Channel Selection and Feature Projection for Cognitive Load Estimation Using Ambulatory EEG

We present an ambulatory cognitive state classification system to assess the subject's mental load based on EEG measurements. The ambulatory cognitive state estimator is utilized in the context of a real-time augmented cognition (AugCog) system that aims to enhance the cognitive performance of a human user through computer-mediated assistance based on assessments of cognitive states using physiological signals including, but not limited to, EEG. This paper focuses particularly on the offline channel selection and feature projection phases of the design and aims to present mutual-information-based techniques that use a simple sample estimator for this quantity. Analyses conducted on data collected from 3 subjects performing 2 tasks (n-back/Larson) at 2 difficulty levels (low/high) demonstrate that the proposed mutual-information-based dimensionality reduction scheme can achieve up to 94% cognitive load estimation accuracy

Epileptic Seizure Classification Using Image-Based Data Representation

Epilepsy is a recurrence of seizures caused by a disorder of the brain in over 3.4 million people nationwide. Some people are able to predict their seizures based off prodrome, which is an early sign or symptom that usually resembles mood changes or a euphoric feeling even days to an hour before occurrence. Consequently, the natural instincts of the body to react to an upcoming attack lends credence to the existence of a pre-ictal state that precedes seizure episodes. Physicians and researchers have thus sought for an automated approach for predicting or detecting seizures. In this research, we evaluate the image-based representation of EEG as a basis for classification and training of machine learning algorithms. We explore only the raw EEG data for images in lossless image file formats, though there are other forms including symbolized and noise-filtered that can be explored. Furthermore, we evaluate different color mapping schemes (symbolized, default, chromatic, and binned) that assign EEG data values to Red-Green-Blue (RGB) pixel values. We report the performance of machine learning algorithms such as Random Forest to accurately classify EEG-based images as either event (with a seizure) or non-event (without a seizure)

Recent Applications in Graph Theory

Graph theory, being a rigorously investigated field of combinatorial mathematics, is adopted by a wide variety of disciplines addressing a plethora of real-world applications. Advances in graph algorithms and software implementations have made graph theory accessible to a larger community of interest. Ever-increasing interest in machine learning and model deployments for network data demands a coherent selection of topics rewarding a fresh, up-to-date summary of the theory and fruitful applications to probe further. This volume is a small yet unique contribution to graph theory applications and modeling with graphs. The subjects discussed include information hiding using graphs, dynamic graph-based systems to model and control cyber-physical systems, graph reconstruction, average distance neighborhood graphs, and pure and mixed-integer linear programming formulations to cluster networks

Brain-Computer Interface

Brain-computer interfacing (BCI) with the use of advanced artificial intelligence identification is a rapidly growing new technology that allows a silently commanding brain to manipulate devices ranging from smartphones to advanced articulated robotic arms when physical control is not possible. BCI can be viewed as a collaboration between the brain and a device via the direct passage of electrical signals from neurons to an external system. The book provides a comprehensive summary of conventional and novel methods for processing brain signals. The chapters cover a range of topics including noninvasive and invasive signal acquisition, signal processing methods, deep learning approaches, and implementation of BCI in experimental problems

Determining Criteria for Distinguishing States of Consciousness

Even though there are many views on consciousness theory in the pertinent literature, there remains a need for a unifying framework for specifying the features of specific states of consciousness. In order to know what kinds of experiences conscious states have in common, researchers need to elicit testimony that is more direct and finer-grained than has been previously available. This dissertation endeavors to fill a gap in current research by addressing concepts and methods for making requisite distinctions. This research illuminates the question of whether specific states of consciousness can be reliably and validly distinguished from each other. In order to do this, 41 individuals, who had experienced significant peak or ecstatic states from a variety of induction methods (most prominently by ingestion of psychedelic substances), were invited to be interviewed. The interview was designed as a conversational-type synthesis of 5 well-known questionnaires pertinent to states of consciousness, but without their explicit and implicit assumptions; that is, the volunteers\u27 responses would not conform to predetermined questions. Encoding their responses allowed me to develop a model that helped to answer the research question ( Are there identifiable features that can reliably and validly distinguish among states of consciousness thought to be distinct from each other? ) by formulating a model in which any given conscious state can be catalogued in terms of its component factors (background, resistances, setting, induction, tradition, energies, and breakthrough events). The results of this study provide much-needed insights into people\u27s internal experiences of their various states, thus forming a basis for improved treatments and analyses. Better understanding of these states can be an impetus for social change by allowing for more incisive analyses and treatments, and also enabling more understanding of other people\u27s inner perspectives

