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.

From filters to features:Scale-space analysis of edge and blur coding in human vision

To make vision possible, the visual nervous system must represent the most informative features in the light pattern captured by the eye. Here we use Gaussian scale-space theory to derive a multiscale model for edge analysis and we test it in perceptual experiments. At all scales there are two stages of spatial filtering. An odd-symmetric, Gaussian first derivative filter provides the input to a Gaussian second derivative filter. Crucially, the output at each stage is half-wave rectified before feeding forward to the next. This creates nonlinear channels selectively responsive to one edge polarity while suppressing spurious or "phantom" edges. The two stages have properties analogous to simple and complex cells in the visual cortex. Edges are found as peaks in a scale-space response map that is the output of the second stage. The position and scale of the peak response identify the location and blur of the edge. The model predicts remarkably accurately our results on human perception of edge location and blur for a wide range of luminance profiles, including the surprising finding that blurred edges look sharper when their length is made shorter. The model enhances our understanding of early vision by integrating computational, physiological, and psychophysical approaches. © ARVO.

Template model for blur coding: the role of early nonlinearity in edge segmentation

We describe a template model for perception of edge blur and identify a crucial early nonlinearity in this process. The main principle is to spatially filter the edge image to produce a 'signature', and then find which of a set of templates best fits that signature. Psychophysical blur-matching data strongly support the use of a second-derivative signature, coupled to Gaussian first-derivative templates. The spatial scale of the best-fitting template signals the edge blur. This model predicts blur-matching data accurately for a wide variety of Gaussian and non-Gaussian edges, but it suffers a bias when edges of opposite sign come close together in sine-wave gratings and other periodic images. This anomaly suggests a second general principle: the region of an image that 'belongs' to a given edge should have a consistent sign or direction of luminance gradient. Segmentation of the gradient profile into regions of common sign is achieved by implementing the second-derivative 'signature' operator as two first-derivative operators separated by a half-wave rectifier. This multiscale system of nonlinear filters predicts perceived blur accurately for periodic and aperiodic waveforms. We also outline its extension to 2-D images and infer the 2-D shape of the receptive fields.

The interplay between microscopic and mesoscopic structures in complex networks

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database. © 2011 Reichardt et al.

Petrographic image analysis and understanding

This study considers the application of image analysis in petrography and investigates the possibilities for advancing existing techniques by introducing feature extraction and analysis capabilities of a higher level than those currently employed. The aim is to construct relevant, useful descriptions of crystal form and inter-crystal relations in polycrystalline igneous rock sections. Such descriptions cannot be derived until the `ownership' of boundaries between adjacent crystals has been established: this is the fundamental problem of crystal boundary assignment. An analysis of this problem establishes key image features which reveal boundary ownership; a set of explicit analysis rules is presented. A petrographic image analysis scheme based on these principles is outlined and the implementation of key components of the scheme considered. An algorithm for the extraction and symbolic representation of image structural information is developed. A new multiscale analysis algorithm which produces a hierarchical description of the linear and near-linear structure on a contour is presented in detail. Novel techniques for symmetry analysis are developed. The analyses considered contribute both to the solution of the boundary assignment problem and to the construction of geologically useful descriptions of crystal form. The analysis scheme which is developed employs grouping principles such as collinearity, parallelism, symmetry and continuity, so providing a link between this study and more general work in perceptual grouping and intermediate level computer vision. Consequently, the techniques developed in this study may be expected to find wider application beyond the petrographic domain.

Dynamic joint sentiment-topic model

Social media data are produced continuously by a large and uncontrolled number of users. The dynamic nature of such data requires the sentiment and topic analysis model to be also dynamically updated, capturing the most recent language use of sentiments and topics in text. We propose a dynamic Joint Sentiment-Topic model (dJST) which allows the detection and tracking of views of current and recurrent interests and shifts in topic and sentiment. Both topic and sentiment dynamics are captured by assuming that the current sentiment-topic-specific word distributions are generated according to the word distributions at previous epochs. We study three different ways of accounting for such dependency information: (1) Sliding window where the current sentiment-topic word distributions are dependent on the previous sentiment-topic-specific word distributions in the last S epochs; (2) skip model where history sentiment topic word distributions are considered by skipping some epochs in between; and (3) multiscale model where previous long- and shorttimescale distributions are taken into consideration. We derive efficient online inference procedures to sequentially update the model with newly arrived data and show the effectiveness of our proposed model on the Mozilla add-on reviews crawled between 2007 and 2011. © 2013 ACM 2157-6904/2013/12-ART5 $ 15.00.

