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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
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...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Modeling with Differential Equations01:25

Modeling 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...

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Related Experiment Video

Updated: May 17, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Fitting Boolean networks from steady state perturbation data.

Anthony Almudevar1, Matthew N McCall, Helene McMurray

  • 1University of Rochester, USA.

Statistical Applications in Genetics and Molecular Biology
|October 24, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian modeling approach for gene regulatory networks, accurately inferring network structures and predicting steady states from perturbation data while quantifying uncertainty.

Related Experiment Videos

Last Updated: May 17, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

  • Systems Biology
  • Computational Biology
  • Genomics

Background:

  • Gene regulatory network reconstruction commonly uses perturbation experiments.
  • Existing methods interpret data as steady states of altered networks, not original ones.

Purpose of the Study:

  • To propose an implicit modeling methodology for gene regulatory network inference using perturbation data.
  • To address the challenge of interpreting steady-state data from perturbed biological systems.

Main Methods:

  • Developed an implicit modeling approach to first model perturbations and predict steady states.
  • Employed a computational Bayesian approach to handle the many-to-one inverse problem and assess model uncertainty.
  • Validated the methodology on synthetic networks and applied it to a real-world gene regulatory network with synergistic gene response data.

Main Results:

  • The Bayesian approach accurately assigned high posterior probability to network structures and steady-state behaviors in synthetic models.
  • Model uncertainty was effectively resolved through additional perturbation experiments.
  • Application to a nine-gene network, responding synergistically to oncogenic mutations, yielded a hypothetical model consistent with known regulatory properties.
  • The methodology demonstrated consistency, with randomized algorithm applications converging to a common posterior density.

Conclusions:

  • Fully Bayesian methods are suitable for gene regulatory network inference, offering accuracy and uncertainty estimation.
  • This approach enhances experimental design for more precise network reconstruction.
  • The implicit modeling accounts for experimental constraints, improving the reliability of inferred gene regulatory networks.