Further Results on Geometric Properties of a Family of Relative Entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the R\'enyi entropy maximization rule of statistical physics.Comment: 7 pages, Prop. 5 modified, in Proceedings of the 2011 IEEE International Symposium on Information Theor

Functional Imaging of Autonomic Regulation: Methods and Key Findings.

Central nervous system processing of autonomic function involves a network of regions throughout the brain which can be visualized and measured with neuroimaging techniques, notably functional magnetic resonance imaging (fMRI). The development of fMRI procedures has both confirmed and extended earlier findings from animal models, and human stroke and lesion studies. Assessments with fMRI can elucidate interactions between different central sites in regulating normal autonomic patterning, and demonstrate how disturbed systems can interact to produce aberrant regulation during autonomic challenges. Understanding autonomic dysfunction in various illnesses reveals mechanisms that potentially lead to interventions in the impairments. The objectives here are to: (1) describe the fMRI neuroimaging methodology for assessment of autonomic neural control, (2) outline the widespread, lateralized distribution of function in autonomic sites in the normal brain which includes structures from the neocortex through the medulla and cerebellum, (3) illustrate the importance of the time course of neural changes when coordinating responses, and how those patterns are impacted in conditions of sleep-disordered breathing, and (4) highlight opportunities for future research studies with emerging methodologies. Methodological considerations specific to autonomic testing include timing of challenges relative to the underlying fMRI signal, spatial resolution sufficient to identify autonomic brainstem nuclei, blood pressure, and blood oxygenation influences on the fMRI signal, and the sustained timing, often measured in minutes of challenge periods and recovery. Key findings include the lateralized nature of autonomic organization, which is reminiscent of asymmetric motor, sensory, and language pathways. Testing brain function during autonomic challenges demonstrate closely-integrated timing of responses in connected brain areas during autonomic challenges, and the involvement with brain regions mediating postural and motoric actions, including respiration, and cardiac output. The study of pathological processes associated with autonomic disruption shows susceptibilities of different brain structures to altered timing of neural function, notably in sleep disordered breathing, such as obstructive sleep apnea and congenital central hypoventilation syndrome. The cerebellum, in particular, serves coordination roles for vestibular stimuli and blood pressure changes, and shows both injury and substantially altered timing of responses to pressor challenges in sleep-disordered breathing conditions. The insights into central autonomic processing provided by neuroimaging have assisted understanding of such regulation, and may lead to new treatment options for conditions with disrupted autonomic function