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

Vectors01:30

Vectors

149
Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
149
Scalar Notation01:28

Scalar Notation

967
Scalar notation is a useful method for simplifying calculations involving vectors. When vectors are added or subtracted, their components can be added or subtracted separately using scalar notation. For instance, force, a vector quantity, can be broken down into its x and y components, called rectangular components, and then the magnitude and direction of these components can be determined using trigonometric functions.
Consider a man pulling a rope from a hook in the northeast direction. The...
967
Scalar and Vectors01:22

Scalar and Vectors

1.8K
In mechanics, commonly used terms like force, speed, velocity, and work can be classified as either scalar or vector quantities. A scalar is a physical quantity that can be described by its magnitude alone and does not require any directional components. Examples of scalar quantities are mass, area, and length.
Scalar quantities with the same physical units can be added or subtracted according to the usual algebra rules for numbers. For example, a class ending 10 min earlier than 50 min lasts...
1.8K
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

490
One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment....
490
Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

4.0K
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
4.0K
Introduction to Scalars01:21

Introduction to Scalars

19.1K
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume,...
19.1K

You might also read

Related Articles

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

Sort by
Same author

Fusion of computational and experimental provenance in RO-Crate.

Journal of integrative bioinformatics·2026
Same author

Region-Aware Wasserstein Distances of Persistence Diagrams and Merge Trees.

IEEE transactions on visualization and computer graphics·2026
Same author

Robust Barycenters of Persistence Diagrams.

IEEE transactions on visualization and computer graphics·2026
Same author

LAMDA: Aiding Visual Exploration of Atomic Displacements in Molecular Dynamics Simulations.

IEEE transactions on visualization and computer graphics·2026
Same author

Topological Autoencoders++: Fast and Accurate Cycle-Aware Dimensionality Reduction.

IEEE transactions on visualization and computer graphics·2025
Same author

BondMatcher: H-Bond Stability Analysis in Molecular Systems.

IEEE transactions on visualization and computer graphics·2025

Related Experiment Video

Updated: Dec 6, 2025

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
09:44

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

Published on: October 16, 2018

10.5K

Localized Topological Simplification of Scalar Data.

Jonas Lukasczyk, Christoph Garth, Ross Maciejewski

    IEEE Transactions on Visualization and Computer Graphics
    |October 13, 2020
    PubMed
    Summary

    This study introduces a localized topological simplification (LTS) algorithm for scalar data, accelerating topological data analysis (TDA) by simplifying only necessary regions. LTS achieves significant speedups and enhances interactivity for data exploration.

    More Related Videos

    Setting Limits on Supersymmetry Using Simplified Models
    07:46

    Setting Limits on Supersymmetry Using Simplified Models

    Published on: November 15, 2013

    8.8K
    Intravital Longitudinal Imaging of Vascular Dynamics in the Calvarial Bone Marrow
    10:49

    Intravital Longitudinal Imaging of Vascular Dynamics in the Calvarial Bone Marrow

    Published on: April 11, 2025

    827

    Related Experiment Videos

    Last Updated: Dec 6, 2025

    Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
    09:44

    Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

    Published on: October 16, 2018

    10.5K
    Setting Limits on Supersymmetry Using Simplified Models
    07:46

    Setting Limits on Supersymmetry Using Simplified Models

    Published on: November 15, 2013

    8.8K
    Intravital Longitudinal Imaging of Vascular Dynamics in the Calvarial Bone Marrow
    10:49

    Intravital Longitudinal Imaging of Vascular Dynamics in the Calvarial Bone Marrow

    Published on: April 11, 2025

    827

    Area of Science:

    • Data analysis
    • Computational geometry
    • Scientific visualization

    Background:

    • Topological data analysis (TDA) requires pre-processing scalar data.
    • Existing global simplification methods can be computationally intensive.
    • Efficient simplification is crucial for interactive data exploration.

    Purpose of the Study:

    • To develop a localized algorithm for topological simplification of scalar data.
    • To improve the speed and interactivity of TDA pipelines.
    • To enable efficient exploration of simplification parameters and their impact on topological features.

    Main Methods:

    • The localized topological simplification (LTS) algorithm processes only regions needing simplification.
    • It flattens and re-embeds sub-/superlevel set components to remove undesired extrema.
    • LTS utilizes shared-memory parallelism for simultaneous region processing.

    Main Results:

    • LTS achieves significant speedups, reducing TDA pipeline execution from minutes to seconds (up to ×36).
    • The algorithm demonstrates high parallel efficiency (70%) through localized processing.
    • An adapted LTS version integrates persistence diagram computation with simplification.

    Conclusions:

    • LTS offers a computationally efficient and parallelizable approach to topological simplification.
    • The method enhances interactivity for exploring scalar data and its topological features.
    • LTS provides substantial benefits for TDA across various scientific domains.