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

Relation between Mathematical Equations and Block Diagrams01:20

Relation between Mathematical Equations and Block Diagrams

383
In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
383
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

746
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
746
Theorems of Pappus and Guldinus01:10

Theorems of Pappus and Guldinus

2.0K
The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
2.0K
Natural and Artificial Concepts01:24

Natural and Artificial Concepts

171
In psychology, concepts can be divided into two categories: natural and artificial. Natural concepts are formed through direct or indirect experiences. For example, consider the concept of snow. If you live in a place with regular snowfall, such as Essex Junction, Vermont, you know snow through direct experiences. You’ve seen it fall, touched it, shoveled it, and played in it. You recognize its texture, appearance, and even its smell. In contrast, if you live on an island like Saint...
171
Dimensional Analysis02:19

Dimensional Analysis

15.1K
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...
15.1K
Kirchhoff's Rules01:21

Kirchhoff's Rules

4.7K
Gustav Kirchhoff (1824–1887) devised two rules known as Kirchhoff's rules to analyze complex circuits, which cannot be analyzed with series-parallel techniques. These rules can be used to analyze any circuit, simple or complex.
Kirchhoff's first rule is called the junction rule. A junction, also known as a node, is a connection of three or more wires. The rule states that the sum of all currents entering a junction must equal the sum of all currents leaving the junction.
4.7K

You might also read

Related Articles

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

Sort by
Same author

Reducing vertices in property graphs.

PloS one·2018
See all related articles

Related Experiment Video

Updated: Jul 11, 2025

Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems
05:47

Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems

Published on: June 13, 2025

241

MMLKG: Knowledge Graph for Mathematical Definitions, Statements and Proofs.

Dominik Tomaszuk1, Łukasz Szeremeta2, Artur Korniłowicz2

  • 1University of Bialystok, Faculty of Computer Science, Bialystok, 15-245, Poland. d.tomaszuk@uwb.edu.pl.

Scientific Data
|November 10, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces the Mizar Mathematical Library Knowledge Graph (MMLKG), a novel approach to organizing mathematical knowledge. MMLKG enhances data interoperability and accessibility for the Mizar Mathematical Library (MML).

More Related Videos

A Knowledge Graph Approach to Elucidate the Role of Organellar Pathways in Disease via Biomedical Reports
07:35

A Knowledge Graph Approach to Elucidate the Role of Organellar Pathways in Disease via Biomedical Reports

Published on: October 13, 2023

1.7K
Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities
10:26

Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities

Published on: September 11, 2021

4.0K

Related Experiment Videos

Last Updated: Jul 11, 2025

Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems
05:47

Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems

Published on: June 13, 2025

241
A Knowledge Graph Approach to Elucidate the Role of Organellar Pathways in Disease via Biomedical Reports
07:35

A Knowledge Graph Approach to Elucidate the Role of Organellar Pathways in Disease via Biomedical Reports

Published on: October 13, 2023

1.7K
Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities
10:26

Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities

Published on: September 11, 2021

4.0K

Area of Science:

  • Computer Science
  • Mathematics
  • Information Science

Background:

  • Knowledge Graphs (KGs) are crucial in various fields, but a lack of interoperable mathematical datasets hinders web integration.
  • The Mizar Mathematical Library (MML) contains valuable mathematical definitions and theorems but is difficult to extract information from for external use.

Purpose of the Study:

  • To address the challenge of interoperability for mathematical datasets on the web.
  • To propose a new data storage and retrieval method for the Mizar Mathematical Library (MML).

Main Methods:

  • Developed the Mizar Mathematical Library Knowledge Graph (MMLKG) using a Knowledge Organization System (KOS) model and KG concepts.
  • Organized mathematical objects into a thesaurus structure.
  • Ensured the data adheres to FAIR data principles (Findable, Accessible, Interoperable, Reusable).

Main Results:

  • MMLKG provides a structured way to organize and access knowledge from the MML.
  • The MMLKG facilitates semantic interoperability, enabling data linking with external sources like Wikidata.
  • The developed knowledge graph is publicly accessible through a Cypher endpoint.

Conclusions:

  • The Mizar Mathematical Library Knowledge Graph (MMLKG) significantly improves the accessibility and interoperability of mathematical knowledge.
  • MMLKG supports the FAIR data principles, promoting wider use and integration of mathematical resources.
  • This work paves the way for enhanced data exchange within the mathematical domain on the web.