Initial Condition and Behavior Patterns in Learning Dynamics: Study of Complexity and Sustainability from Time Series

Learning is an essential part of human life. In it, our sensory organs and neural networks participate and integrate emotional behaviors, indagative and persuasive abilities, along with the ability to selectively acquire information, to mention a fraction of the media used in learning, converge to it. This study presents the results of the observational monitoring of behaviors, displayed by teams of students in learning processes, their interactions, representing them as series of time. These time series contain the dynamics of learning: weak, average, and chaotic, differentiated by the control parameter (connectivity) that is increasing respectively. The exponents of Lyapunov, the entropy of Kolmogorov, the complexity, the loss of information for each series, and the projection horizon of the processes are calculated for each series. The results, approximate, show that the chaotic dynamics propitiate the learning, given that there is an increase of connectivity within the teams breaking patterns or behavioral stereotypes. The entropic character of connectivity allows estimating the complexity of this human activity, exposing its sustainability, which brings irreversible conflicts with nature, given that the universe of nonequilibrium is a connected universe. Finally, the analysis model developed is historically contextualized, in first approximation, in some ancient civilizations

Feature selection for EEG Based biometrics

Department of Human Factors EngineeringEEG-based biometrics identify individuals by using personal and distinctive information in human brain. This thesis aims to evaluate the electroencephalography (EEG) features and channels for biometrics and to propose methodology that identifies individuals. In my research, I recorded fourteen EEG channel signals from thirty subjects. While record EEG signal, subjects were asked to relax and keep eyes closed for 2 minutes. In addition, to evaluate intra-individual variability, we recorded EEG ten times for each subject, and every recording conducted on different days to reduce within-day effects. After acquisition of data, for each channel, I calculated eight features: alpha/beta power ratio, alpha/theta power ratio, beta/theta power ratio, median frequency, PSD entropy, permutation entropy, sample entropy, and maximum Lyapunov exponents. Then, I scored 112 features with three feature selection algorithms: Fisher score, reliefF, and information gain. Finally, I classified EEG data using a linear discriminant analysis (LDA) with a leave-one-out cross validation method. As a result, the best feature set was composed of 23 features that highly ranked on Fisher score and yielded a 18.56% half total error rate. In addition, according to scores calculated by feature selection, EEG channels located on occipital and right temporal areas most contributed to identify individuals. Thus, with suggested methodologies and channels, implementation of efficient EEG-based biometrics is possible.ope

Taming Crowded Visual Scenes

Computer vision algorithms have played a pivotal role in commercial video surveillance systems for a number of years. However, a common weakness among these systems is their inability to handle crowded scenes. In this thesis, we have developed algorithms that overcome some of the challenges encountered in videos of crowded environments such as sporting events, religious festivals, parades, concerts, train stations, airports, and malls. We adopt a top-down approach by first performing a global-level analysis that locates dynamically distinct crowd regions within the video. This knowledge is then employed in the detection of abnormal behaviors and tracking of individual targets within crowds. In addition, the thesis explores the utility of contextual information necessary for persistent tracking and re-acquisition of objects in crowded scenes. For the global-level analysis, a framework based on Lagrangian Particle Dynamics is proposed to segment the scene into dynamically distinct crowd regions or groupings. For this purpose, the spatial extent of the video is treated as a phase space of a time-dependent dynamical system in which transport from one region of the phase space to another is controlled by the optical flow. Next, a grid of particles is advected forward in time through the phase space using a numerical integration to generate a flow map . The flow map relates the initial positions of particles to their final positions. The spatial gradients of the flow map are used to compute a Cauchy Green Deformation tensor that quantifies the amount by which the neighboring particles diverge over the length of the integration. The maximum eigenvalue of the tensor is used to construct a forward Finite Time Lyapunov Exponent (FTLE) field that reveals the Attracting Lagrangian Coherent Structures (LCS). The same process is repeated by advecting the particles backward in time to obtain a backward FTLE field that reveals the repelling LCS. The attracting and repelling LCS are the time dependent invariant manifolds of the phase space and correspond to the boundaries between dynamically distinct crowd flows. The forward and backward FTLE fields are combined to obtain one scalar field that is segmented using a watershed segmentation algorithm to obtain the labeling of distinct crowd-flow segments. Next, abnormal behaviors within the crowd are localized by detecting changes in the number of crowd-flow segments over time. Next, the global-level knowledge of the scene generated by the crowd-flow segmentation is used as an auxiliary source of information for tracking an individual target within a crowd. This is achieved by developing a scene structure-based force model. This force model captures the notion that an individual, when moving in a particular scene, is subjected to global and local forces that are functions of the layout of that scene and the locomotive behavior of other individuals in his or her vicinity. The key ingredients of the force model are three floor fields that are inspired by research in the field of evacuation dynamics; namely, Static Floor Field (SFF), Dynamic Floor Field (DFF), and Boundary Floor Field (BFF). These fields determine the probability of moving from one location to the next by converting the long-range forces into local forces. The SFF specifies regions of the scene that are attractive in nature, such as an exit location. The DFF, which is based on the idea of active walker models, corresponds to the virtual traces created by the movements of nearby individuals in the scene. The BFF specifies influences exhibited by the barriers within the scene, such as walls and no-entry areas. By combining influence from all three fields with the available appearance information, we are able to track individuals in high-density crowds. The results are reported on real-world sequences of marathons and railway stations that contain thousands of people. A comparative analysis with respect to an appearance-based mean shift tracker is also conducted by generating the ground truth. The result of this analysis demonstrates the benefit of using floor fields in crowded scenes. The occurrence of occlusion is very frequent in crowded scenes due to a high number of interacting objects. To overcome this challenge, we propose an algorithm that has been developed to augment a generic tracking algorithm to perform persistent tracking in crowded environments. The algorithm exploits the contextual knowledge, which is divided into two categories consisting of motion context (MC) and appearance context (AC). The MC is a collection of trajectories that are representative of the motion of the occluded or unobserved object. These trajectories belong to other moving individuals in a given environment. The MC is constructed using a clustering scheme based on the Lyapunov Characteristic Exponent (LCE), which measures the mean exponential rate of convergence or divergence of the nearby trajectories in a given state space. Next, the MC is used to predict the location of the occluded or unobserved object in a regression framework. It is important to note that the LCE is used for measuring divergence between a pair of particles while the FTLE field is obtained by computing the LCE for a grid of particles. The appearance context (AC) of a target object consists of its own appearance history and appearance information of the other objects that are occluded. The intent is to make the appearance descriptor of the target object more discriminative with respect to other unobserved objects, thereby reducing the possible confusion between the unobserved objects upon re-acquisition. This is achieved by learning the distribution of the intra-class variation of each occluded object using all of its previous observations. In addition, a distribution of inter-class variation for each target-unobservable object pair is constructed. Finally, the re-acquisition decision is made using both the MC and the AC

