Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy to under-defined or over-defined information systems. To be able to use Shannon entropy, the information is normalized by an affine transformation. The const...

We study and compare the Shannon capacity region and the stable throughput region for a random access system in which source nodes multicast their messages to multiple destination nodes. Under an erasure channel model which accounts for interference and allows for multipacket reception, we first characterize the Shannon capacity region. We then consider a queueing-theoretic formulation and char...

The three most common variations of Fitts’ index of difficulty are the Fitts formulation, the Welford formulation, and the Shannon formulation. A recent paper by Hoffmann [1] critiqued the three and concluded that the Fitts and Welford formulations are valid and that the Shannon formulation is invalid. In this paper, we challenge Hoffmann’s position regarding the Shannon formulation. It is argu...

A common complaint about adaptive prefix coding is that it is much slower than static prefix coding. Karpinski and Nekrich recently took an important step towards resolving this: they gave an adaptive Shannon coding algorithm that encodes each character in O(1) amortized time and decodes it in O(logH) amortized time, where H is the empirical entropy of the input string s. For comparison, Gagie’...

Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...

This essay looks at the historical significance of four APS classic papers that are freely available online: Jolliffe N, Shannon JA, and Smith HW. The excretion of urine in the dog. III. The use of non-metabolized sugars in the measurement of the glomerular filtrate. Am J Physiol 100: 301-312, 1932 (http://ajplegacy.physiology.org/cgi/reprint/100/2/301). Shannon JA. The excretion of inulin by t...

By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...

This study aims to identify and determine species diversity and richness of the Gastropods of intertidal zone of Bushehr seaport coastal field and assess ecological status of the area using Welch index. Sampling was carried out at 6 stations in Bushehr seaport in winter and summer seasons during 2013-2014. Sampling bed sediments was done three times in each station and Gastropod samples were co...