A Stochastic Optimal Control Theory to Model Spontaneous Breathing

Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.

ClimateAP: an application for dynamic local downscaling of historical and future climate data in Asia Pacific

While low-to-moderate resolution gridded climate data are suitable for climate-impact modeling at global and ecosystems levels, spatial analyses conducted at local scales require climate data with increased spatial accuracy. This is particularly true for research focused on the evaluation of adaptive forest management strategies. In this study, we developed an application, Climate AP, to generate scale-free(i.e., specific to point locations) climate data for historical(1901–2015) and future(2011–2100)years and periods. Climate AP uses the best available interpolated climate data for the reference period 1961–1990 as baseline data. It downscales the baseline data from a moderate spatial resolution to scale-free point data through dynamic local elevation adjustments. It also integrates and downscales the historical and future climate data using a delta approach. In the case of future climate data, two greenhouse gas representative concentration pathways(RCP 4.5 and 8.5) and 15 general circulation models are included to allow for the assessment of alternative climate scenarios. In addition, Climate AP generates a large number of biologically relevant climate variables derived from primary monthly variables. The effectiveness of the local downscaling was determined based on the strength of the local linear regression for the estimate of lapse rate. The accuracy of the Climate AP output was evaluated through comparisons of Climate AP output against observations from 1805 weather stations in the Asia Pacific region. The local linear regression explained 70%–80% and 0%–50% of the total variation in monthly temperatures and precipitation, respectively, in most cases. Climate AP reduced prediction error by up to27% and 60% for monthly temperature and precipitation,respectively, relative to the original baselines data. The improvements for baseline portions of historical and futurewere more substantial. Applications and limitations of the software are discussed.