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

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.0K
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...
1.0K
Reflection of Waves01:07

Reflection of Waves

4.0K
When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
4.0K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.3K
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...
1.3K
Regression Toward the Mean01:52

Regression Toward the Mean

6.6K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.6K
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

798
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...
798
Variation01:19

Variation

7.4K
An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...
7.4K

You might also read

Related Articles

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

Sort by
Same author

Deep-Learning-Assisted SICM for Enhanced Real-Time Imaging of Nanoscale Biological Dynamics.

Small methods·2025
Same author

Hadamard Product in Deep Learning: Introduction, Advances and Challenges.

IEEE transactions on pattern analysis and machine intelligence·2025
Same author

Learning-Based Compressive MRI.

IEEE transactions on medical imaging·2018
Same author

Learning Low-Dimensional Signal Models: A Bayesian approach based on incomplete measurements.

IEEE signal processing magazine·2013

Related Experiment Video

Updated: Oct 14, 2025

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

9.3K

Forward-reflected-backward method with variance reduction.

Ahmet Alacaoglu1, Yura Malitsky2, Volkan Cevher1

  • 1École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.

Computational Optimization and Applications
|November 1, 2021
PubMed
Summary

We introduce a new algorithm for solving monotone variational inequalities, achieving convergence without strict assumptions. This method offers optimal convergence rates for both general monotone and strongly monotone cases.

Keywords:
Finite-sum structureMonotone inclusionsSaddle point problemsStochastic variance reductionVariational inequalities

More Related Videos

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
09:27

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

10.2K
Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

3.2K

Related Experiment Videos

Last Updated: Oct 14, 2025

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

9.3K
Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
09:27

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

10.2K
Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

3.2K

Area of Science:

  • Optimization
  • Applied Mathematics
  • Numerical Analysis

Background:

  • Variational inequalities are fundamental in modeling various problems in economics, engineering, and game theory.
  • Existing algorithms often require strong monotonicity or domain boundedness, limiting their applicability.
  • Developing efficient and robust algorithms for variational inequalities remains a key research area.

Purpose of the Study:

  • To propose a novel variance-reduced algorithm for solving monotone variational inequalities.
  • To establish convergence guarantees under weaker conditions than typically required.
  • To analyze the convergence rates for both monotone and strongly monotone cases.

Main Methods:

  • A variance-reduced iterative algorithm is developed.
  • Convergence is proven almost surely without assuming strong monotonicity, cocoercivity, or domain boundedness.
  • Analysis of convergence rates for ergodic averages and linear convergence under strong monotonicity is performed.

Main Results:

  • The proposed algorithm achieves almost sure convergence to a solution for monotone variational inequalities without strong assumptions.
  • In the monotone case, the ergodic average converges at the optimal O(1/k) rate.
  • Under strong monotonicity, the algorithm exhibits linear convergence without needing the strong monotonicity constant.

Conclusions:

  • The developed algorithm offers a more general and efficient approach to solving monotone variational inequalities.
  • The results extend to related problems like monotone inclusions and Bregman projections.
  • This work provides a valuable tool for theoretical analysis and practical applications in optimization and related fields.