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When a network is in an attractor state, the derivative of each and every neuron in that network is zero.
if the connections between neurons are just right, memories started at one point in time can last for much longer. All the cells can maintain their firing rate because all the cells
around them are doing the same. Nothing changes if...
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For working memory to function, the network needs to be good at resisting the influence of such distractors.
‘ring network’, a hand-designed model of a neural circuit that would be ideal for the robust maintenance of working memories.
Attractors in a ring network, on the other hand, are continuous. With continuous attractors, transitioning between similar memories is easy.
A ring network allows for small, sensible errors.
colours lie on a wheel.
gutter-like nature of a continuous attractor – it has low resistance for moving between nearby states, but high resistance to perturbations otherwise.
Because to the biologist, of course, ‘finely tuned’ are dirty words.
The ellipsoid body is centrally placed in the fly brain and it has a unique shape: it has a hole in the middle with cells arranged all around that hole, forming a doughnut made of neurons
It links ions to experiences.
the perceptron is a feedforward (not recurrent) network. Recurrence means that the connections can form loops: neuron A connects to neuron B, which connects back to neuron A, for example.
Eavesdrop on a neuron that should be doing the same thing over and over – for example, one in the motor system that is producing the same movement repeatedly – and you’ll find its activity surprisingly irregular.
how a neuron responded to any given pulse seemed a matter of pure chance.
‘We were struck by the kaleidoscopic appearance of [responses] obtained from large nerves under absolutely constant conditions.’
‘The variability of cortical neuron response[s] is known to be considerable.’
‘Successive presentations of identical stimuli do not yield identical responses,’
neurons have ‘more in common with the ticking of a Geiger counter than of a clock’.
Petri dish they behave remarkably more reliably: stimulating these neurons the same way twice will actually produce similar results.
the very nature of how neurons work makes them noise reducers
the ‘noisiness’ of your athletic ability gets averaged out over time.
If it only uses a quick snapshot of its input, however, the noise will dominate.
So how much time does a neuron combine its inputs over? About 20 milliseconds.
spike only takes about 1 millisecond and a cell can be receiving many at a time from al...
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Neuroscientists William Softky and Christof Koch used a simple mathematical model of a neuron – the ‘leaky integrate-and-fire’ model
Yet the neuron itself – because it integrated these incoming spikes over time – still produced output spikes that were much more regular than the input it received.
When passed through a neuron, noise should get weaker.
Not only is the brain unpredictable, then, but it seems to be encouraging that unpredictability – going against the natural tendency of neurons to squash it.
GABA, as it is more commonly known) was the first identified inhibitory neurotransmitter.
These receptors are like little protein padlocks.
receptor that GABA attaches to, for example, only lets chloride ions into the cell.
Neurons tend to release the same neurotransmitter on to all of their targets, a principle known as Dale’s Law
Neurons that release GABA are called ‘GABAergic’,
‘Whatever the brain does for the mind, we can be sure that GABA plays a major role in it.’
In computers, numbers can only be represented with a certain level of precision.
In general, the stronger that two competing powers are, the bigger the swings in the outcome of their competition.
And the network needs to be self-consistent – that is, each neuron needs to produce the same amount of noise it receives, no more nor less. Could
physics is full of situations where self-consistency is important:
average strength of a connection was roughly equal to one divided by the square root of the number of connections
The auditory cortex, for example, needs to respond to quick changes in
sound frequency to process incoming information. This makes the quick responsiveness of well-balanced neurons a good match.
This counter-intuitive fact that good behaviour can produce bedlam is important.
‘The scientist must always be on the lookout for other explanations than those that have been commonly disseminated.’
Chaotic processes produce outputs that look random but in fact arise from perfect rule-following.
When patients are asleep (particularly in deep dreamless sleep), the EEG makes waves: large movements upwards then downwards extending over a second or more.
When the event of interest – a seizure – occurs, the movements are even starker. The signal traces out big, fast sweeps up and down, three to four times a second, like a kid scribbling frantically with a crayon.
seizure is the opposite of randomness – it is perfect order and predictability.
with the inhibitory connections slightly stronger than excitatory ones – is just off to the right of the middle.
bifurcations.
