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This paper has been withdrawn by the author due to a crucial error in the submission action.

This paper has been withdrawn due to a crucial theoretical and experimental error.

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

This paper has been withdrawn by the author due to rewritting and skipping crucial sign errors.

A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…

This paper has been withdrawn because of serious errors.

The paper has been withdrawn by the author due to a crucial error.

The paper was withdrawn by the author. It contained various errors.

This paper has been withdrawn by the author due to some incorrect presentation in the results and discussion part.

This paper has been withdrawn by the author, due a critical mistake on page 3.

This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

This paper has been withdrawn by the author due to the incorrect argument for the security.

Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.

The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.

This paper has been withdrawn by the author due to a crucial error related with the consideration of regular points

This paper is withdrawn. See quant-ph/9806031 for a discussion.

This paper has been withdrawn by the author due to an error in section 7. There is a new version: arXiv:1011.3352.

This paper has been withdrawn by the author due a crucial error.

This paper has been withdrawn by the authors due to a mistake in one of the proofs

This paper has been withdrawn by the author due to a mistake in the section 4.