A generalization of entropy equation: homogeneous entropies
A generalized coding problem for discrete information sources
A generalized Fannes' inequality.
A generalized residual information measure and its properties.
A Geometrical Problem Arising in a Signal Restoration Algorithm.
A geometry on the space of probabilities (I). The finite dimensional case.
In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω = [1,n] or on P = {p = (p1, ..., pn) ∈ Rn| pi > 0; Σi=1n pi = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in Cn.
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A graphical way to solve the Boolean matrix equations and
A hierarchy for circular codes
We first prove an extremal property of the infinite Fibonacci* word f: the family of the palindromic prefixes {hn | n ≥ 6} of f is not only a circular code but “almost” a comma-free one (see Prop. 12 in Sect. 4). We also extend to a more general situation the notion of a necklace introduced for the study of trinucleotides codes on the genetic alphabet, and we present a hierarchy relating two important classes of codes, the comma-free codes and the circular ones.
A large family of Boolean functions
In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. II. Applications
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. I. General considerations
A log-Sobolev type inequality for free entropy of two projections
We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.
A measure of mutual divergence among a number of probability distributions.
A mixed theory of information. I : symmetric, recursive and measurable entropies of randomized systems of events
A mixed theory of information - VIII: Inset measures depending upon several distributions.
A mixed theory of information - VIII: Inset measures depending upon several distributions. (Short Communication).
A Mixid Theory of Information - IV: Inset-Inaccuracy and Directed Divergence.
A *-mixing convergence theorem for convex set valued processes.