Advanced algorithms for the analysis of data sequences in Matlab

Cílem této práce je se seznámení s možnostmi programu Matlab z hlediska detailní analýzy deterministických dynamických systémů. Jedná se především o analýzu časové posloupnosti a o nalezení Lyapunových exponentů. Dalším cílem je navrhnout algoritmus umožňující specifikovat chování systému na základě znalosti příslušných diferenciálních rovnic. To znamená, nalezení chaotických systémů.This work aims to familiarize with the possibilities of Matlab in terms of detailed analysis of deterministic dynamical systems. This is essentially a analysis of time series and finding Lyapunov exponents. Another objective is to design an algorithm allowing to specify the system behavior based on knowledge of the relevant differential equations. That means finding chaotic systems.

Nonlinear time-series analysis revisited

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems

Non-linear Analysis of Single Electroencephalography (EEG) for Sleep-Related Healthcare Applications

OBJECTIVES: Soft-computing techniques are commonly used to detect medical phenomena and to help with clinical diagnoses and treatment. The purpose of this paper is to analyze the single electroencephalography (EEG) signal with the chaotic methods in order to identify the sleep stages. METHODS: Data acquisition (polysomnography) was performed on four healthy young adults (all males with a mean age of 27.5 years). The evaluated algorithm was designed with a correlation dimension and Lyapunov's exponent using a single EEG signal that detects differences in chaotic characteristics. RESULTS: The change of the correlation dimension and the largest Lyapunov exponent over the whole night sleep EEG was performed. The results show that the correlation dimension and largest Lyapunov exponent decreased from light sleep to deep sleep and they increased during the rapid eye movement stage. CONCLUSIONS: These results suggest that chaotic analysis may be a useful adjunct to linear (spectral) analysis for identifying sleep stages. The single EEG based nonlinear analysis is suitable for u-healthcare applications for monitoring sleepope

Nonlinear analysis of EEG signals at different mental states

BACKGROUND: The EEG (Electroencephalogram) is a representative signal containing information about the condition of the brain. The shape of the wave may contain useful information about the state of the brain. However, the human observer can not directly monitor these subtle details. Besides, since bio-signals are highly subjective, the symptoms may appear at random in the time scale. Therefore, the EEG signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. This work discusses the effect on the EEG signal due to music and reflexological stimulation. METHODS: In this work, nonlinear parameters like Correlation Dimension (CD), Largest Lyapunov Exponent (LLE), Hurst Exponent (H) and Approximate Entropy (ApEn) are evaluated from the EEG signals under different mental states. RESULTS: The results obtained show that EEG to become less complex relative to the normal state with a confidence level of more than 85% due to stimulation. CONCLUSIONS: It is found that the measures are significantly lower when the subjects are under sound or reflexologic stimulation as compared to the normal state. The dimension increases with the degree of the cognitive activity. This suggests that when the subjects are under sound or reflexologic stimuli, the number of parallel functional processes active in the brain is less and the brain goes to a more relaxed stat

The Impact of Coordination Quality on Coordination Dynamics and Team Performance: When Humans Team with Autonomy

abstract: This increasing role of highly automated and intelligent systems as team members has started a paradigm shift from human-human teaming to Human-Autonomy Teaming (HAT). However, moving from human-human teaming to HAT is challenging. Teamwork requires skills that are often missing in robots and synthetic agents. It is possible that adding a synthetic agent as a team member may lead teams to demonstrate different coordination patterns resulting in differences in team cognition and ultimately team effectiveness. The theory of Interactive Team Cognition (ITC) emphasizes the importance of team interaction behaviors over the collection of individual knowledge. In this dissertation, Nonlinear Dynamical Methods (NDMs) were applied to capture characteristics of overall team coordination and communication behaviors. The findings supported the hypothesis that coordination stability is related to team performance in a nonlinear manner with optimal performance associated with moderate stability coupled with flexibility. Thus, we need to build mechanisms in HATs to demonstrate moderately stable and flexible coordination behavior to achieve team-level goals under routine and novel task conditions.Dissertation/ThesisDoctoral Dissertation Engineering 201

Functional connectivity signatures of visual-motor coordination using spectral dynamical analysis

