Coarse-grained analysis of neural networks

What does coarse graining mean?

Very often we have many details about the fine aspects of a system. For example, in theory, we could describe the motion of all the particles of water in a river. However, equally often, it is not the fine details we are interested in, but the coarse ones. Typically, we are only interested in the overall flow of the river, rather than any particular particle in it. Through the use of computer simulation and analytical tools, we can use our knowledge of the fine scale system to approximate it the coarser scale. This is the essence of coarse graining.

How is this relevant to the brain?

We now have a number of detailed mathematical descriptions of individual nerve cells. However, individual neurons convey little information by themselves, it is only when acting in large networks that they can perform functional roles. For example, when we carry out functional brain scans, we see the averaged activity over areas of the brain that while small, contain thousands of cells. Whilst there do exist descriptions of neural tissue at coarser scales, these are based on matching observed behaviour of this tissue, rather than describing the mechanisms producing them.

What do we hope to learn from this?

Certain neural system function by using specific patterns of activity. Typically, these are manifest in the form of persistent localised activity, associated with working memory, and progating activity, linked to the visual system. Through coarse-grained analysis, we hope to understand how mechanisms at the fine scale influence behaviour at the coarse scale. We also hope to understand how the existing coarse scale descriptions can be matched to the fine scale ones.

What are we doing in our research?

We are investigating patterns of activity in simple networks of neurons, using a combination of rigorous mathematics and cutting edge numerical techniques. Although these networks are simple, the behaviour of more complex networks should broadly fit that of the simpler ones. Ultimately, we are interested in understanding how randomness and differences between individual neurons affect the patterns of activity that we observe.