We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian’s Von Neumann entropy as a measure of bipartite entanglement present betw...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Corrosion results in hazardous and expensive damage to pipelines, vehicles, water and wastewater systems, and even home appliances. One of the most extensively practical methods for protecting metals and alloys against corrosion is to use organic inhibitors. The inhibition capability of 2-Mercaptobenzothiazole (2-MBT) against the corrosion of carbon steel in a 2 M NaCl solution was examined by ...

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

Entropy is a measurement of the degree of uncertainty. Meanentropy method can be used for modeling the choice among uncertain outcomes. In this paper, we consider the portfolio selection problem under the assumption that security returns are characterized by type-2 fuzzy variables. Since the expectation and entropy of type-2 fuzzy variables haven’t been well defined, type-2 fuzzy variables need...

background the importance of proper qualitative evaluation of eeg parameters during surgery has been recognized since many years. although none of the characteristics based on the frequency, entropy, and bi spectral characteristics have been regarded as a good predictor for detection of the depth of anesthesia alone. so it seems necessary to study multiple characteristics together. objectives i...

The notion of smooth entropy allows a unifying, generalized formulation of privacy amplification and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the R h y i entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other ...

information on water quality and pollution sources is important for the implementation of sustainable water resource management strategies. in this research, to evaluate spatial variation and the interpretation of large complex water quality data taken at seven different sites along the gorganrood river were subjected to multivariate statistical analysis. the factor analysis generated two signi...