Aging is characterized by the decline and deterioration of functional cells and results in a wide variety of molecular damages and reduced physical and mental capacity. The knowledge on aging process is important because life expectancy is expected to rise until 2050. Aging cannot be considered a homogeneous process and includes different trajectories characterized by states of fitness, frailty, and disability. Frailty is a dynamic condition put between a normal functional state and disability, with reduced capacity to cope with stressors. (...) This geriatric syndrome affects physical, neuropsychological, and social domains and is driven by emotional and spiritual components. Sarcopenia is considered one of the determinants and the biological substrates of physical frailty. Physical and cognitive frailty are separately approached during daily clinical practice. The concept of motoric cognitive syndrome has partially changed this scenario, opening interesting windows toward future approaches. Thus, the purpose of this manuscript is to provide an excursus on current clinical practice, enforced by aneddoctical cases. The analysis of the current state of the art seems to support the urgent need of comprehensive organizational model incorporating physical and cognitive spheres in the same umbrella. (shrink)

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of (...) Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)