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

The Uncertainty Principle04:08

The Uncertainty Principle

33.9K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
33.9K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

2.1K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
2.1K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.5K
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
1.5K
Calculation of First Law Quantities I01:25

Calculation of First Law Quantities I

25
Thermodynamic systems undergoing phase transitions or temperature changes experience energy transfer in the form of heat (q) and work (w). For a reversible phase change at constant temperature (T) and pressure (p), the process involves no chemical reaction but results in energy exchange between distinct phases.The heat transferred during this process corresponds to the latent heat of transition, which is the amount of heat energy absorbed or released by a substance when it changes from one...
25
Uncertainty: Overview00:59

Uncertainty: Overview

1.8K
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
1.8K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

11.9K
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
11.9K

You might also read

Related Articles

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

Sort by
Same author

Automated SCAI staging as a novel decision aid in cardiogenic shock management.

Journal of cardiac failure·2026
Same author

Management Patterns and Outcomes of Invasive Mechanical Ventilation in Patients With Cardiogenic Shock.

JACC. Advances·2025
Same author

PROFET Predicts Continuous Gene Expression Dynamics from scRNA-seq Data to Elucidate Heterogeneity of Cancer Treatment Responses.

bioRxiv : the preprint server for biology·2025
Same author

Cognitive Function and Patient-Reported Outcomes After Cardiogenic Shock.

Journal of the American College of Cardiology·2025
Same author

Out-of-hospital cardiac arrest survival in Black & Hispanic communities since the COVID-19 pandemic.

Resuscitation·2025
Same author

Patient Characteristics, Management and Long-Term Outcomes of Patients With Cardiogenic Shock at a Large Safety Net Hospital.

The American journal of cardiology·2025
Same journal

Anharmonic phonons via quantum thermal bath simulations.

The Journal of chemical physics·2026
Same journal

Quantum simulation of alignment dependent differential cross sections in co-propagating molecular beams at cold collision energies.

The Journal of chemical physics·2026
Same journal

Non-additive ion effects on the coil-globule equilibrium of a generic polymer in aqueous salt solutions.

The Journal of chemical physics·2026
Same journal

Insights into the unexpected small reduction of the temperature of maximum density of water by lithium chloride addition.

The Journal of chemical physics·2026
Same journal

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm-1 states of ethylene.

The Journal of chemical physics·2026
Same journal

Time reversal breaking of colloidal particles in cells.

The Journal of chemical physics·2026
See all related articles

Related Experiment Video

Updated: Mar 10, 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

9.1K

Uncertainty quantification for generalized Langevin dynamics.

Eric J Hall1, Markos A Katsoulakis1, Luc Rey-Bellet1

  • 1Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA.

The Journal of Chemical Physics
|December 18, 2016
PubMed
Summary
This summary is machine-generated.

We developed new finite difference estimators for sensitivity analysis of the generalized Langevin equation (GLE). These methods efficiently analyze complex systems where other techniques fail, offering reduced variance for key parameters.

More Related Videos

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions
10:02

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

4.6K
Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis
14:11

Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis

Published on: March 29, 2016

27.7K

Related Experiment Videos

Last Updated: Mar 10, 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

9.1K
Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions
10:02

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

4.6K
Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis
14:11

Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis

Published on: March 29, 2016

27.7K

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Numerical Analysis

Background:

  • Sensitivity analysis is crucial for understanding complex dynamical systems.
  • The generalized Langevin equation (GLE) models various physical phenomena but presents challenges for traditional sensitivity analysis.
  • Existing methods like likelihood ratio are often inapplicable to key parameters in extended GLE formulations.

Purpose of the Study:

  • To develop efficient finite difference estimators for goal-oriented sensitivity indices in the generalized Langevin equation (GLE).
  • To address limitations of existing sensitivity analysis techniques for extended variable GLE formulations.
  • To provide a framework for variance reduction in sensitivity estimation.

Main Methods:

  • Coupling nominal and perturbed dynamics using common driving noise or a common random path.
  • Developing a general framework for variance reduction through coupling strategies.
  • Demonstrating the optimality of common random path coupling for minimal variance.

Main Results:

  • Efficient finite difference estimators for sensitivity indices were developed.
  • Common random path coupling was shown to be optimal for variance reduction.
  • The proposed estimators were evaluated for particle dynamics examples, showing high efficiency.
  • Reduced variance estimators facilitate global sensitivity analysis and non-local perturbation studies.

Conclusions:

  • The novel finite difference estimators are efficient and applicable to extended GLE models.
  • Common random path coupling offers a statistically optimal approach for variance reduction.
  • These methods enhance the analysis of complex systems and parameter sensitivities in physics and beyond.