Entropy coding is defined to be the compression of a stream of symbols taken from a known symbol set where the probability of occurrence of any symbol from the set at any given point in the stream is constant and independent of any known occurrences of any other symbols. Shannon and Fano showed that the information of such a sequence could be calculated. When measured in bits the information re...

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. The...

A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum ρ-th moment of the number of performed tasks are derived. The case where a sequence of tasks is produced by a source and n tasks are jointly described using nR bits is considered. If R is larger than ...

In this paper, we have developed conditions under which the entropy function and the residual entropy function characterize the distribution. We have also studied some stochastic comparisons based on the entropy measure and established relations between entropy comparisons and comparisons with respect to other measures in reliability. Conditions for decreasing (increasing) uncertainty in a resi...

The concept of uncertain entropy is used to provide a quantitative measurement of the uncertainty associated with uncertain variables. After introducing the definition, this paper gives some examples of entropy of uncertain variables. Furthermore this paper proposes the maximum entropy principle for uncertain variables, that is, out of all the uncertainty distributions satisfying given constrai...

Lactic fermentation and respiration are important metabolic pathways on which life is based. Here, the rate of entropy in a cell associated to fermentation and respiration processes in glucose catabolism of living systems is calculated. This is done for both internal and external heat and matter transport according to a thermodynamic approach based on Prigogine’s formalism. It is shown that the...

The regional evaluation of monitoring stations for water resources can be of great importance due to its role in finding appropriate locations for stations, the maximum gathering of useful information and preventing the accumulation of unnecessary information and ultimately reducing the cost of data collection. Based on the theory of discrete entropy, this study analyzes the density of rain gag...

In physics,heat energy divided by temperature ,entropyis obtained, which means the conversion degree from heat to work. While in science and technology field, entropy generally refers to possible degree of certain matter system status. In social science area, entropy indicates the degree of certain society state, in the field of information theory, entropy expresses uncertain degree. In a word,...

In ergodic theory, the notions of information and entropy are separated from each other. In the existing literature, it is usual to assume the additive nature of information. In this paper, we have proposed a general definition of information in § 2 and studied its properties extensively in § 3. In § 4, information and entropy of countable measurable partitions of a Lebesgue probability space h...