Estimation of potassium levels in hemodialysis patients by T wave nonlinear dynamics and morphology markers

Noninvasive screening of hypo- and hyperkalemia can prevent fatal arrhythmia in end-stage renal disease (ESRD) patients, but current methods for monitoring of serum potassium (K+) have important limitations. We investigated changes in nonlinear dynamics and morphology of the T wave in the electrocardiogram (ECG) of ESRD patients during hemodialysis (HD), assessing their relationship with K+ and designing a K+ estimator. Methods: ECG recordings from twenty-nine ESRD patients undergoing HD were processed. T waves in 2-min windows were extracted at each hour during an HD session as well as at 48 h after HD start. T wave nonlinear dynamics were characterized by two indices related to the maximum Lyapunov exponent (¿t, ¿wt) and a divergence-related index (¿). Morphological variability in the T wave was evaluated by three time warping-based indices (dw, reflecting morphological variability in the time domain, and da and daNL, in the amplitude domain). K+was measured from blood samples extracted during and after HD. Stage-specific and patient-specific K+ estimators were built based on the quantified indices and leave-one-out cross-validation was performed separately for each of the estimators. Results: The analyzed indices showed high inter-individual variability in their relationship with K+. Nevertheless, all of them had higher values at the HD start and 48 h after it, corresponding to the highest K+. The indices ¿ and dw were the most strongly correlated with K+ (median Pearson correlation coefficient of 0.78 and 0.83, respectively) and were used in univariable and multivariable linear K+ estimators. Agreement between actual and estimated K+ was confirmed, with averaged errors over patients and time points being 0.000 ± 0.875 mM and 0.046 ± 0.690 mM for stage-specific and patient-specific multivariable K+ estimators, respectively.ariability allow noninvasive monitoring of [K+] in ESRD patients. Significance: ECG markers have the potential to be used for hypo- and hyperkalemia screening in ESRD patient

Learning Representations from EEG with Deep Recurrent-Convolutional Neural Networks

One of the challenges in modeling cognitive events from electroencephalogram (EEG) data is finding representations that are invariant to inter- and intra-subject differences, as well as to inherent noise associated with such data. Herein, we propose a novel approach for learning such representations from multi-channel EEG time-series, and demonstrate its advantages in the context of mental load classification task. First, we transform EEG activities into a sequence of topology-preserving multi-spectral images, as opposed to standard EEG analysis techniques that ignore such spatial information. Next, we train a deep recurrent-convolutional network inspired by state-of-the-art video classification to learn robust representations from the sequence of images. The proposed approach is designed to preserve the spatial, spectral, and temporal structure of EEG which leads to finding features that are less sensitive to variations and distortions within each dimension. Empirical evaluation on the cognitive load classification task demonstrated significant improvements in classification accuracy over current state-of-the-art approaches in this field.Comment: To be published as a conference paper at ICLR 201

Review and classification of variability analysis techniques with clinical applications

Analysis of patterns of variation of time-series, termed variability analysis, represents a rapidly evolving discipline with increasing applications in different fields of science. In medicine and in particular critical care, efforts have focussed on evaluating the clinical utility of variability. However, the growth and complexity of techniques applicable to this field have made interpretation and understanding of variability more challenging. Our objective is to provide an updated review of variability analysis techniques suitable for clinical applications. We review more than 70 variability techniques, providing for each technique a brief description of the underlying theory and assumptions, together with a summary of clinical applications. We propose a revised classification for the domains of variability techniques, which include statistical, geometric, energetic, informational, and invariant. We discuss the process of calculation, often necessitating a mathematical transform of the time-series. Our aims are to summarize a broad literature, promote a shared vocabulary that would improve the exchange of ideas, and the analyses of the results between different studies. We conclude with challenges for the evolving science of variability analysis

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

Nonlinear Dynamical Systems for Theory And Research In Ergonomics

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin