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What is Variation?01:14

What is Variation?

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Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean.
The range, standard deviation, standard error, and variance are the different measures of variation.
Range: The range is the difference between its maximum and...
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Variation01:19

Variation

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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...
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Conservative Site-specific Recombination and Phase Variation02:53

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Because the DNA segments are cut and reorganized in a direction-specific manner, site-specific recombination has emerged as an efficient genetic engineering technique. Flippase and Cyclization recombinases or Flp and Cre, respectively, are two members of the tyrosine recombinase family derived from bacteriophages, that are used to mediate site-specific DNA insertions, deletions, and targeted expression of proteins in mammalian cell lines.
The recognition sites for Cre recombinase called LoxP...
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Variation of Atmospheric Pressure01:18

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Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
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Comparing Copy Number Variations and SNPs02:26

Comparing Copy Number Variations and SNPs

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Sequencing of the human genome has opened up several best-kept secrets of the genome. Scientists have identified thousands of genome variations that exist within a population. These variations can be a single nucleotide or a larger chromosomal variation.
Copy number variations or CNVs are the structural variations that cover more than 1kb of DNA sequence. The single nucleotide polymorphism (SNP), on the other hand, is a single nucleotide change or a point mutation that is found in more than 1%...
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Coefficient of Variation01:10

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The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
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Updated: Jan 23, 2026

A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
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Variational Approach for Impurity Dynamics at Finite Temperature.

Weizhe Edward Liu1,2, Jesper Levinsen1,2, Meera M Parish1,2

  • 1School of Physics and Astronomy, Monash University, Victoria 3800, Australia.

Physical Review Letters
|June 8, 2019
PubMed
Summary

We developed a new variational method to study impurity dynamics in quantum systems. This approach accurately models experimental results for heavy impurities in a Fermi gas at finite temperatures.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Atomic physics

Background:

  • Studying impurity dynamics in quantum media is crucial for understanding complex many-body systems.
  • Existing methods often struggle with mixed states or dynamical impurities.

Purpose of the Study:

  • To introduce a general variational principle for impurity dynamics in quantum media.
  • To provide a method applicable to mixed states, including thermal states.
  • To model experimental observations of impurities in Fermi gases.

Main Methods:

  • Utilizing the Heisenberg picture and approximate time-dependent impurity operators.
  • Developing a variational approach consistent with conservation laws.
  • Applying the method to heavy impurities in a finite-temperature Fermi gas.

Main Results:

  • The variational method accurately models Ramsey interference experiments.
  • The approach shows consistency with finite-temperature Green's function methods.
  • Successful modeling of ^{40}K atoms in a ^{6}Li Fermi gas.

Conclusions:

  • The developed variational principle offers a powerful tool for studying impurity dynamics.
  • This method enables investigations of impurities with dynamical degrees of freedom.
  • The approach is applicable to arbitrary quantum-mechanical mediums.