We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ−sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ−sensitivity of the logarithmic transformation of the...

Although the Gini coefficient is an ideal measure of income inequality, it may be applied to measure the aging inequality in a society. In this paper, an attempt has been made to develop alternative measures of aging inequality based on the Gini index. The study uses the secondary population data of Asian countries collected from the international data base, US census Bureau. From the analysis ...

Novelty is an important psychological construct that affects both perceptual and behavioral processes. Here, we propose a lexical novelty score (LNS) for a song’s lyric, based on the statistical properties of a corpus of 275,905 lyrics (available at www.smcnus.org/lyrics/). A lyric-level LNS was derived as a function of the inverse document frequencies of its unique words. An artist-level LNS w...

Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, t...