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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)
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 2 / 18
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
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: 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
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: 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
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: 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
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 5 / 18
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
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 6 / 18
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
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 7 / 18
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
1Image from Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 9 / 18
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.
1Image from Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 10 / 18
Results: Power-law Scaling in Experiment
Avalanche size and duration follow power law (P (D) ∼ D−τ , P (s) ∼ s−α)
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 11 / 18
Results: Power-law Scaling in SimulationResults 2: Electric Boogaloo
Avalanche size and duration follow power law (P (D) ∼ D−τ , P (s) ∼ s−α)
1Image from Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 12 / 18
Results: Power-law Avalanches
Relationship between avalanche size and duration given by s ∼ D−β,where β = α−1
τ−1
1Image from Shew, 2015T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 13 / 18
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
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 14 / 18
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
T. Miller, A. Miller, V. Nguyen, M. Nakib Adaptation & Criticality in Visual Cortex December 9, 2016 17 / 18
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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