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

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

1.2K
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
1.2K
Poisson Probability Distribution01:09

Poisson Probability Distribution

12.4K
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...
12.4K
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

1.2K
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
1.2K
Binomial Probability Distribution01:15

Binomial Probability Distribution

16.6K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
16.6K
Microsoft Excel: Pearson's Correlation01:18

Microsoft Excel: Pearson's Correlation

2.7K
Microsoft Excel is a powerful tool for statistical analysis, including calculating Pearson's correlation coefficient, which measures the strength and direction of a linear relationship between two continuous variables. Pearson's correlation coefficient, often denoted as "r," ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, meaning as one variable increases, the other does too. A value close to -1 indicates a strong negative correlation, implying...
2.7K
Spearman's Rank Correlation Test01:20

Spearman's Rank Correlation Test

1.6K
Spearman's rank correlation test, also known as Spearman's rho, is a nonparametric method for assessing the strength and direction of association between two variables. This test is particularly valuable when the data distribution is unknown or when the assumption of normality does not hold. Named after the English psychologist and statistician Dr. Charles Edward Spearman, it serves as the nonparametric counterpart to Pearson's correlation coefficient.
Spearman's test calculates correlation by...
1.6K

You might also read

Related Articles

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

Sort by
Same author

Late metachronous contralateral torsion after testicular torsion without contralateral orchiopexy: a mid- to long-term follow-up study.

Pediatric surgery international·2026
Same author

Case Report of an Infectious Aortic Aneurysm Following Intravesical Bacillus Calmette-Guérin Therapy After Transurethral Resection of a Bladder Tumor.

IJU case reports·2026
Same author

Preoperative Gamma-Glutamyltransferase-to-Lymphocyte Ratio as an Independent Prognostic Biomarker in Patients Undergoing Radical Cystectomy for Bladder Cancer.

Medicina (Kaunas, Lithuania)·2026
Same author

A case of primary malignant melanoma of the ureter.

International cancer conference journal·2025
Same author

Association Between Endogenous Equol Production and the Onset of Overactive Bladder in Postmenopausal Women.

Journal of clinical medicine·2025
Same author

α Annealing of ant colony optimization in the infinite-range Ising model.

Physical review. E·2025

Related Experiment Video

Updated: Mar 29, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K

Correlation function for generalized Pólya urns: Finite-size scaling analysis.

Shintaro Mori1, Masato Hisakado2

  • 1Department of Physics, Kitasato University, Kitasato 1-15-1, Sagamihara, Kanagawa 252-0373, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
Summary

This study reveals a universality class for generalized Pólya urn transitions by analyzing correlation functions. The findings describe continuous phase transitions and universal scaling behavior in the system.

More Related Videos

Assembly and Characterization of Polyelectrolyte Complex Micelles
08:44

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

11.7K
Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
09:16

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

15.0K

Related Experiment Videos

Last Updated: Mar 29, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K
Assembly and Characterization of Polyelectrolyte Complex Micelles
08:44

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

11.7K
Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
09:16

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

15.0K

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Probability Theory

Background:

  • The Pólya urn model is a fundamental stochastic process used to model sampling with replacement and evolving probabilities.
  • Understanding phase transitions in such systems is crucial for diverse fields, including statistical mechanics and machine learning.
  • Previous studies have explored Pólya urn dynamics, but a comprehensive universality class for generalized versions remained elusive.

Purpose of the Study:

  • To establish a universality class for the phase transitions of a generalized Pólya urn model.
  • To investigate the asymptotic behavior of the normalized correlation function C(t) using finite-size scaling analysis.
  • To characterize the system's behavior across different parameter regimes, particularly near critical points.

Main Methods:

  • Analyzed the asymptotic behavior of the normalized correlation function C(t) using finite-size scaling.
  • Studied a generalized Pólya urn where ball addition probabilities depend on the current proportion of red balls.
  • Investigated the system's dynamics in the (J,h) parameter plane, identifying regions with one or two stable fixed points.

Main Results:

  • Identified a boundary [J(c)(h),h] in the (J,h) plane separating regions with distinct stable fixed point behaviors.
  • Demonstrated that the correlation function C(t) exhibits power-law scaling C(t)∼c+c'·t^(l-1) dependent on the parameter J.
  • Revealed a continuous phase transition at h=0, characterized by logarithmic corrections and universal scaling functions C(t)≃(lnt)^(-α')g[(1-l)lnt].

Conclusions:

  • The generalized Pólya urn exhibits a universality class for its phase transitions, characterized by specific scaling behaviors.
  • The system displays continuous phase transitions with universal scaling functions and length scales related to the slope of the probability function.
  • The findings provide a theoretical framework for understanding complex stochastic systems with evolving probabilities and critical phenomena.