Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Discrete and hybrid methods for the diagnosis of distributed systems

Many important activities of modern society rely on the proper functioning of complex systems such as electricity networks, telecommunication networks, manufacturing plants and aircrafts. The supervision of such systems must include strong diagnosis capability to be able to effectively detect the occurrence of faults and ensure appropriate corrective measures can be taken in order to recover from the faults or prevent total failure. This thesis addresses issues in the diagnosis of large complex systems. Such systems are usually distributed in nature, i.e. they consist of many interconnected components each having their own local behaviour. These components interact together to produce an emergent global behaviour that is complex. As those systems increase in complexity and size, their diagnosis becomes increasingly challenging. In the first part of this thesis, a method is proposed for diagnosis on distributed systems that avoids a monolithic global computation. The method, based on converting the graph of the system into a junction tree, takes into account the topology of the system in choosing how to merge local diagnoses on the components while still obtaining a globally consistent result. The method is shown to work well for systems with tree or near-tree structures. This method is further extended to handle systems with high clustering by selectively ignoring some connections that would still allow an accurate diagnosis to be obtained. A hybrid system approach is explored in the second part of the thesis, where continuous dynamics information on the system is also retained to help better isolate or identify faults. A hybrid system framework is presented that models both continuous dynamics and discrete evolution in dynamical systems, based on detecting changes in the fundamental governing dynamics of the system rather than on residual estimation. This makes it possible to handle systems that might not be well characterised and where parameter drift is present. The discrete aspect of the hybrid system model is used to derive diagnosability conditions using indicator functions for the detection and isolation of multiple, arbitrary sequential or simultaneous events in hybrid dynamical networks. Issues with diagnosis in the presence of uncertainty in measurements due sensor or actuator noise are addressed. Faults may generate symptoms that are in the same order of magnitude as the latter. The use of statistical techniques,within a hybrid system framework, is proposed to detect these elusive fault symptoms and translate this information into probabilities for the actual operational mode and possibility of transition between modes which makes it possible to apply probabilistic analysis on the system to handle the underlying uncertainty present

Decentralised Algorithms for Wireless Networks.

Designing and managing wireless networks is challenging for many reasons. Two of the most crucial in 802.11 wireless networks are: (a) variable per-user channel quality and (b) unplanned, ad-hoc deployment of the Access Points (APs). Regarding (a), a typical consequence is the selection, for each user, of a different bit-rate, based on the channel quality. This in turn causes the so-called performance “anomaly”, where the users with lower bit-rate transmit for most of the time, causing the higher bit-rate users to receive less time for transmission (air time). Regarding (b), an important issue is managing interference. This can be mitigated by selecting different channels for neighbouring APs, but needs to be carried out in a decentralised way because often APs belong to different administrative domains, or communication between APs is unfeasible. Tools for managing unplanned deployment are also becoming important for other small cell networks, such as femtocell networks, where decentralised allocation of scrambling codes is a key task

Out-of-equilibrium economic dynamics and persistent polarisation

Most of economics is equilibrium economics of one sort or another. The study of outof- equilibrium economics has largely been neglected. This thesis, engaging with ideas and techniques from complexity science, develops frameworks and tools for out-of-equilibrium modelling. We initially focus our attention on models of exchange before examining methods of agent-based modelling. Finally we look at a set of models for social dynamics with nontrivial micro-macro interrelationships. Chapter 2 introduces complexity science and relevant economic concepts. In particular we examine the idea of complex adaptive systems, the application of complexity to economics, some key ideas from microeconomics, agent-based modelling and models of segregation and/or polarisation. Chapter 3 develops an out-of-equilibrium, fully decentralised model of bilateral exchange. Initially we study the limiting properties of our out-of-equilibrium dynamic, characterising the conditions required for convergence to pairwise and Pareto optimal allocation sets. We illustrate problems that can arise for a rigid version of the model and show how even a small amount of experimentation can overcome these. We investigate the model numerically characterising the speed of convergence and changes in ex post wealth. In chapter 4 we now explicitly model the trading structure on a network. We derive analytical results for this general network case. We investigate the e�ect of network structure on outcomes numerically and contrast the results with the fully connected case of chapter 3. We look at extensions of the model including a version with an endogenous network structure and a versions where agents can learn to accept a `worthless' but widely available good in exchanges. Chapter 5 outlines and demonstrates a new approach to agent-based modelling which draws on a number techniques from contemporary software engineering. We develop a prototype framework to illustrate how the ideas might be applied in practice in order to address methodological gaps in many current approaches. We develop example agent-based models and contrast the approach with existing agent-based modelling approaches and the kind of purpose built models which were used for the numerical results in chapters 3 and 4. Chapter 6 develops a new set of models for thinking about a wide range of social dynamics issues including human capital acquisition and migration. We analyse the models initially from a Nash equilibrium perspective. Both continuum and �nite versions of the model are developed and related. Using the criterion of stochastic stability we think about the long run behaviour of a version of the model. We introduce agent heterogeneity into the model. We conclude with a fully dynamic version of the model (using techniques from chapter 5) which looks at endogenous segregation

