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

Probability Distributions01:32

Probability Distributions

13.1K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
13.1K
Geometric Sequences01:30

Geometric Sequences

358
In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...
358
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

18.6K
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...
18.6K
Poisson Probability Distribution01:09

Poisson Probability Distribution

12.3K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
12.3K
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

360
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...
360
Graphs of Polar Equations01:17

Graphs of Polar Equations

399
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
399

You might also read

Related Articles

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

Sort by
Same author

The Ethics of Digital Touch.

IEEE transactions on haptics·2025
Same author

Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine.

European journal of psychotraumatology·2025
Same author

It Sounds Cool: Exploring Sonification of Mid-Air Haptic Textures Exploration on Texture Judgments, Body Perception, and Motor Behaviour.

IEEE transactions on haptics·2023
Same author

"I See Where This is Going": A Psychophysical Study of Directional Mid-Air Haptics and Apparent Tactile Motion.

IEEE transactions on haptics·2023
Same author

Using Virtual Objects With Hand-Tracking: The Effects of Visual Congruence and Mid-Air Haptics on Sense of Agency.

IEEE transactions on haptics·2023
Same author

Does It par-Tickle?: Investigating the Relationship Between Mid-Air Haptics and Visual Representations of Surface Textures.

IEEE transactions on haptics·2023
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Mar 22, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.6K

Random geometric graphs with general connection functions.

Carl P Dettmann1, Orestis Georgiou2

  • 1School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.

Physical Review. E
|April 15, 2016
PubMed
Summary
This summary is machine-generated.

This study analyzes the connectivity of random geometric graphs, crucial for wireless networks. It develops a new method to calculate graph connectivity probability using boundary components, simplifying analysis for complex connection functions.

More Related Videos

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.6K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.1K

Related Experiment Videos

Last Updated: Mar 22, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.6K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.6K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.1K

Area of Science:

  • Random geometric graphs
  • Network connectivity analysis
  • Wireless communication networks

Background:

  • Introduces the Gilbert model of random geometric graphs with nodes placed via Poisson point process.
  • Discusses probabilistic connection models using a connection function H(r) for wireless ad hoc networks.
  • Highlights the importance of graph connectivity in various applications beyond wireless networks.

Purpose of the Study:

  • To express the connection probability of dense networks in convex domains (2D/3D) for general connection functions.
  • To analyze connectivity by considering contributions from boundary components.
  • To simplify the understanding of network connectivity by identifying key parameters.

Main Methods:

  • Develops a theoretical framework to express connectivity probability in terms of boundary component contributions.
  • Applies the framework to dense random geometric graphs in convex domains.
  • Utilizes moments of the connection function as key analytical quantities.

Main Results:

  • Derives a formula for connection probability dependent on boundary components for general connection functions.
  • Identifies that only moments of the connection function are essential for determining connectivity.
  • Achieves good agreement with previous studies and numerical simulations.

Conclusions:

  • The study provides a generalized method for analyzing random geometric graph connectivity.
  • The derived approach simplifies complex connectivity calculations by focusing on boundary effects and function moments.
  • The findings are applicable to dense networks in various dimensions and support existing research and simulations.