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

Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

58
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...
58
Population Growth00:57

Population Growth

26.5K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
26.5K
Geometric Sequences01:30

Geometric Sequences

68
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...
68
Life Histories01:29

Life Histories

21.9K
Overview
21.9K
Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

60
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
60
Graphs of Functions01:30

Graphs of Functions

53
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...
53

You might also read

Related Articles

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

Sort by
Same author

Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach.

Journal of mathematical biology·2023
Same author

SHIFTING POWERS IN SPIVEY'S BELL NUMBER FORMULA.

Quaestiones mathematicae : journal of the South African Mathematical Society·2022
Same author

AVALANCHES IN A SHORT-MEMORY EXCITABLE NETWORK.

Advances in applied probability·2021
Same author

Favorite Sites of a Persistent Random Walk.

Journal of mathematical analysis and applications·2021
Same author

A Markovian influence graph formed from utility line outage data to mitigate large cascades.

IEEE transactions on power systems : a publication of the Power Engineering Society·2020
Same author

Staircase patterns in words: subsequences, subwords, and separation number.

European journal of combinatorics = Journal europeen de combinatoire = Europaische Zeitschrift fur Kombinatorik·2020

Related Experiment Video

Updated: Nov 15, 2025

ODELAY: A Large-scale Method for Multi-parameter Quantification of Yeast Growth
11:19

ODELAY: A Large-scale Method for Multi-parameter Quantification of Yeast Growth

Published on: July 3, 2017

8.5K

Horizontal visibility graph of a random restricted growth sequence.

Toufik Mansour1, Reza Rastegar2, Alexander Roitershtein3

  • 1Department of Mathematics, University of Haifa, 199 Abba Khoushy Ave, 3498838 Haifa, Israel.

Advances in Applied Mathematics
|March 5, 2021
PubMed
Summary

We analyzed random sequences and set partitions using horizontal visibility graphs. We derived formulas for node degrees based on Stirling and Bernoulli numbers.

Keywords:
horizontal visibility graphpartitions of a setrestricted growth function

More Related Videos

Heuristic Mining of Hierarchical Genotypes and Accessory Genome Loci in Bacterial Populations
08:03

Heuristic Mining of Hierarchical Genotypes and Accessory Genome Loci in Bacterial Populations

Published on: December 7, 2021

2.6K
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.5K

Related Experiment Videos

Last Updated: Nov 15, 2025

ODELAY: A Large-scale Method for Multi-parameter Quantification of Yeast Growth
11:19

ODELAY: A Large-scale Method for Multi-parameter Quantification of Yeast Growth

Published on: July 3, 2017

8.5K
Heuristic Mining of Hierarchical Genotypes and Accessory Genome Loci in Bacterial Populations
08:03

Heuristic Mining of Hierarchical Genotypes and Accessory Genome Loci in Bacterial Populations

Published on: December 7, 2021

2.6K
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.5K

Area of Science:

  • Graph theory
  • Combinatorics
  • Statistical mechanics

Background:

  • Horizontal visibility graphs (HVGs) offer a unique perspective on time series and sequence analysis.
  • Understanding the structural properties of HVGs derived from random processes is crucial for statistical analysis.

Purpose of the Study:

  • To investigate the distributional properties of horizontal visibility graphs.
  • To analyze graphs generated from random restrictive growth sequences and random set partitions of size n.

Main Methods:

  • Developing theoretical frameworks to analyze graph properties.
  • Applying combinatorial methods to derive explicit formulas.
  • Utilizing properties of Stirling and Bernoulli numbers.

Main Results:

  • Formulas for the expected degree of nodes in the studied HVGs.
  • The derived formulas are explicit functions of Stirling and Bernoulli numbers.
  • Characterization of graph properties based on sequence and partition characteristics.

Conclusions:

  • The study provides a mathematical framework for understanding HVGs from random sequences.
  • The results offer insights into the relationship between combinatorial structures and graph properties.
  • The derived formulas can be applied in various fields utilizing sequence analysis and graph theory.