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The Decisive Commanding
Neural Network In the
Parietal Cortex
By
Hsiu-Ming Chang (張修明)
Shadlen & Newsom, 2001, J.Neurosci.
Monkeys are trained to perform
the motion discrimination task by
eye saccades.
For each neuron,
a response
field (RF) is
determined
Shadlen & Newsom, 2001, J.Neurosci.
Electrodes are inserted into the lateral intraparietal cortex
Shadlen & Newsom, 2001, J.Neurosci.
Single neurons favoring a specific direction of the eye movement
are found
Shadlen & Newsom, 2001, J.Neurosci.
Activity elevated on a decision to
move the eye to a specific
direction
Activity attenuated on a decision to
move the eye away from a specific
direction
Shadlen & Newsom, 2001, J.Neurosci.
The neural activity
reaches the maximum
just before the saccadic
eye movement
The neural activity
follows the strength
of the information
Shadlen & Newsom, 2001, J.Neurosci.
The reaction time is longer than the decay time of NMDA receptor activation
The reaction with error decisions takes longer time than with the correct ones
Roitman & Shadlen , 2002, J.Neurosci.
The decision process is simulated in a theoretical network
The resting potential VL, firing threshold Vth,
and reset potential Vreset were set respectively to
−70mV, −50mV and −55mV.
Else
Wong & Wang, 2006, J. Neurosci
where g was the peak synaptic conductance,
S the synaptic gating variable (fraction of open channels),
VE = 0 the reversal potential of excitatory connectivity, and VI = −70mV the
reversal potential for inhibitory synapses.
w was a dimensionless potentiation factor due to structured excitatory synapses
The relatively strong synapses, a potentiation factor w = w+ = 1.7 is chosen1. A
“depression” factor w = w− = 1−f(w+−1)/(1−f) < 1 for the synapses between
two different selective populations, and for synapses between the nonselective
population to selective ones. For all other connections, w = 1.
Wong & Wang, 2006, J. Neurosci
In units of μS, grec,AMPA = 0.0005, gext,AMPA = 0.0021, gNMDA = 0.000165, and
grec,AMPA = 0.00004, gext,AMPA = 0.00162, gNMDA = 0.00013 to the interneurons. For
inhibitory synapses to pyramidal cells and interneurons, gGABA, are 0.0013μS
and 0.001μS respectively.
Wong & Wang, 2006, J. Neurosci
S is the synaptic gating variable ~ open probability
The time constants were τAMPA = 2ms,τNMDA,decay = 100ms, τNMDA,rise
= 2ms, τGABA = 5ms, andα = 0.5ms−1. The rise time for AMPA and GABA
(< 1ms) were assumed to be instantaneous. Spikes from external of the
network were assumed to go through AMPA receptors.
Wong & Wang, 2006, J. Neurosci
Approximations are made
to simplify calculations
For a total of 2000 neurons with 400
Inhibitory ones
Wong & Wang, 2006, J. Neurosci
F(yi)= Yi /(tNMDA(1-yi)),
and yi is the steady state of Si.
where i 1, 2, 3 denotes the two selective, and one nonselective excitatory
populations,
I is the inhibitory population. ri(t) is the instantaneous mean firing rate of the
presynaptic excitatory population i,
rI(t) is the mean firing rate of the inhibitory population.
S and its associated are the average synaptic gating variable and its
corresponding decay time constant, respectively.
Wong & Wang, 2006, J. Neurosci
the firing rate r of a leaky integrate-and-fire (LIF) neuron
receiving noisy input
r=
Isyn is the total synaptic input to a single cell, and cE,I is the gain factor. gE,I is a
noise factor that determines the shape of the “curvature” of . If gE,I is large,
would act like a linearthreshold function with IE,I/c as the threshold current.
The values are, for pyramidal cells, IE = 125 Hz, gE = 0.16 s, and cE = 310(VnC)-1;
and for interneurons, II =177Hz, gI = 0.087 s, and cI = 615(VnC)-1
Wong & Wang, 2006, J. Neurosci
Assuming the interspike intervals to be nearly Poisson,
the average gating variable can be fitted by a simple
function
where 0.641 and r is the presynaptic firing rate. Then
F(y(r))= g r
Wong & Wang, 2006, J. Neurosci
Further reduction is achieved if approximations, r is time independent and
NMDA receptors have a decay time constant much longer than others, are
made.
Under a wide range of conditions, the firing rate of the
nonselective population changes only by a modest amount,
assumed at a constant mean rate of 2 Hz.
Applying linear approximation of the input– output transfer
function of the inhibitory cell.
where g2 = 2 and r0 = 11.5 Hz.
Wong & Wang, 2006, J. Neurosci
Assuming that all other variables achieve their steady states much faster
than the NMDA gating variable SNMDA, which dominates the time
evolution of the system.
where i 1, 2 labels the two
excitatory populations
After approximations, only two equations are left for solving
Wong & Wang, 2006, J. Neurosci
the standard set of parameters for the two-variable model is as
follows: JN,11 = 0.1561 nA = JN,22, JN,12 = 0.0264 nA = JN,21, JA,11
= 9.9026*10-4 nC = JA,22, JA,12 = 6.5177*10-5 nA Hz-1 = JA,21 and I0 =
0.2346 nA.
Wong & Wang, 2006, J. Neurosci
Input signal are applied to 15% of the total excitatory neurons
where JA,ext = 0.2243 * 10-3 nA * Hz-1 is the
average synaptic coupling with AMPARs and
c’ is the degree of coherence
where s2noise is the variance of the noise, and is a Gaussian
white noise with zero mean and unit variance. Unless
specified, noise is fixed at 0.007 nA.
Wong & Wang, 2006, J. Neurosci
A decision is made when the threshold the reached
Wong & Wang, 2006, J. Neurosci
The theoretical model reproduces the experimental results
Stimulation
Coherence
Increases
The accuracy
Error takes
Longer time
To act
Wong & Wang, 2006, J. Neurosci
The coherence dependent responses are also demonstrated
Wong & Wang, 2006, J. Neurosci
Stronger stimulation results in shorter reaction time
Wong & Wang, 2006, J. Neurosci
Working memory
Wong & Wang, 2006, J. Neurosci
Wong & Wang, 2006, J. Neurosci
Stimulation
induces
disturbance
on the state
of the network
and creates
transient
unstable
Wong & Wang, 2006, J. Neurosci
Coherent
stimulation
separate
two nullclines
and reduce
the number
of attractors
Wong & Wang, 2006, J. Neurosci
Stronger recurrent current reduces the reaction time and accuracy
Wong & Wang, 2006, J. Neurosci
Increase the AMPA
Component in the
Recurrent current
Results in shorter
Reaction time but
Less accuracy
Wong & Wang, 2006, J. Neurosci
Wong & Wang, 2006, J. Neurosci
Decision
Without
Working
Memory
(instinct ?)
Wong & Wang, 2006, J. Neurosci
A logical elaboration of the decision making process
In a neural system is demonstrated
The functional significant neural activity is represented
in a form of synchronization.
Decision is made when the neural network reaches a
steady state in activity
The purpose for the vast number of neurons in the ensemble
redundancy
noise reduction (higher precision)
The biological evidence of theoretical derivation of w is still
ambiguous.
The abrupt rise and drop of neural activity near the sccadic
movement have not been simulated (interneuron factor ?)