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

Coordination Number and Geometry02:57

Coordination Number and Geometry

15.6K
For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
15.6K
Curvilinear Motion: Normal and Tangential Components01:27

Curvilinear Motion: Normal and Tangential Components

1.2K
When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
1.2K
Torque Free Motion01:15

Torque Free Motion

942
The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...
942
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

1.6K
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
1.6K
Gastrointestinal Motility Disorders01:20

Gastrointestinal Motility Disorders

1.6K
Gastrointestinal or GI motility disorders are characterized by irregular gastrointestinal tract movements, disrupting food transit from the mouth to the anus. They are caused by damage or dysfunction in gut muscles or nerves. These disorders can cause symptoms such as severe constipation, diarrhea, abdominal pain, and swallowing difficulties. Disorders can affect any segment of the GI tract and range widely in severity, from common conditions like GERD to life-threatening conditions like...
1.6K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

13.7K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
13.7K

You might also read

Related Articles

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

Sort by
Same author

Reconsideration of Information-Theoretic Principles-Perspective from the Dual Probability Distribution.

Entropy (Basel, Switzerland)·2026
Same author

Onsager's Non-Equilibrium Thermodynamics as Gradient Flow in Information Geometry.

Entropy (Basel, Switzerland)·2025
Same author

180th Anniversary of Ludwig Boltzmann.

Entropy (Basel, Switzerland)·2025
Same author

Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives.

Entropy (Basel, Switzerland)·2025
Same author

Multi-Additivity in Kaniadakis Entropy.

Entropy (Basel, Switzerland)·2024
Same author

On the Kaniadakis Distributions Applied in Statistical Physics and Natural Sciences.

Entropy (Basel, Switzerland)·2023
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: May 5, 2026

One Dimensional Turing-Like Handshake Test for Motor Intelligence
14:05

One Dimensional Turing-Like Handshake Test for Motor Intelligence

Published on: December 15, 2010

24.8K

Non-Metricity in Information Geometry.

Tatsuaki Wada1, Antonio Maria Scarfone2,3

  • 1Region of Electrical and Electronic Systems Engineering, Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi-shi 316-8511, Japan.

Entropy (Basel, Switzerland)
|May 4, 2026
PubMed
Summary
This summary is machine-generated.

This study explores non-metricity in information geometry using Weyl geometry and gradient flow. It reveals how a scalar field characterizes Weyl

Keywords:
Weyl geometrygradient flowinformation geometrynon-metricityα connection

More Related Videos

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

14.0K
Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

8.8K

Related Experiment Videos

Last Updated: May 5, 2026

One Dimensional Turing-Like Handshake Test for Motor Intelligence
14:05

One Dimensional Turing-Like Handshake Test for Motor Intelligence

Published on: December 15, 2010

24.8K
MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

14.0K
Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

8.8K

Area of Science:

  • Information Geometry
  • Differential Geometry
  • Theoretical Physics

Background:

  • Non-metricity is crucial in information geometry, influencing gradient flow dynamics.
  • Weyl geometry provides a framework for understanding these geometric properties.

Purpose of the Study:

  • To investigate the role of non-metricity in information geometry through gradient flow analysis.
  • To derive the explicit expression of the alpha connection using non-metricity and the Fisher metric.

Main Methods:

  • Utilizing concepts from Weyl geometry to analyze gradient flow.
  • Deriving the alpha connection based on the non-metricity condition: ∇k(α)gij = αCkij.
  • Employing a scalar field derived from a potential function.

Main Results:

  • The Amari-Centsov tensor (Ck ij) is identified as the non-metricity tensor for the alpha connection and Fisher metric.
  • An explicit expression for the alpha connection is derived.
  • The scalar field is shown to characterize Weyl's gauge field, non-metricity, and potential function dynamics during gradient flow.

Conclusions:

  • Non-metricity significantly impacts gradient flow in information geometry.
  • The scalar field derived from potential functions offers a unified characterization of geometric properties within the Weyl geometry framework.