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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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 particular...
Uncertainty: Overview00:59

Uncertainty: Overview

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.
Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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Updated: May 22, 2026

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

How far can stochastic and deterministic views be reconciled?

Eric Bertin1

  • 1Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46 Allée d'Italie, F-69007 Lyon, France. eric.bertin@ens-lyon.fr

Progress in Biophysics and Molecular Biology
|May 8, 2012
PubMed
Summary

This study explains stochastic and deterministic processes, highlighting their similarities and differences. Surprisingly, their practical behaviors can be much closer than initially assumed.

Related Experiment Videos

Last Updated: May 22, 2026

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

Area of Science:

  • Mathematical Modeling
  • Probability Theory
  • Complex Systems

Background:

  • Stochastic processes involve randomness, while deterministic processes follow predictable paths.
  • Understanding these processes is crucial in various scientific disciplines.
  • A clear distinction is often assumed between random and predictable system behaviors.

Purpose of the Study:

  • To offer a pedagogical comparison of stochastic and deterministic processes.
  • To introduce fundamental mathematical concepts for describing stochastic processes.
  • To demonstrate that the practical differences between stochastic and deterministic behaviors can be minimal.

Main Methods:

  • Comparative analysis of process definitions.
  • Introduction to the mathematical formalisms of stochastic processes.
  • Illustrative examples highlighting behavioral similarities.

Main Results:

  • Identified key similarities and differences in process dynamics.
  • Presented basic mathematical tools for stochastic process analysis.
  • Empirically suggested that the practical gap between stochastic and deterministic systems is often smaller than theoretical distinctions imply.

Conclusions:

  • Stochastic and deterministic processes share more practical similarities than commonly perceived.
  • Basic mathematical frameworks can effectively describe stochastic phenomena.
  • The distinction between randomness and predictability may be less pronounced in applied contexts.