Functional Connectivity

Biological neural networks are quite complicated in the sense of a function map from input to output. On the other hand, the building blocks of such networks are simple neurons which are the atomic “functions” of the whole network.

As a physicist, we have been working with harmonic oscillators. Single oscillators have its frequency of oscillations. Coupled oscillators have their eigenmode, which are hidden collective behaviors of the oscillators. It seems that each oscillator is oscillating chaotically. As we find the eigenmodes, we find the collective patterns. Each oscillator joins some if not all of the collective patterns.

This idea inspires us. If we look at the spiking of each neuron, we might not be able to identify the patterns. However, for coupled neurons, we have to find their collective modes to really identify the hidden patterns. This idea works for very small networks, the eigenvalues and eigenvectors of which can be found easily. For super large networks, it becomes mission impossible.

In any case, we can persue the idea that the network is composed of basic functional units. There are many levels and aspects of brain connectivity 1.

  1. Graph theory:
    • clustering techniques
    • community detection, which is quite interesting.
  2. Morphometric methods
  3. Functional brain connectivity:
    • computing cross-correlations in the time or frequency domain;
    • mutual information;
    • spectral coherence.

Community Detection

The article [^BrainConnectivity] mentioned that eigenspectrum is used in community detection.

In social science and complex networks, community detection is a well researched field. A bunch of methods have been developped.

  • Q modularity 1;
  • Hyperbolic mapping 2;
  • Statistical mechanics method such as Gibbs distribution 3;

Here are some facts about brain network.

  1. It’s similar to small world network 1.
  2. There are functional hubs 1.
  3. Segregation and integration might be key to a functional neural network [BrainConnectivity]_.


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Lei Ma (2020). 'Functional Connectivity', Intelligence, 05 April. Available at: