The electroencephalogram (EEG) during the re-establishment of consciousness after general anesthesia and surgery varies starkly between patients. Can the EEG during this emergence period provide a means of estimating the underlying biological processes underpinning the return of consciousness? Can we use a model to infer these biological processes from the EEG patterns? A frontal EEG was recorded from 84 patients. Ten patients were chosen for state-space analysis. Five showed archetypal emergences; which consisted of a progressive decrease in alpha power and increase peak alpha frequency before return of responsiveness. The five non-archetypal emergences showed almost no spectral EEG changes (even as the volatile general anesthetic decreased) and then an abrupt return of responsiveness. We used Bayesian methods to estimate the likelihood of an EEG pattern corresponding to the position of the patient on a 2-dimensional manifold in a state space of excitatory connection strength vs. change in intrinsic resting neuronal membrane conductivity. We could thus visualize the trajectory of each patient in the state-space during their emergence period. The patients who followed an archetypal emergence displayed a very consistent pattern; consisting of progressive increase in conductivity, and a temporary period of increased connection strength before return of responsiveness. The non-archetypal emergence trajectories remained fixed in a region of phase space characterized by a relatively high conductivity and low connection strength throughout emergence. This unexpected progressive increase in conductivity during archetypal emergence may be due to an abating of the surgical stimulus during this period. Periods of high connection strength could represent forays into dissociated consciousness, but the model suggests all patients reposition near the fold in the state space to take advantage of bi-stable cortical dynamics before transitioning to consciousness.

Determining safe aircraft trajectories that avoid hazardous weather regions and other aircraft while efficiently using the available airspace is an important problem. Although tactical weather forecast maps have been available, their use in automated aircraft trajectory generation has not been fully explored or implemented. We consider aircraft trajectory generation using forecast data available from the Corridor Integrated Weather System product. The forecasts, updated at regular intervals, are used to design no-fly regions. We propose a receding horizon trajectory generation based on the dynamic nature of the forecast. Our method uses current environment information and incrementally updated forecast to update and optimize the trajectories. Simulations are shown based on forecast weather and indicate the advantage of taking into account time-varying forecasts in the planning horizon.

This work presents a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. We show that the mapping produced from human data robustly separates rapid eye movement sleep (REM) from slow wave sleep (SWS). A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.

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This work presents a probabilistic method for inferring the parameter ranges in a biologically relevant mathematical model of the cortex most likely to be producing seizures observed in an electrocorticogram (ECoG) signal from a human subject. Additionally, this method produces a probabilistic pathway of the temporal evolution of physiological state in the cortex over the course of individual seizures, leveraging a model of the cortex that describes cortical physiology. We describe ways in which these methods and results offer insights into seizure etiology and have the potential to suggest new treatment options. To directly account for the stochastic and noisy nature of the mathematical model and the ECoG signal, we use a probabilistic Bayesian framework to map features of ECoG segments onto a distribution of likelihoods over physiologically-relevant parameter states. A Hidden Markov Model (HMM) is then introduced to incorporate the belief that cortical physiology has both temporal continuity and also a degree of reproducibility between individual seizures. By inspecting the ratio of likelihoods between HMMs run under two possible parameter regions, both of which produce seizures in the model, we determine which physiological parameter regions are more likely to be causing the observed seizures. We show that between individual seizures, there is consistency in these likelihood ratios between hypothesized regions, in the temporal pathways calculated, and in the separation of seizure from non-seizure time segment likelihood maps.

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An adaptive controller design is proposed and simulated for parameter identification and oscillation control in microbubble systems. Lyapunov's direct method and a Lyapunov-like analysis are used to show stability and convergence of trajectory tracking and parameter adaptation. The method allows for the determination of microbubble contrast agent shell thickness or material parameters in a nondestructive manner.

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