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

Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

427
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
427
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

1.3K
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
1.3K
Modeling with Differential Equations01:25

Modeling with Differential Equations

227
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
227
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

397
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
397
Exponential Equations with Logarithms: Problem Solving01:29

Exponential Equations with Logarithms: Problem Solving

250
In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...
250
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

321
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
321

You might also read

Related Articles

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

Sort by
Same author

Peer influence decay and behavioral diffusion in adolescent networks: A simulation approach.

Science (New York, N.Y.)·2026
Same author

Jasmonate signaling and prey nutrient availability trigger distinct biochemical responses in the Drosera capensis feeding cycle.

Plant physiology·2026
Same author

Mimicking oxidative damage in γS-crystallin with site-specific incorporation of 5-hydroxytryptophan.

Biophysical reports·2026
Same author

Jasmonate-induced prey response in the carnivorous plant <i>Drosera capensis</i>.

bioRxiv : the preprint server for biology·2025
Same author

The Computer-Assisted Sequence Annotation (CASA) workflow for enzyme discovery.

Applications in plant sciences·2025
Same author

Mini-αA-crystallin protects a client lens protein from catastrophic aggregation due to heat stress.

Protein science : a publication of the Protein Society·2025

Related Experiment Video

Updated: Mar 30, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K

A Novel Simulation Method for Binary Discrete Exponential Families, with Application to Social Networks.

Carter T Butts1

  • 1Departments of Sociology, Statistics, and EECS, and Institute for Mathematical Behavioral Sciences; University of California, Irvine; SSPA 2145; Irvine, CA 92697-5100; buttsc@uci.edu.

The Journal of Mathematical Sociology
|November 21, 2015
PubMed
Summary

We developed a novel approximate sampling method for binary discrete exponential families, offering fixed execution time and quality guarantees. This method improves upon Markov chain Monte Carlo (MCMC) for social network analysis and random graph generation.

Keywords:
discrete exponential familiesrandom graphsstatistical simulation

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

3.8K
Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.4K

Related Experiment Videos

Last Updated: Mar 30, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K
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
Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.4K

Area of Science:

  • Computational Sociology
  • Statistical Modeling
  • Network Science

Background:

  • Stochastic models for binary data are crucial in sociology, modeling behaviors and social networks.
  • Exact sampling is challenging due to data dependence, leading to approximate Markov chain Monte Carlo (MCMC) methods.
  • MCMC methods have variable execution times and uncertain draw quality.

Purpose of the Study:

  • To introduce a novel approximate sampling method for binary discrete exponential families.
  • To provide fixed execution time and well-defined quality guarantees for sampling.
  • To apply the method to random graph generation and social network simulation.

Main Methods:

  • Developed a new approximate sampling procedure for binary discrete exponential families.
  • Demonstrated the method's application in generating random graphs.
  • Utilized geographical covariates and dyadic dependence mechanisms for social network simulation.

Main Results:

  • The novel method offers fixed execution time, unlike MCMC.
  • The procedure provides well-defined quality guarantees for approximate sampling.
  • Successfully simulated a large-scale social network using the new method.

Conclusions:

  • The proposed sampling method is a viable and advantageous alternative to MCMC for binary discrete exponential families.
  • This approach enhances the simulation of complex social networks and random graphs.
  • Offers improved reliability and efficiency in computational sociology research.