Jove
Visualize
Contact Us

Related Concept Videos

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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

174
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...
174
Multicompartment Models: Overview01:14

Multicompartment Models: Overview

354
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
354
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

148
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...
148
Mechanistic Models: Overview of Compartment Models01:21

Mechanistic Models: Overview of Compartment Models

245
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
245
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

179
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,...
179
Predicting Products: Substitution vs. Elimination02:52

Predicting Products: Substitution vs. Elimination

13.0K
When a nucleophile and an alkyl halide react, nucleophilic substitution and β-elimination reactions compete to generate products.
The following factors can influence the mechanisms competing against each other:
13.0K

You might also read

Related Articles

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

Sort by
Same author

Empirical discovery of multiscale transfer of information in dynamical systems.

Physical review. E·2026
Same author

Machine learning enhanced Hankel dynamic-mode decomposition.

Chaos (Woodbury, N.Y.)·2023
Same author

Detection of functional communities in networks of randomly coupled oscillators using the dynamic-mode decomposition.

Physical review. E·2021
Same author

Characterizing coherent structures in Bose-Einstein condensates through dynamic-mode decomposition.

Physical review. E·2019
Same author

Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles
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 Experiment Videos

Dynamic-mode decomposition and optimal prediction.

Christopher W Curtis1, Daniel Jay Alford-Lago2

  • 1Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182, USA.

Physical Review. E
|February 19, 2021
PubMed
Summary
This summary is machine-generated.

Memory-dependent dynamic mode decomposition (MDDMD) extends traditional dynamic mode decomposition (DMD) to analyze complex systems with incomplete data. This new method effectively captures the averaged dynamics of unobserved variables using partial measurements.

Related Experiment Videos

Area of Science:

  • Data-driven modeling
  • Dynamical systems theory
  • Nonlinear time series analysis

Background:

  • Dynamic Mode Decomposition (DMD) is a standard technique for analyzing time-series data.
  • Traditional DMD requires complete measurements of all system dimensions.
  • Incomplete data presents challenges for analyzing complex dynamical systems.

Purpose of the Study:

  • To extend the Dynamic Mode Decomposition (DMD) algorithm for systems with partial observations.
  • To incorporate memory effects from unobserved variables into the DMD framework.
  • To develop a robust method for analyzing complex dynamics from limited data.

Main Methods:

  • Incorporation of Mori-Zwanzig decomposition to derive memory kernels.
  • Projection of unresolved variable dynamics onto resolved dimensions.
  • Development of Memory-Dependent Dynamic Mode Decomposition (MDDMD).

Main Results:

  • MDDMD successfully approximates ensemble-averaged dynamics from partial measurements.
  • The derived memory kernels effectively represent the influence of unobserved dynamics.
  • Numerical examples validate the accuracy of the MDDMD approach.

Conclusions:

  • MDDMD offers a powerful extension to DMD for systems with incomplete data.
  • The method provides accurate insights into the averaged dynamics of complex systems.
  • MDDMD enhances the applicability of DMD in scenarios with partial observations.