Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Stochastic and Optimal Distributed Control for Energy Optimization and Spatially Invariant Systems

Improving energy efficiency and grid responsiveness of buildings requires sensing, computing and communication to enable stochastic decision-making and distributed operations. Optimal control synthesis plays a significant role in dealing with the complexity and uncertainty associated with the energy systems. The dissertation studies general area of complex networked systems that consist of interconnected components and usually operate in uncertain environments. Specifically, the contents of this dissertation include tools using stochastic and optimal distributed control to overcome these challenges and improve the sustainability of electric energy systems. The first tool is developed as a unifying stochastic control approach for improving energy efficiency while meeting probabilistic constraints. This algorithm is applied to demonstrate energy efficiency improvement in buildings and improving operational efficiency of virtualized web servers, respectively. Although all the optimization in this technique is in the form of convex optimization, it heavily relies on semidefinite programming (SP). A generic SP solver can handle only up to hundreds of variables. This being said, for a large scale system, the existing off-the-shelf algorithms may not be an appropriate tool for optimal control. Therefore, in the sequel I will exploit optimization in a distributed way. The second tool is itself a concrete study which is optimal distributed control for spatially invariant systems. Spatially invariance means the dynamics of the system do not vary as we translate along some spatial axis. The optimal H2 [H-2] decentralized control problem is solved by computing an orthogonal projection on a class of Youla parameters with a decentralized structure. Optimal H∞ [H-infinity] performance is posed as a distance minimization in a general L∞ [L-infinity] space from a vector function to a subspace with a mixed L∞ and H∞ space structure. In this framework, the dual and pre-dual formulations lead to finite dimensional convex optimizations which approximate the optimal solution within desired accuracy. Furthermore, a mixed L2 [L-2] /H∞ synthesis problem for spatially invariant systems as trade-offs between transient performance and robustness. Finally, we pursue to deal with a more general networked system, i.e. the Non-Markovian decentralized stochastic control problem, using stochastic maximum principle via Malliavin Calculus

Experiments on networks of coupled opto-electronic oscillators and physical random number generators

In this thesis, we report work in two areas: synchronization in networks of coupled oscillators and the evaluation of physical random number generators. A ``chimera state'' is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is spontaneously broken into coherent and incoherent parts. We report a study of chimera states and cluster synchronization in two different opto-electronic experiments. The first experiment is a traditional network of four opto-electronic oscillators coupled by optical fibers. We show that the stability of the observed chimera state can be determined using the same group-theoretical techniques recently developed for the study of cluster synchrony. We present three novel results: (i) chimera states can be experimentally observed in small networks, (ii) chimera states can be stable, and (iii) at least some types of chimera states (those with identically synchronized coherent regions) are closely related to cluster synchronization. The second experiment uses a single opto-electronic feedback loop to investigate the dynamics of oscillators coupled in large complex networks with arbitrary topology. Recent work has demonstrated that an opto-electronic feedback loop can be used to realize ring networks of coupled oscillators. We significantly extend these capabilities and implement networks with arbitrary topologies by using field programmable gate arrays (FPGAs) to design appropriate digital filters and time delays. With this system, we study (i) chimeras in a five-node globally-coupled network, (ii) synchronization of clusters that are not predicted by network symmetries, and (iii) optimal networks for cluster synchronization. The field of random number generation is currently undergoing a fundamental shift from relying solely on pseudo-random algorithms to employing physical entropy sources. The standard evaluation practices, which were designed for pseudo-random number generators, are ill-suited to quantify the entropy that underlies physical random number generation. We review the state of the art in the evaluation of physical random number generation and recommend a new paradigm: quantifying entropy generation and understanding the physical limits for harvesting entropy from sources of randomness. As an illustration of our recommendations, we evaluate three common optical entropy sources: single photon time-of-arrival detection, chaotic lasers, and amplified spontaneous emission

Self-organised multi-objective network clustering for coordinated communications in future wireless networks

