Parameter estimation of Stochastic Logistic Model : Levenberg-Marquardt Method

In this paper, we estimate the drift and diffusion parameters of the stochas- tic logisticmodels for the growth of Clostridium Acetobutylicum P262 using Levenberg- Marquardt optimization method of non linear least squares. The parameters are esti- mated for five different substrates. The solution of the deterministic models has been approximated using Fourth Order Runge-Kutta and for the solution of the stochastic differential equations, Milstein numerical scheme has been used. Small values of Mean Square Errors (MSE) of stochastic models indicate good fits. Therefore the use of stochastic models are shown to be appropriate in modelling cell growth of Clostridium Acetobutylicum P26

Local convergence of the Levenberg-Marquardt method under H\"{o}lder metric subregularity

We describe and analyse Levenberg-Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity of the function defining the equation and H\"older continuity of its gradient mapping. Further, we analyse the local convergence of the method under the additional assumption that the \L{}ojasiewicz gradient inequality holds. We finally report encouraging numerical results confirming the theoretical findings for the problem of computing moiety conserved steady states in biochemical reaction networks. This problem can be cast as finding a solution of a system of nonlinear equations, where the associated mapping satisfies the \L{}ojasiewicz gradient inequality assumption.Comment: 30 pages, 10 figure

A pH-based pedotransfer function for scaling saturated hydraulic conductivity reduction: improved estimation of hydraulic dynamics in HYDRUS

Hydraulic conductivity is a key soil property governing agricultural production and is thus an important parameter in hydrologic modeling. The pH scaling factor for saturated hydraulic conductivity (Ks) reduction in the HYDRUS model was reviewed and evaluated for its ability to simulate Ks reduction. A limitation of the model is the generalization of Ks reduction at various levels of electrolyte concentration for different soil types, i.e., it is not soil specific. In this study, a new generalized linear regression model was developed to estimate Ks reduction for a larger set of Australian soils compared with three American soils. A nonlinear pedotransfer function was also produced, using the Levenberg–Marquardt optimization algorithm, by considering the pH and electrolyte concentration of the applied solution as well as the soil clay content. This approach improved the estimation of the pH scaling factor relating to Ks reduction for individual soils. The functions were based on Ks reduction in nine contrasting Australian soils using two sets of treatment solutions with Na adsorption ratios of 20 and 40; total electrolyte concentrations of 8, 15, 25, 50, 100, 250, and 500 mmolc L−1; and pH values of 6, 7, 8, and 9. A comparison of the experimental data and model outputs indicates that the models performed objectively well and successfully described the Ks reduction due to the pH. Further, a nonlinear function provided greater accuracy than the generalized function for the individual soils of Australia and California. This indicates that the nonlinear model provides an improved estimation of the pH scaling factor for Ks reduction in specific soils in the HYDRUS model and should therefore be considered in future HYDRUS developments and applications

Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization

We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous coverage of the state space.Comment: 18 pages, 6 figure