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

Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

152
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
152
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

161
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
161
Conservative Site-specific Recombination and Phase Variation02:53

Conservative Site-specific Recombination and Phase Variation

6.2K
Because the DNA segments are cut and reorganized in a direction-specific manner, site-specific recombination has emerged as an efficient genetic engineering technique. Flippase and Cyclization recombinases or Flp and Cre, respectively, are two members of the tyrosine recombinase family derived from bacteriophages, that are used to mediate site-specific DNA insertions, deletions, and targeted expression of proteins in mammalian cell lines.
The recognition sites for Cre recombinase called LoxP...
6.2K
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

360
The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
360
Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

482
In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero:
482
Fault Types01:18

Fault Types

150
When analyzing a single line-to-ground fault from phase A to ground at a three-phase bus, it is important to consider the fault impedance. This impedance is zero for a bolted fault, equal to the arc impedance for an arcing fault, and represents the total fault impedance for a transmission-line insulator flashover. To derive sequence and phase currents, fault conditions are translated from the phase domain to the sequence domain.
For line-to-line faults occurring between phases B and C, the...
150

You might also read

Related Articles

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

Sort by
Same author

Enhancement of hidden Markov model analyses for improved inference of archaic introgression in modern humans.

Molecular biology and evolution·2026
Same author

Estimating Gene Conversion Tract Length and Rate From PacBio HiFi Data.

Molecular biology and evolution·2025
Same author

Phase-type distributions in mathematical population genetics: An emerging framework.

Theoretical population biology·2024
Same author

Phase-type distributions in population genetics.

Theoretical population biology·2019
Same author

A general framework for moment-based analysis of genetic data.

Journal of mathematical biology·2019

Related Experiment Video

Updated: Oct 13, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.2K

Multivariate phase-type theory for the site frequency spectrum.

Asger Hobolth1, Mogens Bladt2, Lars Nørvang Andersen3

  • 1Department of Mathematics, Aarhus University, Ny Munkegade 118, building 1530, 8000, Aarhus C, Denmark. asger@math.au.dk.

Journal of Mathematical Biology
|November 16, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces multivariate phase-type theory to precisely calculate genetic diversity metrics derived from the site frequency spectrum (SFS). This approach offers an analytical solution for mutation rate estimators and neutrality tests, improving genetic diversity analysis.

Keywords:
Coalescent theoryMutation ratePhase-type distributionSite frequency spectrum

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.1K
A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

25.5K

Related Experiment Videos

Last Updated: Oct 13, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.2K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.1K
A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

25.5K

Area of Science:

  • Population Genetics
  • Statistical Genetics
  • Computational Biology

Background:

  • Linear functions of the site frequency spectrum (SFS) are crucial for analyzing genetic diversity.
  • Estimators of mutation rate and neutrality tests rely on SFS distributions.
  • Current methods often approximate these distributions using simulations.

Purpose of the Study:

  • To apply multivariate phase-type theory for characterizing and calculating SFS linear function distributions.
  • To provide an analytical framework for genetic diversity estimators and neutrality tests.
  • To develop a computationally tractable method for SFS distribution analysis.

Main Methods:

  • Utilizing multivariate phase-type theory to model SFS linear functions.
  • Demonstrating that mutation rate estimators follow discrete phase-type distributions.
  • Deriving probability generating functions for neutrality tests using continuous multivariate phase-type theory and numerical inversion.

Main Results:

  • Mutation rate estimators are shown to be distributed according to discrete phase-type distributions.
  • Neutrality tests are generally not discrete phase-type distributed, requiring continuous phase-type theory.
  • An analytically tractable formula for the probability generating function of the SFS was derived.

Conclusions:

  • Multivariate phase-type theory provides an exact method for calculating SFS linear function distributions.
  • This methodology offers improvements over simulation-based approximations for genetic diversity analysis.
  • Software and code are available for implementing these phase-type methods in R.