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

Evaluating Limits by Direct Substitution01:29

Evaluating Limits by Direct Substitution

109
In the analysis of functions that represent continuous physical phenomena, it is often necessary to determine the output value as the input approaches a specific point. When a combination of algebraic terms defines the function and exhibits no discontinuities or abrupt changes near the point of interest, the limit of the function can be evaluated directly. This process, known as direct substitution, involves replacing the variable in the expression with the value it approaches.Direct...
109
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.5K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
2.5K
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

1.1K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
1.1K
Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

5.0K
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:
5.0K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.1K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.1K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

316
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
316

You might also read

Related Articles

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

Sort by
Same author

Single-cell and spatial omics in plants: from cellular atlases to regulatory mechanisms.

Journal of experimental botany·2026
Same author

Constitutive and inducible oleoresin defenses share genetic architectures and mechanisms in Pinus taeda.

The New phytologist·2026
Same author

Transcriptomic and functional analyses uncover a conserved effector driving genotype-dependent virulence in the <i>Sphaerulina musiva-Populus trichocarpa</i> interaction.

mBio·2026
Same author

Integrated epidemiological and molecular data inform the relationship between precancer and cancer states of esophageal adenocarcinoma.

Nature medicine·2026
Same author

Spatio-temporal dynamics of Hendra virus in Australia reveal stable maintenance of diverse viral clades among Pteropus bats.

Nature microbiology·2026
Same author

Training thermodynamic computers by gradient descent.

Proceedings of the National Academy of Sciences of the United States of America·2026

Related Experiment Video

Updated: Jan 1, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K

Direct evaluation of dynamical large-deviation rate functions using a variational ansatz.

Daniel Jacobson1, Stephen Whitelam2

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review. E
|December 25, 2019
PubMed
Summary

This study introduces a novel importance sampling method for calculating large-deviation rate functions in continuous-time Markov chains. The technique provides tighter bounds and exact rate functions for dynamical observables without prior knowledge of rare events.

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

443
Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

4.9K

Related Experiment Videos

Last Updated: Jan 1, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

443
Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

4.9K

Area of Science:

  • Statistical Physics
  • Computational Chemistry
  • Theoretical Physics

Background:

  • Large-deviation theory analyzes rare events in stochastic systems.
  • Continuous-time Markov chains model complex dynamical systems.
  • Calculating large-deviation rate functions for dynamical observables is computationally challenging.

Purpose of the Study:

  • To develop a simple importance sampling method for bounding and computing large-deviation rate functions.
  • To provide a physically transparent framework for analyzing rare dynamical events.
  • To enable accurate calculation of rate functions for time-extensive observables.

Main Methods:

  • Constructing a reference model as a variational ansatz for conditioned system behavior.
  • Direct simulation of the reference model to obtain bounds on rate functions.
  • Estimating the tightness of the bounds and recovering exact rate functions.
  • Applying the method to network and lattice models for currents and counting observables.

Main Results:

  • The method provides upper bounds on large-deviation rate functions.
  • Bounds obtained are tighter than those from Level 2.5 large deviations.
  • Exact rate functions can be recovered by correcting the bounds.
  • Demonstrated applicability to various network and lattice models.

Conclusions:

  • The proposed importance sampling method offers a transparent and effective framework for large-deviation analysis.
  • It surpasses existing approximation methods in bound tightness.
  • The approach is versatile and applicable to diverse dynamical systems and observables.