some properties of lattice without and with remote connections

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some properties of lattice without and with
remote connections marko puljic december, 2002
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dynamics of neurons and neuron populations
microscopic pulse and wave state variables
describe the activity of the single neurons that
contribute to the population. neuron converts
incoming pulses to waves, sums them, converts its
integrated wave to a pulse train, and transmits
that train to all its axonal branches. states
mesoscopic state variables describe the
collective activities in the pulse and wave
modes. states
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Transition rules (2D lattice d2, k4,5,6,7,8
noise lt 0.5)

• j(B)noise if less than majority active
  neighbors, 1-noise otherwise -arousal
• r(B)noise if more than majority active
  neighbors, 1-noise otherwise -depression

1 - noise
noise
1 - noise
noise
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how do the mesoscopic states (density) change
with time and noise? density number of active
cells / total number of cells
no axons (density vs. time)
noise 0.13
noise 0.2
noise 0.136
noise 0.135
noise 0.12
noise 0.08
axons (density vs. time) 15 (1) possible neighbor
noise 0.16
noise 0.155
noise 0.15
noise 0.145
noise 0.135
noise 0.14
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why shift happens? (outward with the addition of
the remote neighbors)
low noise - low likelihood of site being
inactive remote neighbor will be likely
active (by majority rule it makes site harder to
turn inactive)
1 - noise
noise
increase the noise to lower the density
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adding remote neighbors causes the increase in
critical noise changing the connection
architecture changes the critical nose, (not same
to have one site with 4 neighbors and 4 with
one) there is lower and upper bound for the
critical noise, when the lattice has no remote
neighbors and when lattice is fully connected
it is possible to simulate critical noise between
lower (0.13428) and upper bound (0.233) to any
desired precision by arbitrary lattice size and
connection architecture, (for infinite precision
lattice size goes to infinity).
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• oscillations
• wait time for the jump
• relationship with the lattice size
• relationship with the noise
• relationship with the remote connections
• how long does it take for the jump to go to
  another phase, (number of runs)
• relationship with the lattice size
• relationship with the noise
• relationship with the remote connections
• jump description

density
1-µ
µ
time
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