In this thesis, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral drive by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.

Wireless networks and power distribution grids are experiencing increasing demands on their efficiency and reliability. Judicious methods for allocating scarce resources such as power and bandwidth are of paramount importance. As a result, nonlinear optimization and signal processing tools have been incorporated into the design of contemporary networks. This thesis develops schemes for efficient resource allocation (RA) in such dynamic networks, with an emphasis in stochasticity, which is accounted for in the problem formulation as well as in the algorithms and schemes to solve those problems. Stochastic optimization and decomposition techniques are investigated to develop low-complexity algorithms with specific applications in cross-layer design of wireless communications, cognitive radio (CR) networks and smart power distribution systems. The costs and constraints on the availability of network resources, together with diverse quality of service (QoS) requirements, render network design, management, and operation challenging ...

The overriding aim of this thesis is to investigate the benefits of focusing time-frequency analysis on particular regions of the time-frequency plane. The thesis examines aspects of such a regionalisation in the analysis of both deterministic signals and stochastic processes. The majority of deterministic energetic time-frequency representations are non-parametric indicating the distribution of the energy of a signal in the time-frequency plane but providing no further information about the time-frequency structure. This thesis develops a semi-parametric time-frequency model to simultaneously describe the time-frequency energetic structure of a signal and provide an indication of its time-frequency complexity. The model aims to identify ‘timefrequency components’ within the signal to indicate how their energy is distributed in the time-frequency plane and thereby to probabilistically associate every location in the plane with each identified component. The thesis investigates a number of applications of the ...

In this thesis we focus on the development of energy-efficient adaptive algorithms for Wireless Sensor Networks. Its contributions can be arranged in two main lines. Firstly, we focus on the efficient management of energy resources in WSNs equipped with finite-size batteries and energy-harvesting devices. To that end, we propose a censoring scheme by which the nodes are able to decide if a message transmission is worthy or not given their energetic condition. In order to do so, we model the system using a Markov Decision Process and use this model to derive optimal policies. Later, these policies are analyzed in simplified scenarios in order to get insights of their features. Finally, using Stochastic Approximation, we develop low-complexity censoring algorithms that approximate the optimal policy, with less computational complexity and faster convergence speed than other approaches such as Q-learning. Secondly, we ...

Recent advances in many fields ranging from engineering to natural science, require increasingly complicated optimization tasks in the experiment design, for which the target objectives are generally in the form of black-box functions that are expensive to evaluate. In a common formulation of this problem, a designer is expected to solve the black-box optimization tasks via sequentially attempting candidate solutions and receiving feedback from the system. This thesis considers Bayesian optimization (BO) as the black-box optimization framework, and investigates the enhancements on BO from the aspects of efficiency, adaptation and reliability. Generally, BO consists of a surrogate model for providing probabilistic inference and an acquisition function which leverages the probabilistic inference for selecting the next candidate solution. Gaussian process (GP) is a prominent non-parametric surrogate model, and the quality of its inference is a critical factor on the optimality performance ...

Advanced mobile communication systems are characterized by a dense deployment of different types of wireless access points. Since these systems are primarily limited by interference, multiple-input multiple-output (MIMO) techniques as well as coordinated transmission and detection schemes are necessary to mitigate this limitation. Thus, mobile communication systems become more complex which requires that also the mathematical tools for their theoretical analysis must evolve. These must be able to take the most important system characteristics into account, such as fading, path loss, and interference. The aim of this thesis is to develop such tools based on large random matrix theory and to demonstrate their usefulness with the help of several practical applications, such as the performance analysis of network MIMO and large-scale MIMO systems, the design of low-complexity polynomial expansion detectors, and the study of random beamforming techniques as well as ...

In the current heterogeneous communication environments, the great variety of multimedia systems and applications combined with fast evolution of networking architectures and topologies, give rise to new research problems related to the various elements of the communication chain. This includes, the ever present problem in video communications, which results from the need for coping with transmission errors and losses. In this context, video streaming with path diversity appeared as a novel communication framework, involving different technological fields and posing several research challenges. The research work carried out in this thesis is a contribution to robust video coding and adaptation techniques in the field of Multiple Description Coding (MDC) for multipath video streaming. The thesis starts with a thorough study of MDC and its theoretical basis followed by a description of the most important practical implementation aspects currently available in literature. ...

Multiple antennas at the base station side can be used to enhance the spectral efficiency and energy efficiency of the next generation wireless technologies. Indeed, massive multi-input multi-output (MIMO) is seen as one promising technology to bring the aforementioned benefits for fifth generation wireless standard, commonly known as 5G New Radio (5G NR). In this monograph, we will explore a wide range of potential topics in multi-user MIMO (MU-MIMO) relevant to 5G NR, • Sum rate maximizing beamforming (BF) design and robustness to partial channel state information at the transmitter (CSIT) • Asymptotic analysis of the various BF techniques in massiveMIMO and • Bayesian channel estimationmethods using sparse Bayesian learning. While massive MIMO has the aforementioned benefits, it makes the acquisition of the channel state information at the transmitter (CSIT) very challenging. Since it requires large amount of uplink (UL) ...

