Changing Connectomes, MIT press
- connectomics is about graphs, different gradations of graphs, different mathematical properties, how graphs created during development
- can be graphs of neurons, voxels, regions
Characteristics of a graph: unit level
- node/edge betweenness - how frequently node/edge is a part of a shortest path
Characteristics of a graph: aggregate level
- connectedness =
2 * E / (N * (N - 1)) how many edges are there out of possible edges
- average shortest path
- global efficiency = average of inverse of length of shortest path, if no edge and distance is infinite then it contributes 0
- average neihbourhood connectivity
- frequency of triples of different configurations. some configurations are more common that others in regions of bran and animals
thoughts: how about to try to use connectomics theory to understand CPU architecture? will it works well? what we are missing?
- clusters - connected a lot within
Major networks types
- random, random edges, not realistic
- regular, high connectivity between neighbors
- small-world, high connectivity between neighbors, sometimes long connections
- modular, some connections within group and some between groups
- hierarchical, multi-level modular
- each neuron/node in graph have constant spacial position, which dictates which nodes it can connect to and how much it would cost, as well as physical properties of pressure, etc.
- physical Eluclidian distance between nodes is inversely proportional to probability of connectedness
- most of axons are straight lines
- different animals have different graphs of neural networks
Graphs of brains available
- fly, drosophilia, full
- pigeon, some partial but good. more anatomically distributed than numans. two levels just as humans. has central core.
- macaque, rhesus monkey
- patterns formation is complex on how they developed (like CNN layers)
- Alan Turing was working on CNN like patterns in 1952, guiding molecules called morphogenes lead to formation of patterns
- apoptosis - deletion of neurons and connections, occurs by programmed cell death or external factors (neuromorphic death)
- if non apoptosis happens brain can not develop, there are studies on mice
- layer formation — the more layer the more neurons and input. mice to human increased surface size 1000x but thickness only 2x
- structural — how connections change. don’t change much after development.
- functional - connections get stronger or weaker. change a lot.
how connected? axons can be very long. how they are guided? many theories. establish first major pathways, then new paths follow them. use chemical signals to guide axons.
- patches of connected neurons on surface
- 10cm is 100ms for normal fiber and 10ms for myelinated factor
- degree influence synchronisation
- wide range of delays depending on brain system, hierarchy of delays and speeds
- stimulation works and can lead to lasting changes
- Kuramoto oscilators
- Proportional-Differentional Feedback control technique
- control theory
- Lead-DBS - model of deep brain stimulation as population level
- VERTEX - model of electrical stimulation at neuronal level