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Related Concept Videos

Correlation01:09

Correlation

In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Critical Region, Critical Values and Significance Level01:16

Critical Region, Critical Values and Significance Level

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the test...
Critical Values01:31

Critical Values

A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...
Absolute and Local Extreme Values01:22

Absolute and Local Extreme Values

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...
Correlations02:20

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...

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Related Experiment Video

Updated: Jun 21, 2026

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

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Published on: August 1, 2011

Correlations in avalanche critical points.

Benedetta Cerruti1, Eduard Vives

  • 1Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

Avalanche dynamics show a unique correlation between waiting times and previous event sizes in the random-field Ising model. This finding, observed at T=0, mirrors patterns seen in earthquakes and forest fires.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Avalanche dynamics and power-law statistics are common in natural phenomena like earthquakes and solar flares.
  • Similar behaviors are observed in condensed-matter systems, including ferromagnets and martensites.

Purpose of the Study:

  • To investigate avalanche dynamics in the random-field Ising model at zero temperature (T=0).
  • To identify unique correlations in avalanche behavior not present in other models.

Main Methods:

  • Studied the prototypical random-field Ising model.
  • Analyzed system behavior at T=0.

Main Results:

  • Discovered a significant correlation between waiting intervals and the preceding avalanche size.
  • This correlation is absent in other avalanche models but present in real-world systems like earthquakes and forest fires.

Conclusions:

  • The observed correlation suggests a specific type of critical point.
  • This critical point is likely located at the termination of a first-order discontinuity between high and low activity regimes.