Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

MEG and complex systems

MEG beamformer algorithms work by making the assumption that correlated and spatially distinct local field potentials do not develop in the human brain. Despite this assumption, images produced by such algorithms concur with those from other non-invasive and invasive estimates of brain function. In this paper we set out to develop a method that could be applied to raw MEG data to explicitly test his assumption. We show that a promax rotation of MEG channel data can be used as an approximate estimator of the number of spatially distinct correlated sources in any frequency band.

Understanding policy implementation processes as self-organizing systems

Implementation studies and related research in organizational theory can be enhanced by drawing on the field of complex systems to understand better and, as a consequence, more successfully manage change. This article reinterprets data previously published in the British Journal of Management to reveal a new contribution, that policy implementation processes should be understood as a self-organizing system in which adaptive abilities are extremely important for stakeholders. In other words, national policy is reinterpreted at the local level, with each local organization uniquely mixing elements of national policy with their own requirements making policy implementation unpredictable and more sketchy. The original article explained different paces and directions of change in terms of traditional management processes: leadership, politics, implementation and vision. By reinterpreting the data, it is possible to reveal that deeper level processes, which are more emergent, are also at work influencing change, which the authors label possibility space. Implications for theory, policy and practice are identified.

A methodology for analysis and control of discrete event dynamic systems

The rapid developments in computer technology have resulted in a widespread use of discrete event dynamic systems (DEDSs). This type of system is complex because it exhibits properties such as concurrency, conflict and non-determinism. It is therefore important to model and analyse such systems before implementation to ensure safe, deadlock free and optimal operation. This thesis investigates current modelling techniques and describes Petri net theory in more detail. It reviews top down, bottom up and hybrid Petri net synthesis techniques that are used to model large systems and introduces on object oriented methodology to enable modelling of larger and more complex systems. Designs obtained by this methodology are modular, easy to understand and allow re-use of designs. Control is the next logical step in the design process. This thesis reviews recent developments in control DEDSs and investigates the use of Petri nets in the design of supervisory controllers. The scheduling of exclusive use of resources is investigated and an efficient Petri net based scheduling algorithm is designed and a re-configurable controller is proposed. To enable the analysis and control of large and complex DEDSs, an object oriented C++ software tool kit was developed and used to implement a Petri net analysis tool, Petri net scheduling and control algorithms. Finally, the methodology was applied to two industrial DEDSs: a prototype can sorting machine developed by Eurotherm Controls Ltd., and a semiconductor testing plant belonging to SGS Thomson Microelectronics Ltd.

Design and implementation of graphical user interfaces for complex simulations

The development of increasingly powerful computers, which has enabled the use of windowing software, has also opened the way for the computer study, via simulation, of very complex physical systems. In this study, the main issues related to the implementation of interactive simulations of complex systems are identified and discussed. Most existing simulators are closed in the sense that there is no access to the source code and, even if it were available, adaptation to interaction with other systems would require extensive code re-writing. This work aims to increase the flexibility of such software by developing a set of object-oriented simulation classes, which can be extended, by subclassing, at any level, i.e., at the problem domain, presentation or interaction levels. A strategy, which involves the use of an object-oriented framework, concurrent execution of several simulation modules, use of a networked windowing system and the re-use of existing software written in procedural languages, is proposed. A prototype tool which combines these techniques has been implemented and is presented. It allows the on-line definition of the configuration of the physical system and generates the appropriate graphical user interface. Simulation routines have been developed for the chemical recovery cycle of a paper pulp mill. The application, by creation of new classes, of the prototype to the interactive simulation of this physical system is described. Besides providing visual feedback, the resulting graphical user interface greatly simplifies the interaction with this set of simulation modules. This study shows that considerable benefits can be obtained by application of computer science concepts to the engineering domain, by helping domain experts to tailor interactive tools to suit their needs.

T-cell epitope prediction and immune complex simulation using molecular dynamics:state of the art and persisting challenges

Atomistic Molecular Dynamics provides powerful and flexible tools for the prediction and analysis of molecular and macromolecular systems. Specifically, it provides a means by which we can measure theoretically that which cannot be measured experimentally: the dynamic time-evolution of complex systems comprising atoms and molecules. It is particularly suitable for the simulation and analysis of the otherwise inaccessible details of MHC-peptide interaction and, on a larger scale, the simulation of the immune synapse. Progress has been relatively tentative yet the emergence of truly high-performance computing and the development of coarse-grained simulation now offers us the hope of accurately predicting thermodynamic parameters and of simulating not merely a handful of proteins but larger, longer simulations comprising thousands of protein molecules and the cellular scale structures they form. We exemplify this within the context of immunoinformatics.

Convergence and knowledge processing in multi-agent systems

Multi-agent systems are complex systems comprised of multiple intelligent agents that act either independently or in cooperation with one another. Agent-based modelling is a method for studying complex systems like economies, societies, ecologies etc. Due to their complexity, very often mathematical analysis is limited in its ability to analyse such systems. In this case, agent-based modelling offers a practical, constructive method of analysis. The objective of this book is to shed light on some emergent properties of multi-agent systems. The authors focus their investigation on the effect of knowledge exchange on the convergence of complex, multi-agent systems.

The dynamics of a genetic algorithm under stabilizing selection

A formalism recently introduced by Prugel-Bennett and Shapiro uses the methods of statistical mechanics to model the dynamics of genetic algorithms. To be of more general interest than the test cases they consider. In this paper, the technique is applied to the subset sum problem, which is a combinatorial optimization problem with a strongly non-linear energy (fitness) function and many local minima under single spin flip dynamics. It is a problem which exhibits an interesting dynamics, reminiscent of stabilizing selection in population biology. The dynamics are solved under certain simplifying assumptions and are reduced to a set of difference equations for a small number of relevant quantities. The quantities used are the population's cumulants, which describe its shape, and the mean correlation within the population, which measures the microscopic similarity of population members. Including the mean correlation allows a better description of the population than the cumulants alone would provide and represents a new and important extension of the technique. The formalism includes finite population effects and describes problems of realistic size. The theory is shown to agree closely to simulations of a real genetic algorithm and the mean best energy is accurately predicted.

Public key cryptography and error correcting codes as Ising models

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.

Resource allocation in sparse graphs

Resource allocation in sparsely connected networks, a representative problem of systems with real variables, is studied using the replica and Bethe approximation methods. An efficient distributed algorithm is devised on the basis of insights gained from the analysis and is examined using numerical simulations,showing excellent performance and full agreement with the theoretical results. The physical properties of the resource allocation model are discussed.

Exploring innovation in policy-making within central government:the case of the UK's Highways Agency

The first and main contribution of this article is its access to the decision-making processes which drive innovation in policy-making within central government. The article will present a detailed case history of how the innovation came about and conclude by highlighting analytic possibilities for future research. The policy in focus is the UK’s Traffic Management Act 2004, which passed responsibility for managing incidents on major roads from the police to the Highways Agency (HA), and has been interpreted as a world first in traffic management. The article tracks the Traffic Management Act 2004 from problem identification to a preliminary evaluation. It is then suggested that future research could explain organizational change more theoretically. By taking a longitudinal and multi-level approach, the research falls into a processual account of organizational change. The second contribution of the article is to highlight two novel ways in which this approach is being applied to policy-making, through an institutional processualist research programme on public management reform and empirical investigations using complex systems to explain policy change.