The continuous Legendre transform, its inverse transform, and applications.
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives
We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
The effect of Gaussian blurring on the extraction of peaks and pits from digital elevation models.
The entropy and redundancy of normalized database structures
The entropy of Łukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
The entropy of Łukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
The fundamental equation of information and its generalizations.
The general solution of a functional equation related to the mixed theory of information.
The geometric structure of the inverse gamma distribution.
The information geometric descriptions of denormalized thermodynamic manifolds.
The irrelevant information principle for collective probabilistic reasoning
Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, , as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach...
The multidimensional -transform and its use in solution of partial difference equations
The mutual information estimation in the sampling with replacement
The mutual information. Estimation in the sampling without replacement
The noncommutative Hilbert transform approach to free entropy
The Number of Steps in a Finite Jacobi Algorithm.
The Paley-Wiener-Levinson theorem revisited.
The partial inner product space method: a quick overview.
The performance analysis of the adaptive two-stage DFB narrowband interference suppression filter in DSSS receiver