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大型线性常微分方程系统的参数估计与变量选择：矩阵方法AI 解读

Ordinary differential equations (ODEs) are widely used to model the dynamic behavior of a complex system. Parameter estimation and variable selection for a "Big System" with linear ODEs are very challenging due to the need of nonlinear optimization in an ultra-high dimensional parameter space. In this article, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies…

广义常微分方程模型AI 解读

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in…

动态基因调控网络建模的稀疏可加常微分方程AI 解读

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and…

结合混合效应建模的高维常微分方程动态基因调控网络识别AI 解读

Gene regulation is a complicated process. The interaction of many genes and their products forms an intricate biological network. Identification of this dynamic network will help us understand the biological process in a systematic way. However, the construction of such a dynamic network is very challenging for a high-dimensional system. In this article we propose to use a set of ordinary differential equations (ODE), coupled with dimensional reduction by clustering and…

兼顾数值误差与测量误差的非线性常微分方程系数筛估计AI 解读

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…

在回归测量误差框架下估计微分方程模型参数AI 解读

Differential equation (DE) models are widely used in many scientific fields that include engineering, physics and biomedical sciences. The so-called "forward problem", the problem of simulations and predictions of state variables for given parameter values in the DE models, has been extensively studied by mathematicians, physicists, engineers and other scientists. However, the "inverse problem", the problem of parameter estimation based on the measurements of output…

确定性动态模型中时变系数的高效局部估计及 HIV-1 应用AI 解读

Recently deterministic dynamic models have become very popular in biomedical research and other scientific areas; examples include modeling human immunodeficiency virus (HIV) dynamics, pharmacokinetic/pharmacodynamic analysis, tumor cell kinetics, and genetic network modeling. In this article we propose estimation methods for the time-varying coefficients in deterministic dynamic systems that are usually described by a set of differential equations. Three two-stage local…

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