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

Random Error01:04

Random Error

7.6K
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
7.6K
Wilcoxon Signed-Ranks Test for Matched Pairs01:09

Wilcoxon Signed-Ranks Test for Matched Pairs

431
The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must...
431
Randomized Experiments01:13

Randomized Experiments

8.8K
The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
8.8K
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

503
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 0s. In...
503
Random Variables01:09

Random Variables

17.1K
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...
17.1K
Random and Systematic Errors01:20

Random and Systematic Errors

14.2K
Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
14.2K

You might also read

Related Articles

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

Sort by
Same author

Overlap locking and nonperturbative effects in spin glasses.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Predictability of complex networks.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Rare trajectories in a prototypical mean-field disordered model: Insights into landscape and instantons.

Physical review. E·2026
Same author

Sampling the space of solutions of an artificial neural network.

Physical review. E·2025
Same author

Critical exponents of the spin-glass transition in a field at zero temperature.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Build an international AI 'telescope' to curb the power of big tech companies.

Nature·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: Jan 5, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.9K

Fluctuations in the random-link matching problem.

Enrico M Malatesta1, Giorgio Parisi2, Gabriele Sicuro3

  • 1Bocconi Institute for Data Science and Analytics, Bocconi University, Milano 20136, Italy.

Physical Review. E
|October 24, 2019
PubMed
Summary
This summary is machine-generated.

We analyzed fluctuations in the random-link matching problem using replica and cavity methods. Our study provides exact expressions for the variance and large deviation function of the optimal cost.

More Related Videos

Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction
16:23

Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction

Published on: February 26, 2014

14.8K
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
11:22

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

10.5K

Related Experiment Videos

Last Updated: Jan 5, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.9K
Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction
16:23

Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction

Published on: February 26, 2014

14.8K
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
11:22

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

10.5K

Area of Science:

  • Statistical physics
  • Combinatorial optimization
  • Random graph theory

Background:

  • The random-link matching problem is a fundamental problem in combinatorial optimization.
  • Understanding the fluctuations of the optimal cost is crucial for analyzing the problem's behavior.
  • Previous studies have explored various aspects of this problem, but a complete understanding of its fluctuations remains elusive.

Purpose of the Study:

  • To investigate the fluctuations of the optimal cost in the random-link matching problem.
  • To derive exact expressions for the variance and the large deviation function of the optimal cost.
  • To compare the effectiveness of the replica and cavity methods in analyzing this problem.

Main Methods:

  • The study employs the replica approach, a powerful technique in statistical physics for analyzing disordered systems.
  • The cavity method, another established technique, is also utilized for its complementary strengths.
  • Both methods are applied to derive analytical expressions for the desired quantities.

Main Results:

  • The exact expression for the variance of the optimal cost is derived using replica arguments.
  • The large deviation function of the optimal cost is derived through two independent methods: the replica method and the cavity method.
  • The consistency of results obtained from both methods validates their application.

Conclusions:

  • The replica and cavity methods provide accurate and consistent results for analyzing the random-link matching problem.
  • The derived expressions for variance and the large deviation function offer deeper insights into the problem's statistical properties.
  • This work contributes to a more comprehensive understanding of random matching problems in statistical physics and optimization.