QUANTITATIVE LAWS June 13 -June 24

1. A NEURAL MECHANISM
FOR THE EMERGENCE OF
NON-CRITICAL POWER LAWS
Serena Di Santo
21/06/2016
Lake Como School

2. tissue on array local field potentials thresholded signals
A NEURAL MECHANISM
FOR THE EMERGENCE OF
NON-CRITICAL POWER LAWS
c r i t i c a l

3. WILSON-COWAN MODEL
AND BALANCED AMPLIFICATION OF FLUCTUATIONS
E
I
wI
wI
wE
wE
@tE = ↵E + (1 E)f(s)
@tI = ↵I + (1 I)f(s)
f(s) = ✓[tanh(s)]
s = wEE wII + h
'
Benayoun M, Cowan JD, van Drongelen W, Wallace E, (2010) PLoS Comput Biol
Murphy BK, Miller K, (2009) Neuron
wE wI
E
I
not balanced
+
p
↵E + (1 E)f(s)⌘E
+
p
↵I + (1 I)f(s)⌘I

4. NON NORMAL FORMS AND A NOISE INDUCED ZERO MODE
Linear
stability close to
the fixed point…
Non Diagonalizable
Non orthogonal Eigenvect
Define Pseudospectra
˙⇢ = a⇢ b⇢2
+ h +
p
⇢⌘(t)
T U N N
E
L
I N
G
Amplificated fluctuations
+noise
☞
NON
NORMAL
FORM
AT
A 6= AAT
Pst(⇢) ⇠
1
⇢1 2h
2

5. SIMILAR PHENOMENON, DIFFERENT REGULATORY MECHANISM:
TSODYKS-MARKRAM MODEL FOR SYNAPTIC PLASTICITY
˙R =
1
⌧
(Rm
R) u⇢R⇢ b⇢2 c⇢3 + !⇢R +
p
⇢⌘˙⇢ = a⇢ b⇢2 c⇢3 + h + !⇢R +
p
⇢⌘
NON-NORMAL FORMS ☞AMPLIFICATION OF FLUCTUATIONS ☞
NOISE INDUCED ZERO MODE☞ ☞NON-CRITICAL POWER LAWS

6. THANKS TO
MIGUEL ANGEL Muñoz & PABLO Villegas