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Harmonic Mean

Harmonic Mean

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...

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Related Experiment Video

Updated: Jun 11, 2025

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Published on: March 21, 2019

Dynamic Functional Connectome Harmonics.

Hoyt Patrick Taylor¹, Pew-Thian Yap^2,3

¹Department of Computer Science, University of North Carolina, Chapel Hill, NC, USA.

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention

|October 9, 2024

Summary

This summary is machine-generated.

This study introduces functional connectome harmonics, revealing stable brain organization across timescales. These harmonics identify reproducible brain states and offer a novel method for measuring cortical flexibility.

Keywords:

dynamic functional connectivity flexibility harmonics

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Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

Area of Science:

Neuroscience
Computational Neuroscience
Brain Imaging

Background:

Functional connectivity (FC) gradients map brain organization but typically use static FC.
The influence of timescale on FC topography and principal axes remains underexplored.
Momentary brain states may underlie dynamic FC organization.

Purpose of the Study:

To compute functional connectome harmonics using varying timescales.
To investigate the stability of principal FC axes across different time windows.
To develop a novel method for assessing cortical flexibility using time-varying connectome harmonics.

Main Methods:

Solved for normal modes of functional connectivity to derive functional connectome harmonics.
Computed harmonics using time windows of varying lengths.
Developed a vertex-resolution cortical flexibility metric based on time-varying harmonics.

Main Results:

Functional connectome harmonics are stable across timescales.
Harmonics correspond to meaningful, reproducible brain states with stable inter-relationships.
The novel cortical flexibility method shows qualitative agreement with existing literature.

Conclusions:

The principal axes of functional connectivity are invariant to timescale.
Functional connectome harmonics provide a robust representation of brain states and dynamics.
This approach offers a new avenue for studying brain flexibility and organization.