Polychronization

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In neuroscience, the term polychronization describes the process of generating reproducible time-locked but not synchronous spiking patterns with millisecond precision. The term is derived from Greek poly meaning many and chronos meaning time or clock. Spiking neurons with axonal conduction delays and spike timing dependent plasticity (STDP) can spontaneously self-organize into groups and exhibit multiple polychronous patterns. These patterns represent memory, and their number often exceeds the number of neurons, or even synapses, in the network.

Related words: polychrony, polychronize

1 Polychrony
2 Polychronized spiking
3 Polychronized Group
4 Complexity
5 External links

[edit] Polychrony

Polychrony occurs when events happen with consistent pattern of timing within themselves. To illustrate, consider the following situation. Every day Bob, Bill and Berta go to school according to these constraints:

Bob goes to school first
Bill goes to school 5 minutes after Bob
Berta goes to school 20 minutes after Bill

The three events are clearly not synchronized, but they are polychronized, because they occur at fixed intervals from another and they occur regularly. Extending that example to neurons, assume we have four neurons A,B,C,D with the following constraints:

A,B,C have synaptic connections with D
A takes 10 ms to signal D
B takes 20 ms to signal D
C takes 50 ms to signal D

If they fire according to the below scheduleding sequence they will be polychronized

C fires at time 0
B fires at time 30
A fires at time 40

Polychrony does not imply that events finish at the same time, we could have a situation such as this:

C fires first
B fires 60 seconds later
A fires 400 seconds later

and still be polychronized. As long as they are firing with a consistent pattern of timing within themselves, we say that the events are polychronized. It should be noted that synchrony, is a special case of polychrony, with the interval between the multiple events being zero.

[edit] Polychronized spiking

Classical neural computation involves neurons and synapses, and inter-neuronal information being passed on via their firing rates. Therefore, in order for the connection between two neurons to become stronger, the presynaptic neuron has to fire off more quickly to the postsynaptic neuron. Likewise, if the presynaptic neuron fires off less rapidly, its connection with the postsynaptic neuron will become weaker. Eugene Izhikevich does not refute this model, but proposes the following addition to it:

If neurons A, B and C are polychronized such that their spikes arrive at neuron D at the same time, their respective connections with D will be strengthened more so than had they arrived independently

[edit] Polychronized Group

Any two or more neurons which are polychronized, and arrive at a distinct postsynaptic neuron at the same time form a polychronized group. To avoid redundancy, the largest possible group must be taken. If we have a situation like the one below:

We have 6 neurons A,B,C,D,E,F
A,B,C,E,F have synaptic connections with D
A takes 10 ms to signal D
B takes 20 ms to signal D
C takes 50 ms to signal D
E takes 16 ms to signal D
F takes 12 ms to signal D

and they fire off in the following sequence:

C fires at time 0
B fires at time 30
A fires at time 40
E fires at time 60
F fires at time 64

Then neurons A,B,C form a polychronous group of size 3 and neurons E,F form a polychronous group of size 2.

[edit] Complexity

An intriguing consequence of this view is that the number of polychronous groups exceeds the number of neurons in the brain. At any given time, a neuron can be a member of more than one group, therefore the capacity of the brain may be larger than once conjectured. At any given time there can be on the order of $2 n$ groups because of subset construction.