The aim of this paper is to present some ideas how to relax the notion of the optimal solution of the stochastic optimization problem. In the deterministic case, ε-minimal solutions and level-minimal solutions are considered as desired relaxations. We call them approximative solutions and we introduce some possibilities how to combine them with randomness. Relations among random versions of approximative solutions and their consistency are presented in this paper. No measurability is assumed, therefore, treatment convenient for nonmeasurable objects is employed.
The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the characterization and quantitative representation of such uncertainties and measures of information produced by sources of the considered type.
The analysis of information coding in neurons requires methods that measure different properties of neuronal signals. In this paper we review the recently proposed measure of randomness and compare it to the coefficient of variation, which is the frequently employed measure of variability of spiking neuronal activity. We focus on the problem of the spontaneous activity of neurons, and we hypothetize that under defined conditions, spontaneous activity is more random than evoked activity. This hypothesis is supported by contrasting variability and randomness obtained from experimental recordings of olfactory receptor neurons in rats., L. Košťál, P. Lánský., and Obsahuje biblografii a biblografické odkazy