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Related Concept Videos

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...
Correlation and Causation01:27

Correlation and Causation

Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
Correlation versus Causation
If the dependent variable increases or decreases when the independent variable increases, there is a positive or negative...
Control Systems01:10

Control Systems

Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
At the heart...
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:
Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...

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Related Experiment Video

Updated: May 15, 2026

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance
09:01

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance

Published on: May 7, 2014

Effect of correlations on network controllability.

Márton Pósfai1, Yang-Yu Liu, Jean-Jacques Slotine

  • 1Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA, USA.

Scientific Reports
|January 17, 2013
PubMed
Summary
This summary is machine-generated.

Controlling complex networks requires understanding driver nodes. Network structure, specifically degree correlations, influences the number of driver nodes needed, while clustering and modularity do not. This research bridges the gap between theoretical predictions and real-world network control.

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Last Updated: May 15, 2026

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance
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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Area of Science:

  • Complex systems
  • Network science
  • Control theory

Background:

  • Controllability of dynamical systems depends on external signals applied to driver nodes.
  • The minimal number of driver nodes is crucial for efficient network control.
  • Real-world networks often show a discrepancy between predicted and observed driver node counts.

Purpose of the Study:

  • To investigate how network characteristics influence the minimal number of driver nodes required for controllability.
  • To analyze the impact of clustering, modularity, and degree correlations on network control.
  • To reconcile theoretical predictions with empirical observations of driver nodes in real networks.

Main Methods:

  • Analysis of dynamical systems and network controllability.
  • Mathematical modeling of network properties like clustering, modularity, and degree correlations.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • Clustering and modularity do not significantly affect the number of driver nodes needed for control.
  • The dependence of driver nodes on degree correlation coefficients can be linear, quadratic, or absent, depending on correlation symmetries.
  • The study provides insights into the relationship between network structure and control requirements.

Conclusions:

  • Network symmetries, particularly in matching problems, are key determinants of control node requirements.
  • Understanding these structural impacts helps in predicting and optimizing control strategies for complex systems.
  • The findings contribute to closing the gap between theoretical models and practical applications in network control.