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Related Concept Videos

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...
Construction of Root Locus01:15

Construction of Root Locus

The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
For positive gain values, the root locus exists on the real axis to the left of an odd number of finite open-loop poles or zeros. The root locus starts at the open-loop poles and traces the paths of the closed-loop poles as the gain increases.
Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is observed...
Properties of the Root Locus01:05

Properties of the Root Locus

The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on the...
Control System Problem01:21

Control System Problem

In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.

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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Finding a periodic attractor of a Boolean network.

Tatsuya Akutsu1, Sven Kosub, Avraham A Melkman

  • 1Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan. takutsu@kuicr.kyoto-u.ac.jp

IEEE/ACM Transactions on Computational Biology and Bioinformatics
|June 13, 2012
PubMed
Summary
This summary is machine-generated.

This study presents efficient algorithms for finding periodic attractors in Boolean networks (BNs), crucial for computational systems biology. Polynomial and sub-exponential time solutions are developed for specific BN subclasses, advancing attractor computation.

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Area of Science:

  • Computational Systems Biology
  • Theoretical Computer Science
  • Bioinformatics

Background:

  • Boolean networks (BNs) are widely used to model gene regulatory networks.
  • Finding periodic attractors in BNs is computationally challenging (NP-hard).
  • Specialized subclasses of BNs offer tractable solutions for attractor analysis.

Purpose of the Study:

  • To develop efficient algorithms for finding periodic attractors in specific Boolean network subclasses.
  • To address the computational complexity of attractor detection in systems biology models.
  • To provide practical solutions for analyzing the dynamics of biological systems modeled by BNs.

Main Methods:

  • Algorithm development for finding period-2 attractors in OR-function BNs (polynomial time).
  • Algorithm development for finding period-2 attractors in AND/OR-function BNs (O(1.985^n) time).
  • Algorithm development for fixed-period attractors in nested canalyzing function BNs with constant treewidth (O(n(2^p(w+1))) time).

Main Results:

  • A polynomial-time algorithm for a specific class of OR-function BNs.
  • A sub-exponential time algorithm for AND/OR-function BNs.
  • An efficient algorithm for nested canalyzing functions with bounded treewidth.

Conclusions:

  • Efficient computation of periodic attractors is feasible for biologically relevant subclasses of Boolean networks.
  • The developed algorithms significantly improve upon general NP-hard complexity for these specific cases.
  • These findings facilitate more effective computational analysis of biological system dynamics.