On linear recursion and pseudorandomness
On linguistic dynamical systems, families of graphs of large girth, and cryptography.
On -dimensional unified -Jensen difference divergence measures and their applications
On measurable solutions of a functional equation and its application to information theory
On measurable solutions of a functional equation and their application to information theory
In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon’s entropy and entropy of type is given.
On measures of relative ‘useful’ information
On metric divergences of probability measures
Standard properties of -divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of -divergences, or the metricity of their powers. This paper extends the previously known family of -divergences with these properties. The extension consists of a continuum of -divergences which are squared metric distances and which are mostly new but include...
On middle universal weak and cross inverse property loops with equal length of inverse cycles.
On minimal factorisations of sporadic groups.
On minimal length factorizations of finite groups.
On minimal logarithmic signatures of finite groups.
On minimal redundancy codes.
A code X over the alphabet A is complete if the submonoid X* generated by X meets all two-sided ideals of A*. If one measures the cost of a finite code X over A, with respect to a given information source S, by the quantity gamma(X) = <X> ln |A|, we say that X is completely optimal for S if it does not exist any code X', over an arbitrary alphabet, such that gamma (X') < gamma (X). One can show that for |X| ≤ 5 a completely optimal code has to be complete. However for |X| >...
On multiscale denoising of spherical functions: basic theory and numerical aspects.
On non-additive measures of inaccuracy
On pointwise adaptive curve estimation based on inhomogeneous data
We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point x0 with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists of a local polynomial...
On Proactive Verifiable Secret Sharing Schemes
The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at the 11th Workshop on Selected Areas in Cryptography (SAC) 2004This paper investigates the security of Proactive Secret Sharing Schemes. We first consider the approach of using commitment to 0 in the renewal phase in order to refresh the player's shares and we present two types of...
On probability of first order formulas in a given model
On real quadratic number fields suitable for cryptography.
On recursive filters inverse to finite sequences in the minimum mean square sense
On Schur-convexity of expectation of weighted sum of random variables with applications.