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Related Concept Videos

Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Positive and Negative Feedback Loops01:18

Positive and Negative Feedback Loops

Animal organs and organ systems constantly adjust to internal and external changes through a process called homeostasis ("steady state"). Examples of these changes include regulation of the level of glucose or calcium in the blood or internal responses to external temperatures. Homeostasis requires  maintaining an internal dynamic equilibrium:
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.
Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
Thevinin's Theorem01:15

Thevinin's Theorem

Thévenin's theorem plays a pivotal role in electrical circuit analysis, offering a solution to the challenges posed by variable loads within a circuit. In practical applications, it is common to encounter circuits where certain elements remain fixed while others fluctuate, often referred to as the "load." A typical household electrical outlet serves as a prime example of a variable load, as it can be connected to a variety of appliances, each with its own unique electrical characteristics.

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Related Experiment Video

Updated: May 22, 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

Evolving sensitivity balances Boolean Networks.

Jamie X Luo1, Matthew S Turner

  • 1Centre for Complexity Science, University of Warwick, Coventry, West Midlands, United Kingdom.

Plos One
|May 16, 2012
PubMed
Summary
This summary is machine-generated.

Boolean Networks (BNs) modeling gene regulatory networks (GRNs) show maximum sensitivity to mutations when topologically balanced. Evolved networks feature long limit cycles, easily destabilized by mutations, relevant to stem cell differentiation.

Related Experiment Videos

Last Updated: May 22, 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:

  • Computational Biology
  • Systems Biology
  • Network Science

Background:

  • Boolean Networks (BNs) are utilized as simplified models for complex Gene Regulatory Networks (GRNs).
  • Understanding the stability and dynamics of BNs is crucial for deciphering cellular processes.
  • The Ergodic Set concept, as defined by Ribeiro and Kauffman, offers a framework for analyzing long-term BN dynamics.

Purpose of the Study:

  • To investigate the sensitivity of Boolean Networks (BNs) to mutations, specifically loss of interaction.
  • To define and quantify BN sensitivity using the Ergodic Set structure.
  • To explore the relationship between network topology, dynamics, and sensitivity in the context of GRNs.

Main Methods:

  • Definition of BN sensitivity as the mean change in Ergodic Set structure under all possible loss-of-interaction mutations.
  • In silico experiments employing selective evolution to optimize BNs for sensitivity.
  • Analysis of network topology (inhibitory vs. excitatory interactions) and dynamic properties (limit cycles).

Main Results:

  • Maximum sensitivity to mutations is achievable in BNs.
  • Evolved sensitive BNs tend to be topologically balanced, with an equal number of inhibitory and excitatory interactions.
  • The dominant evolutionary strategy for sensitivity involves creating Ergodic Sets dominated by a single, long limit cycle that is easily destabilized.

Conclusions:

  • Network sensitivity is a tunable property that can be evolved in BNs.
  • Topological balance and specific dynamic structures (long limit cycles) are key to achieving high sensitivity.
  • The findings suggest potential parallels between evolved sensitive networks and the dynamics of pluripotent stem cells during differentiation.