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

Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Transformers with Off-Nominal Turns Ratios01:25

Transformers with Off-Nominal Turns Ratios

In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the rated...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Relation between Mathematical Equations and Block Diagrams01:20

Relation between Mathematical Equations and Block Diagrams

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.

You might also read

Related Articles

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

Sort by
Same author

Spatial and environmental drivers of Varroa destructor detection in New South Wales, Australia.

Scientific reports·2025
Same author

Exploring Genetic Engineering Through a Deliberation in Biochemistry.

Biochemistry and molecular biology education : a bimonthly publication of the International Union of Biochemistry and Molecular Biology·2025
Same author

A generalizable 3D framework and model for self-supervised learning in medical imaging.

NPJ digital medicine·2025
Same author

Integrating 12 Spatial and Single Cell Technologies to Characterise Tumour Neighbourhoods and Cellular Interactions in three Skin Cancer Types.

bioRxiv : the preprint server for biology·2025
Same author

Investigation of erythema migrans patients identifies Borrelia species and Neoehrlichia mikurensis with implications for clinical assessment.

Scientific reports·2025
Same author

Erratum: Opportunities and challenges for people-centered multi-hazard early warning systems: Perspectives from the Global South.

iScience·2025

Related Experiment Video

Updated: May 22, 2026

A Rapid Method for Modeling a Variable Cycle Engine
04:58

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

Alternative to Ritt's pseudodivision for finding the input-output equations of multi-output models.

Nicolette Meshkat1, Chris Anderson, Joseph J DiStefano

  • 1UCLA, Department of Mathematics, Los Angeles, CA 90095, United States. nmeshkat@math.ucla.edu

Mathematical Biosciences
|May 26, 2012
PubMed
Summary

A new method using Gröbner Bases simplifies structural identifiability analysis for dynamic systems. This approach offers a more efficient way to determine model parameters compared to traditional differential algebra techniques.

More Related Videos

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

Related Experiment Videos

Last Updated: May 22, 2026

A Rapid Method for Modeling a Variable Cycle Engine
04:58

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

Area of Science:

  • Systems Biology
  • Computational Mathematics
  • Control Theory

Background:

  • Structural identifiability analysis is crucial for validating dynamic system models.
  • Differential algebra methods, particularly Ritt's pseudodivision, are standard but computationally intensive.
  • The characteristic set and its input-output subset are key to traditional identifiability analysis.

Purpose of the Study:

  • To introduce a simpler and more efficient algorithm for a critical step in structural identifiability analysis.
  • To leverage Gröbner Bases as an alternative to Ritt's pseudodivision.
  • To provide a theoretical foundation and practical validation for the proposed method.

Main Methods:

  • Development of a novel algorithm based on Gröbner Bases for computing the characteristic set.
  • Mathematical proof establishing the correctness and reduced derivative requirements of the Gröbner Bases approach.
  • Application and testing of the algorithm on various biosystem models.

Main Results:

  • The proposed Gröbner Bases algorithm provides a more efficient alternative to Ritt's pseudodivision.
  • A reduced upper bound on derivative requirements was proven for the new method.
  • Demonstrated efficacy across multiple complex biosystem models.

Conclusions:

  • Gröbner Bases offer a computationally advantageous approach for structural identifiability analysis.
  • The new method simplifies a key step in differential algebra-based model analysis.
  • This advancement facilitates more accessible and efficient dynamic system model validation.