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Related Concept Videos

Randomized Experiments01:13

Randomized Experiments

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...
Random Variables01:09

Random Variables

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...
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
Random Sampling Method01:09

Random Sampling Method

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...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

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Related Experiment Video

Updated: Jun 14, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Random number generators tested on quantum Monte Carlo simulations.

Kenta Hongo1, Ryo Maezono, Kenichi Miura

  • 1School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan. kenta_hongo@mac.com

Journal of Computational Chemistry
|March 26, 2010
PubMed
Summary
This summary is machine-generated.

New random number generators (RNGs), MRG8 and MT19937, efficiently compute molecular ground state energies using Monte Carlo methods, matching high-quality RANLUX results with less computational cost.

Related Experiment Videos

Last Updated: Jun 14, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

  • Computational Chemistry
  • Stochastic Methods

Background:

  • Accurate random number generation is crucial for stochastic simulations in computational chemistry.
  • High-quality pseudorandom number generators (RNGs) like RANLUX are computationally intensive.
  • Evaluating molecular ground state energies requires reliable and efficient RNGs.

Purpose of the Study:

  • To compare the performance of novel RNGs against established ones for molecular energy calculations.
  • To assess the computational efficiency and accuracy of MRG8 and MT19937 generators.
  • To validate the suitability of these RNGs for variational and diffusion Monte Carlo methods.

Main Methods:

  • Monte Carlo simulations (variational and diffusion methods) were employed for ground state energy calculations.
  • Multiple pseudorandom number generators were tested: MRG8, MT19937, RANLUX (levels 0-4), and RANDU.
  • Performance was evaluated based on accuracy (statistical error bars) and computational cost.

Main Results:

  • MRG8 and MT19937 generators achieved results comparable to the highest luxury level of RANLUX (RANLUX-4).
  • Both MRG8 and MT19937 demonstrated lower computational costs than RANLUX for sequence generation.
  • The notoriously poor RANDU generator was included for comparative baseline.

Conclusions:

  • MRG8 and MT19937 are efficient and accurate RNGs suitable for molecular ground state energy calculations.
  • These generators offer a viable alternative to computationally expensive methods like RANLUX.
  • The findings support the use of advanced RNGs to improve the efficiency of quantum Monte Carlo simulations.