Adaptation to Sensory Input Tunes Visual Cortex to Criticality · cerebral cortex in rats2 Several simulations imply critical adaptation exists 3 Power Law in Rat Cerebral Cortex

Adaptation to Sensory Input Tunes Visual Cortex toCriticality

Woodrow L. Shew, Wesley P. Clawson, Jeff Pobst, Yahya Karimipanah,Nathaniel C. Wright, and Ralf Wessel

Tim Miller, August Miller, Viviana Nguyen, and Mayisha Nakib

University of Illinois PHYS 596 Team 8

Shew, Woodrow L., Clawson, Wesley P., Pobst, Jeff, Karimipanah, Yahya, Wright, Nathaniel C.,Wessel, Ralf. Adaptation to sensory input tunes visual cortex to criticality. Nature Physics. 11,659-663 (2015)

December 9, 2016

T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 1 / 18

Nerves self-organize to critical point

Nature Physics 22 June 2015

Hypothesis: Nerves self-organize tocritical point to optimize informationprocessing

Experimentally and computationallytest if strong sensory input causesvisual cortex to tune to signal

Confirm predicted scaling lawstheoretically expected at criticality

Red-eared turtle brainsharvested for experiment

0Image taken from Korzeniec, Monika ”Trachemys scripta elegans” Wikimedia Commons(2006)


Critical behavior occurs at phase transitions

Critical point marks transition between two distinct phases/types ofbehavior

Phase transitions often break symmetries of system

Consequently, critical point often marks transition between a moreordered and a less ordered state ⇒ “edge of chaos”

Example: sandpile model1

1Bak et al., 1987; image from Hesse & Gross, 2014T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 3 / 18

Hallmarks of criticality

Branching parameter σ ≈ 1

Critical slowing down

Avalanche size S and durationT follow power-law distributions:D(S) ∼ S−τ , D(T ) ∼ T−α

Scale-invariance (self-similarity)Figure: Branching parameter σ isdefined as the # of peaks in activity attime t+ ∆t (descendants) divided bythe # of peaks at time t (ancestors).1

1Image from Beggs & Plenz, 2003T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 4 / 18





Scale-invariance (self-similarity)Figure: Relaxation time τ as a function oftemperature T for a magnetic nanoparticlesystem. Inset: τ vs. (T/Tg − 1), where Tgis the transition temperature.1

1Image from Djurberg et al., 1997T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 4 / 18





Scale-invariance (self-similarity)Figure: Distribution of avalanche sizesfor sandpile model. Linear relationshipon log-log scale indicates a powerlaw.1

1Image from Bak et al., 1988T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 4 / 18





Scale-invariance (self-similarity)Figure: Cross-section of avalanchesfrom simulation of crackling noise inmagnets. Avalanches appear similaracross spatial scales.1

1Image from Sethna et al., 2001T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 4 / 18

Neuronal networks self-organize to operate at criticality

Systems at criticality are believed tooptimize aspects of memory andinformation processing

Verified in models of cellularautomata,1 cellular proteininteractions,2 and neuronal networks3

Led to criticality hypothesis: neuronalnetworks self-organize to the criticalpoint of a phase transition

Figure: In a neuronal networkmodel, transmittedinformation peaks at σ slightlygreater than 1, which isindicative of critical behavior.4

1Langton, 19902Kauffman & Johnsen, 1991; Kauffman, 19933E.g., Chialvo & Bak, 19994Image from Beggs & Plenz, 2003


History of Criticality and Previous Rat Brain Experiment

Idea that neural networks adaptto criticality around since 19981

Previous experiments focus oncerebral cortex in rats2

Several simulations implycritical adaptation exists 3

Power Law in Rat Cerebral Cortex

Straight line on log plot indicates powerlaw.

1Packard, 19882Beggs 2008, Image also from Beggs3Rybarsch 2014


2013 Sand Pile Simulation but for Neurons

Authors follow up there owntheoretical studies from 2013

higher capacity to carry signalsless signal distortion

Applications in understandingneurological disease: seizures, possiblyautism 4

New Paper: Unlike prior experiments,this deals directly with incomingsignals from external source - vision

4Beggs 20085Image from Shew, 2013


Experimental Methods: Preparing the Turtle Brain

Brain, optic nerves, and eyes surgicallyremoved from 9 red eared turtles

One eye cut in half and drained toexpose retina

Microelectrodes array inserted into theeye

Videos projected onto retina using aprojector and lenses to stimulate brain

Microelectrodes used to measuresignals through visual cortex.

1Image from Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 8 / 18

Experimental Methods: Analyzing the Turtle Brain

Scaling laws of neuronalavalanches were studiedto determine whether ornot the network wasoperating in the criticalregime

Specifically, avalanchesize and duration wereconsidered


Methods: Integrate-and-Fire DynamicsComputational Component

1000 Neurons with all-to-all connectivity each with external input

Integrate-and-fire dynamics with differing synaptic weights leading toprobabilistic firing in discrete time

After firing, firing connections are depressed temporarily.

Above is a depiction of the connectivity of the system. All-to-allconnectivity means every neuron influences every other neuron.


Results: Power-law Scaling in Experiment

Avalanche size and duration follow power law (P (D) ∼ D−τ , P (s) ∼ s−α)


Results: Power-law Scaling in SimulationResults 2: Electric Boogaloo

Avalanche size and duration follow power law (P (D) ∼ D−τ , P (s) ∼ s−α)


Results: Power-law Avalanches

Relationship between avalanche size and duration given by s ∼ D−β,where β = α−1

τ−1


Things that made us mad!

Paper only shows data for oneturtle (others in supplementary),but it does have this:

β parameters for all turtles

q values are reported but errorson fit parameters are not

Deviation between distributionsonly in supplementaryinformation

1Image Mandy Barton’s Pintrest2Image Shew, 2015


Things that made us mad!

Why all to allconnections?

Why every neuronreceives signal fromoutside?

Bi-modaldistribution obviousduring the transientperiod forsimulation, but notin experiment

1Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 15 / 18

Things that made us glad!

Clear concise prose

Figures organized neatlyall in one spot per section

Authors email you backvery quickly

Here’s the entire experiment inone snapshot

1Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 16 / 18

Citation Evaluation

Paper has been cited 13 times (according to the SCOPUS database)

Cited by 6 experimental papersCited by 7 theoretical papers

Criticality has been found in other organisms including mice andhumans


Critical Behavior Confirmed!

Combines experimentaland computationalmethods

Avalanche size andduration follow power law,and other criterioncharacteristic of criticalbehavior after transientperiod.

Would be nice if errors onfit parameters werereported

Legacy: OngoingNewer work: different network and twonerves compared along with local area

4Nathaniel C. Wright, Mahmood S. Hoseini, Ralf Wessel, Biorxiv Nov 2016T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 18 / 18

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Adaptation to Sensory Input Tunes Visual Cortex to Criticality · cerebral cortex in rats2 Several simulations imply critical adaptation exists 3 Power Law in Rat Cerebral Cortex