A NEURAL MECHANISM FOR THE EMERGENCE OF NON-CRITICAL POWER LAWS - Serena Di Santo

A NEURAL MECHANISM FOR THE EMERGENCE OF

NON-CRITICAL POWER LAWS

Serena Di Santo

21/06/2016Lake Como School

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

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

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 NE LI N G

Amplificated fluctuations+noise

☞

NON NORMAL FORM

ATA 6= AAT

Pst(⇢) ⇠1

⇢1�2h�2

SIMILAR PHENOMENON, DIFFERENT REGULATORY MECHANISM: TSODYKS-MARKRAM MODEL FOR SYNAPTIC PLASTICITY

R =1

⌧(Rm �R)� u⇢R⇢ = a⇢� 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

THANKS TO

MIGUEL ANGEL Muñoz & PABLO Villegas