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This paper has been withdrawn by the author due to the incorrect application of the divergence theorem to Eqs 7, 8 and 9.
This paper has been withdrawn by the authors due to a crucial error in calculation.
This paper has been withdrawn at the author's request.
This paper has been withdrawn by the author due to the need for further revision.
This paper has been withdrawn by the authors as they feel it inappropriate to publish this paper for the time being.
This paper has been withdrawn by the author due to an error in the computation of E(n,x) on page 6 which appears to be essential for the result. The author is currently trying to correct this proof
This paper has been withdrawn by the author due to a crucial problem associated with Figs. 2 and 3.
We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of $d$-dimensional bounded monotonic functions under $L^p$ norms. It is interesting to see that both the metric entropy and bracketing entropy…
This paper has been withdrawn by the first author due to incomplete bibliography and incorporation of multiple formats in the same file.
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
This paper has been withdrawn by the authors.
This paper has been withdrawn due to an error in one of the equations in the extended portion.
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
This paper has been withdrawn by the author, due to an error in relation (11).
This paper has been withdrawn by the authors due to a crucial error in equation 12.
Characterising the capacity region for a network can be extremely difficult, especially when the sources are dependent. Most existing computable outer bounds are relaxations of the Linear Programming bound. One main challenge to extend…
This paper has been withdrawn by the author, due to a crucial error in page 5.
This paper has been withdrawn by the authors due to a fatal flaw in the central proof.
This paper was withdrawn by the author because severe errors were discovered.
Several groups have recently investigated the flow of information in high-energy collisions, from the entanglement entropy of the proton yielding classical Shannon entropy of its parton distribution functions (pdfs), through jet splitting…