SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems

We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential $A\rho^{2\zeta-2}-B\rho^{\zeta-2}$. We show that in these cases the non-compact (compact) algebra corresponds to so(2,1) (su(2))

Pathways from agriculture-to-nutrition: Design and conduct of the National PoSHAN surveys of Nepal

Pathways through which agricultural production may influence markets, household food security, dietary patterns and nutritional status remain incompletely understood. While cross-sectional surveys are common, national, population-based, standardized data collection systems that annually monitor markets, local services, food security, dietary intake and nutritional status may be needed to understand time trends and relationships. We describe the design and methods of an annual nationally representative series of surveys of households with preschool aged children in 7 Village Development Committees (VDCs) sampled across each agroecological zone (mountains, hills and plains) in Nepal. Our sampling methodology yielded 21 VDCs, 63 wards (3 per VDC) and 40 markets in 2013, 2014 and 2016. Each year between ~ 4286-5097 consenting households were assessed for agricultural practices, socioeconomic conditions and food security; diet by 7-day food frequency and nutritional status by anthropometry (weight, height and arm circumference) of women (n=4509-5458) and children (n=5401- 5468) using standardized procedures. Due to a major earthquake in April 2015, a truncated sample (wards n=27) was reached in 2015. Three VDCs, each representing a centroid of surveyed VDCs in each zone, served as year-round sentinel sites in which we conducted six surveys of seasonal conditions from 2013-2015. Representative, sameseason, same-site surveys offer a feasible national framework for assessing annual status and trends in agricultural, food security and nutritional conditions to identify opportunities for policy and program interventions and observe population responses along a continuum leading from agriculture to nutrition

Mapping child growth failure across low- and middle-income countries

Childhood malnutrition is associated with high morbidity and mortality globally1. Undernourished children are more likely to experience cognitive, physical, and metabolic developmental impairments that can lead to later cardiovascular disease, reduced intellectual ability and school attainment, and reduced economic productivity in adulthood2. Child growth failure (CGF), expressed as stunting, wasting, and underweight in children under five years of age (0�59 months), is a specific subset of undernutrition characterized by insufficient height or weight against age-specific growth reference standards3�5. The prevalence of stunting, wasting, or underweight in children under five is the proportion of children with a height-for-age, weight-for-height, or weight-for-age z-score, respectively, that is more than two standard deviations below the World Health Organization�s median growth reference standards for a healthy population6. Subnational estimates of CGF report substantial heterogeneity within countries, but are available primarily at the first administrative level (for example, states or provinces)7; the uneven geographical distribution of CGF has motivated further calls for assessments that can match the local scale of many public health programmes8. Building from our previous work mapping CGF in Africa9, here we provide the first, to our knowledge, mapped high-spatial-resolution estimates of CGF indicators from 2000 to 2017 across 105 low- and middle-income countries (LMICs), where 99 of affected children live1, aggregated to policy-relevant first and second (for example, districts or counties) administrative-level units and national levels. Despite remarkable declines over the study period, many LMICs remain far from the ambitious World Health Organization Global Nutrition Targets to reduce stunting by 40 and wasting to less than 5 by 2025. Large disparities in prevalence and progress exist across and within countries; our maps identify high-prevalence areas even within nations otherwise succeeding in reducing overall CGF prevalence. By highlighting where the highest-need populations reside, these geospatial estimates can support policy-makers in planning interventions that are adapted locally and in efficiently directing resources towards reducing CGF and its health implications. © 2020, The Author(s)