arXiv subjects

Vivi Andasari

Publications and source records attributed to Vivi Andasari.

2 recordsLinked to original sources

arXiv2025

Systems of ODEs Parameters Estimation by Using Stochastic Newton-Raphson and Gradient Descent Methods

Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when dealing with nonlinear and high-dimensional models. In this paper, we propose novel methodologies for parameter estimation in systems of ODEs by using the Newton-Raphson (NR) method and Gradient Descent (GD) method. By leveraging the discrete derivative and Taylor expansion, the problem is formulated in a way that enables the application of both methods, allowing for flexible, efficient solutions. Additionally, we extend these approaches to stochastic versions - Stochastic Newton-Raphson (SNR) and Stochastic Gradient Descent (SGD) - to handle large-scale systems with reduced computational cost. The proposed methods are evaluated by using numerical examples, including both linear and nonlinear parameter models, and compare the results to the well-known Nonlinear Least Squares (NLS) method. While NR converges rapidly to the optimal solution, GD demonstrates robustness in handling chaotic systems, though it may occasionally lead to suboptimal results. Overall, the proposed methods provide improved accuracy in parameter estimation for ODE systems, outperforming NLS in terms of error metrics such as bias, mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination R2. These methods offer a valuable tool for fitting ODE models, particularly in scenarios involving big data and complex dynamics.

math.NA↗

arXiv2016

Effects of 3D Geometries on Cellular Gradient Sensing and Polarization

During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases, and is determined by intracellular signaling networks. It results in directional forces through actin polymerization and myosin contractions. Many existing mathematical models of cell polarization are formulated in terms of reaction-diffusion systems of interacting molecules, and are often defined in one or two spatial dimensions. In this paper, we introduce a 3D reaction-diffusion model of interacting molecules in a single cell, and find that cell geometry has an important role affecting the capability of a cell to polarize, or change polarization when an external signal changes direction. Our results suggest a geometrical argument why more roundish cells can repolarize more effectively than cells which are elongated along the direction of the original stimulus, and thus enable roundish cells to turn faster, as has been observed in experiments. On the other hand, elongated cells preferentially polarize along their main axis even when a gradient stimulus appears from another direction. Furthermore, our 3D model can accurately capture the effect of binding and unbinding of important regulators of cell polarization to and from the cell membrane. This spatial separation of membrane and cytosol, not possible to capture in 1D or 2D models, leads to marked differences of our model from comparable lower-dimensional models.

physics.bio-ph↗