On Shannon-McMillan's limit theorem for pairs of stationary random processes
On Simple Stochastic Models
On solution sets of information inequalities
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
On some applications of the ag inequality in information theory.
On some Basic Properties of the Kolmogorov Complexity
On Some Functional Equations And Their Applications
On some functional equations and their applications.
On Some Functional Equations Concerning Entropy, Directed Divergence and Inaccuracy.
On some functional equations from additive and nonadditive measures (III).
In this series, this paper is devoted to the study of two related functional equations primarily connected with weighted entropy and weighted entropy of degree beta (which are weighted additive and weighted beta additive respectively) which include as special cases Shannon's entropy, inaccuracy (additive measures) and the entropy of degree beta (nonadditive) respectively. These functional equations which arise mainly from the representation and these 'additive' properties are solved for fixed m...
On some functional equations from additive and nonadditive measures. IV.
On some functional equations of Jessen, Karpf, and Thorup.
On some generalized functional equations in information theory.
On some new measures of uncertainty, inaccuracy and information and their characterizations
On some subsemigroups of a free semigroup.
On specificity and entropy measures.
On spectral bandwidth of a stationary random process
The irregularity coefficient is one of the numerical characteristics of the spectral bandwith of a stationary random process. Its basic properties are investigated and the application to the dichotomic classification of a process into narrow-band and wide-band ones is given. Further, its behaviour is analyzed for sufficiently wide classes of stationary processes whose spectral densities frequently appear both in theory and applications.
On symmetry and reversible symmetry concerning generalized directed divergence
On the algebraic structure of fuzzy sets of type 2
On the amount of information contained in a sequence of independent observations
On the amount of information resulting from empirical and theoretical knowledge.
We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set P of predicates and a probability space (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 0). Since this is a first step in this area, our approach is as simple as possible, but still nontrivial, as it is demonstrated by examples. More realistic approach...