Consistent Digital Curved Rays and Pseudoline Arrangements

Representing a family of geometric objects in the digital world where each object is represented by a set of pixels is a basic problem in graphics and computational geometry. One important criterion is the consistency, where the intersection pattern of the objects should be consistent with axioms of the Euclidean geometry, e.g., the intersection of two lines should be a single connected component. Previously, the set of linear rays and segments has been considered. In this paper, we extended this theory to families of curved rays going through the origin. We further consider some psudoline arrangements obtained as unions of such families of rays

MEASURING HUMAN WELLBEING AND ADVANCING SUSTAINABLE DEVELOPMENT: HOW CREDIBLE ARE THE UNDP'S HUMAN DEVELOPMENT REPORTS?

The broad objectives of the Human Development Report (HDR) and the estimates of human wellbeing are to identify policies that reduce poverty, economic and gender inequalities inequalities and increase human wellbeing. Since inception in 1990, the HDR and the methodological and measurement issues relating to the now well known Human Development Index (HDI) have undergone several transformations. This paper empirically looks at reliability of databases from HDRs with a special focus on the estimations methodology and data revisions of the HDI, recent growth trend in HDI and real income. It also looks selectively at major shift in policy directions for sustainable development in the HDRs. This paper notes that the databases in the HDRs exhibit significant measurement errors and inadequacies. The measurement errors are more conspicuous in case of data pertaining to low-income developing countries. This paper also notes that besides database problems, issues relating to policy revisions in the recent Reports raise serious questions of credibility with the Reports.Human Development Index, PPP GDP per capita, Low Income Countries, wellbeing.

Anomalous Diffusion In Microrheology: A Comparative Study

We present a comparative study on two theoretical descriptions of microrheological experiments. Using a generalized Langevin equation (GLE), we analyze the origin of the power-law behavior of the main properties of a viscoelastic medium. Then, we discuss the equivalence of the GLE with a generalized Fokker-Planck equation (GFPE), and how more general GFPE's can be derived from a thermo-kinetic formalism. These complementary theories lead to a justification for the physical nature of the Hurst exponent of fractional kinetics. Theory is compared with experiments.Comment: 7 pages, 3 figure

A FDR-preserving field theory for interacting Brownian particles: one-loop theory and MCT

We develop a field theoretical treatment of a model of interacting Brownian particles. We pay particular attention to the requirement of the time reversal invariance and the fluctuation-dissipation relationship (FDR). The method used is a modified version of the auxiliary field method due originally to Andreanov, Biroli and Lefevre [J. Stat. Mech. P07008 (2006)]. We recover the correct diffusion law when the interaction is dropped as well as the standard mode coupling equation in the one-loop order calculation for interacting Brownian particle systems.Comment: 66 pages, 8 figures, submitted to J. Stat. Mec