The fifth generation (5G) cellular system is being developed with a vision of 1000 times more capacity than the fourth generation (4G) systems to cope with ever increasing mobile data traffic. Interference mitigation plays an important role in improving the much needed overall capacity especially in highly interference-limited dense deployment scenarios envisioned for 5G. Coordinated multi-point (CoMP) is identified as a promising interference mitigation technique where multiple base stations (BS) can cooperate for joint transmission/reception by exchanging user/control data and perform joint signal processing to mitigate inter-cell interference and even exploit it as a useful signal. CoMP is already a key feature of long term evolution-advanced (LTE-A) and envisioned as an essential function for 5G. However, CoMP cannot be realized for the whole network due to its computational complexity, synchronization requirement between coordinating BSs and high backhaul capacity requirement. BSs need to be clustered into smaller groups and CoMP can be activated within these smaller clusters. This PhD thesis aims to investigate optimum dynamic CoMP clustering solutions in 5G and beyond wireless networks with massive small cell (SC) deployment. Truly self-organised CoMP clustering algorithms are investigated, aiming to improve much needed spectral efficiency and other network objectives especially load balancing in future wireless networks. Low complexity, scalable, stable and efficient CoMP clustering algorithms are designed to jointly optimize spectral efficiency, load balancing and limited backhaul availability. Firstly, we provide a self organizing, load aware, user-centric CoMP clustering algorithm in a control and data plane separation architecture (CDSA) proposed for 5G to maximize spectral efficiency and improve load balancing. We introduce a novel re-clustering algorithm for user equipment (UE) served by highly loaded cells and show that unsatisfied UEs due to high load can be significantly reduced with minimal impact on spectral efficiency. Clustering with load balancing algorithm exploits the capacity gain from increase in cluster size and also the traffic shift from highly loaded cells to lightly loaded neighbours. Secondly, we develop a novel, low complexity, stable, network-centric clustering model to jointly optimize load balancing and spectral efficiency objectives and tackle the complexity and scalability issues of user-centric clustering. We show that our clustering model provide high spectral efficiency in low-load scenario and better load distribution in high-load scenario resulting in lower number of unsatisfied users while keeping spectral efficiency at comparably high levels. Unsatisfied UEs due to high load are reduced by $68.5\%$ with our algorithm when compared to greedy clustering model. In this context, the unique contribution of this work that it is the first attempt to fill the gap in literature for multi-objective, network-centric CoMP clustering, jointly optimizing load balancing and spectral efficiency. Thirdly, we design a novel multi-objective CoMP clustering algorithm to include backhaul-load awareness and tackle one of the biggest challenges for the realization of CoMP in future networks i.e. the demand for high backhaul bandwidth and very low latency. We fill the gap in literature as the first attempt to design a clustering algorithm to jointly optimize backhaul/radio access load and spectral efficiency and analyze the trade-off between them. We employ 2 novel coalitional game theoretic clustering methods, 1-a novel merge/split/transfer coalitional game theoretic clustering algorithm to form backhaul and load aware BS clusters where spectral efficiency is still kept at high level, 2-a novel user transfer game model to move users between clusters to improve load balancing further. Stability and complexity analysis is provided and simulation results are presented to show the performance of the proposed method under different backhaul availability scenarios. We show that average system throughout is increased by 49.9% with our backhaul-load aware model in high load scenario when compared to a greedy model. Finally, we provide an operator's perspective on deployment of CoMP. Firstly, we present the main motivation and benefits of CoMP from an operator's viewpoint. Next, we present operational requirements for CoMP implementation and discuss practical considerations and challenges of such deployment. Possible solutions for these experienced challenges are reviewed. We then present initial results from a UL CoMP trial and discuss changes in key network performance indicators (KPI) during the trial. Additionally, we propose further improvements to the trialed CoMP scheme for better potential gains and give our perspective on how CoMP will fit into the future wireless networks

Evolutionary Game Theory: Theoretical Concepts and Applications to Microbial Communities

Ecological systems are complex assemblies of large numbers of individuals, interacting competitively under multifaceted environmental conditions. Recent studies using microbial laboratory communities have revealed some of the self-organization principles underneath the complexity of these systems. A major role of the inherent stochasticity of its dynamics and the spatial segregation of different interacting species into distinct patterns has thereby been established. It ensures the viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of “social” behavior. A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the mathematical tools and a conceptual framework for a deeper understanding of these ecological systems. We give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of microbial systems. Intrinsic fluctuations, stemming from the discreteness of individuals, are ubiquitous, and can have an important impact on the stability of ecosystems. In the absence of speciation, extinction of species is unavoidable. It may, however, take very long times. We provide a general concept for defining survival and extinction on ecological time-scales. Spatial degrees of freedom come with a certain mobility of individuals. When the latter is sufficiently high, bacterial community structures can be understood through mapping individual-based models, in a continuum approach, onto stochastic partial differential equations. These allow progress using methods of nonlinear dynamics such as bifurcation analysis and invariant manifolds. We conclude with a perspective on the current challenges in quantifying bacterial pattern formation, and how this might have an impact on fundamental research in non-equilibrium physics

Module hierarchy and centralisation in the anatomy and dynamics of human cortex

Systems neuroscience has recently unveiled numerous fundamental features of the macroscopic architecture of the human brain, the connectome, and we are beginning to understand how characteristics of brain dynamics emerge from the underlying anatomical connectivity. The current work utilises complex network analysis on a high-resolution structural connectivity of the human cortex to identify generic organisation principles, such as centralised, modular and hierarchical properties, as well as specific areas that are pivotal in shaping cortical dynamics and function. After confirming its small-world and modular architecture, we characterise the cortex’ multilevel modular hierarchy, which appears to be reasonably centralised towards the brain’s strong global structural core. The potential functional importance of the core and hub regions is assessed by various complex network metrics, such as integration measures, network vulnerability and motif spectrum analysis. Dynamics facilitated by the large-scale cortical topology is explored by simulating coupled oscillators on the anatomical connectivity. The results indicate that cortical connectivity appears to favour high dynamical complexity over high synchronizability. Taking the ability to entrain other brain regions as a proxy for the threat posed by a potential epileptic focus in a given region, we also show that epileptic foci in topologically more central areas should pose a higher epileptic threat than foci in more peripheral areas. To assess the influence of macroscopic brain anatomy in shaping global resting state dynamics on slower time scales, we compare empirically obtained functional connectivity data with data from simulating dynamics on the structural connectivity. Despite considerable micro-scale variability between the two functional connectivities, our simulations are able to approximate the profile of the empirical functional connectivity. Our results outline the combined characteristics a hierarchically modular and reasonably centralised macroscopic architecture of the human cerebral cortex, which, through these topological attributes, appears to facilitate highly complex dynamics and fundamentally shape brain function