Visual-motor coordination is an essential function of human motion control, which requires interactions of multiple brain regions. Visual tracking is a behavioural task that requires intensive visual-motor coordination, which makes it a good paradigm to study the underlying mechanism of visual-motor coordination. In this research, tracking paradigm was used to study the visual-motor coordination, and both behaviour and electroencephalography (EEG) functional connectivity were analysed. The behavioural analysis explored the anticipatory characteristic of human motion control. In the tracking paradigm, participants were asked to trace a target moving with constant speed along a circular trajectory. Two different types of tracking paradigm were applied in the research. Firstly, the full visibility tracking trials were performed, in which participants had the full visibility of the target movement. Participants showed weak anticipatory behaviour in the full visibility tracking trials. In order to observe stronger anticipatory behaviour, the intermittent tracking trials were then performed, in which two target-invisible zones were added. It was found that participants applied two distinctive control modes of visual-motor coordination in the target-visible zone and target-invisible zone, respectively. The result showed that the target-invisible zone made participants perform anticipatory control of visual tracking. In order to identify the brain activities related to visual processing and motion control separately in the visual-motor feedback loops, two reference conditions were designed and compared with the tracking trials. The functional connectivity was defined using phase-locking synchrony, and both static and dynamical features of the network were investigated. For static analysis, the time-averaged graphical properties of functional connectivity were investigated. To investigate dynamical properties, a new dynamical network analysis method was developed based on eigenvector representation of functional connectivity. Both static and dynamic analyses demonstrated significant differences between cortical functional connectivity networks of open and closed visual-motor loop. Additionally, the dynamical network analysis also revealed that the EEG network related to visualmotor coordination undergoes a meta-stable state dynamics in the prime eigenvector space. This method can also potentially be applied to other network system to reveal the meta-stable states structure

A Study of Nonlinear Dynamics of EEG Responses to Simulated Unmanned Vehicle Tasks

In the contemporary world, mental workload becomes higher as technology evolves and task demand becomes overwhelming. The operators of a system are usually required to complete tasks with higher complicity within a shorter period of time. Continuous operation under a high level of mental workload can be a major source of risk and human error, thus put the operator in a hazardous working environment. Therefore, it is necessary to monitor and assess mental workload. In this study, an unmanned vehicle operation with visual detection tasks was investigated by means of nonlinear analysis of EEG time series. Nonlinear analysis is considered more advantageous compared with traditional power spectrum analysis of EEG. Besides, nonlinear analysis is more capable to capture the nature of EEG data and human performance, which is a process that subjects to constant changes. By examining the nonlinear dynamics of EEG, it is more likely to obtain a deeper understanding of brain activity. The objective of this study is to investigate the mental workload under different task levels through the examination of brain activity via nonlinear dynamics of EEG time series in simulated unmanned ground vehicle visual detection tasks. The experiment was conducted by the team lead by Dr. Lauren Reinerman Jones at Institute for Simulation & Training, University of Central Florida. One hundred and fifty subjects participated the experiment to complete four visual detection task scenarios (1) change detection, (2) threat detection task, (3) dual task with different change detection task rates, and (4) dual task with different threat detection task rates. Their EEG was recorded during performing the tasks at nine EEG channels. This study develops a massive data processing program to calculate the largest Lyapunov exponent, correlation dimension of the EEG data. This study also develops the program for performing 0-1 test on the EEG data in Python language environment. The result of this study verifies the existence of chaotic dynamics in EEG time series, reveals the change in brain activity as the effect of changing task demand in more detailed level, and obtains new insights from the psychophysiological mental workload measurement used in the preliminary study. The results of this study verified the existence of the chaotic dynamics in the EEG time series. This study also supported the hypothesis that EEG data exhibits change in the level of nonlinearity corresponding to differed task levels. The nonlinear analysis of EEG time series data is able to discriminate the change in brain activity derived from the changes in task load. All nonlinear dynamics analysis techniques used in this study is able to find the difference of nonlinearity in EEG among task levels, as well as between single task scenario and dual task scenario

Mathematical modelling and brain dynamical networks

In this thesis, we study the dynamics of the Hindmarsh-Rose (HR) model which studies the spike-bursting behaviour of the membrane potential of a single neuron. We study the stability of the HR system and compute its Lyapunov exponents (LEs). We consider coupled general sections of the HR system to create an undirected brain dynamical network (BDN) of Nn neurons. Then, we study the concepts of upper bound of mutual information rate (MIR) and synchronisation measure and their dependence on the values of electrical and chemical couplings. We analyse the dynamics of neurons in various regions of parameter space plots for two elementary examples of 3 neurons with two different types of electrical and chemical couplings. We plot the upper bound Ic and the order parameter rho (the measure of synchronisation) and the two largest Lyapunov exponents LE1 and LE2 versus the chemical coupling gn and electrical coupling gl. We show that, even for small number of neurons, the dynamics of the system depends on the number of neurons and the type of coupling strength between them. Finally, we evolve a network of Hindmarsh-Rose neurons by increasing the entropy of the system. In particular, we choose the Kolmogorov-Sinai entropy: HKS (Pesin identity) as the evolution rule. First, we compute the HKS for a network of 4 HR neurons connected simultaneously by two undirected electrical and two undirected chemical links. We get different entropies with the use of different values for both the chemical and electrical couplings. If the entropy of the system is positive, the dynamics of the system is chaotic and if it is close to zero, the trajectory of the system converges to one of the fixed points and loses energy. Then, we evolve a network of 6 clusters of 10 neurons each. Neurons in each cluster are connected only by electrical links and their connections form small-world networks. The six clusters connect to each other only by chemical links. We compare between the combined effect of chemical and electrical couplings with the two concepts, the information flow capacity Ic and HKS in evolving the BDNs and show results that the brain networks might evolve based on the principle of the maximisation of their entropies