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

Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

597
The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
597
Ranks01:02

Ranks

223
Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
223
Probability in Statistics01:14

Probability in Statistics

12.4K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
12.4K
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

174
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
174
Random Variables01:09

Random Variables

11.4K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
11.4K
Probability Distributions01:32

Probability Distributions

6.7K
 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...
6.7K

You might also read

Related Articles

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

Sort by
Same author

Structural and Electrochemical Properties of 4-Methyl-4'-(<i>n</i>-mercaptoalkyl) Biphenyls Self-Assembled on the Au(100)-(1 × 1) Surface.

Langmuir : the ACS journal of surfaces and colloids·2025
Same author

In Situ Synthesis of a Hydroxyapatite and Reduced Graphene Oxide Composite for Potential Electrochemical Biosensing Applications.

ACS omega·2025
Same author

Hyperbolic random geometric graphs: Structural and spectral properties.

Physical review. E·2025
Same author

Dissipative fractional standard maps: Riemann-Liouville and Caputo.

Chaos (Woodbury, N.Y.)·2025
Same author

Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties.

Physical review. E·2024
Same author

Topological and spectral properties of random digraphs.

Physical review. E·2024
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: May 29, 2025

Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.4K

Singular-value statistics of directed random graphs.

J A Méndez-Bermúdez1, R Aguilar-Sánchez2

  • 1Universidad Nacional Autónoma de Honduras, Benemérita Universidad Autónoma de Puebla, Instituto de Física, Puebla 72570, Mexico and Escuela de Física, Facultad de Ciencias, Honduras.

Physical Review. E
|February 7, 2025
PubMed
Summary
This summary is machine-generated.

Singular-value statistics effectively analyze non-Hermitian random matrices in directed graphs. This method distinguishes graph models and identifies transitions from isolated to complete networks.

More Related Videos

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

10.2K
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

2.1K

Related Experiment Videos

Last Updated: May 29, 2025

Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.4K
Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

10.2K
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

2.1K

Area of Science:

  • * Physics
  • * Mathematics
  • * Network Science

Background:

  • * Singular-value statistics (SVS) is an emerging tool from random matrix theory.
  • * SVS has shown promise in characterizing non-Hermitian random matrix ensembles.
  • * Its application to complex network structures remains an active area of research.

Purpose of the Study:

  • * To numerically investigate the SVS of non-Hermitian adjacency matrices in directed random graphs.
  • * To evaluate the utility of SVS in distinguishing between different graph models and network properties.
  • * To explore the relationship between SVS measures and graph structural transitions.

Main Methods:

  • * Numerical simulations of directed Erdös-Rényi and random geometric graphs.
  • * Generation of non-Hermitian adjacency matrices from diluted real Ginibre ensembles.
  • * Analysis of singular-value-spacing ratio (r) and minimum singular value (λmin).

Main Results:

  • * The ensemble average of the singular-value-spacing ratio (〈r〉) effectively captures the transition from sparse to dense graphs.
  • * The probability density function of the minimum singular value (λmin) clearly differentiates between various graph models.
  • * SVS provides a robust method for analyzing the spectral properties of non-Hermitian random matrix ensembles in graph theory.

Conclusions:

  • * Singular-value statistics offer a powerful lens for understanding the spectral properties of non-Hermitian random matrices within graph structures.
  • * The analyzed SVS measures (〈r〉 and λmin) serve as sensitive indicators of graph topology and model distinctions.
  • * This study highlights the potential of SVS as a versatile tool in network science and random matrix theory.