. On the other hand, the United States Geological Survey (USGS) and British Antarctic Survey (BAS) archives hold a large number of historic aerial stereo-photographs of the AP, dating back to the early 1940s. These images contain a valuable source of information and have been used to demonstrate widespread retreat of glaciers in this region. Less effort has been made so far to use this stereo-photography for the extraction of elevation data to compare it with recent elevation information to determine glacier volume change from which mass changes may be estimated. This dissertation seeks to close this research gap and to extend the number of mass balance records for the AP, by investigating, measuring, and analysing historical glacier elevation change in the AP using digital elevation models (DEMs) derived from USGS and BAS airborne (1948-2005) and ASTER spaceborne (2001-2010) stereo imagery. To ensure reliable and accurate measurements of surface elevation change, extracted DEMs need to be registered in a precise manner. The lack of ground control information in the AP is a major obstacle for this and can result in inaccurate absolute orientations of DEMs. If uncorrected, possible offsets between DEMs introduce significant error and i can lead to an over- or underestimation of glacier change. Thus, in order to precisely co-register corresponding historic and modern DEMs an iterative robust least squares surface matching algorithm was applied. The underlying surface matching approach was previously developed for small-scale coastal erosion studies at Newcastle University. Within the context of this work it has been successfully modified and improved to enable large scale glacier change assessment in areas of steep topography which is typical for the AP. For a total of 12 glaciers in the AP, located along the western coast between 64° and 71° S, DEMs from the historic archive stereo-imagery were successfully extracted and combined with DEMs derived from modern aerial and ASTER satellite imagery. The improved surface matching approach allowed precise co-registration of these DEMs and enabled the accurate measurement of glacier surface mass balance at the lower portion of the glaciers. Widespread frontal glacier surface lowering, of up to 50 m, has been observed on 12 glaciers with a mean lowering rate of 0.28 ± 0.03 m/yr over a period of 37 years (1970-2007). Higher rates, of up to 0.6 m/yr, were observed in the north-western Peninsula. Two glaciers which have multi-epoch coverage show a significantly larger-than-average lowering since about 1990. These results are in close correspondence with an increase in positive degree days over the last four decades and suggest that much of this lowering can be attributed to atmospheric forcing. However, the observed spatial and temporal variations in the lowering rates suggests that the pattern of surface change is not a simple one and that a regional upscaling is not straight forward. The glaciers represent only 1.2 % of all estimated glaciers in the AP and only the glacier fronts (~20 % of each glacier) were studied. Observations also show an elevation increase at some higher altitude locations within a few km of the glacier fronts, raising the potential that the lowering may have been at least partially compensated for by increased high-altitude accumulation.British Geological Survey BUFI and NER

