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.

L'Australie et la Nouvelle-Zélande:deux puissances régionales contraintes à l’action

Somehow, almost despite themselves, Australia and New Zealand have become regional powers. First burdened with colonial duties then abandoned by their mother country, Australia and New Zealand had little choice but to ensure their own security and development, a goal necessarily founded on regional action, although their geostrategic environment would sometimes impact differently on each power. However, growing instability in the South Pacific from the end of the 1990s constrained both to seek new and stronger roles in the region. Between neo-colonialism and the imperatives of regional security, Australia and New Zealand were left with no other choice but to react.

Design methodology for the servo control of high speed multi-axis machinery (BL): decoupling and synchronisation of a generic machine by blockwise decentralised MIMO control

Traditional machinery for manufacturing processes are characterised by actuators powered and co-ordinated by mechanical linkages driven from a central drive. Increasingly, these linkages are replaced by independent electrical drives, each performs a different task and follows a different motion profile, co-ordinated by computers. A design methodology for the servo control of high speed multi-axis machinery is proposed, based on the concept of a highly adaptable generic machine model. In addition to the dynamics of the drives and the loads, the model includes the inherent interactions between the motion axes and thus provides a Multi-Input Multi-Output (MIMO) description. In general, inherent interactions such as structural couplings between groups of motion axes are undesirable and needed to be compensated. On the other hand, imposed interactions such as the synchronisation of different groups of axes are often required. It is recognised that a suitable MIMO controller can simultaneously achieve these objectives and reconciles their potential conflicts. Both analytical and numerical methods for the design of MIMO controllers are investigated. At present, it is not possible to implement high order MIMO controllers for practical reasons. Based on simulations of the generic machine model under full MIMO control, however, it is possible to determine a suitable topology for a blockwise decentralised control scheme. The Block Relative Gain array (BRG) is used to compare the relative strength of closed loop interactions between sub-systems. A number of approaches to the design of the smaller decentralised MIMO controllers for these sub-systems has been investigated. For the purpose of illustration, a benchmark problem based on a 3 axes test rig has been carried through the design cycle to demonstrate the working of the design methodology.

Study of synchronisation in chains of coupled non-linear oscillators and resonators

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Probabilistic synchronisation of pinning control

This paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty. A probabilistic control method for adaptive synchronization is presented. All required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength, the state and control values. Robustness of the probabilistic controller is proved via the Liapunov method. Furthermore, based on the residual error of the network states we introduce the definition of stochastic pinning controllability. A coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments. The theoretical derivation is complemented by its validation on two representative examples.

Le(s) temps du compte rendu sportif

Cellard (1979 : 19) avançait de façon quelque peu impressionniste que ‘le passé simple se rencontrait beaucoup plus souvent dans les comptes rendus de rencontres sportives de notre journal que dans toute autre catégorie de textes’. Même si un tel passé perfectif serait le vecteur idéal du rapport d’un exploit sportif au déroulement chronologique, la réalité des textes nous offre un panorama nettement diversifié. Une compétition acharnée se joue avec d’autres tiroirs verbaux (passé composé, imparfait, présent) qui, chacun, offre une présentation différente des procès. Après une brève présentation théorique de chaque tiroir, nous entamerons une étude de corpus basée sur des textes de presse francophone. Nous conclurons que le panorama temporel du compte rendu sportif contemporain pourrait résulter de contraintes extra-linguistiques comme le type de publication et l’évolution des médias.

La guerre des Balkans:élites nationales et discours transnationaux dans la française, allemande et britannique

Cet article repose sur une étude de la presse de lEstablishment en France, en Allemagne et au Royaume-Uni, au cours de la guerre des Balkans en 1999. Les sources sont la Frankfurter Allgemeine Zeitung, Le Monde et le Financial Times. Lobjectif est de voir en quoi la manière de rapporter les événements révèle des priorités politiques des diverses élites qui lisent ces journaux, ainsi que de leur perception de lordre international. Le résultat des travaux indique lexistence dun certain degré de synchronisation dans la façon dont la presse a concentré lattention de lopinion publique ; il indique aussi quil existe des différences sensibles entre ces journaux français, allemand et britannique, en termes de contenu et de perspectives. Malgré lexistence dun discours transnational, la sphère publique européenne demeure fragmentée. This article is based on a study of the press in France, Germany and the United Kingdom, during the Balkans war in 1999. The sources are the Frankfurter Allgemeine Zeitung, Le Monde and the Financial Times. The objectve is to see how report events reveal the priorities of the various political elites who read these newspapers, as well as their perception of international lordre. The outcome of the study indicates some degree of synchronization in the way the press has focused mindfulness of public opinion and that it also indicates there are significant differences between the French newspapers, German and British, in terms of content and perspectives. Despite the existence of a transnational speech, the European public sphere remains fragmented.

GLM-beamformer method demonstrates stationary field, alpha ERD and gamma ERS co-localisation with fMRI BOLD response in visual cortex

Recently, we introduced a new 'GLM-beamformer' technique for MEG analysis that enables accurate localisation of both phase-locked and non-phase-locked neuromagnetic effects, and their representation as statistical parametric maps (SPMs). This provides a useful framework for comparison of the full range of MEG responses with fMRI BOLD results. This paper reports a 'proof of principle' study using a simple visual paradigm (static checkerboard). The five subjects each underwent both MEG and fMRI paradigms. We demonstrate, for the first time, the presence of a sustained (DC) field in the visual cortex, and its co-localisation with the visual BOLD response. The GLM-beamformer analysis method is also used to investigate the main non-phase-locked oscillatory effects: an event-related desynchronisation (ERD) in the alpha band (8-13 Hz) and an event-related synchronisation (ERS) in the gamma band (55-70 Hz). We show, using SPMs and virtual electrode traces, the spatio-temporal covariance of these effects with the visual BOLD response. Comparisons between MEG and fMRI data sets generally focus on the relationship between the BOLD response and the transient evoked response. Here, we show that the stationary field and changes in oscillatory power are also important contributors to the BOLD response, and should be included in future studies on the relationship between neuronal activation and the haemodynamic response. © 2005 Elsevier Inc. All rights reserved.

Computer control of machines utilising independent drive mechanisms

The thesis describes an investigation into methods for the specification, design and implementation of computer control systems for flexible manufacturing machines comprising multiple, independent, electromechanically-driven mechanisms. An analysis is made of the elements of conventional mechanically-coupled machines in order that the operational functions of these elements may be identified. This analysis is used to define the scope of requirements necessary to specify the format, function and operation of a flexible, independently driven mechanism machine. A discussion of how this type of machine can accommodate modern manufacturing needs of high-speed and flexibility is presented. A sequential method of capturing requirements for such machines is detailed based on a hierarchical partitioning of machine requirements from product to independent drive mechanism. A classification of mechanisms using notations, including Data flow diagrams and Petri-nets, is described which supports capture and allows validation of requirements. A generic design for a modular, IDM machine controller is derived based upon hierarchy of control identified in these machines. A two mechanism experimental machine is detailed which is used to demonstrate the application of the specification, design and implementation techniques. A computer controller prototype and a fully flexible implementation for the IDM machine, based on Petri-net models described using the concurrent programming language Occam, is detailed. The ability of this modular computer controller to support flexible, safe and fault-tolerant operation of the two intermittent motion, discrete-synchronisation independent drive mechanisms is presented. The application of the machine development methodology to industrial projects is established.

Collective behaviour in a square lattice of driven Duffing resonators coupled to van der Pol oscillators

The global and local synchronisation of a square lattice composed of alternating Duffing resonators and van der Pol oscillators coupled through displacement is studied. The lattice acts as a sensing device in which the input signal is characterised by an external driving force that is injected into the system through a subset of the Duffing resonators. The parameters of the system are taken from MEMS devices. The effects of the system parameters, the lattice architecture and size are discussed.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Development and application of magnetoencephalographic methods in the investigation of the human visual system

This thesis is an exploration of the organisation and functioning of the human visual system using the non-invasive functional imaging modality magnetoencephalography (MEG). Chapters one and two provide an introduction to the ‘human visual system and magnetoencephalographic methodologies. These chapters subsequently describe the methods by which MEG can be used to measure neuronal activity from the visual cortex. Chapter three describes the development and implementation of novel analytical tools; including beamforming based analyses, spectrographic movies and an optimisation of group imaging methods. Chapter four focuses on the use of established and contemporary analytical tools in the investigation of visual function. This is initiated with an investigation of visually evoked and induced responses; covering visual evoked potentials (VEPs) and event related synchronisation/desynchronisation (ERS/ERD). Chapter five describes the employment of novel methods in the investigation of cortical contrast response and demonstrates distinct contrast response functions in striate and extra-striate regions of visual cortex. Chapter six use synthetic aperture magnetometry (SAM) to investigate the phenomena of visual cortical gamma oscillations in response to various visual stimuli; concluding that pattern is central to its generation and that it increases in amplitude linearly as a function of stimulus contrast, consistent with results from invasive electrode studies in the macaque monkey. Chapter seven describes the use of driven visual stimuli and tuned SAM methods in a pilot study of retinotopic mapping using MEG; finding that activity in the primary visual cortex can be distinguished in four quadrants and two eccentricities of the visual field. Chapter eight is a novel implementation of the SAM beamforming method in the investigation of a subject with migraine visual aura; the method reveals desynchronisation of the alpha and gamma frequency bands in occipital and temporal regions contralateral to observed visual abnormalities. The final chapter is a summary of main conclusions and suggested further work.

Investigation of the neural correlates of recognition memory using magnetoencephalography

Neuroimaging literature has identified several regions involved in encoding and recognition processes. A review of the literature illustrated considerable variations in the precise location and mechanisms of these processes, and it was these variations that were investigated in the studies in this thesis. Magnetoencephalography (MEG) was used as the neuroimaging tool and a preliminary study identified Synthetic Aperture Magnetometry (SAM) and not a traditional dipole fitting technique, as an appropriate tool for identifying the multiple cortical regions involved in recognition memory. It has been suggested that there is hemispheric asymmetry in encoding and recognition processes. There are two main hypotheses: the first suggesting that there is task-specificity, the second that this specificity is determined by stimulus modality. A series of experiments was completed with two main aims: first to produce consistent and complementary recognition memory data with MEG, and second to determine whether there exists any hemispheric asymmetry in recognition memory. The results obtained from five experiments demonstrated activation of prefrontal and middle temporal structures, which were consistent with those reported in previous neuroimaging studies. It was suggested that this diverse activation may be explained by the involvement of a semantic network during recognition memory processes. In support of this, a subsequent study involving a semantic encoding task demonstrated that category-specific differences in cortical activation also existed in the recognition memory phase. Controlling for the involvement of such semantic processes produced predominantly bilateral activation. It was suggested that the apparent hemispheric asymmetry findings reported in the literature may be due to the 'coarse' temporal analysis available with earlier imaging techniques, which over-simplified the networks reported by being unable to recognise the early complex processes associated with semantic processing which these MEG studies were able to identify. The importance of frequency-specific activations, specifically theta synchronisation and alpha desynchronisation, in memory processes was also investigated.

Accommodation and intraocular pressure

The relationship between accommodation and intraocular pressure (lOP) has not been addressed as a research question for over 20 years, when measurement of both of these parameters was less advanced than today. Hence the central aim of this thesis was to evaluate the effects of accommodation on lOP. The instrument of choice throughout this thesis was the Pulsair EasyEye non-contact tonometer (NCT) due principally to its slim-line design which allowed the measurement of lOP in one eye and simultaneous stimulation of accommodation in the other eye. A second reason for using the Pulsair EasyEye NCT was that through collaboration with the manufacturers (Keeler, UK) the instrument's operational technology was made accessible. Hence, the principle components underpinning non-contact lOP measures of 0.1mmHg resolution (an order of magnitude greater than other methods) were made available. The relationship between the pressure-output and corneal response has been termed the pressure-response relationship, aspects of which have been shown to be related to ocular biometric parameters. Further, analysis of the components of the pressure-response relationship together with high-speed photography of the cornea during tonometry has enhanced our understanding of the derivation of an lOP measure with the Pulsair EasyEye NCT. The NCT samples the corneal response to the pressure pulse over a 19 ms cycle photoelectronically, but computes the subject's lOP using the data collected in the first 2.34 ms. The relatively instantaneous nature of the lOP measurement renders the measures susceptible to variations in the steady-state lOP caused by the respiratory and cardiac cycles. As such, the variance associated with these cycles was minimised by synchronising the lOP measures with the cardiac trace and maintaining a constant pace respiratory cycle at 15 breathes/minute. It is apparent that synchronising the lOP measures with the peak, middle or trough of the cardiac trace significantly reduced the spread of consecutive measures. Of the 3 locations investigated, synchronisation with the middle location demonstrated the least variance (coeflicient of variation = 9.1%) and a strong correlation (r = 0.90, p = <0.001) with lOP values obtained with Goldmann contact tonometry (n = 50). Accordingly lOP measures synchronised with the middle location of the cardiac cycle were taken in the RE while the LE fixated low (L; zero D), intermediate (I; 1.50 D) and high (H; 4 D) accommodation targets, Quasi-continuous measures of accommodation responses were obtained during the lOP measurement period using the portable infrared Grand Seiko FR-5000 autorefractor. The lOP reduced between L and I accommodative levels by approximately 0.61 mmHg (p <0.00 I). No significant reduction in IOP between L and H accommodation levels was elicited (p = 0.65) (n = 40). The relationship between accommodation and lOP was characterised by substantial inter-subject variations. Myopes demonstrated a tendency to show a reduction in IOP with accommodation which was significant only with I accommodation levels when measured with the NCT (r = 0.50, p = 0.01). However, the relationship between myopia and lOP change with accommodation reached significance for both I (r = 0.61, p= 0.003) and H (r = 0.531, p= 0.0 1) accommodation levels when measured with the Ocular blood Flow Analyser (OBFA). Investigation of the effects of accommodation on the parameters measured by the OBFA demonstrated that with H accommodation levels the pulse amplitude (PA) and pulse rate (PR) responses differed between myopes and emmetropes (PA: p = 0.03; PR: p = 0.004). As thc axial length increased there was a tendency for the pulsatile ocular blood flow (POBF) to reduce with accommodation, which was significant only with H accommodation levels (r = 0.38, p = 0.02). It is proposed that emmetropes arc able to regulate the POBF responses to changes in ocular perfusion pressure caused by changes in lOP with I (r = 0.77, p <0.001) and H (r = 0.73, p = 0.001) accommodation levels. However, thc relationship between lOP and POBF changes in the myopes was not correlated for both I (r = 0.33, p = 0.20) and H (r = 0.05, p = 0.85) accommodation levels. The thesis presents new data on the relationships between accommodation, lOP and parameters of the OBFA,: and provides evidence for possible lOP and choroidal blood flow regulatory mechanisms. Further the data highlight possible deficits in the vascular regulation of the myopic eye during accommodation, which may play a putative role in the aetiology of myopia development.