Post-quantum blockchain for internet of things domain

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonIn the evolving realm of quantum computing, emerging advancements reveal substantial challenges and threats to existing cryptographic infrastructures, particularly impacting blockchain technologies. These are pivotal for securing the Internet of Things (IoT) ecosystems. The traditional blockchain structures, integral to myriad IoT applications, are susceptible to potential quantum computations, emphasizing an urgent need for innovations in post-quantum blockchain solutions to reinforce security in the expansive domain of IoT. This PhD thesis delves into the crucial exploration and meticulous examination of the development and implementation of post-quantum blockchain within the IoT landscape, focusing on the incorporation of advanced post-quantum cryptographic algorithms in Hyperledger Fabric, a forefront blockchain platform renowned for its versatility and robustness. The primary aim is to discern viable post-quantum cryptographic solutions capable of fortifying blockchain systems against impending quantum threats enhancing security and reliability in IoT applications. The research comprehensively evaluates various post-quantum public-key generation and digital signature algorithms, performing detailed analyses of their computational time and memory usage to identify optimal candidates. Furthermore, the thesis proposes an innovative lattice-based digital signature scheme Fast-Fourier Lattice-based Compact Signature over NTRU (Falcon), which leverages the Monte Carlo Markov Chain (MCMC) algorithm as a trapdoor sampler to augment its security attributes. The research introduces a post-quantum version of the Hyperledger Fabric blockchain that integrates post-quantum signatures. The system utilizes the Open Quantum Safe (OQS) library, rigorously tested against NIST round 3 candidates for optimal performance. The study highlights the capability to manage IoT data securely on the post-quantum Hyperledger Fabric blockchain through the Message Queue Telemetry Transport (MQTT) protocol. Such a configuration ensures safe data transfer from IoT sensors directly to the blockchain nodes, securing the processing and recording of sensor data within the node ledger. The research addresses the multifaceted challenges of quantum computing advancements and significantly contributes to establishing secure, efficient, and resilient post-quantum blockchain infrastructures tailored explicitly for the IoT domain. These findings are instrumental in elevating the security paradigms of IoT systems against quantum vulnerabilities and catalysing innovations in post-quantum cryptography and blockchain technologies. Furthermore, this thesis introduces strategies for the optimization of performance and scalability of post-quantum blockchain solutions and explores alternative, energy-efficient consensus mechanisms such as the Raft and Stellar Consensus Protocol (SCP), providing sustainable alternatives to the conventional Proof-of-Work (PoW) approach. A critical insight emphasized throughout this thesis is the imperative of synergistic collaboration among academia, industry, and regulatory bodies. This collaboration is pivotal to expedite the adoption and standardization of post-quantum blockchain solutions, fostering the development of interoperable and standardized technologies enriched with robust security and privacy frameworks for end users. In conclusion, this thesis furnishes profound insights and substantial contributions to implementing post-quantum blockchain in the IoT domain. It delineates original contributions to the knowledge and practices in the field, offering practical solutions and advancing the state-of-the-art in post-quantum cryptography and blockchain research, thereby paving the way for a secure and resilient future for interconnected IoT systems

Reinforcement Learning

Brains rule the world, and brain-like computation is increasingly used in computers and electronic devices. Brain-like computation is about processing and interpreting data or directly putting forward and performing actions. Learning is a very important aspect. This book is on reinforcement learning which involves performing actions to achieve a goal. The first 11 chapters of this book describe and extend the scope of reinforcement learning. The remaining 11 chapters show that there is already wide usage in numerous fields. Reinforcement learning can tackle control tasks that are too complex for traditional, hand-designed, non-learning controllers. As learning computers can deal with technical complexities, the tasks of human operators remain to specify goals on increasingly higher levels. This book shows that reinforcement learning is a very dynamic area in terms of theory and applications and it shall stimulate and encourage new research in this field

Building networks of Markov decision processes to achieve synchronised behaviour from complex multi-agent systems

Complex multi-agent systems, consisting of multiple decision making agents as part of a larger collective, are particularly complex control problems, because of the potential for emergent (and potentially undesirable or even unsafe) behaviours to arise from the interaction between separate agents. When a number of autonomous systems interact with one another, be they robotic systems, intelligent software agents, or autonomous vehicles, they can become a complex multi-agent system, potentially prone to emergent behaviours. Understanding, controlling and assuring complex multi-agent systems is a difficult challenge for the systems engineer, through all stages of the engineering lifecycle. There is often no simple mechanism to control the behaviour of the whole, and no established formal techniques for system proving. The underpinning mathematics is too far removed from the systems of years gone by for established techniques to be transferrable. This thesis takes a fresh look at this topic using the mathematical framework of complexity science and theoretical aspects of systems science to begin to tackle this knotty problem domain. Synchronised robotics is a concept introduced for this PhD to describe systems consisting of multiple robotic appendages acting independently based on simple control logic, but unbeknownst to the individual robots also acting as part of a carefully choreographed collective system. Synchronised robotics provides an ideal application area from which to develop and explore an exemplar scenario. Production line robotics are the chosen exemplar. This thesis shows how systems science principles can be utilised to represent all kinds of complex multi-agent system, with different internal network structures between decision nodes mirroring the myriad of ways that a systems architect might choose to construct his or her system. It then proceeds to show how to generalise the Markov Decision Process (MDP) formulation to these networks, to produce models of interactive autonomy. This novel approach to systems design and proving is brought to life through application to the production line robotics exemplar, for which a mathematical model based on the processes and techniques described has been built, tested, and initial results obtained demonstrating the potential efficacy of the approach for capturing the complex behaviours displayed, providing a control mechanism with improved resilience to correcting undesirable emergent behaviours, and pointing a way towards a potential future system proving tool for multi-agent systems