Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

391
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
391
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

1.4K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
1.4K
Linearization and Approximation01:26

Linearization and Approximation

154
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...
154
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

5.1K
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.
For data that follow a straight line, the standard method for fitting is the linear...
5.1K
Quadratic Models01:23

Quadratic Models

299
Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
299
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

132
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
132

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

PRIME: Phase reversed interleaved multi-Echo acquisition enables highly accelerated distortion-corrected diffusion MRI.

Medical image analysis·2026
Same author

Diffusion skewness imaging using Q-space trajectory imaging with positivity constraints.

Physics in medicine and biology·2026
Same author

Effect of a consistent reconstruction algorithm on inter-scanner reproducibility in diffusion MRI.

Medical physics·2025
Same author

Rapid whole brain motion-robust mesoscale in-vivo MR imaging using multi-scale implicit neural representation.

Medical image analysis·2025
Same author

Maximum-entropy and subspace methods for high-resolution relaxation-diffusion distribution estimation.

Imaging neuroscience (Cambridge, Mass.)·2025
Same author

Likelihood-free posterior estimation and uncertainty quantification for diffusion MRI models.

Imaging neuroscience (Cambridge, Mass.)·2025
Same journal

Combinatorial and Hodge Laplacians: Similarities and Differences.

SIAM review. Society for Industrial and Applied Mathematics·2026
Same journal

Trajectory stratification of stochastic dynamics.

SIAM review. Society for Industrial and Applied Mathematics·2021
Same journal

Research and Education in Computational Science and Engineering.

SIAM review. Society for Industrial and Applied Mathematics·2018
Same journal

AN EVOLUTIONARY MODEL OF TUMOR CELL KINETICS AND THE EMERGENCE OF MOLECULAR HETEROGENEITY DRIVING GOMPERTZIAN GROWTH.

SIAM review. Society for Industrial and Applied Mathematics·2018
Same journal

CSTG: An Effective Framework for Cost-sensitive Sparse Online Learning.

SIAM review. Society for Industrial and Applied Mathematics·2018
Same journal

Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations.

SIAM review. Society for Industrial and Applied Mathematics·2013
See all related articles

Related Experiment Video

Updated: Mar 21, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.1K

Linear Models Based on Noisy Data and the Frisch Scheme.

Lipeng Ning1, Tryphon T Georgiou2, Allen Tannenbaum3

  • 1Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115.

SIAM Review. Society for Industrial and Applied Mathematics
|May 12, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces novel numerical techniques for identifying linear relationships in noisy data, focusing on the Frisch-Kalman dictum for optimal structure discovery. It offers new proofs and methods for noise reduction in large datasets.

Keywords:
factor analysisidentificationlinear models

More Related Videos

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

3.0K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K

Related Experiment Videos

Last Updated: Mar 21, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.1K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

3.0K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K

Area of Science:

  • Statistics
  • Data Science
  • Econometrics

Background:

  • Identifying linear relationships in data with measurement errors is crucial for uncovering structure.
  • Historical foundations include work by Spearman and Frisch, with related concepts in errors-in-variables and factor analysis.
  • Independent measurement errors are a common assumption in this domain.

Purpose of the Study:

  • To present modern numerical techniques for identifying linear relations among variables with noisy measurements.
  • To provide alternative proofs for key results in the field.
  • To explore the Frisch-Kalman dictum for noise identification and rank minimization.

Main Methods:

  • Reviewing fundamental contributions and providing modern proofs.
  • Applying novel numerical techniques based on the Frisch-Kalman dictum (rank minimization).
  • Discussing trace minimization heuristics, convex relaxations, and theoretical rank bounds for global optimality.

Main Results:

  • Development of modern viewpoints and numerical techniques for noise identification.
  • Guarantees for global optimality through convex relaxations and rank bounds.
  • Exploration of complementary viewpoints focusing on optimal quadratic estimation error.

Conclusions:

  • The study offers advanced methods for structure discovery in noisy datasets.
  • It bridges classical insights with modern computational approaches.
  • Novel regularization schemes are presented for improved noise modeling and relation identification.