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Related Concept Videos

Linearization and Approximation01:26

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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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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
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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.
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Linear equations form the foundation of many algebraic and real-world applications, characterized by their simplicity and utility. A linear equation is an algebraic statement in which each term is either a constant or a product of a constant and a single variable. These equations represent straight lines when plotted on a Cartesian coordinate plane, reflecting a constant rate of change between two quantities.A typical linear equation in one variable has the form: ax + b = c, where a, b, and c...
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Updated: Mar 9, 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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Estimating monotonic rates from biological data using local linear regression.

Colin Olito1, Craig R White2, Dustin J Marshall2

  • 1Centre for Geometric Biology, School of Biological Sciences, Monash University, Clayton, VIC 3800, Australia colin.olito@gmail.com.

The Journal of Experimental Biology
|January 5, 2017
PubMed
Summary
This summary is machine-generated.

Researchers can now objectively estimate biological rates from complex data using the new R package LoLinR. This tool enhances reproducible research by employing local linear regression for non-linear time series analysis.

Keywords:
AutocorrelationBiological ratesLinearityLocal linear regressionReproducible researchTime series

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Area of Science:

  • Biological Sciences
  • Physiology
  • Biogeochemistry

Background:

  • Estimating biological rates is crucial for fundamental biological questions.
  • Current methods often use linear regression on non-linear, noisy time series data, leading to inaccuracies.
  • Manual truncation of non-linearities is a common but subjective approach.

Purpose of the Study:

  • Introduce the R package LoLinR for objective and reproducible estimation of monotonic biological rates.
  • Provide a flexible toolkit for analyzing non-linear time series data.
  • Demonstrate the application of LoLinR using metabolic rate data.

Main Methods:

  • Implementation of local linear regression techniques.
  • Utilizing the R package LoLinR.
  • Analysis of non-linear and noisy time series data.

Main Results:

  • LoLinR enables objective and reproducible estimation of monotonic biological rates.
  • The package provides statistically robust methods for time series analysis.
  • Demonstrated applicability in estimating metabolic rates.

Conclusions:

  • LoLinR offers a reliable method for estimating biological rates from non-linear time series.
  • The package promotes reproducible research across various biological disciplines.
  • Facilitates accurate analysis of complex biological data.