We study the entropy of the set traced by an n-step simple symmetric random walk on Z. We show that for d ≥ 3, the entropy is of order n. For d = 2, the entropy is of order n/ log n. These values are essentially governed by the size of the boundary of the trace.

Second order lower bounds for the entropy function expressed in terms of the index of coincidence are derived. Equivalently, these bounds involve entropy and Rényi entropy of order 2. The constants found either explicitly or implicitly are best possible in a natural sense. The inequalities developed originated with certain problems in universal prediction and coding which are briefly discussed.

This work is concerned with the proof of the existence and uniqueness of the entropy weak solution to the following nonlinear hyperbolic equation: u t + div(vf (u)) = 0 in IR N 0; T ], with initial data u(:; 0) = u 0 (:) in IR N. where u 0 2 L 1 (IR N) is a given function, v is a divergence-free bounded function of class C 1 from IR N 0; T ] to IR N , and f is a function of class C 1 from IR to...

In image processing, one of the most efficient techniques for image segmentation is entropy-based thresholding. In this work it was applied a generalized entropy formalism that represents a recent development in statistical mechanics. We propose, for the first time, an image thresholding method using a nonextensive entropy regarding the presence of nonadditive information content in some image ...

We introduce the entropy rate of multidimensional cellular automata. This number is invariant under shift–commuting isomorphisms; as opposed to the entropy of such CA, it is always finite. The invariance property and the finiteness of the entropy rate result from basic results about the entropy of partitions of multidimensional cellular automata. We prove several results that show that entropy ...

Topological entropy can be an indicator of complicated (chaotic) behavior in dynamical systems. Whether the topological entropy of a dynamical system is positive or not is of primary significance, due to the fact that positive topological entropy implies that one can assert that the system is chaotic. As the concept of topological entropy is concerned, it is hard, as remarked by [8], to get a g...

Shannon entropy is increasingly used in many applications. In this article, an estimator of the entropy of a continuous random variable is proposed. Consistency and scale invariance of variance and mean squared error of the proposed estimator is proved and then comparisons are made with Vasicek's (1976), van Es (1992), Ebrahimi et al. (1994) and Correa (1995) entropy estimators. A simulation st...

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

We propose a system for measuring entropy 1 variations, S, in thermal systems using pyroelectric sensors. 2 These sensors convert time-dependent temperature variations 3 into electrical current. Consequently, heat and temperature 4 variations are obtained, and sensor entropy is inferred. Various 5 polyvinylidene fluoride and lead zirconate titanate sensors have 6 been tested. Two types of measu...

The use of the digital signal processing procedure of decimation is introduced as a tool to detect patterns of information entropy distribution and is applied to information entropy in influenza A segment 7. Decimation was able to reveal patterns of entropy accumulation in archival and emerging segment 7 sequences that were not apparent in the complete, undecimated data. The low entropy accumul...