Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge--Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurement error. The B-spline is used to approximate the time-varying coefficients, and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach. Our results show that if the maximum step size of the $p$-order numerical algorithm goes to zero at a rate faster than $n^{-1/(p\wedge4)}$, the numerical error is negligible compared to the measurement error. This result provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. Moreover, we have shown that the numerical solution-based NLS estimator and the sieve NLS estimator are strongly consistent. The sieve estimator of constant parameters is asymptotically normal with the same asymptotic co-variance as that of the case where the true ODE solution is exactly known, while the estimator of the time-varying parameter has the optimal convergence rate under some regularity conditions. The theoretical results are also developed for the case when the step size of the ODE numerical solver does not go to zero fast enough or the numerical error is comparable to the measurement error. We illustrate our approach with both simulation studies and clinical data on HIV viral dynamics.Comment: Published in at http://dx.doi.org/10.1214/09-AOS784 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Neural Generalized Ordinary Differential Equations with Layer-varying Parameters

Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or Neural-ODE model. In this study, we propose a neural generalized ordinary differential equation (Neural-GODE) model with layer-varying parameters to further extend the Neural-ODE to approximate the discrete ResNets. Specifically, we use nonparametric B-spline functions to parameterize the Neural-GODE so that the trade-off between the model complexity and computational efficiency can be easily balanced. It is demonstrated that ResNets and Neural-ODE models are special cases of the proposed Neural-GODE model. Based on two benchmark datasets, MNIST and CIFAR-10, we show that the layer-varying Neural-GODE is more flexible and general than the standard Neural-ODE. Furthermore, the Neural-GODE enjoys the computational and memory benefits while performing comparably to ResNets in prediction accuracy

A pathway to the green revolution in emerging economies: how does green technological innovation affect green growth and ecological sustainability?

Green technological innovation (G.T.I.) contributes to making economic growth compatible with ecological sustainability (E.S.). Thus, in light of environmental challenges and attempts of emerging economies’ progress toward a green revolution, this study examines the effects of G.T.I. on green growth (G.G). and E.S. for 25 emerging economies from 1990 to 2018. It also investigates the moderating role of G.T.I. on the impacts of energy intensity and foreign direct investment (F.D.I.) on G.G. and E.S. to illustrate the energy rebound effect and pollution haven hypothesis. The Fully modified least square (F.M.O.L.S.), the Dynamic least square (D.O.L.S.), and the Pooled mean group autoregressive distributed lag (P.M.G./A.R.D.L.) estimators are used. The findings imply that G.T.I. positively impacts G.G. and E.S. in emerging economies. Conversely, F.D.I. and energy intensity have adverse effects on G.G. and E.S. However, the negative effects of F.D.I. and energy intensity on G.G. and E.S. are decreasing with respect to G.T.I., implying that emerging countries promoting G.T.I. minimize the pollution haven effects of F.D.I. and mitigate the negative effect of energy intensity. Therefore, G.T.I. is a vital factor to facilitate the pathway to the green revolution in emerging economies. Policy implications are forwarded based on the findings of the study

Enhanced Microscale Hydrodynamic Near-cloaking using Electro-osmosis

In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the cloaking conditions and relationship of shapes are quantified more accurately. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking

A mathematical theory of microscale hydrodynamic cloaking and shielding by electro-osmosis

In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being annulus or confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the condition that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding

Evidence of areca nut consumption in the United States mainland: a cross‑sectional study

Background Areca nut (AN) is an addictive substance consumed in the Southeast region and is highly associated with oral premalignant lesions and oral cancer. The impact of AN use in the United States (US) is largely unknown, but the products are readily available and probably used by a significant fraction of Asian immigrants or descendants living in the US. We aimed at assessing AN use prevalence among the Asian community in Houston, Texas. Methods A cross-sectional questionnaire was used to interview adult individuals (≥ 18 years of age) who self-identified as Asian immigrants or descendants residing in Houston. Means, frequencies, and proportions were reported. Factors associated with AN use were evaluated using logistic regression. Results We surveyed 275 individuals (58% women, 43% between 35–54 years old, 67% born outside of the US, and 6% concurrent smokers). Among respondents, 91% were familiar with AN products, 17% self-reported ever use of AN products in the US, and 31% had friends/family members who were AN ever users. AN use was significantly associated with being Indian Subcontinent immigrants or descendants (ISID) (OR = 3·9; CI: 1·10,13·81; p = 0·035) and having friends/family members using AN products (OR = 6·2; CI: 1·69, 22·69; p = 0·006). Conclusions Our findings provide quantitative data on the prevalence of AN ever use and context for future AN prevention and cessation interventions specific to the Southeast Asian groups living in the US mainland. This is crucial for the prevention and control of oral cancer and other detrimental conditions related to AN consumption