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Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful additionto the well-established methods for characterizing time-invariants in non-Hermitian systems.

Using establishment-level data, we examine the impact of the Indian government's employment guarantee program on labor and firm behavior. We exploit the staggered implementation of the program for identification and find that the program led to a 10% reduction in the permanent workforce in firms. Firms responded to the adverse labor-supply shock by resorting to increased mechanization. This significantly increased the firms' cost of production, leading to a decline in net profits and productivity. These effects manifested primarily in firms paying low wages, firms having low labor productivity and greater sales volatility, and firms located in states with pro-employer labor regulations.

Using establishment-level employment and operating data, we examine the impact of the Indian government's employment guarantee program on labor and firm behavior. We exploit the staggered implementation of the program for identification and find that the program led to a 10% reduction in permanent workforce in firms. Firms responded to the adverse labor supply shock by resorting to increased mechanization. This significantly increases the firms' cost of production, thereby leading to a decline in net profits and productivity. These effects manifest primarily in firms paying low wages, having low labor productivity and greater sales volatility, and firms located in states with pro-employer labor regulations.

BACKGROUND: Incomplete immunisation coverage causes preventable illness and death in both developing and developed countries. Identification of factors that might modulate coverage could inform effective immunisation programmes and policies. We constructed a performance indicator that could quantitatively approximate measures of the susceptibility of immunisation programmes to coverage losses, with an aim to identify correlations between trends in vaccine coverage and socioeconomic factors. METHODS: We undertook a data-driven time-series analysis to examine trends in coverage of diphtheria, tetanus, and pertussis (DTP) vaccination across 190 countries over the past 30 years. We grouped countries into six world regions according to WHO classifications. We used Gaussian process regression to forecast future coverage rates and provide a vaccine performance index: a summary measure of the strength of immunisation coverage in a country. FINDINGS: Overall vaccine coverage increased in all six world regions between 1980 and 2010, with variation in volatility and trends. Our vaccine performance index identified that 53 countries had more than a 50% chance of missing the Global Vaccine Action Plan (GVAP) target of 90% worldwide coverage with three doses of DTP (DTP3) by 2015. These countries were mostly in sub-Saharan Africa and south Asia, but Austria and Ukraine also featured. Factors associated with DTP3 immunisation coverage varied by world region: personal income (Spearman's ρ=0·66, p=0·0011) and government health spending (0·66, p<0·0001) were informative of immunisation coverage in the Eastern Mediterranean between 1980 and 2010, whereas primary school completion was informative of coverage in Africa (0·56, p<0·0001) over the same period. The proportion of births attended by skilled health staff correlated significantly with immunisation coverage across many world regions. INTERPRETATION: Our vaccine performance index highlighted countries at risk of failing to achieve the GVAP target of 90% coverage by 2015, and could aid policy makers' assessments of the strength and resilience of immunisation programmes. Weakening correlations with socioeconomic factors show a need to tackle vaccine confidence, whereas strengthening correlations point to clear factors to address. FUNDING: UK Engineering and Physical Sciences Research Council.

Background Incomplete immunisation coverage causes preventable illness and death in both the developing and developed world. Identifying factors that may modulate coverage can inform effective immunisation programmes and policies. Methods We perform a data-driven analysis of unprecedented scale, examining time-varying trends in Diphtheriatetanus-pertussis coverage across 190 countries over the past three decades. Gaussian process regression is employed to forecast future coverage rates and provide a Vaccine Performance Index: a summary measure of the strength of immunisation coverage in a country. Findings Overall vaccine coverage has increased in all five world regions between 1980 and 2010, with marked variation in volatility and trends. Our Vaccine Performance Index identifies 53 countries with a less than 50% chance of missing the Global Vaccine Action Plan (GVAP) target of 90% worldwide DTP3 coverage by 2015, in agreement with recent immunisation data. These countries are mostly sub-Saharan and South Asian, but Austria and Ukraine in Europe also feature. Factors associated with DTP3 immunisation coverage vary by world-region: personal income (! = 0.66, ' < 0.001) and government health spending (! = 0.66, ' < 0.01) are particularly informative in the Eastern Mediterranean between 1980 and 2010, whilst primary school completion is informative in Africa (! = 0.56, ' < 0.001) over the same time. The fraction of births attended by skilled health staff is significantly informative across many world regions Interpretation A Vaccine Performance Index can highlight countries at risk identifying the strength and resilience of immunisation programmes. Weakening correlations with socio-economic factors indicate a need to tackle vaccine confidence whereas strengthening correlations points to clear factors to address.

INTRODUCTION:There is a renewed global interest in improving community health worker (CHW) programmes. For CHW programmes to be effective, key intervention design factors which contribute to the performance of CHWs need to be identified. The recent WHO guidelines recommends the combination of financial and non-financial incentives to improve CHW performance. However, evidence gaps remain as to what package of incentives will improve their performance in different country contexts. This study aims to evaluate CHW incentive preferences to improve performance and retention which will strengthen CHW programmes and help governments leverage limited resources appropriately. METHODS AND ANALYSIS:A discrete choice experiment (DCE) will be conducted with CHWs in Bangladesh, Haiti, Kenya and Uganda with different levels of maturity of CHWs programmes. This will be carried out in two phases. Phase 1 will involve preliminary qualitative research including focus group discussions (FGDs) and key informant interviews to develop the DCE design which will include attributes relevant to the CHW country settings. Phase 2 will involve a DCE survey with CHWs, presenting them with a series of job choices with varying attribute levels. An orthogonal design will be used to generate the choice sets for the surveys. The surveys will be administered in locally-appropriate languages to at least 150 CHWs from each of the cadres in each country. Conditional and mixed multinomial logit (MMNL) models will be used for the estimation of stated preferences. ETHICS AND DISSEMINATION:This study has been reviewed and approved by the Population Council's Institutional Review Board in New York, and appropriate ethics review boards in Kenya, Uganda, Bangladesh and Haiti. The results of the study will be disseminated through in-country dissemination workshops, meetings with country-level stakeholders and policy working groups, print media, online blogs and peer-reviewed journals.