Diffusion with resetting in arbitrary spatial dimension

We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state which exhibits non-Gaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate $r^*$ which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as $\exp -A (\log t)^d$ where $A$ is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.Comment: 21 pages, 3 figures, submitted to Journal of Physics

Intersociety Literacy Comparisons

literates, isolated illiterates, proximate illiterates, literacy measures, illustration, policy implication

Measuring polarization by reduced-form indices

An abbreviated or reduced-form monotonic polarization index is an increasing function of the between-group term and a decreasing function of the within-group term of a population subgroup decomposable inequality index. The between-group term represents the „identification? component of polarization and the within-group term can be regarded as an inverse indicator of the „alienation? component of polarization. An ordering for ranking alternative distributions of income using such polarizations indices has been developed. Several polarization indices of the said type have been characterized using intuitively reasonable axioms. Finally, we also consider the dual problem of retrieving the inequality index from the specified form of a polarization index.Polarization, ordering, axioms, indices, characterization, duality.

Measuring Financial Inclusion : An Axiomatic Approach

This paper clearly demonstrates that the axiomatic measurement approach developed in the human development literature can be usefully applied to the measurement of financial inclusion. A conceptual framework for aggregating data on financial services in different dimensions is developed. The suggested index of financial inclusion allows calculation of percentage contributions of different dimensions to the overall achievement. This in turn enables us to identify the dimensions of inclusion that are more/less susceptible to overall inclusion and hence to isolate the dimensions that deserve attention from a policy perspective. The paper also illustrates the index using cross-country and sub-national level data.financial inclusion, axioms, index, policy, application

Multidimensional poverty and material deprivation

We examine the measurement of multidimensional poverty and material deprivation following the counting approach. In contrast to earlier contributions, dimensions of well-being are not forced to be equally important but different weights can be assigned to different dimensions. We characterize a class of individual measures reflecting this feature. In addition, we axiomatize an aggregation procedure to obtain a class of indices for entire societies allowing for different degrees of inequality aversion in poverty. We apply the proposed measures to European Union member states where the concept of material deprivation was initiated.Multidimensional poverty measurement, material deprivation, equity

Target Shortfall Orderings and Indices

Given any income distribution, to each income we associate a subgroup containing all persons whose incomes are not higher than this income and a person's target shortfall in a subgroup is the gap between the subgroup highest income and his own income. We then develop an absolute target shortfall ordering, which, under constancy of population size and total income, implies the Lorenz and Cowell-Ebert complaint orderings. Under the same restrictions, one distribution dominates the other by this ordering if and only if the dominated distribution can be obtained from the dominant one by a sequence of rank preserving progressive transfers, where each transfer is shared equally by all persons poorer than the donor of the transfer. The relationship of the ordering with the absolute deprivation and differential orderings, and its consistency with ranking of distributions by absolute target shortfall indices are explored. Well-known inequality indices like the absolute Gini index and the standard deviation are interpreted as absolute target shortfall indices. Finally, the possibility of a relative target shortfall ordering is also discussed.Target shortfall orderings, transfer, indices

Measuring financial inclusion: An Axiomatic approach

This paper clearly demonstrates that the axiomatic measurement approach developed in the human development literature can be usefully applied to the measurement of financial inclusion. A conceptual framework for aggregating data on financial services in different dimensions is developed. The suggested index of financial inclusion allows calculation of percentage contributions of different dimensions to the overall achievement. This in turn enables us to identify the dimensions of inclusion that are more/less susceptible to overall inclusion and hence to isolate the dimensions that deserve attention from a policy perspective. The paper also illustrates the index using cross-country and sub-national level data.Financial inclusion, axioms, index, policy, application

The Measurement of Social Exclusion

This paper develops an axiomatic approach to the measurement of social exclusion. At the individual level, social exclusion is viewed in terms of deprivation of the person concerned with respect to different functionings in the society. At the aggregate level we treat social exclusion as a function of individual exclusions. The class of subgroup decomposable social exclusion measures using a set of independent axioms is identified. We then look at the problem of ranking exclusion profiles by exclusion dominance principle under certain restrictions. Finally, applications of decomposable and non-decomposable measures suggested in the paper using European Union and Italian data are also considered.Social Exclusion, Axioms, Characterization, Dominance, Application, Policy