Individual-Based Modeling and Nonlinear Analysis for Complex Systems with Application to Theoretical Ecology

One approach to understanding the behaviour of complex systems is individual-based modeling, which provides a bottom-up approach allowing for the consideration of the traits and behaviour of individual organisms. Ecosystem models aim to characterize the major dynamics of ecosystems, in order to synthesize the understanding of such systems and to allow predictions of their behaviour. Moreover, ecosystem simulations have the potential to help scientists address theoretical questions as well as helping with ecological resource management. Because in reality biologists do not have much data regarding variations in ecosystems over long periods of time, using the results of ecological computer simulation for making reasonable predictions can help biologists to better understand the long-term behaviour of ecosystems. Different versions of ecosystem simulations have been developed to investigate several questions in ecology such as how speciation proceeds in the absence of experimenter-defined functions. I have investigated some of these questions relying on complex interactions between the many individuals involved in the system, as well as long-term evolutionary patterns and processes such as speciation and macroevolution. Most scientists now believe that natural phenomena have to be looking as a chaotic system. In the past few years, chaos analysis techniques have gained increasing attention over a variety of applications. I have analyzed results of complex models to see whether chaotic behaviour can emerge, since any attempt to model a realistic system needs to have the capacity to generate patterns as complex as the ones that are observed in real systems. To further understand the complex behaviour of real systems, a new algorithm for long-term prediction of time series behaviour is also proposed based on chaos analysis. We evaluated the performance of our new method with respect to the prediction of the Dow-Jones industrial index time series, epileptic seizure and global temperature anomaly

Linear and nonlinear approaches to unravel dynamics and connectivity in neuronal cultures

