Currently displaying 1 – 13 of 13

Showing per page

Order by Relevance | Title | Year of publication

Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models

Papáček, ŠtěpánMatonoha, Ctirad — 2023

Programs and Algorithms of Numerical Mathematics

Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of...

On two methods for the parameter estimation problem with spatio-temporal FRAP data

Papáček, ŠtěpánJablonský, JiříMatonoha, Ctirad — 2015

Programs and Algorithms of Numerical Mathematics

FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model...

On the optimization of initial conditions for a model parameter estimation

Matonoha, CtiradPapáček, ŠtěpánKindermann, Stefan — 2017

Programs and Algorithms of Numerical Mathematics

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence...

On estimation of diffusion coefficient based on spatio-temporal FRAP images: An inverse ill-posed problem

Kaňa, RadekMatonoha, CtiradPapáček, ŠtěpánSoukup, Jindřich — 2013

Programs and Algorithms of Numerical Mathematics

We present the method for determination of phycobilisomes diffusivity (diffusion coefficient D ) on thylakoid membrane from fluorescence recovery after photobleaching (FRAP) experiments. This was usually done by analytical models consisting mainly of a simple curve fitting procedure. However, analytical models need some unrealistic conditions to be supposed. Our method, based on finite difference approximation of the process governed by the Fickian diffusion equation and on the minimization of an...

Primal interior point method for minimization of generalized minimax functions

Ladislav LukšanCtirad MatonohaJan Vlček — 2010

Kybernetika

In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. (i. e. interior point method that uses explicitly computed approximations of Lagrange multipliers instead of their updates). Next we describe the basic algorithm and give more details concerning its implementation...

Primal interior-point method for large sparse minimax optimization

Ladislav LukšanCtirad MatonohaJan Vlček — 2009

Kybernetika

In this paper, we propose a primal interior-point method for large sparse minimax optimization. After a short introduction, the complete algorithm is introduced and important implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus the large sparse nonconvex minimax optimization problems can be solved successfully. The results of extensive computational experiments given in this paper confirm efficiency and robustness of the proposed...

On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks

Ctirad MatonohaŠtěpán PapáčekVolodymyr Lynnyk — 2022

Applications of Mathematics

We develop and test a relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both the methods, being (i) the standard quasi-steady-state approximation method, and (ii) the novel so-called delayed quasi-steady-state approximation method, firstly proposed by Vejchodský (2014), are extensively presented. Both theoretical and numerical issues related to the setting of delays are discussed. Namely, for one slightly...

On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy

Jurjen Duintjer TebbensCtirad MatonohaAndreas MatthiosŠtěpán Papáček — 2019

Applications of Mathematics

A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter...

Page 1

Download Results (CSV)