Abstract The change in entropy is calculated due to propagation of blast waves, produced by the explosion of spherical charge in sea water, using the energy hypothesis of Thomas. The release of energy is considered as instantaneous and the gravitation of earth is taken into account, assuming the earth to be a sphere of uniform density. For the sake of simplicity, effect of rotation of the earth...

We study the asymptotic behavior of compressible isentropic flow through porous medium with general L∞ initial data. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. Recent progress gives a definte answer to this conjectu...

Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of first occurrence of the respective symbol in the original sequence. Since a pattern is the result of data processing on the original sequence, its entropy c...

We have derived generalized ideal gas equations for a structureful universe consisting of all forms of matters. We have assumed a universe that contains superclusters. Superclusters are then made of clusters. Each cluster can be further divided into smaller ones and so on. We have derived an expression for the entropy of such a universe. Our model is rather independent of the geometry of the in...

The genetic information in cells is stored in DNA sequences, represented by a string of four letters, each corresponding to a definite type of nucleotides. Genomic DNA sequences are very abundant in periodic patterns, which play important biological roles. The complexity of genetic sequences can be estimated using the information-theoretic methods. Low complexity regions are of particular inter...

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study...

A thought experiment is proposed that reveals a difference between Fitts’ index of difficulty and Shannon’s entropy, in the quantification of the information content of a series of rapid aimed movements. This implies that the contemporary Shannon formulation of the index of difficulty is similar to, but not identical to, entropy. Preliminary work is reported toward developing a model that resol...

Since the pioneering work of Shannon, entropy, mutual information, association, divergence measures and kernels on distributions have found a broad range of applications in many areas of machine learning. Entropies provide a natural notion to quantify the uncertainty of random variables, mutual information and association indices measure the dependence among its arguments, divergences and kerne...

We introduce a methodology for sensitivity analysis of evidence variables in Gaussian Bayesian networks. Knowledge of the posterior probability distribution of the target variable in a Bayesian network, given a set of evidence, is desirable. However, this evidence is not always determined; in fact, additional information might be requested to improve the solution in terms of reducing uncertaint...

Based on the Markov model and the basic theory of information entropy, this paper puts forward a new method for optimizing the location of observation points in order to obtain more information from limited geological investigation. According to the existing data from observation points data, classification of tunnel geological lithology was performed, and various lithology distribution were de...