On-board Obstacle Avoidance in the Teleoperation of Unmanned Aerial Vehicles

Teleoperation von Drohnen in Umgebungen ohne GPS-Verbindung und wenig Bewegungsspielraum stellt den Operator vor besondere Herausforderungen. Hindernisse in einer unbekannten Umgebung erfordern eine zuverlässige Zustandsschätzung und Algorithmen zur Vermeidung von Kollisionen. In dieser Dissertation präsentieren wir ein System zur kollisionsfreien Navigation einer ferngesteuerten Drohne mit vier Propellern (Quadcopter) in abgeschlossenen Räumen. Die Plattform ist mit einem Miniaturcomputer und dem Minimum an Sensoren ausgestattet. Diese Ausstattung genügt den Anforderungen an die Rechenleistung. Dieses Setup ermöglicht des Weiteren eine hochgenaue Zustandsschätzung mit Hilfe einer Kaskaden-Architektur, sehr gutes Folgeverhalten bezüglich der kommandierten Geschwindigkeit, sowie eine kollisionsfreie Navigation. Ein Komplementärfilter berechnet die Höhe der Drohne, während ein Kalman-Filter Beschleunigung durch eine IMU und Messungen eines Optical-Flow Sensors fusioniert und in die Softwarearchitektur integriert. Eine RGB-D Kamera stellt dem Operator ein visuelles Feedback, sowie Distanzmessungen zur Verfügung, um ein Roboter-zentriertes Modell umliegender Hindernisse mit Hilfe eines Bin-Occupancy-Filters zu erstellen. Der Algorithmus speichert die Position dieser Hindernisse, auch wenn sie das Sehfeld des Sensors verlassen, mit Hilfe des geschätzten Zustandes des Roboters. Das Prinzip des Ausweich-Algorithmus basiert auf dem Ansatz einer modell-prädiktiven Regelung. Durch Vorhersage der wahrscheinlichen Position eines Hindernisses werden die durch den Operator kommandierten Sollwerte gefiltert, um eine mögliche Kollision mit einem Hindernis zu vermeiden. Die Plattform wurde experimentell sowohl in einer räumlich abgeschlossenen Umgebung mit zahlreichen Hindernissen als auch bei Testflügen in offener Umgebung mit natürlichen Hindernissen wie z.B. Bäume getestet. Fliegende Roboter bergen das Risiko, im Fall eines Fehlers, sei es ein Bedienungs- oder Berechnungsfehler, durch einen Aufprall am Boden oder an Hindernissen Schaden zu nehmen. Aus diesem Grund nimmt die Entwicklung von Algorithmen dieser Roboter ein hohes Maß an Zeit und Ressourcen in Anspruch. In dieser Arbeit präsentieren wir zwei Methoden (Software-in-the-loop- und Hardware-in-the-loop-Simulation) um den Entwicklungsprozess zu vereinfachen. Via Software-in-the-loop-Simulation konnte der Zustandsschätzer mit Hilfe simulierter Sensoren und zuvor aufgenommener Datensätze verbessert werden. Eine Hardware-in-the-loop Simulation ermöglichte uns, den Roboter in Gazebo (ein bekannter frei verfügbarer ROS-Simulator) mit zusätzlicher auf dem Roboter installierter Hardware in Simulation zu bewegen. Ebenso können wir damit die Echtzeitfähigkeit der Algorithmen direkt auf der Hardware validieren und verifizieren. Zu guter Letzt analysierten wir den Einfluss der Roboterbewegung auf das visuelle Feedback des Operators. Obwohl einige Drohnen die Möglichkeit einer mechanischen Stabilisierung der Kamera besitzen, können unsere Drohnen aufgrund von Gewichtsbeschränkungen nicht auf diese Unterstützung zurückgreifen. Eine Fixierung der Kamera verursacht, während der Roboter sich bewegt, oft unstetige Bewegungen des Bildes und beeinträchtigt damit negativ die Manövrierbarkeit des Roboters. Viele wissenschaftliche Arbeiten beschäftigen sich mit der Lösung dieses Problems durch Feature-Tracking. Damit kann die Bewegung der Kamera rekonstruiert und das Videosignal stabilisiert werden. Wir zeigen, dass diese Methode stark vereinfacht werden kann, durch die Verwendung der Roboter-internen IMU. Unsere Ergebnisse belegen, dass unser Algorithmus das Kamerabild erfolgreich stabilisieren und der rechnerische Aufwand deutlich reduziert werden kann. Ebenso präsentieren wir ein neues Design eines Quadcopters, um dessen Ausrichtung von der lateralen Bewegung zu entkoppeln. Unser Konzept erlaubt die Neigung der Propellerblätter unabhängig von der Ausrichtung des Roboters mit Hilfe zweier zusätzlicher Aktuatoren. Nachdem wir das dynamische Modell dieses Systems hergeleitet haben, synthetisierten wir einen auf Feedback-Linearisierung basierten Regler. Simulationen bestätigen unsere Überlegungen und heben die Verbesserung der Manövrierfähigkeit dieses neuartigen Designs hervor.The teleoperation of unmanned aerial vehicles (UAVs), especially in cramped, GPS-restricted, environments, poses many challenges. The presence of obstacles in an unfamiliar environment requires reliable state estimation and active algorithms to prevent collisions. In this dissertation, we present a collision-free indoor navigation system for a teleoperated quadrotor UAV. The platform is equipped with an on-board miniature computer and a minimal set of sensors for this task and is self-sufficient with respect to external tracking systems and computation. The platform is capable of highly accurate state-estimation, tracking of the velocity commanded by the user and collision-free navigation. The robot estimates its state in a cascade architecture. The attitude of the platform is calculated with a complementary filter and its linear velocity through a Kalman filter integration of inertial and optical flow measurements. An RGB-D camera serves the purpose of providing visual feedback to the operator and depth measurements to build a probabilistic, robot-centric obstacle state with a bin-occupancy filter. The algorithm tracks the obstacles when they leave the field of view of the sensor by updating their positions with the estimate of the robot's motion. The avoidance part of our navigation system is based on the Model Predictive Control approach. By predicting the possible future obstacles states, the UAV filters the operator commands by altering them to prevent collisions. Experiments in obstacle-rich indoor and outdoor environments validate the efficiency of the proposed setup. Flying robots are highly prone to damage in cases of control errors, as these most likely will cause them to fall to the ground. Therefore, the development of algorithm for UAVs entails considerable amount of time and resources. In this dissertation we present two simulation methods, i.e. software- and hardware-in-the-loop simulations, to facilitate this process. The software-in-the-loop testing was used for the development and tuning of the state estimator for our robot using both the simulated sensors and pre-recorded datasets of sensor measurements, e.g., from real robotic experiments. With hardware-in-the-loop simulations, we are able to command the robot simulated in Gazebo, a popular open source ROS-enabled physical simulator, using computational units that are embedded on our quadrotor UAVs. Hence, we can test in simulation not only the correct execution of algorithms, but also the computational feasibility directly on the robot's hardware. Lastly, we analyze the influence of the robot's motion on the visual feedback provided to the operator. While some UAVs have the capacity to carry mechanically stabilized camera equipment, weight limits or other problems may make mechanical stabilization impractical. With a fixed camera, the video stream is often unsteady due to the multirotor's movement and can impair the operator's situation awareness. There has been significant research on how to stabilize videos using feature tracking to determine camera movement, which in turn is used to manipulate frames and stabilize the camera stream. However, we believe that this process could be greatly simplified by using data from a UAV’s on-board inertial measurement unit to stabilize the camera feed. Our results show that our algorithm successfully stabilizes the camera stream with the added benefit of requiring less computational power. We also propose a novel quadrotor design concept to decouple its orientation from the lateral motion of the quadrotor. In our design the tilt angles of the propellers with respect to the quadrotor body are being simultaneously controlled with two additional actuators by employing the parallelogram principle. After deriving the dynamic model of this design, we propose a controller for this platform based on feedback linearization. Simulation results confirm our theoretical findings, highlighting the improved motion capabilities of this novel design with respect to standard quadrotors

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic