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

State Space Representation01:27

State Space Representation

154
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
154
Transfer Function to State Space01:23

Transfer Function to State Space

176
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
176
State Space to Transfer Function01:21

State Space to Transfer Function

157
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
157
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

5.2K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
5.2K
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

433
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
433
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

187
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
187

You might also read

Related Articles

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

Sort by
Same author

Centering Equity During Health Technology Innovation: Scoping Review of Methods and Research Adjustments to Promote Inclusive Coproduction.

Journal of medical Internet research·2026
Same author

Comparative effectiveness of rituximab versus ocrelizumab in relapsing multiple sclerosis on clinical relapses and radiological outcomes in British Columbia, Canada.

Multiple sclerosis (Houndmills, Basingstoke, England)·2026
Same author

Impact of multiple sclerosis disease-modifying therapies on chronic lesion tissue expansion.

Multiple sclerosis (Houndmills, Basingstoke, England)·2026
Same author

Acute and longitudinal magnetic resonance imaging abnormalities in antibody-mediated encephalitis.

Brain communications·2026
Same author

Circulatory immune cell counts and clinical outcomes in multiple sclerosis relapse versus remission.

Journal of the neurological sciences·2026
Same author

Non-linear measures of movement variability in multiple sclerosis: a clinical narrative review of Lyapunov exponent and entropy applications in balance and gait.

Frontiers in neurology·2026

Related Experiment Video

Updated: May 17, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.6K

Multiple Sclerosis Classification Using the Local Divergence Exponent: Parameters Selection for State-Space

L Eduardo Cofré Lizama1,2, Liuhua Peng3, Tomas Kalincik4,5

  • 1Department of Allied Health, School of Health Sciences, Swinburne University of Technology, Hawthorn, Melbourne, VIC 3122, Australia.

Sensors (Basel, Switzerland)
|May 14, 2025
PubMed
Summary
This summary is machine-generated.

Local Divergence Exponent (LDE) calculations can effectively distinguish people with multiple sclerosis (pwMS) from controls. Using fixed parameters for LDE calculation simplifies its use as a mobility biomarker in MS.

Keywords:
Lyapunovdynamicmultiple sclerosisstabilitystate space

More Related Videos

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.6K
Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
06:40

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

10.1K

Related Experiment Videos

Last Updated: May 17, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.6K
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.6K
Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
06:40

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

10.1K

Area of Science:

  • Biomedical Engineering
  • Neurology
  • Rehabilitation Science

Background:

  • Walking stability is impaired in people with multiple sclerosis (pwMS).
  • Previous studies using the local divergence exponent (LDE) to assess walking stability in pwMS show varied results due to differing calculation methods.
  • Standardizing LDE calculation is crucial for reliable comparisons and clinical application.

Purpose of the Study:

  • To investigate how different state space reconstruction parameters for LDE calculation impact the classification accuracy of pwMS.
  • To identify optimal parameters for LDE calculation to serve as a reliable mobility biomarker in multiple sclerosis.

Main Methods:

  • 55 pwMS and 23 controls underwent a 5-minute walking test.
  • LDE was calculated using three parameter sets (trial-specific, median, fixed d=5/τ=10) and various sensor data (vertical, mediolateral, anteroposterior accelerations, norm, 3D) from sternum and lumbar sensors.
  • Quadratic Discriminant Analysis (QDA) was used to compare classification accuracy across different LDE calculation methods.

Main Results:

  • The highest classification accuracy (84%) was achieved using LDE from sternum-mounted norm acceleration data with fixed parameters (d=5, τ=10), incorporating walking speed as a covariate.
  • LDE calculations using lumbar sensors yielded lower classification accuracy compared to sternum sensors.

Conclusions:

  • Fixed parameters (d=5, τ=10) for LDE calculation using sternum norm acceleration data provide the best classification of pwMS.
  • Standardizing LDE calculation parameters simplifies its implementation as a mobility biomarker for multiple sclerosis.
  • This study provides evidence supporting a consensus for LDE calculation methodology in MS research and clinical practice.