On the Inequality ... .
On the Inequality ...pi f(pi) > piif(qi).
On the invertibility of finite linear transducers
Linear finite transducers underlie a series of schemes for Public Key Cryptography (PKC) proposed in the 90s of the last century. The uninspiring and arid language then used, condemned these works to oblivion. Although some of these schemes were afterwards shown to be insecure, the promise of a new system of PKC relying on different complexity assumptions is still quite exciting. The algorithms there used depend heavily on the results of invertibility of linear transducers. In this paper we introduce...
On the Jensen-Shannon divergence and the variation distance for categorical probability distributions
We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence...
On the joint 2-adic complexity of binary multisequences
Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences with given joint 2-adic complexity.
On the joint 2-adic complexity of binary multisequences∗
Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences...
On the jump set of solutions of the total variation flow
On the Largest Solution of a Functional Equation Connected to sum Form Information Measures on Open Domain-i
On the mean and the variance of estimates of Kullback information and relative “useful” information measures
In this paper the mean and the variance of the Maximum Likelihood Estimator (MLE) of Kullback information measure and measure of relative "useful" information are obtained.
On the modified entropy equation.
On the Multiresolution analysis of abstract Hilbert spaces
On the optimality of a new class of 2D recursive filters
The purpose of this paper is to prove the minimum variance property of a new class of 2D, recursive, finite-dimensional filters. The filtering algorithms are derived from general basic assumptions underlying the stochastic modelling of an image as a 2D gaussian random field. An appealing feature of the proposed algorithms is that the image pixels are estimated one at a time; this makes it possible to save computation time and memory requirement with respect to the filtering procedures based on strip...
On the optimum decision rule for the radar signal processing
On the physical and communication properties of a thermodynamical communication channel
On the pseudoinverse of a sum of symmetric matrices with applications to estimation
On the Quotient Function Employed in the Blind Source Separation Problem
MSC 2010: 42C40, 94A12On the blind source separation problem, there is a method to use the quotient function of complex valued time-frequency informations of two ob-served signals. By studying the quotient function, we can estimate the number of sources under some assumptions. In our previous papers, we gave a mathematical formulation which is available for the sources with-out time delay. However, in general, we can not ignore the time delay. In this paper, we will reformulate our basic theorems...
On the reception of binary phase shift keyed sequences by an autocorrelation receiver
On the regularity condition for decomposable communication channels
On the relationship between quasi-affine systems and the à trous algorithm.
We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasi-affine counterparts associated with a fairly general class of scaling functions that includes the class of compactly supported...
On the Rényi dimension