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

Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

337
An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
337
Graphs of Functions01:30

Graphs of Functions

444
Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
444
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

571
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
571
Second Derivatives and the Shape of a Graph01:29

Second Derivatives and the Shape of a Graph

175
The second derivative of a function provides essential information about a graph's curvature and how it changes over an interval. It helps determine whether a function is concave upward or concave downward and identifies points where the curvature changes. These properties are fundamental in analyzing real-world scenarios, such as changes in road elevation, population growth, and economic trends.A function f(x) is considered concave upward on an interval if its graph lies above all its tangent...
175
Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

332
The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
332
First Derivatives and the Shape of a Graph01:22

First Derivatives and the Shape of a Graph

136
In calculus, the concept of the first derivative plays a crucial role in understanding the behavior of a function over its domain. The first derivative, denoted as f’(x), provides insight into how a function changes at any given point, much like a cyclist adjusting speed along a winding trail. By analyzing the first derivative, mathematicians can determine where a function is increasing, decreasing, or reaching critical points.The first derivative provides a precise method for classifying...
136

You might also read

Related Articles

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

Sort by
Same author

The effects of three kinds of non-steroidal anti-inflammatory drugs on postoperative pain and on the serum levels of tumour necrosis factor-α and substance P in paediatric patients following orthopaedic hip surgery.

Archives of medical science : AMS·2026
Same author

Palladium(II)-Catalyzed Selective C-H Silylation: Access to Divergent Silicon-Containing 8-Methylquinolines.

The Journal of organic chemistry·2026
Same author

Hormonal and laboratory predictors of patent foramen ovale in cryptogenic ischemic events: a SHAP-enhanced logistic regression approach.

Frontiers in neurology·2026
Same author

Mega-floods over the past 30,000 years in western yunnan, southwest China.

Scientific reports·2026
Same author

[Carbon Emission Accounting and Emission Reduction Path Analysis of Urban Wastewater Treatment Plants： A Case of a Wastewater Treatment Plant in Shenyang City].

Huan jing ke xue= Huanjing kexue·2025
Same author

Design, synthesis and biological evaluation of novel dualaction statin conjugates with triglyceride and cholesterol lowering activities.

Molecular diversity·2025
Same journal

Turbulent flow in a vortex separator with a directed pipe inlet.

Scientific reports·2026
Same journal

Systematic characteristic evaluation of clay-based cementitious material derived from calcium carbide residue and waste tile powder.

Scientific reports·2026
Same journal

Retraction Note: Improvement of a rapid diagnostic application of monoclonal antibodies against avian influenza H7 subtype virus using Europium nanoparticles.

Scientific reports·2026
Same journal

Applying large language models to spam detection in the Kazakh low-resource language setting.

Scientific reports·2026
Same journal

An open-source 3D printing system enabling in-situ freeze-thaw processing of hydrogels.

Scientific reports·2026
Same journal

An enhanced EfficientNet framework for automated waste classification using cosine annealing and label smoothing.

Scientific reports·2026
See all related articles

Related Experiment Video

Updated: Mar 12, 2026

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
09:49

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

4.9K

Non-uniform Evolving Hypergraphs and Weighted Evolving Hypergraphs.

Jin-Li Guo1, Xin-Yun Zhu1, Qi Suo1

  • 1Business School, University of Shanghai for Science and Technology, Shanghai 200093, PR China.

Scientific Reports
|November 16, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a novel non-uniform evolving hypergraph model with nonlinear preferential attachment. The research reveals scale-free behavior in both hyperdegree and hyperstrength distributions for weighted evolving hypergraphs.

More Related Videos

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
15:00

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

4.5K

Related Experiment Videos

Last Updated: Mar 12, 2026

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
09:49

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

4.9K
Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
15:00

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

4.5K

Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Evolving hypergraphs model complex relationships beyond pairwise interactions.
  • Existing models often assume uniform hyperedge sizes and simple attachment rules.
  • Understanding the dynamics of large-scale, evolving networks is crucial for various scientific domains.

Purpose of the Study:

  • To propose a non-uniform evolving hypergraph model with nonlinear preferential attachment and attractiveness.
  • To develop a model for weighted evolving hypergraphs incorporating node and hyperedge dynamics.
  • To analyze the emergent properties, specifically scale-free distributions, of these models.

Main Methods:

  • Development of a non-uniform evolving hypergraph model with batch node arrivals via a Poisson process.
  • Mathematical derivation of the characteristic equation for hyperdegrees and analysis of hyperdegree changes.
  • Construction of a coupled model for weighted evolving hypergraphs, integrating weight evolution.
  • Application of Poisson process theory and derived equations to obtain stationary distributions.

Main Results:

  • The non-uniform evolving hypergraph model exhibits a stationary average hyperdegree distribution.
  • The weighted evolving hypergraph model demonstrates scale-free behavior for both hyperdegree and hyperstrength distributions.
  • The size of each hyperedge is non-uniform due to random variables governing node and existing node selection.

Conclusions:

  • The proposed non-uniform evolving hypergraph model provides a more realistic representation of complex systems.
  • The weighted evolving hypergraph model successfully captures scale-free properties, common in real-world networks.
  • This work offers a theoretical framework for analyzing dynamic and weighted higher-order networks.