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instructions

Neurons transmit information electrochemically. When the soma, or cell body, of the neuron switches from being inactive (grey circle) to being active (yellow circle), the neuron transmits a signal down the axon, and then to other neurons at synapses (arrows). These other neurons may or may not become active, depending upon their receptor activation threshold.

A neuron with a positive (white numbered circle) activation threshold needs to receive a signal from a certain number of other neurons for itself to become active. Thus, a neuron with a +1 activation threshold requires at least one active synapse, while a +3 activation threshold requires at least three active synapses.

Neuron Instructions, Table 1

A neuron with a negative (black numbered circle) activation threshold needs a lack of inhibitor signal from a certain number of other neurons for itself to become active. In other words, it needs a certain number of synaptic connections to inactive neurons to become active. Thus, a neuron with a –1 activation threshold requires at least one inactive synapse, while a –3 activation threshold requires at least three inactive synapses.

Neuron Instructions, Table 2

The maximum activation threshold (positive or negative) for a neuron is equal to the number of incoming synaptic connections (arrows pointing to it). No neurons have an activation threshold of zero.

In each of these puzzles, you are given a set of neurons in one or more activation states. You need to determine how to assign the available receptor activation thresholds to the neurons in the bottom row so that the neurons behave as given. The same arrangement of activation thresholds must work for every given activation state.


examples

Here is an example, along with the available receptor activation thresholds.

Neuron Example A

Each neuron in the bottom row has a few possible receptor activation thresholds, listed below.

Neuron Example A, Table 1

The neuron at left, for example, could have a +1 threshold or a –1 threshold, since it has one active and one inactive synaptic connection, and it itself is active. Compare this with the neuron on the right, which similarly has one active and one inactive synaptic connection, yet is not active. This neuron consequently has a +2 or –2 threshold.


Some of these activation threshold possibilities can be immediately eliminated, because they are not available.

Neuron Example A, Table 2

Note that only one of the neurons could possibly have a +3 activation threshold, so that must be assigned to that neuron.

Neuron Example A, Table 3

The neurons at the ends have only one possible activation threshold available.

Neuron Example A, Table 4

This leaves one neuron and one activation threshold left.

Neuron Example A, Table 5

The solution will be shown like this:

Neuron Example A, Solution


Here is another example which has two activation states, along with the available activation thresholds.

Neuron Example B

For the first state, each neuron in the bottom row has a few possible receptor activation thresholds, listed below. Some of these are unavailable, while the +3 activation threshold can only be assigned to one neuron.

Neuron Example B, State A, Table 1

The remaining activation thresholds can be assigned to the other neurons in two possible ways.

Neuron Example B, State A, Table 2

Looking at the second state, each neuron in the bottom row again has a few possible receptor activation thresholds, listed below. Some of these are unavailable, while the –1 activation threshold can only be assigned to one neuron.

Neuron Example B, State B, Table 1

The remaining activation thresholds can again be assigned to the other neurons in two possible ways.

Neuron Example B, State B, Table 2

Comparing the two sets of outcomes, only one of these possible arrangements works for both activation states.

Neuron Example B, Solution


solving tips

Just because a neuron has a certain number of active synaptic connections (arrows coming from yellow circles), doesn't mean that number is its activation threshold. For example, if a neuron is active and has two active synaptic connections, that doesn't necessarily mean it has an activation threshold of +2. It could have an activation threshold of +1, because it is receiving more than enough signal from the two synaptic connections to become active. Similarly, remember there are negative activation thresholds as well, which rely on the absence of active synaptic connections (or presence of inactive synaptic connections).

The above examples list all potential activation thresholds and narrow that list using the available choices. Another strategy would be to see which available activation thresholds can be assigned to which neurons, looking specifically for those that can only be assigned to one particular neuron. Maximum activation thresholds, if available, may be the most obvious candidates to investigate, but any threshold could be unique to a particular neuron.