We are interesting in the error exponent for source coding with fidelity criterion. For each fixed distortion level ∆, the maximum attainable error exponent at rate R, as a function of R, is called the reliability function. The minimum rate achieving the given error exponent is called the minimum achievable rate. For memoryless sources with finite alphabet, Marton (1974) gave an expression of t...

The performance of maximum-likelihood (ML) decoded binary linear block codes over the AWGN channel is addressed via the tangential-sphere bound (TSB) and some of its improved variations. The paper focuses on the derivation of the error exponents of these bounds. Although it was previously exemplified that some variations of the TSB suggest an improvement over the TSB for finite-length codes, it...

In this work, we give a rigorous explicit formula for the Lyapunov exponent for some binary infinite products of random 2 × 2 real matrices. All these products are constructed using only two types of matrices, A and B, which are chosen according to a stochastic process. The matrix A is singular, namely its determinant is zero. This formula is derived by using a particular decomposition for the ...

We estimated Hurst exponent of twelve stock index series from across the glove using daily values of for past ten years and found that the Hurst exponent value of the full series is around 0.50 confirming market efficiency. But the Hurst exponent value is found to vary widely when the full series is split into smaller series of 60 trading days. Later, we tried to find relationship between Hurst...

a watershed management program is usually based on the results of watershed modeling. accurate modeling results are decided by the appropriate parameters and input data. precipitation is the most important input for watershed modeling. precipitation characteristics usually exhibit significant spatial variation, even within small watersheds. therefore, properly describing the spatial variation o...

We examined the Hurst exponent of heart rate time series and its relation with the subjective measures of valence and arousal in two groups of subjects. The electrocardiogram (ECG) and the subjective valence and arousal were measured during the administration of emotional film stimuli (happiness, sadness, anger and fear). The results showed that there is a difference in the Hurst exponent for t...

We investigate the dynamical origin for the occurrence of asynchronous hyperchaos and chaos via blowout bifurcations in coupled chaotic systems. An asynchronous hyperchaotic or chaotic attractor with a positive or negative second Lyapunov exponent appears through a blowout bifurcation. It is found that the sign of the second Lyapunov exponent of the newly born asynchronous attractor, exhibiting...

In this paper, we report on persistence results of reactive-wetting advancing interfaces performed with mercury on silver at room temperature. Earlier kinetic roughening studies of reactive-wetting systems at room temperature as well as at high temperatures revealed some limited information on the spatiotemporal behavior of these systems. However, by calculating the persistence exponent, we wer...

Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Bro...