A Shift-Dependent Measure of Extended Cumulative Entropy and Its Applications in Blind Image Quality Assessment

Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy (ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past version. These results contain stochastic order, upper and lower bounds, the symmetry property and some relationships with other reliability functions. We also discuss some properties of conditional weighted ECE under some assumptions. Finally, we propose a nonparametric estimator of this new measure and study its practical results in blind image quality assessment

Fractal Dimensions of the Hydrodynamic Modes of Diffusion

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.Comment: 20 pages, 6 figures, submitted to Nonlinearit

The structure and determinants of inequality and poverty reduction in Ghana, 1988-92

Using three rounds of the Ghana Living Standard Survey, conducted between 1988 and 1992, the authors present findings that shed light on the structure of inequality among different socioeconomic groups in different geographic areas, in the context of poverty reduction. First, poverty reduction can be attributed mainly to improvements in both average levels of income and the pattern of its distribution in the informal and nonfarm sectors in other cities and rural areas outside the capital city, Accra. Second, an analysis of different measures of inequality reveals that the most important changes in the degree of inequality took place at the lower end of the distribution. But the direction of change was different in Accra compared with the localities outside Accra. In Accra, while inequality increased overall, the inequality in the lower part of the distribution increased much more. In other cities, there was a more or less uniform improvement all along the distribution. But in the rural areas, there was a significant improvement at the lower end, but a deterioration at the upper end. Third, structural adjustment - which aimed to cut back public sector employment and stimulate activities in the private sector - raised living standards in rural areas and other cities, but not in Accra. The public sector is much larger in Accra than in other cities and rural areas. Contraction of the public sector in other cities and rural areas was compensated for by income growth in the informal and nonfarm sectors. But contraction of Accra's large public sector dominated the local economy, so living standards declined in both formal and informal sectors. Accra's economy will probably grow as its private and informal sectors grow. Fourth, major shifts in the population occurred in all localities from the formal to the informal sector, but the magnitude of the shift was largest in Accra - in fact, several times more than in the other localities. The deterioration of the income at the lower part of the distribution in both the formal and the informal sectors is mainly responsible for the decline in the welfare of the low income households in Accra. These findings suggest that an integrated regional strategy, taking into account the local socioeconomic structure, is necessary for achieving economic growth and poverty reduction in all regions. Anotherimportant finding: The poor do not benefit as much from education as the nonpoor do because there is very low return (in income) to primary education, the highest level most poor Ghanaians can hope for. Education helps increase, rather than decrease, inequality, so primary education for the poor should be designed to provide them with income-earning skills. Developing economic strategies for sustainable poverty reduction will require further research on activities in the informal sector. Another issue that requires investigation is the role of different administrative regions in the determination of household welfare that seems to have changed over the period under study. Findings from such an analysis will facilitate the design of appropriate regional strategies for poverty reduction in Ghana.Poverty Impact Evaluation,Public Health Promotion,Health Systems Development&Reform,Health Economics&Finance,Services&Transfers to Poor,Poverty Assessment,Achieving Shared Growth,Inequality,Rural Poverty Reduction,Services&Transfers to Poor

Advancing Shannon entropy for measuring diversity in systems

From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science. Part of the challenge is measuring it. Shannon entropy H has been used to re-think diversity within probability distributions, based on the notion of information. However, there are two major limitations to Shannon's approach. First, it cannot be used to compare diversity distributions that have different levels of scale. Second, it cannot be used to compare parts of diversity distributions to the whole. To address these limitations, we introduce a re-normalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c. Given a probability density p(x), Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of ^pc(x) up to cumulative probability c. We illustrate the utility of our approach by re-normalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions for energy of sub-atomic particles. The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions

Scanning and Sequential Decision Making for Multi-Dimensional Data - Part I: the Noiseless Case

We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image is compressed by coding the error sequence resulting from scandicting it. Thus, it is natural to ask what is the optimal method to scan and predict a given image, what is the resulting minimum prediction loss, and whether there exist specific scandiction schemes which are universal in some sense. Specifically, we investigate the following problems: First, modeling the data array as a random field, we wish to examine whether there exists a scandiction scheme which is independent of the field's distribution, yet asymptotically achieves the same performance as if this distribution was known. This question is answered in the affirmative for the set of all spatially stationary random fields and under mild conditions on the loss function. We then discuss the scenario where a non-optimal scanning order is used, yet accompanied by an optimal predictor, and derive bounds on the excess loss compared to optimal scanning and prediction. This paper is the first part of a two-part paper on sequential decision making for multi-dimensional data. It deals with clean, noiseless data arrays. The second part deals with noisy data arrays, namely, with the case where the decision maker observes only a noisy version of the data, yet it is judged with respect to the original, clean data.Comment: 46 pages, 2 figures. Revised version: title changed, section 1 revised, section 3.1 added, a few minor/technical corrections mad