This dissertation develops false discovery rate (FDR) controlling machine learning algorithms for large-scale high-dimensional data. Ensuring the reproducibility of discoveries based on high-dimensional data is pivotal in numerous applications. The developed algorithms perform fast variable selection tasks in large-scale high-dimensional settings where the number of variables may be much larger than the number of samples. This includes large-scale data with up to millions of variables such as genome-wide association studies (GWAS). Theoretical finite sample FDR-control guarantees based on martingale theory have been established proving the trustworthiness of the developed methods. The practical open-source R software packages TRexSelector and tlars, which implement the proposed algorithms, have been published on the Comprehensive R Archive Network (CRAN). Extensive numerical experiments and real-world problems in biomedical and financial engineering demonstrate the performance in challenging use-cases. The first three main parts of this dissertation present ...

The theory of statistical signal processing finds a wide variety of applications in the fields of data communications, such as in channel estimation, equalization and symbol detection, and sensor array processing, as in beamforming, and radar systems. Indeed, a large number of these applications can be interpreted in terms of a parametric estimation problem, typically approached by a linear filtering operation acting upon a set of multidimensional observations. Moreover, in many cases, the underlying structure of the observable signals is linear in the parameter to be inferred. This dissertation is devoted to the design and evaluation of statistical signal processing methods under realistic implementation conditions encountered in practice. Traditional statistical signal processing techniques intrinsically provide a good performance under the availability of a particularly high number of observations of fixed dimension. Indeed, the original optimality conditions cannot be theoretically guaranteed ...

In the last decade, cooperation among multiple terminals has been seen as one of the more promising strategies to improve transmission speed in wireless communications networks. Basically, the idea is to mimic an antenna array and apply distributed versions of well-known space-diversity techniques. In this context, the simplest cooperative scheme is the relay channel: all the terminals (relays) that overhear a point-to-point communication between a source and a destination may decide to aid the source by forwarding (relaying) its message. In a mobile system, it is common to assume that the relays do not have any information about the channel between them and the destination. Under this hypothesis, the best solution to exploit the diversity offered by multiple transmitting antennas is to use space-time coding (STC). However, classical STC's are designed for systems with a fixed and usually low number ...

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...

The brain is the substrate of a complex dynamic system providing a remarkably varied range of functionalities, going from simple perception to higher-level cognition. Disturbances in its complex dynamics can cause an equally vast variety of mental disorders. One such brain disorder is schizophrenia, a neurodevelopmental disease characterized by abnormal perception of reality that manifests in symptoms like hallucinations or delusions. Even though the brain is known to be affected in schizophrenia, the exact pathophysiology underlying its developmental course is still mostly unknown. In this thesis, we develop and apply methods to look into ongoing brain function measured through magnetic resonance imaging (MRI) and evaluate the potential of these approaches for improving our understanding of psychosis vulnerability and schizophrenia. We focus on patients with chromosome 22q11.2 deletion syndrome (22q11DS), a genetic disorder that comes with a 30fold increased risk for ...

A large variety of important tasks in low­-level vision, image analysis and pat­tern recognition can be formulated as discrete labeling problems where one seeks to optimize some measure of the quality of the labeling. For example such is the case in optical flow estimation, stereo matching, image restoration to men­tion only a few of them. Discrete Markov Random Fields are ideal candidates for modeling these labeling problems and, for this reason, they are ubiquitous in computer vision. Therefore, an issue of paramount importance, that has at­tracted a significant amount of computer vision research over the past years, is how to optimize discrete Markov Random Fields efficiently and accurately. The main theme of this thesis is concerned exactly with this issue. Two novel MRF op­timization schemes are thus presented, both of which manage to extend current state-­of­-the­-art techniques in significant ways. ...

MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) CHANNELS constitute a unified way of modeling a wide range of different physical communication channels, which can then be handled with a compact and elegant vector-matrix notation. The two paradigmatic examples are wireless multi-antenna channels and wireline Digital Subscriber Line (DSL) channels. Research in antenna arrays (also known as smart antennas) dates back to the 1960s. However, the use of multiples antennas at both the transmitter and the receiver, which can be naturally modeled as a MIMO channel, has been recently shown to offer a significant potential increase in capacity. DSL has gained popularity as a broadband access technology capable of reliably delivering high data rates over telephone subscriber lines. A DSL system can be modeled as a communication through a MIMO channel by considering all the copper twisted pairs within a binder as a whole rather ...