[eng] In the present thesis, we propose to explore neuronal circuits at the mesoscale, an approach in which one monitors small populations of few thousand neurons and concentrates in the emergence of collective behavior. In our case, we carried out such an exploration both experimentally and numerically, and by adopting an analysis perspective centered on time series analysis and dynamical systems. Experimentally, we used neuronal cultures and prepared more than 200 of them, which were monitored using fluorescence calcium imaging. By adjusting the experimental conditions, we could set two basic arrangements of neurons, namely homogeneous and aggregated. In the experiments, we carried out two major explorations, namely development and disintegration. In the former we investigated changes in network behavior as it matured; in the latter we applied a drug that reduced neuronal interconnectivity. All the subsequent analyses and modeling along the thesis are based on these experimental data. Numerically, the thesis comprised two aspects. The first one was oriented towards a simulation of neuronal connectivity and dynamics. The second one was oriented towards the development of linear and nonlinear analysis tools to unravel dynamic and connectivity aspects of the measured experimental networks. For the first aspect, we developed a sophisticated software package to simulate single neuronal dynamics using a quadratic integrate–and–fire model with adaptation and depression. This model was plug into a synthetic graph in which the nodes of the network are neurons, and the edges connections. The graph was created using spatial embedding and realistic biology. We carried out hundreds of simulations in which we tuned the density of neurons, their spatial arrangement and the characteristics of the fluorescence signal. As a key result, we observed that homogeneous networks required a substantial number of neurons to fire and exhibit collective dynamics, and that the presence of aggregation significantly reduced the number of required neurons. For the second aspect, data analysis, we analyzed experiments and simulations to tackle three major aspects: network dynamics reconstruction using linear descriptions, dynamics reconstruction using nonlinear descriptors, and the assessment of neuronal connectivity from solely activity data. For the linear study, we analyzed all experiments using the power spectrum density (PSD), and observed that it was sufficiently good to describe the development of the network or its disintegration. PSD also allowed us to distinguish between healthy and unhealthy networks, and revealed dynamical heterogeneities across the network. For the nonlinear study, we used techniques in the context of recurrence plots. We first characterized the embedding dimension m and the time delay δ for each experiment, built the respective recurrence plots, and extracted key information of the dynamics of the system through different descriptors. Experimental results were contrasted with numerical simulations. After analyzing about 400 time series, we concluded that the degree of dynamical complexity in neuronal cultures changes both during development and disintegration. We also observed that the healthier the culture, the higher its dynamic complexity. Finally, for the reconstruction study, we first used numerical simulations to determine the best measure of ‘statistical interdependence’ among any two neurons, and took Generalized Transfer Entropy. We then analyzed the experimental data. We concluded that young cultures have a weak connectivity that increases along maturation. Aggregation increases average connectivity, and more interesting, also the assortativity, i.e. the tendency of highly connected nodes to connect with other highly connected node. In turn, this assortativity may delineates important aspects of the dynamics of the network. Overall, the results show that spatial arrangement and neuronal dynamics are able to shape a very rich repertoire of dynamical states of varying complexity.[cat] L’habilitat dels teixits neuronals de processar i transmetre informació de forma eficient depèn de les propietats dinàmiques intrínseques de les neurones i de la connectivitat entre elles. La present tesi proposa explorar diferents tècniques experimentals i de simulació per analitzar la dinàmica i connectivitat de xarxes neuronals corticals de rata embrionària. Experimentalment, la gravació de l’activitat espontània d’una població de neurones en cultiu, mitjançant una càmera ràpida i tècniques de fluorescència, possibilita el seguiment de forma controlada de l’activitat individual de cada neurona, així com la modificació de la seva connectivitat. En conjunt, aquestes eines permeten estudiar el comportament col.lectiu emergent de la població neuronal. Amb l’objectiu de simular els patrons observats en el laboratori, hem implementat un model mètric aleatori de creixement neuronal per simular la xarxa física de connexions entre neurones, i un model quadràtic d’integració i dispar amb adaptació i depressió per modelar l’ampli espectre de dinàmiques neuronals amb un cost computacional reduït. Hem caracteritzat la dinàmica global i individual de les neurones i l’hem correlacionat amb la seva estructura subjacent mitjançant tècniques lineals i no–lineals de series temporals. L’anàlisi espectral ens ha possibilitat la descripció del desenvolupament i els canvis en connectivitat en els cultius, així com la diferenciació entre cultius sans dels patològics. La reconstrucció de la dinàmica subjacent mitjançant mètodes d’incrustació i l’ús de gràfics de recurrència ens ha permès detectar diferents transicions dinàmiques amb el corresponent guany o pèrdua de la complexitat i riquesa dinàmica del cultiu durant els diferents estudis experimentals. Finalment, a fi de reconstruir la connectivitat interna hem testejat, mitjançant simulacions, diferents quantificadors per mesurar la dependència estadística entre neurona i neurona, seleccionant finalment el mètode de transferència d’entropia gereralitzada. Seguidament, hem procedit a caracteritzar les xarxes amb diferents paràmetres. Malgrat presentar certs tres de xarxes tipus ‘petit món’, els nostres cultius mostren una distribució de grau ‘exponencial’ o ‘esbiaixada’ per, respectivament, cultius joves i madurs. Addicionalment, hem observat que les xarxes homogènies presenten la propietat de disassortativitat, mentre que xarxes amb un creixent nivell d’agregació espaial presenten assortativitat. Aquesta propietat impacta fortament en la transmissió, resistència i sincronització de la xarxa

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described