Jove
Visualize
Contact Us

Related Concept Videos

Reynolds Transport Theorem01:24

Reynolds Transport Theorem

1.3K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.3K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.7K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.7K
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

353
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...
353
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

308
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...
308
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

181
In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
181
Short-distance Transport of Resources02:12

Short-distance Transport of Resources

16.3K
Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
16.3K

You might also read

Related Articles

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

Sort by
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
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 Video

Updated: Aug 22, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

637

Sparse Regularized Optimal Transport with Deformed q-Entropy.

Han Bao1, Shinsaku Sakaue2

  • 1Graduate School of Informatics and The Hakubi Center for Advanced Research, Kyoto University, Kyoto 604-8103, Japan.

Entropy (Basel, Switzerland)
|November 11, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces q-algebra deformed entropy for optimal transport, achieving sparse solutions unlike standard methods. Sparsity increases as the deformation parameter q approaches zero, balancing interpretability with computational efficiency.

Keywords:
Sinkhorn algorithmconvex analysisentropyoptimal transportquasi-Newton method

More Related Videos

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

28.6K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.5K

Related Experiment Videos

Last Updated: Aug 22, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

637
Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

28.6K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.5K

Area of Science:

  • Mathematical Optimization
  • Statistical Mechanics
  • Computational Mathematics

Background:

  • Optimal transport measures distances between probability distributions.
  • Regularized optimal transport, like Sinkhorn, reduces computational complexity but yields dense solutions.
  • Dense solutions can hinder the interpretability of transport plans.

Purpose of the Study:

  • To introduce a novel deformed entropy based on q-algebra for optimal transport.
  • To achieve sparse solutions in optimal transport for improved interpretability.
  • To analyze the trade-off between solution sparsity and computational convergence speed.

Main Methods:

  • Utilizing q-algebra to define a deformed entropy function.
  • Applying the deformed entropy as a regularizer in the optimal transport problem.
  • Theoretical analysis of the optimization process, including convergence properties with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.

Main Results:

  • The q-algebra deformed entropy generates sparsely supported optimal transport solutions.
  • Sparsity of the solutions increases as the deformation parameter q approaches zero.
  • Larger values of q correlate with faster convergence rates during optimization.

Conclusions:

  • Deformed entropy offers a method to control sparsity in optimal transport solutions.
  • The parameter q in q-algebra deformed entropy governs the trade-off between solution sparsity and convergence speed.
  • This approach enhances the interpretability of transport plans derived from optimal transport.