Contributions to Collective Dynamical Clustering-Modeling of Discrete Time Series

The analysis of sequential data is important in business, science, and engineering, for tasks such as signal processing, user behavior mining, and commercial transactions analysis. In this dissertation, we build upon the Collective Dynamical Modeling and Clustering (CDMC) framework for discrete time series modeling, by making contributions to clustering initialization, dynamical modeling, and scaling. We first propose a modified Dynamic Time Warping (DTW) approach for clustering initialization within CDMC. The proposed approach provides DTW metrics that penalize deviations of the warping path from the path of constant slope. This reduces over-warping, while retaining the efficiency advantages of global constraint approaches, and without relying on domain dependent constraints. Second, we investigate the use of semi-Markov chains as dynamical models of temporal sequences in which state changes occur infrequently. Semi-Markov chains allow explicitly specifying the distribution of state visit durations. This makes them superior to traditional Markov chains, which implicitly assume an exponential state duration distribution. Third, we consider convergence properties of the CDMC framework. We establish convergence by viewing CDMC from an Expectation Maximization (EM) perspective. We investigate the effect on the time to convergence of our efficient DTW-based initialization technique and selected dynamical models. We also explore the convergence implications of various stopping criteria. Fourth, we consider scaling up CDMC to process big data, using Storm, an open source distributed real-time computation system that supports batch and distributed data processing. We performed experimental evaluation on human sleep data and on user web navigation data. Our results demonstrate the superiority of the strategies introduced in this dissertation over state-of-the-art techniques in terms of modeling quality and efficiency

EXPERIMENTAL-COMPUTATIONAL ANALYSIS OF VIGILANCE DYNAMICS FOR APPLICATIONS IN SLEEP AND EPILEPSY

Epilepsy is a neurological disorder characterized by recurrent seizures. Sleep problems can cooccur with epilepsy, and adversely affect seizure diagnosis and treatment. In fact, the relationship between sleep and seizures in individuals with epilepsy is a complex one. Seizures disturb sleep and sleep deprivation aggravates seizures. Antiepileptic drugs may also impair sleep quality at the cost of controlling seizures. In general, particular vigilance states may inhibit or facilitate seizure generation, and changes in vigilance state can affect the predictability of seizures. A clear understanding of sleep-seizure interactions will therefore benefit epilepsy care providers and improve quality of life in patients. Notable progress in neuroscience research—and particularly sleep and epilepsy—has been achieved through experimentation on animals. Experimental models of epilepsy provide us with the opportunity to explore or even manipulate the sleep-seizure relationship in order to decipher different aspects of their interactions. Important in this process is the development of techniques for modeling and tracking sleep dynamics using electrophysiological measurements. In this dissertation experimental and computational approaches are proposed for modeling vigilance dynamics and their utility demonstrated in nonepileptic control mice. The general framework of hidden Markov models is used to automatically model and track sleep state and dynamics from electrophysiological as well as novel motion measurements. In addition, a closed-loop sensory stimulation technique is proposed that, in conjunction with this model, provides the means to concurrently track and modulate 3 vigilance dynamics in animals. The feasibility of the proposed techniques for modeling and altering sleep are demonstrated for experimental applications related to epilepsy. Finally, preliminary data from a mouse model of temporal lobe epilepsy are employed to suggest applications of these techniques and directions for future research. The methodologies developed here have clear implications the design of intelligent neuromodulation strategies for clinical epilepsy therapy

Quantifying the Dynamics of Coupled Networks of Switches and Oscillators

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems

Inferring neural dynamics during burst suppression using a neurophysiology-inspired switching state-space model

Burst suppression is an electroencephalography (EEG) pattern associated with profoundly inactivated brain states characterized by cerebral metabolic depression. Its distinctive feature is alternation between short temporal segments of near-isoelectric inactivity (suppressions) and relatively high-voltage activity (bursts). Prior modeling studies suggest that burst-suppression EEG is a manifestation of two alternating brain states associated with consumption (during a burst) and production (during a suppression) of adenosine triphosphate (ATP). This finding motivates us to infer latent states characterizing alternating brain states and underlying ATP kinetics from instantaneous power of multichannel EEG using a switching state-space model. Our model assumes Gaussian distributed data as a broadcast network manifestation of one of two global brain states. The two brain states are allowed to stochastically alternate with transition probabilities that depend on the instantaneous ATP level, which evolves according to first-order kinetics. The rate constants governing the ATP kinetics are allowed to vary as first-order autoregressive processes. Our latent state estimates are determined from data using a sequential Monte Carlo algorithm. Our neurophysiology-informed model not only provides unsupervised segmentation of multi-channel burst-suppression EEG but can also generate additional insights on the level of brain inactivation during anesthesia.Comment: To appear in the proceedings of the 2020 IEEE Asilomar Conference on Signals, Systems, and Computer

Coordination dynamics in the sensorimotor loop

The last two decades have witnessed radical changes of perspective about the nature of intelligence and cognition, leaving behind some of the assumptions of computational functionalism. From the myriad of approaches seeking to substitute the old rule-based symbolic perception of mind, we are especially interested in two of them. The first is Embodied and Situated Cognition, where the advances in modeling complex adaptive systems through computer simulations have reconfigured the way in which mechanistic, embodied and interactive explanations can conceptualize the mind. We are particularly interested in the concept of sensorimotor loop, which brings a new perspective about what is needed for a meaningful interaction with the environment, emphasizing the role of the coordination of effector and sensor activities while performing a concrete task. The second one is the framework of Coordination Dynamics, which has been developed as a result of the increasing focus of neuroscience on self-organized oscillatory brain dynamics. It provides formal tools to study the mechanisms through which complex biological systems stabilize coordination states under conditions in which they would otherwise become unstable. We will merge both approaches and define coordination in the sensorimotor loop as the main phenomena behind the emergence of cognitive behavior. At the same time, we will provide methodological tools and concepts to address this hypothesis. Finally, we will present two case studies based on the proposed approach: 1. We will study the phenomenon known as “intermittent behavior”, which is observed in organisms at different levels (from microorganisms to higher animals). We will propose a model that understands intermittent behavior as a general strategy of biologica organization when an organism has to adapt to complex changing environments, and would allow to establish effective sensorimotor loops even in situations of instable engagement with the world. 2. We will perform a simulation of a phonotaxis task performed by an agent with an oscillator network as neural controller. The objective will be to characterize robust adaptive coupling between perceptive activity and the environmental dynamics just through phase information processing. We will observe how the robustness of the coupling crucially depends of how the sensorimotor loop structures and constrains both the emergent neural and behavioral patterns. We will hypothesize that this structuration of the sensorimotor space, in which only meaningful behavioral patterns can be stabilized, is a key ingredient for the emergence of higher cognitive abilities