Kinetic modeling studies of heterogeneously catalyzed biodiesel synthesis reactions

The heterogeneously catalyzed transesterification reaction for the production of biodiesel from triglycerides was investigated for reaction mechanism and kinetic constants. Three elementary reaction mechanisms Eley-Rideal (ER), Langmuir-Hinshelwood-Hougen-Watson (LHHW), and Hattori with assumptions, such as quasi-steady-state conditions for the surface species and methanol adsorption, and surface reactions as the rate-determining steps were applied to predict the catalyst surface coverage and the bulk concentration using a multiscale simulation framework. The rate expression based on methanol adsorption as the rate limiting in LHHW elementary mechanism has been found to be statistically the most reliable representation of the experimental data using hydrotalcite catalyst with different formulations. © 2011 American Chemical Society.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.

Full-vectorial modeling of femtosecond pulses for laser inscription of photonic structures

During the last decade, microfabrication of photonic devices by means of intense femtosecond (fs) laser pulses has emerged as a novel technology. A common requirement for the production of these devices is that the refractive index modification pitch size should be smaller than the inscribing wavelength. This can be achieved by making use of the nonlinear propagation of intense fs laser pulses. Nonlinear propagation of intense fs laser pulses is an extremely complicated phenomenon featuring complex multiscale spatiotemporal dynamics of the laser pulses. We have utilized a principal approach based on finite difference time domain (FDTD) modeling of the full set of Maxwell's equations coupled to the conventional Drude model for generated plasma. Nonlinear effects are included, such as self-phase modulation and multiphoton absorption. Such an approach resolves most problems related to the inscription of subwavelength structures, when the paraxial approximation is not applicable to correctly describe the creation of and scattering on the structures. In a representative simulation of the inscription process, the signature of degenerate four wave mixing has been found. © 2012 Optical Society of America.

Scaling and Multiscaling Exponents in Networks and Flows

The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refining measurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant heirarchical structures,e.g. rainfall, turbulence, etc. The heirarchical structure is reflected in the occurence of a natural separation of scales which collectively manifest at some basic unit scale. Thus proper data analysis and inference require a mathematical framework which couples the variability over multiple decades of scale in which basic theoretical benchmarks can be identified and calculated. This continues the main theme of the research in this area of applied probability over the past twenty years.

Stochastic anti-resonance in a fibre Raman amplifier

Stochastic anti-resonance, that is resonant enhancement of randomness caused by polarization mode beatings, is analyzed both numerically and analytically on an example of fibre Raman amplifier with randomly varying birefringence. As a result of such anti-resonance, the polarization mode dispersion growth causes an escape of the signal state of polarization from a metastable state corresponding to the pulling of the signal to the pump state of polarization.This phenomenon reveals itself in abrupt growth of gain fluctuations as well as in dropping of Hurst parameter and Kramers length characterizing long memory in a system and noise induced escape from the polarization pulling state. The results based on analytical multiscale averaging technique agree perfectly with the numerical data obtained by direct numerical simulations of underlying stochastic differential equations. This challenging outcome would allow replacing the cumbersome numerical simulations for real-world extra-long high-speed communication systems.

Identification of the degradation mechanisms of organic solar cells:active layer and interfacial layers

Organic Solar Cells (OSCs) represent a photovoltaic technology with multiple interesting application properties. However, the establishment of this technology into the market is subject to the achievement of operational lifetimes appropriate to their application purposes. Thus, comprehensive understanding of the degradation mechanisms occurring in OSCs is mandatory in both selecting more intrinsically stable components and/or device architectures and implementing strategies that mitigate the encountered stability issues. Inverted devices can suffer from mechanical stress and delamination at the interface between the active layer, e.g. poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester (P3HT:PCBM), and the hole transport layer, e.g. poly(3,4-ethylenedioxythiophene):poly(p-styrene sulfonate) (PEDOT:PSS). This work proposes the incorporation of a thin adhesive interlayer, consisting of a diblock copolymer composed of a P3HT block and a thermally-triggerable, alkyl-protected PSS block. In this context, the synthesis of poly(neopentyl p-styrene sulfonate) (PNSS) with controlled molar mass and low dispersity (Ð ≤ 1.50) via Reversible Addition-Fragmentation chain Transfer (RAFT) polymerisation has been extensively studied. Subsequently, Atomic Force Microscopy (AFM) was explored to characterise the thermal deprotection of P3HT-b-PNSS thin layers to yield amphiphilic P3HT-b-PSS, indicating that surface deprotection prior to thermal treatment could occur. Finally, structural variation of the alkyl protecting group in PSS allowed reducing the thermal treatment duration from 3 hours (P3HT-b-PNSS) to 45 minutes for the poly(isobutyl p-styrene sulfonate) (PiBSS) analogous copolymer. Another critical issue regarding the stability of OSCs is the sunlight-driven chemical degradation of the active layer. In the study herein, the combination of experimental techniques and theoretical calculations has allowed identification of the structural weaknesses of poly[(4,4’- bis(2-ethylhexyl) dithieno [3,2-b:2’,3’-d]silole)-2,6-diyl-alt-(4,7-bis(2-thienyl)-2,1,3-benzothiadiazole)-5,5’-diyl], Si-PCPDTBT, upon photochemical treatment in air. Additionally, the study of the relative photodegradation rates in air of a series of polymers with systematically modified backbones and/or alkyl side chains has shown no direct correlation between chemical structure and stability. It is proposed instead that photostability is highly dependent on the crystalline character of the deposited films. Furthermore, it was verified that photostability of blends based on these polymers is dictated by the (de)stabilising effect that [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) has over each polymer. Finally, a multiscale analysis on the degradation of solar cells based on poly[4,4' bis(2- ethylhexyl) dithieno[3,2-b:2',3'-d]silole)-2,6-diyl-alt-[2,5 bis(3 tetradecylthiophen 2-yl)thiazole[5,4-d]thiazole)-1,8-diyl] and PCBM, indicated that by judicious selection of device layers, architectures, and encapsulation materials, operational lifetimes up to 3.3 years with no efficiency losses can be successfully achieved.

