The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. Nonlinear adaptive control system design with asymptotically stable parameter estimation error Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations.
ORCAFLEX HOCKLING SERIES
In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied.
However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. Ghasemi, Omid Lindsey, Merry L Yang, Tianyi Nguyen, Nguyen Huang, Yufei Jin, Yu-Fang Bayesian parameter estimation for nonlinear modelling of biological pathways.
0 kommentar(er)
