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Synthetic Disvision of Polynomials

Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
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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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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

List-decoding methods for inferring polynomials in finite dynamical gene network models.

Janis Dingel1, Olgica Milenkovic

  • 1Institute for Communications Engineering, Technische Universität München, Munich, Germany. janis.dingel@tum.de

Bioinformatics (Oxford, England)
|April 30, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces stochastic polynomial dynamical systems (SPDSs) for reverse engineering gene regulatory networks from gene expression data. SPDSs improve network analysis with small, noisy datasets, outperforming existing algebraic methods.

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Area of Science:

  • Systems Biology
  • Computational Biology
  • Bioinformatics

Background:

  • Reverse engineering gene expression profiles is crucial in systems biology.
  • Existing methods struggle with noisy, small datasets common in high-throughput measurements.
  • Novel approaches are needed for robust network analysis from limited data.

Purpose of the Study:

  • To introduce a new algebraic modeling framework, Stochastic Polynomial Dynamical Systems (SPDSs).
  • To enable accurate reconstruction of gene regulatory network dynamics from microarray data.
  • To address limitations of current methods when dealing with small sample sizes and errors.

Main Methods:

  • Developed the SPDSs framework, assuming quantized expression data and polynomial update functions.
  • Employed a reverse engineering algorithm based on coding theory, specifically list-decoding for Reed-Muller codes.
  • Validated the method on synthetic data and real microarray expression datasets (E. coli SOS repair system, RegulonDB transcription factor network).

Main Results:

  • SPDSs effectively capture gene regulatory network dynamics from microarray data.
  • List-decoding based SPDSs significantly outperform other algebraic reverse engineering methods.
  • The framework provides valuable insights into gene influence on network dynamics.

Conclusions:

  • SPDSs offer a powerful new approach for reverse engineering gene regulatory networks.
  • The method is robust to noise and effective with limited biological data.
  • Publicly available software will facilitate application in systems biology research.