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

Dimensional Analysis02:19

Dimensional Analysis

18.1K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
18.1K
Downsampling01:20

Downsampling

291
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
291
Problem Solving: Dimensional Analysis01:08

Problem Solving: Dimensional Analysis

5.1K
Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
5.1K
Correlation of Experimental Data01:23

Correlation of Experimental Data

329
Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity,...
329
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

454
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...
454
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

353
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
353

You might also read

Related Articles

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

Sort by
Same author

CMV Immune Responses and Cognitive Impairment in People with HIV.

The Journal of infectious diseases·2026
Same author

Comparing the Effectiveness of High Intensity Interval Training vs Continuous Moderate Intensity Exercise on Physical Function Among Older Adults With HIV.

Open forum infectious diseases·2026
Same author

Generalized coarsened confounding for causal effects: a large-sample framework.

Journal of causal inference·2026
Same author

A Weighted Survival Regression Framework for Incorporating External Prediction Information.

Journal of statistical theory and practice·2025
Same author

A surrogate endpoint-based provisional approval causal roadmap, illustrated by vaccine development.

Biostatistics (Oxford, England)·2025
Same author

Exposures from Oil and Gas Development and Childhood Leukemia Risk in Colorado: A Population-Based Case-Control Study.

Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology·2025
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Oct 2, 2025

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

8.2K

Sufficient Dimension Reduction: An Information-Theoretic Viewpoint.

Debashis Ghosh1

  • 1Department of Biostatistics and Informatics, Colorado School of Public Health, Aurora, CO 80045, USA.

Entropy (Basel, Switzerland)
|February 25, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces an information-theoretic framework to interpret sufficient dimension reduction (SDR) techniques. This approach offers a more assumption-lean understanding of SDR methods and their connections to information theory.

Keywords:
central subspaceinformation bottlenecksingle-index model

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

2.6K
An Operant Intra-/Extra-dimensional Set-shift Task for Mice
08:35

An Operant Intra-/Extra-dimensional Set-shift Task for Mice

Published on: January 22, 2016

12.4K

Related Experiment Videos

Last Updated: Oct 2, 2025

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

8.2K
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

2.6K
An Operant Intra-/Extra-dimensional Set-shift Task for Mice
08:35

An Operant Intra-/Extra-dimensional Set-shift Task for Mice

Published on: January 22, 2016

12.4K

Area of Science:

  • Statistics
  • Information Theory
  • Machine Learning

Background:

  • Sufficient dimension reduction (SDR) is a statistical methodology focused on uncovering essential regression relationships within high-dimensional data.
  • Existing SDR approaches are motivated by data-driven subspace identification and model-free data analysis.
  • Nonlinear extensions of SDR have garnered significant interest in statistical research.

Purpose of the Study:

  • To develop a novel interpretation of sufficient dimension reduction (SDR) techniques.
  • To leverage information theory as a framework for understanding SDR.
  • To establish connections between SDR and existing results in information theory.

Main Methods:

  • The study employs an information-theoretic approach to interpret SDR methodologies.
  • This framework aims to provide a more assumption-lean understanding of SDR's function.
  • Connections are explored between the proposed information-theoretic interpretation and established information theory literature.

Main Results:

  • A new perspective on interpreting sufficient dimension reduction (SDR) techniques is established through information theory.
  • The information-theoretic framework facilitates a deeper, assumption-lean understanding of how SDR methods function.
  • The study highlights and elaborates on the links between SDR and information theory principles.

Conclusions:

  • The proposed information-theoretic framework offers a robust and assumption-lean interpretation of sufficient dimension reduction (SDR).
  • This approach enhances the theoretical understanding of SDR and its relationship with information theory.
  • The findings pave the way for novel applications and further research at the intersection of SDR and information theory.