Fuzzy Subset Theory in the Measurement of Poverty

What has not been explored in the traditional measures of poverty is the extensive set of categorical variables that indicate standard of living and are already available from existing survey data. What precluded researchers from deriving poverty and welfare gauges from these data is the difficulty of incorporating these indicators in their measurement. This article offers a new approach to the traditional measures that allow these available data to be readily utilized. While accounting for the multi-dimensionality of the poverty phenomenon, the approach still provides formalism in the use of other variable parallel to and complementary with income and expenditure.poverty, econometric modeling, data and statistics

From Linear to Nonlinear Response in Spin Glasses: Importance of Mean-Field-Theory Predictions

Deviations from spin-glass linear response in a single crystal Cu:Mn 1.5 at % are studied for a wide range of changes in magnetic field, $\Delta H$. Three quantities, the difference $TRM-(MFC-ZFC)$, the effective waiting time, $t_{w}^{eff}$, and the difference $TRM(t_{w})-TRM(t_{w}=0)$ are examined in our analysis. Three regimes of spin-glass behavior are observed as $\Delta H$ increases. Lines in the $(T,\Delta H)$ plane, corresponding to ``weak'' and ``strong'' violations of linear response under a change in magnetic field, are shown to have the same functional form as the de Almeida-Thouless critical line. Our results demonstrate the existence of a fundamental link between static and dynamic properties of spin glasses, predicted by the mean-field theory of aging phenomena.Comment: 9 pages, 10 figure