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

Solution Concentration and Dilution02:59

Solution Concentration and Dilution

135.1K
The relative amount of a given solution component is known as its concentration. Often, though not always, a solution contains one component with a concentration that is significantly greater than that of all other components. This component is called the solvent and may be viewed as the medium in which the other components are dispersed or dissolved. Solutions in which water is the solvent are, of course, very common on our planet. A solution in which water is the solvent is called an aqueous...
135.1K
Band Theory02:35

Band Theory

17.3K
When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...
17.3K
Scientific Laws and Theories02:31

Scientific Laws and Theories

89.3K
Scientific Laws
89.3K
Attribution Theory00:56

Attribution Theory

13.8K
Behavior is a product of both the situation (e.g., cultural influences, social roles, and the presence of bystanders) and of the person (e.g., personality characteristics). Subfields of psychology tend to focus on one influence or behavior over others. Situationism is the view that our behavior and actions are determined by our immediate environment and surroundings. In contrast, dispositionism holds that our behavior is determined by internal factors (Heider, 1958).
13.8K
The Atomic Theory of Matter02:59

The Atomic Theory of Matter

129.6K
The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter was composed of small, finite particles that they called atomos, meaning “indivisible.” Later, Aristotle and others came to the conclusion that matter consisted of various combinations of the four “elements” — fire, earth, air, and water — and could be infinitely divided. Interestingly, these philosophers...
129.6K
Standard Deviation01:10

Standard Deviation

28.0K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
28.0K

You might also read

Related Articles

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

Sort by
Same author

Epidemic threshold and localization of the SIS model on directed complex networks.

Physical review. E·2026
Same author

Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures.

Physical review. E·2025
Same author

Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks.

Physical review letters·2025
Same author

Effects of clustering heterogeneity on the spectral density of sparse networks.

Physical review. E·2024
Same author

Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies: a general framework [Invited].

Biomedical optics express·2024
Same author

Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise.

Physical review. E·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: Feb 10, 2026

Isolation and Quantification of Botulinum Neurotoxin From Complex Matrices Using the BoTest Matrix Assays
12:25

Isolation and Quantification of Botulinum Neurotoxin From Complex Matrices Using the BoTest Matrix Assays

Published on: March 3, 2014

16.6K

Large-deviation theory for diluted Wishart random matrices.

Isaac Pérez Castillo1, Fernando L Metz2

  • 1Department of Quantum Physics and Photonics, Institute of Physics, UNAM, P.O. Box 20-364, 01000 Mexico City, Mexico and London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, United Kingdom.

Physical Review. E
|May 20, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a new theory for eigenvalue fluctuations in sparse random matrices using the replica approach. The findings accurately predict eigenvalue distributions in large datasets across various scientific fields.

More Related Videos

Preparation of Complaint Matrices for Quantifying Cellular Contraction
11:38

Preparation of Complaint Matrices for Quantifying Cellular Contraction

Published on: December 14, 2010

18.3K
Cortisol Extraction from Sturgeon Fin and Jawbone Matrices
06:01

Cortisol Extraction from Sturgeon Fin and Jawbone Matrices

Published on: September 10, 2019

8.7K

Related Experiment Videos

Last Updated: Feb 10, 2026

Isolation and Quantification of Botulinum Neurotoxin From Complex Matrices Using the BoTest Matrix Assays
12:25

Isolation and Quantification of Botulinum Neurotoxin From Complex Matrices Using the BoTest Matrix Assays

Published on: March 3, 2014

16.6K
Preparation of Complaint Matrices for Quantifying Cellular Contraction
11:38

Preparation of Complaint Matrices for Quantifying Cellular Contraction

Published on: December 14, 2010

18.3K
Cortisol Extraction from Sturgeon Fin and Jawbone Matrices
06:01

Cortisol Extraction from Sturgeon Fin and Jawbone Matrices

Published on: September 10, 2019

8.7K

Area of Science:

  • Statistical Physics
  • Machine Learning
  • Data Science

Background:

  • Sparse random matrices are crucial for analyzing large datasets in physics, biology, and economics.
  • Understanding eigenvalue fluctuations in these matrices is key to data processing and analysis.

Purpose of the Study:

  • To develop a theoretical framework for eigenvalue fluctuations in diluted Wishart random matrices.
  • To derive analytical expressions for eigenvalue distribution properties.

Main Methods:

  • Utilizing the replica approach from disordered systems theory.
  • Deriving the cumulant generating function for eigenvalue counts.
  • Analyzing large-deviation probabilities and rate functions.

Main Results:

  • An analytical expression for the cumulant generating function of the number of eigenvalues smaller than x.
  • Explicit results for the mean, variance, and third cumulant of eigenvalue counts.
  • Demonstrated excellent agreement between theoretical predictions and numerical diagonalization.

Conclusions:

  • The developed theory provides an exact and compelling framework for analyzing eigenvalue fluctuations in sparse random matrices.
  • This work validates and extends previous findings on sparse random matrix theory.