An energy based nanomechnical properties evaluation method for cementitious materials

Advances in multiscale material modeling of structural concrete have created an upsurge of interest in the accurate evaluation of mechanical properties and volume fractions of its nano constituents. The task is accomplished by analyzing the response of a material to indentation, obtained as an outcome of a nanoindentation experiment, using a procedure called the Oliver and Pharr (OP) method. Despite its widespread use, the accuracy of this method is often questioned when it is applied to the data from heterogeneous materials or from the materials that show pile-up and sink-in during indentation, which necessitates the development of an alternative method. ^ In this study, a model is developed within the framework defined by contact mechanics to compute the nanomechanical properties of a material from its indentation response. Unlike the OP method, indentation energies are employed in the form of dimensionless constants to evaluate model parameters. Analysis of the load-displacement data pertaining to a wide range of materials revealed that the energy constants may be used to determine the indenter tip bluntness, hardness and initial unloading stiffness of the material. The proposed model has two main advantages: (1) it does not require the computation of the contact area, a source of error in the existing method; and (2) it incorporates the effect of peak indentation load, dwelling period and indenter tip bluntness on the measured mechanical properties explicitly. ^ Indentation tests are also carried out on samples from cement paste to validate the energy based model developed herein by determining the elastic modulus and hardness of different phases of the paste. As a consequence, it has been found that the model computes the mechanical properties in close agreement with that obtained by the OP method; a discrepancy, though insignificant, is observed more in the case of C-S-H than in the anhydrous phase. Nevertheless, the proposed method is computationally efficient, and thus it is highly suitable when the grid indentation technique is required to be performed. In addition, several empirical relations are developed that are found to be crucial in understanding the nanomechanical behavior of cementitious materials.^

Análise wavelet e modelo de manchas em curvas de luz estelares dos telescópios espaciais Kepler e CoRoT

Analogous to sunspots and solar photospheric faculae, which visibility is modulated by stellar rotation, stellar active regions consist of cool spots and bright faculae caused by the magnetic field of the star. Such starspots are now well established as major tracers used to estimate the stellar rotation period, but their dynamic behavior may also be used to analyze other relevant phenomena such as the presence of magnetic activity and its cycles. To calculate the stellar rotation period, identify the presence of active regions and investigate if the star exhibits or not differential rotation, we apply two methods: a wavelet analysis and a spot model. The wavelet procedure is also applied here to study pulsation in order to identify specific signatures of this particular stellar variability for different types of pulsating variable stars. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern vii signature in the local wavelet map of pulsating stars over the entire time span was also detected. The second method is based on starspots detection during transits of an extrasolar planet orbiting its host star. As a planet eclipses its parent star, we can detect physical phenomena on the surface of the star. If a dark spot on the disk of the star is partially or totally eclipsed, the integrated stellar luminosity will increase slightly. By analyzing the transit light curve it is possible to infer the physical properties of starspots, such as size, intensity, position and temperature. By detecting the same spot on consecutive transits, it is possible to obtain additional information such as the stellar rotation period in the planetary transit latitude, differential rotation, and magnetic activity cycles. Transit observations of CoRoT-18 and Kepler-17 were used to implement this model.