A Convergent Overlapping Domain Decomposition Method for Total Variation Minimization

This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.Comment: Matlab code and numerical experiments of the methods provided in this paper can be downloaded at the web-page: http://homepage.univie.ac.at/carola.schoenlieb/webpage_tvdode/tv_dode_numerics.ht

The Hyper-log-chromaticity space for illuminant invariance

Variation in illumination conditions through a scene is a common issue for classification, segmentation and recognition applications. Traffic monitoring and driver assistance systems have difficulty with the changing illumination conditions at night, throughout the day, with multiple sources (especially at night) and in the presence of shadows. The majority of existing algorithms for color constancy or shadow detection rely on multiple frames for comparison or to build a background model. The proposed approach uses a novel color space inspired by the Log-Chromaticity space and modifies the bilateral filter to equalize illumination across objects using a single frame. Neighboring pixels of the same color, but of different brightness, are assumed to be of the same object/material. The utility of the algorithm is studied over day and night simulated scenes of varying complexity. The objective is not to provide a product for visual inspection but rather an alternate image with fewer illumination related issues for other algorithms to process. The usefulness of the filter is demonstrated by applying two simple classifiers and comparing the class statistics. The hyper-log-chromaticity image and the filtered image both improve the quality of the classification relative to the un-processed image

Energy-Aware Real-Time Scheduling on Heterogeneous and Homogeneous Platforms in the Era of Parallel Computing

Multi-core processors increasingly appear as an enabling platform for embedded systems, e.g., mobile phones, tablets, computerized numerical controls, etc. The parallel task model, where a task can execute on multiple cores simultaneously, can efficiently exploit the multi-core platform\u27s computational ability. Many computation-intensive systems (e.g., self-driving cars) that demand stringent timing requirements often evolve in the form of parallel tasks. Several real-time embedded system applications demand predictable timing behavior and satisfy other system constraints, such as energy consumption. Motivated by the facts mentioned above, this thesis studies the approach to integrating the dynamic voltage and frequency scaling (DVFS) policy with real-time embedded system application\u27s internal parallelism to reduce the worst-case energy consumption (WCEC), an essential requirement for energy-constrained systems. First, we propose an energy-sub-optimal scheduler, assuming the per-core speed tuning feature for each processor. Then we extend our solution to adapt the clustered multi-core platform, where at any given time, all the processors in the same cluster run at the same speed. We also present an analysis to exploit a task\u27s probabilistic information to improve the average-case energy consumption (ACEC), a common non-functional requirement of embedded systems. Due to the strict requirement of temporal correctness, the majority of the real-time system analysis considered the worst-case scenario, leading to resource over-provisioning and cost. The mixed-criticality (MC) framework was proposed to minimize energy consumption and resource over-provisioning. MC scheduling has received considerable attention from the real-time system research community, as it is crucial to designing safety-critical real-time systems. This thesis further addresses energy-aware scheduling of real-time tasks in an MC platform, where tasks with varying criticality levels (i.e., importance) are integrated into a common platform. We propose an algorithm GEDF-VD for scheduling MC tasks with internal parallelism in a multiprocessor platform. We also prove the correctness of GEDF-VD, provide a detailed quantitative evaluation, and reported extensive experimental results. Finally, we present an analysis to exploit a task\u27s probabilistic information at their respective criticality levels. Our proposed approach reduces the average-case energy consumption while satisfying the worst-case timing requirement

Investigating quantum many-body systems with tensor networks, machine learning and quantum computers

(English) We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM.(Español) En esta tesis, realizamos simulaciónes cuánticas en ordenadores clásicos y cuánticos y diseñamos un marco de aprendizaje automático en el que podemos construir diagramas de fase de sistemas cuánticos de muchas partículas de manera no supervisada. Las simulaciones clásicas se realizan con métodos de red de tensores de última generación en una y dos dimensiones espaciales. Para sistemas unidimensionales, utilizamos estados de productos de matrices (MPS) que tienen muchas ventajas prácticas y pueden optimizarse utilizando el eficiente algoritmo del grupo de renormalización de matrices de densidad (DMRG). Los datos para sistemas bidimensionales se obtienen mediante los denominados estados de pares entrelazados proyectados (PEPS) optimizados a través de la evolución en tiempo imaginario. Los datos, en forma de observables, espectros de entrelazamiento o partes de los vectores de estado de estas simulaciones, se introducen luego en un algoritmo de aprendizaje profundo (DL) donde realizamos la detección de anomalías para construir el diagrama de fase. Extendemos esta noción a los ordenadores cuánticos e introducimos la detección de anomalías cuánticas variacionales. Aquí, primero simulamos el estado fundamental y luego lo procesamos utilizando el aprendizaje automático cuántico (QML). Tanto las rutinas de simulación como el QML se realizan en el mismo dispositivo, lo que demostramos tanto en una simulación clásica como en un ordenador cuántico real de IBM.Postprint (published version

Systems of difference equations as a model for the Lorenz system

We consider systems of difference equations as a model for the Lorenz system of differential equations. Using the power series whose coefficients are the solutions of these systems, we define three real functions, that are approximation for the solutions of the Lorenz system

Reservoir Computing for Learning in Structured Domains

The study of learning models for direct processing complex data structures has gained an increasing interest within the Machine Learning (ML) community during the last decades. In this concern, efficiency, effectiveness and adaptivity of the ML models on large classes of data structures represent challenging and open research issues. The paradigm under consideration is Reservoir Computing (RC), a novel and extremely efficient methodology for modeling Recurrent Neural Networks (RNN) for adaptive sequence processing. RC comprises a number of different neural models, among which the Echo State Network (ESN) probably represents the most popular, used and studied one. Another research area of interest is represented by Recursive Neural Networks (RecNNs), constituting a class of neural network models recently proposed for dealing with hierarchical data structures directly. In this thesis the RC paradigm is investigated and suitably generalized in order to approach the problems arising from learning in structured domains. The research studies described in this thesis cover classes of data structures characterized by increasing complexity, from sequences, to trees and graphs structures. Accordingly, the research focus goes progressively from the analysis of standard ESNs for sequence processing, to the development of new models for trees and graphs structured domains. The analysis of ESNs for sequence processing addresses the interesting problem of identifying and characterizing the relevant factors which influence the reservoir dynamics and the ESN performance. Promising applications of ESNs in the emerging field of Ambient Assisted Living are also presented and discussed. Moving towards highly structured data representations, the ESN model is extended to deal with complex structures directly, resulting in the proposed TreeESN, which is suitable for domains comprising hierarchical structures, and Graph-ESN, which generalizes the approach to a large class of cyclic/acyclic directed/undirected labeled graphs. TreeESNs and GraphESNs represent both novel RC models for structured data and extremely efficient approaches for modeling RecNNs, eventually contributing to the definition of an RC framework for learning in structured domains. The problem of adaptively exploiting the state space in GraphESNs is also investigated, with specific regard to tasks in which input graphs are required to be mapped into flat vectorial outputs, resulting in the GraphESN-wnn and GraphESN-NG models. As a further point, the generalization performance of the proposed models is evaluated considering both artificial and complex real-world tasks from different application domains, including Chemistry, Toxicology and Document Processing

Modelling and Statistics of Spatial Point Processes

Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult