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We revisit the variational characterization of conservative diffusion as entropic gradient flow and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of Langevin--Smoluchowski type, the Fokker--Planck probability density flow maximizes the rate of relative entropy dissipation, as measured by the distance traveled in the ambient space of probability measures with finite second moments, in terms of the quadratic Wasserstein metric. We obtain novel, stochastic-process versions of these features, valid along almost every trajectory of the diffusive motion in the backwards direction of time, using a very direct perturbation analysis. By averaging our trajectorial results with respect to the underlying measure on path space, we establish the maximal rate of entropy dissipation along the Fokker--Planck flow and measure exactly the deviation from this maximum that corresponds to any given perturbation. A bonus of our trajectorial approach is that it derives the HWI inequality relating relative entropy (H), Wasserstein distance (W), and relative Fisher information (I). [ABSTRACT FROM AUTHOR]

Background Cerebral palsy (CP) is the most common motor impairment in childhood and often accompanied by a broad spectrum of comorbidities. Data are sparse concerning visual impairment (VI) and functional classification among CP children. Objective The objective of this study was to analyze the prevalence of VI among children with CP and to investigate a possible association between VI and Gross Motor Function Classification System (GMFCS) and the Bimanual Fine Motor Function (BFMF). Methods In this hospital-based study, records of 200 children with CP aged 2 to 17 years were reviewed. Results Overall, VI was found in 59.5% of children with CP. Prevalence of VI was higher when compared with non-CP children. A correlation between GMFCS as well as BFMF and severity of VI was found. Children with severe CP were at greater risk for severe VI, especially cerebral VI compared with children with mild CP. Conclusion VI is a significant problem in children with CP and is correlated with motor function. Children with CP should undergo detailed ophthalmologic and orthoptic assessment to enable early intervention. [ABSTRACT FROM AUTHOR]