On the accurate estimation of free energies using the jarzynski equality.

The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, ΔF^J . Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator ΔF^FD . Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy ΔF^ML considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to ΔF^J . We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional ΔF^ML∗ to the Bennett acceptance ratio ( ΔF^BAR ) estimator. We show that, for Gaussian unidirectional work distributions, ΔF^FD is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that ΔF^ML and ΔF^ML∗ perform better than ΔF^J and ΔF^BAR , for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc.

Impact of Universal Health Coverage on Child Growth and Nutrition in Argentina.

OBJECTIVES: To estimate trends of undernutrition (stunting and underweight) among children younger than 5 years covered by the universal health coverage programs Plan Nacer and Programa Sumar. METHODS: From 2005 to 2013, Plan Nacer and Programa Sumar collected high-quality information on birth and visit dates, age (in days), gender, weight (in kg), and height (in cm) for 1.4 million children in 6386 health centers (13 million records) with broad coverage of vulnerable populations in Argentina. RESULTS: The prevalence of stunting and underweight decreased 45.0% (from 20.6% to 11.3%) and 38.0% (from 4.0% to 2.5%), respectively, with differences between rural versus urban areas, gender, regions, age, and seasons. CONCLUSIONS: Undernutrition prevalence substantially decreased in 2 programs in Argentina as a result of universal health coverage.