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

Randomized Experiments01:13

Randomized Experiments

8.8K
The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
8.8K
Random Variables01:09

Random Variables

17.1K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
17.1K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.6K
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...
1.6K
Random Sampling Method01:09

Random Sampling Method

14.0K
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
14.0K
Law of Independent Assortment02:03

Law of Independent Assortment

62.0K
While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
62.0K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.2K
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...
1.2K

You might also read

Related Articles

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

Sort by
Same author

Generative-model-based null-space iterative reconstruction for atomic electron tomography with sparse data.

Nature communications·2026
Same author

Platelet-Collagen Interactions in Hemostatic Mechanisms.

Advanced healthcare materials·2026
Same author

Solid Pseudopapillary Neoplasms of the Pancreas with Delayed Ovarian Metastasis During Pregnancy: A Case Report and Literature Review.

International journal of women's health·2026
Same author

Association between serum vitamin D levels and cardiovascular disease risk in patients with hyperuricemia: A cross-sectional study.

PloS one·2026
Same author

Water kefir grain polysaccharides: Ultrasonic-assisted extraction optimization, structural characterization, bioactivities, and application in goat yogurt.

Ultrasonics sonochemistry·2026
Same author

Ziyuglycoside II ameliorates chemotherapy-induced neutropenia by promoting neutrophil differentiation and functional recovery via SPI1 and C/EBPϵ transcriptional regulation.

Frontiers in immunology·2026
Same journal

A Comprehensive Numerical Model of Thrombus Embolization: Fluid-Thrombus Interactions Through a Coupled Computational Fluid Dynamics - Peridynamics Framework.

Computer methods in applied mechanics and engineering·2026
Same journal

Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions.

Computer methods in applied mechanics and engineering·2026
Same journal

An optimal Petrov-Galerkin framework for operator networks.

Computer methods in applied mechanics and engineering·2026
Same journal

Multi-level <math><mi>k</mi></math> -nearest neighbors algorithm for direct point cloud-based engineering analysis.

Computer methods in applied mechanics and engineering·2026
Same journal

Full-field surrogate modeling of cardiac electrophysiology encoding geometric variability.

Computer methods in applied mechanics and engineering·2026
Same journal

ValveFit: An analysis-suitable B-spline-based surface fitting framework for patient-specific modeling of tricuspid valves.

Computer methods in applied mechanics and engineering·2025
See all related articles

Related Experiment Video

Updated: Dec 28, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.9K

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.

Huan Lei1, Jing Li1, Peiyuan Gao1

  • 1Pacific Northwest National Laboratory, Richland, WA 99352.

Computer Methods in Applied Mechanics and Engineering
|February 11, 2020
PubMed
Summary
This summary is machine-generated.

We introduce a new Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework. DSRAR accurately quantifies uncertainty propagation in complex systems using limited data, even with non-Gaussian probability distributions.

Keywords:
arbitrary randomnesscompressed sensingdata-drivenmutual dependencesparsity enhancementuncertainty quantification

More Related Videos

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

933
Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
07:35

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

7.9K

Related Experiment Videos

Last Updated: Dec 28, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.9K
Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

933
Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
07:35

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

7.9K

Area of Science:

  • Computational mathematics
  • Uncertainty quantification
  • Scientific computing

Background:

  • Quantifying uncertainty propagation in high-dimensional systems is challenging due to complex input probability distributions.
  • Traditional methods struggle with limited data and arbitrary dependencies between random variables.
  • Existing polynomial chaos expansions often assume mutual independence, limiting their applicability.

Purpose of the Study:

  • To develop a general framework for constructing surrogate models for arbitrary probability measures, handling dependent random inputs.
  • To create a data-driven method for building multivariate polynomial bases that maintain orthogonality for non-Gaussian distributions.
  • To enable accurate uncertainty quantification with limited training data in complex, high-dimensional systems.

Main Methods:

  • Developed a Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework.
  • Constructed multivariate polynomial bases for arbitrary, mutually dependent probability measures.
  • Implemented a sparsity-enhancing rotation procedure ensuring basis orthogonality for rotated random vectors.

Main Results:

  • The DSRAR framework accurately recovers sparse representations of target functions using limited training data.
  • Demonstrated effectiveness in high-dimensional (O(10)) conformational spaces for partial differential equations and molecular systems.
  • Successfully applied to systems with implicitly represented and explicitly given non-Gaussian probability measures.

Conclusions:

  • The DSRAR framework offers a robust solution for uncertainty quantification in systems with complex, arbitrary probability distributions.
  • This data-driven approach overcomes limitations of traditional methods, especially with limited data and dependent random inputs.
  • The method shows significant potential for applications in computational mathematics and scientific computing.