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

Survival Tree01:19

Survival Tree

157
Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
Constructing a...
157
Compacting Factor test01:22

Compacting Factor test

246
The compacting factor test is a method used to assess the workability of concrete. It is  especially suitable for concrete mixes containing aggregates up to one and a half inches in size. This test involves specialized equipment consisting of two truncated cone-shaped hoppers and a cylinder, all with polished interior surfaces to minimize friction.
The procedure begins by placing concrete into the upper hopper without any compaction. Once filled, the bottom door of this hopper is opened,...
246
Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

2.0K
Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
2.0K
Method of Sections: Problem Solving II01:30

Method of Sections: Problem Solving II

1.2K
Consider an arbitrary truss structure composed of diagonal, vertical, and horizontal members fixed to the wall. To calculate the force acting on members CB, GB, and GH, method of sections can be used. The loads and lengths of the horizontal and vertical members are known parameters, as shown in the figure.
1.2K
F Distribution01:19

F Distribution

3.8K
The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...
3.8K
Identifying Statistically Significant Differences: The F-Test01:14

Identifying Statistically Significant Differences: The F-Test

2.0K
The F-test is used to compare two sample variances to each other or compare the sample variance to the population variance. It is used to decide whether an indeterminate error can explain the difference in their values. The underlying assumptions that allow the use of the F-test include the data set or sets are normally distributed, and the data sets are independent of each other. The test statistic F is calculated by dividing one variance by another. In other words, the square of one standard...
2.0K

You might also read

Related Articles

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

Sort by
Same author

Order-Dependent dissimilarity measures on phylogenetic trees.

Journal of mathematical biology·2026
Same author

Incidentally detected retropharyngeal cystic parathyroid adenoma in trauma imaging: A diagnostic challenge.

Journal of clinical imaging science·2025
Same author

Comparison of intraoperative and postoperative metrics in robotic vs. laparoscopic liver resections by difficulty - Retrospective cohort analysis of a multi-institutional database.

HPB : the official journal of the International Hepato Pancreato Biliary Association·2025
Same author

Comparative analysis of three approaches for minimally invasive incision-dominant hepatectomy: a multi-center analysis of patients undergoing resection of segments VII and VIII in the AMILES registry.

HPB : the official journal of the International Hepato Pancreato Biliary Association·2025
Same author

New lung ultrasound system for rapid triage of pulmonary disease without a radiologist or sonographer.

BMC pulmonary medicine·2025
Same author

External validation of Tampa Difficulty Scoring System for robotic liver resection using Americas Minimally Invasive Liver Surgery Registry (AMILES).

Surgical endoscopy·2025
Same journal

Slow Evolution Towards Generalism in a Model of Variable Dietary Range.

Bulletin of mathematical biology·2026
Same journal

CBINN: Cancer Biology-Informed Neural Network for Unknown Parameter Estimation and Missing Physics Identification.

Bulletin of mathematical biology·2026
Same journal

A Cost-Sensitive Behavioral Modeling Analysis of the Early Identification and Control of Infectious Diseases.

Bulletin of mathematical biology·2026
Same journal

Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.

Bulletin of mathematical biology·2026
Same journal

The Exact Hypergeometric Posterior Method for Accurate Inference of Population Size from Mark-Recapture Data.

Bulletin of mathematical biology·2026
Same journal

Modeling, Analysis, and Optimal Control of Leukemic Cell Population Dynamics Under Therapy.

Bulletin of mathematical biology·2026
See all related articles

Related Experiment Video

Updated: Sep 8, 2025

Author Spotlight: Advancements in X-ray CT Tool Chain for Tree Core Analysis
06:56

Author Spotlight: Advancements in X-ray CT Tool Chain for Tree Core Analysis

Published on: September 22, 2023

1.2K

The GFB Tree and Tree Imbalance Indices.

Sean Cleary1, Mareike Fischer2, Katherine St John3

  • 1Department of Mathematics, The City College of New York, New York, 10031, USA.

Bulletin of Mathematical Biology
|September 5, 2025
PubMed
Summary
This summary is machine-generated.

We introduce new tree imbalance indices derived from subtree sizes, showing complete and greedy from the bottom (GFB) trees minimize them, while caterpillar trees maximize them. The GFB tree is the unique minimizer for the s-shape statistic.

Keywords:
GFB treePhylogenetic treeTree balanceYule model

More Related Videos

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

3.4K
Leaf Area Index Estimation Using Three Distinct Methods in Pure Deciduous Stands
09:04

Leaf Area Index Estimation Using Three Distinct Methods in Pure Deciduous Stands

Published on: August 29, 2019

13.7K

Related Experiment Videos

Last Updated: Sep 8, 2025

Author Spotlight: Advancements in X-ray CT Tool Chain for Tree Core Analysis
06:56

Author Spotlight: Advancements in X-ray CT Tool Chain for Tree Core Analysis

Published on: September 22, 2023

1.2K
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

3.4K
Leaf Area Index Estimation Using Three Distinct Methods in Pure Deciduous Stands
09:04

Leaf Area Index Estimation Using Three Distinct Methods in Pure Deciduous Stands

Published on: August 29, 2019

13.7K

Area of Science:

  • Phylogenetics
  • Computer Science
  • Graph Theory

Background:

  • Tree balance is crucial in phylogenetics and computer science.
  • Over 25 balance/imbalance indices exist to rank rooted binary trees.
  • Subtree-size based measures are common for quantifying tree structure.

Purpose of the Study:

  • Introduce a new family of tree imbalance indices.
  • Identify minimizers and maximizers for these indices.
  • Characterize greedy from the bottom (GFB) trees and analyze specific statistics.

Main Methods:

  • Investigated subtree-size based measures satisfying concavity and monotonicity.
  • Analyzed complete trees and greedy from the bottom (GFB) trees.
  • Derived asymptotic bounds for s-shape and Q-shape statistics under specific tree distributions.

Main Results:

  • Complete/GFB trees minimize a wide range of imbalance indices; caterpillar trees maximize them.
  • The GFB tree is the unique minimizer for the s-shape statistic.
  • Established an equivalence between GFB trees and complete trees.

Conclusions:

  • The study yields an infinite family of novel imbalance indices.
  • Provides a new characterization of GFB trees.
  • Offers insights into the behavior of tree imbalance statistics under different distributions.