Related Experiment Video
Updated: Jul 12, 2026
05:00
New Features in Visual Dynamics 3.0
Published on: August 9, 2024
Automated smoother for the numerical decoupling of dynamics models
Marco Vilela1, Carlos C H Borges, Susana Vinga
1Department of Computatinal and Applied Mathematics, Laboratório Nacional de Computação Científica, Petrópolis, Rio de Janeiro, Brazil. mvilela@mdanderson.org
BMC Bioinformatics
|August 23, 2007
Summary
This study introduces a robust, automated method for extracting signals from biological time series data. The new approach uses an improved Whittaker
Area of Science:
- Systems Biology
- Computational Biology
- Biophysics
Background:
- Model reverse engineering of complex biological systems relies on structure identification.
- Biochemical Systems Theory (BST) simplifies this by using kinetic-order coefficients to define network topology.
- Previous numerical decoupling methods using artificial neural networks (ANN) introduced bias.
Purpose of the Study:
- To develop a robust, fully automated procedure for signal extraction from time series data.
- To adapt and improve upon existing methods for biological system modeling.
- To overcome limitations of ANN-based approaches in dynamic model identification.
Main Methods:
- Reformulation of the Whittaker's smoother within information theory.
- Development of adaptive signal segmentation for nonstationary noise.
- Application to metabolic profiles from in-vivo NMR experiments.
Main Results:
- A robust, fully automated signal extraction solution is proposed.
- The adapted Whittaker's smoother eliminates parametric bias in time course smoothing.
- The method enables differentiation crucial for numerical decoupling of differential equations.
Conclusions:
- The developed method effectively extracts signals from time series with nonstationary noise.
- It facilitates the numerical decoupling of differential equations for mechanistic model reverse engineering.
- This constitutes a general tool for analyzing multivariate experimental time series in biology.
Related Concept Videos
01:25Modeling with Differential Equations
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:21Partial Differential Equations
A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
01:20Separable Differential Equations
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
01:24Fast Decoupled and DC Powerflow
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
01:20Relation between Mathematical Equations and Block Diagrams
In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.