Related Experiment Video
Updated: Oct 15, 2025
07:26
Designing Automated, High-throughput, Continuous Cell Growth Experiments Using eVOLVER
Published on: May 19, 2019
12.3K
Large Deviations for Subcritical Bootstrap Percolation on the Erdős-Rényi Graph.
1Department of Mathematics, University of British Columbia, Vancouver, BC Canada.
Journal of Statistical Physics
|November 1, 2021
Summary
This study analyzes bootstrap percolation on random graphs, revealing the probability of widespread infection from small initial sets. We identify the most efficient infection pathways for unexpected large-scale spread.
Area of Science:
- Probability theory
- Statistical physics
- Network science
Background:
- Bootstrap percolation models infection spread on graphs.
- Erdős-Rényi random graphs are a fundamental model for network structure.
- Previous work established critical conditions for widespread infection.
Purpose of the Study:
- Investigate atypical, large-deviation events in bootstrap percolation.
- Quantify the probability of unexpected infection spread from small initial sets.
- Identify the most efficient pathways for such large deviations.
Main Methods:
- Analysis of bootstrap percolation dynamics on Erdős-Rényi random graphs.
- Large deviation theory to calculate rate functions.
- Identification of minimum-cost trajectories for rare events.
Main Results:
- Calculated the rate function for small initial sets causing unexpected large infections.
- Identified the least-cost trajectory for realizing these large deviations.
- Characterized the probability of rare, extensive infection spread.
Conclusions:
- Provides a deeper understanding of extreme events in random network percolation.
- Offers insights into the dynamics of rare but significant spread phenomena.
- Contributes to the statistical analysis of complex systems.
Keywords:
Bootstrap percolationDiscrete calculus of variationsLarge deviationsPhase transitionRandom graphsMore Related Videos
Related Concept Videos
01:17Wald-Wolfowitz Runs Test II
347
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...
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
347
01:10Entropy Change in Reversible Processes
2.8K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.8K
01:24Bootstrapping
691
The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
691
01:15Chebyshev's Theorem to Interpret Standard Deviation
4.6K
Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
4.6K
01:02Quantifying and Rejecting Outliers: The Grubbs Test
2.7K
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...
2.7K
01:16Unusual Results
3.4K
Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ from the mean, μ is considered unusual.
Maximum unusual value =...
According to the range rule of thumb, any value above or below two standard deviations, 2σ from the mean, μ is considered unusual.
Maximum unusual value =...
3.4K