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Linearization and Approximation

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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...

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Updated: Jun 21, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Published on: October 28, 2022

An approximation algorithm for the minimum breakpoint linearization problem.

Xin Chen¹, Yun Cui

¹Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. chenxin@ntu.edu.sg

IEEE/ACM Transactions on Computational Biology and Bioinformatics

|August 1, 2009

Summary

This summary is machine-generated.

This study introduces a new approximation algorithm for the Minimum Breakpoint Linearization (MBL) problem in genome rearrangement. The algorithm provides a guaranteed performance bound for ordering genes on a chromosome from partial data.

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Linearization of the Bradford Protein Assay

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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Linearization of the Bradford Protein Assay

Linearization of the Bradford Protein Assay

Published on: April 12, 2010

Area of Science:

Computational Biology
Genomics
Bioinformatics

Background:

Genetic mapping often yields partial gene orders, necessitating methods to infer complete chromosomal sequences.
Genome rearrangement problems, including Minimum Breakpoint Linearization (MBL), are crucial for understanding genome evolution and structure.
The MBL problem aims to find a total gene order minimizing breakpoint distance to a reference, but is known to be NP-hard.

Purpose of the Study:

To develop an efficient approximation algorithm for the Minimum Breakpoint Linearization (MBL) problem.
To provide a theoretical performance guarantee for inferring total gene order from partial data.

Main Methods:

Formulation of the Minimum Breakpoint Linearization (MBL) problem within genome rearrangement.
Development of a novel approximation algorithm with a specific performance bound.
Analysis of the algorithm's approximation ratio: {m(2)+m/2}, where m is the number of combined gene maps.

Main Results:

The proposed algorithm achieves an {m(2)+m/2}-approximation for the MBL problem.
This represents an improvement over existing heuristic approaches by providing a quantifiable performance guarantee.
The algorithm effectively addresses the challenge of inferring total gene order from incomplete genetic mapping data.

Conclusions:

The developed algorithm offers a significant advancement in solving the NP-hard MBL problem.
It provides a practical and theoretically sound method for reconstructing complete gene orders from partial genomic information.
This contributes to more accurate genome assembly and comparative genomics studies.