Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple paradigmatic case of equal strength, all-to-all sine coupling of phase oscillators subject to a sinusoidal external drive, is considered. The stationary states and their stability are determined. Using the stability information and numerical experiments, parameter space phase diagrams showing when different types of system behavior apply are constructed, and the bifurcations marking transitions between different types of behavior are delineated. The analysis is supported by results of direct numerical simulation of an ensemble of oscillators.

Markers from local field potentials, neurochemicals, skin conductance, and hormone concentrations have been proposed as a means of closing the loop in Deep Brain Stimulation (DBS) therapy for treating neuropsychiatric and movement disorders. Developing a closed-loop DBS controller based on peripheral signals would require: (i) the recovery of a biomarker from the source neural stimuli underlying the peripheral signal variations; (ii) the estimation of an unobserved brain or central nervous system related state variable from the biomarker. The state variable is application-specific. It is emotion-related in the case of depression or post-traumatic stress disorder, and movement-related for Parkinson's or essential tremor. We present a method for closing the DBS loop in neuropsychiatric disorders based on the estimation of sympathetic arousal from skin conductance measurements. We deconvolve skin conductance via an optimization formulation utilizing sparse recovery and obtain neural impulses from sympathetic nerve fibers stimulating the sweat glands. We perform this deconvolution via a two-step coordinate descent procedure that recovers the sparse neural stimuli and estimates physiological system parameters simultaneously. We next relate an unobserved sympathetic arousal state to the probability that these neural impulses occur and use Bayesian filtering within an Expectation-Maximization framework for estimation. We evaluate our method on a publicly available data-set examining the effect of different types of stress on peripheral signal changes including body temperature, skin conductance and heart rate. A high degree of arousal is estimated during cognitive tasks, as are much lower levels during relaxation. The results demonstrate the ability to decode psychological arousal from neural activity underlying skin conductance signal variations. The complete pipeline from recovering neural stimuli to decoding an emotion-related brain state using skin conductance presents a promising methodology for the ultimate realization of a closed-loop DBS controller. Closed-loop DBS treatment would additionally help reduce unnecessary power consumption and improve therapeutic gains.

The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R 2 above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.

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Human emotion represents a complex neural process within the brain. The ability to automatically recognize emotions from physiological signals has the potential to impact humanity in multiple ways through applications in human-machine interaction, remote health monitoring, smart living environments and entertainment. We present a marked point process-based Bayesian filtering approach to track sympathetic arousal from skin conductance features. The rate at which individual skin conductance responses (SCRs) occur and their respective amplitudes encode important information regarding an individual's psychological arousal level. We develop a state-space model relating a latent neuropsychological arousal state to the rate at which neural impulses underlying SCRs occur and the impulse amplitudes. We simultaneously estimate both arousal and the state-space model parameters within an expectation-maximization framework. We evaluate our method on both simulated and experimental data. Results on simulated data indicate the method's ability to accurately estimate an unobserved state from marked point process observations. The experimental data include studies involving mental stress artificially-induced in laboratory environments, real-world driver stress and Pavlovian fear conditioning. Results on experimental data outperform previous Bayesian filtering approaches in terms of a lower sensitivity to small impulses and avoiding overfitting. The filter is thus able to estimate emotional arousal from skin conductance features and is a promising approach for everyday emotion recognition applications.

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