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

Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

215
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
215
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

1.1K
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
1.1K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

360
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...
360
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.1K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
20.1K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

382
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.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
382
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

1.3K
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...
1.3K

You might also read

Related Articles

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

Sort by
Same author

A novel application of neural networks to identify potentially effective combinations of biologic factors for enhancement of bone fusion/repair.

PloS one·2022
Same author

Deriving testable hypotheses through an analogy between individual and collective memory.

Progress in brain research·2022
Same author

Differences in olfactory bulb mitral cell spiking with ortho- and retronasal stimulation revealed by data-driven models.

PLoS computational biology·2021
Same author

Computational modeling of the monoaminergic neurotransmitter and male neuroendocrine systems in an analysis of therapeutic neuroadaptation to chronic antidepressant.

European neuropsychopharmacology : the journal of the European College of Neuropsychopharmacology·2019
Same author

Computational Analysis of Therapeutic Neuroadaptation to Chronic Antidepressant in a Model of the Monoaminergic Neurotransmitter and Stress Hormone Systems.

Frontiers in pharmacology·2019
Same author

Exploring the Correlation between the Cognitive Benefits of Drug Combinations in a Clinical Database and the Efficacies of the Same Drug Combinations Predicted from a Computational Model.

Journal of Alzheimer's disease : JAD·2019
Same journal

Desert lizards modulate nutritional responses to match seasonal biological needs.

Royal Society open science·2026
Same journal

Multi-generational fidelity, ecological and social determinants of roosting in a cooperatively breeding bird (<i>Argya squamiceps</i>).

Royal Society open science·2025
Same journal

Multifaceted polarization and information reliability in climate change discussions on social media platforms.

Royal Society open science·2025
Same journal

Comparing the kinematics related to inflicted head injury between violent shaking of a 6-week-old and a 1-year-old infant surrogate.

Royal Society open science·2025
Same journal

Partner choice increases observed reciprocity-based cooperation but decreases unobserved stake-based cooperation.

Royal Society open science·2025
Same journal

Importation models for travel-related SARS-CoV-2 cases reported in Newfoundland and Labrador during the COVID-19 pandemic.

Royal Society open science·2025
See all related articles

Related Experiment Video

Updated: Feb 21, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.7K

A geometric method for eigenvalue problems with low-rank perturbations.

Thomas J Anastasio1, Andrea K Barreiro2, Jared C Bronski3

  • 1Department of Molecular and Integrative Physiology and Beckman Institute, University of Illinois Urbana-Champaign, Urbana, IL 61820, USA.

Royal Society Open Science
|October 10, 2017
PubMed
Summary
This summary is machine-generated.

This study analyzes the spectrum of operators with low-rank perturbations using differential geometry. The novel approach simplifies spectral analysis for complex systems in neuroscience and applied mathematics.

Keywords:
Aronszajn–Krein formulabifurcation theoryrank-one perturbations

More Related Videos

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.9K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Related Experiment Videos

Last Updated: Feb 21, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.7K
Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.9K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Area of Science:

  • Mathematical Physics
  • Applied Mathematics
  • Computational Neuroscience

Background:

  • Many applied problems involve operators that are low-rank perturbations of well-understood operators.
  • Analyzing the spectrum of non-normal operators is crucial for understanding system dynamics.
  • Existing methods may not efficiently handle low-rank perturbations.

Purpose of the Study:

  • To develop a method for completely analyzing the spectrum of low-rank (rank one or two) non-normal perturbations of operators.
  • To apply this method to specific problems in computational neuroscience and applied mathematics.

Main Methods:

  • Utilizing the low-rank perturbation structure of the operator.
  • Applying concepts from classical differential geometry, specifically the envelope of a family of curves.
  • Analyzing the spectrum by relating it to the geometric properties of the perturbed operator.

Main Results:

  • A complete spectral analysis was achieved for operators with rank one or two perturbations.
  • The method was successfully applied to three distinct problems: an oculomotor integrator model, a continuum integrator model, and a phase separation model.
  • The differential geometry approach provided a powerful tool for spectral determination.

Conclusions:

  • The envelope method offers an effective and complete approach to spectral analysis of low-rank perturbed operators.
  • This technique has broad applicability in fields dealing with such mathematical structures.
  • The study provides a unified framework for analyzing diverse applied problems with similar mathematical underpinnings.