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Related Concept Videos

Transient and Steady-state Response01:24

Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

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Related Experiment Video

Updated: May 24, 2026

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting.

Patrick B Warren1, Rosalind J Allen

  • 1Unilever R&D Port Sunlight, Quarry Road East, Bebington, Wirral, CH63 3JW, United Kingdom. patrick.warren@unilever.com

The Journal of Chemical Physics
|March 20, 2012
PubMed
Summary

This study introduces trajectory reweighting for efficient parameter sensitivity analysis in biochemical network models. The novel method avoids repeated simulations, enabling faster computation of sensitivity coefficients for stochastic models.

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Last Updated: May 24, 2026

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Area of Science:

  • Biochemistry
  • Computational Biology
  • Systems Biology

Background:

  • Parameter sensitivity analysis is crucial for biochemical network modeling.
  • Stochastic simulations present computational challenges for sensitivity analysis due to repeated simulations.

Purpose of the Study:

  • To develop a computationally efficient method for parameter sensitivity analysis in stochastic simulations.
  • To avoid the need for multiple simulations by using trajectory reweighting.

Main Methods:

  • Trajectory reweighting to compute sensitivity coefficients without parameter perturbation.
  • Simultaneous computation of multiple sensitivity coefficients.
  • Application of the Girsanov measure transform principles.

Main Results:

  • A novel method for computing sensitivity coefficients in stochastic simulations.
  • Enables computation of steady-state sensitivity coefficients from a single simulation run.
  • Demonstrated application to signaling networks and genetic switches.

Conclusions:

  • The trajectory reweighting method significantly enhances the efficiency of parameter sensitivity analysis for biochemical networks.
  • The approach simplifies the analysis of stochastic models, particularly those with linear propensity functions.
  • Facilitates deeper insights into biochemical signaling and genetic regulatory systems.