Christopher Kello Cognitive and Information Sciences Thanks to NSF DARPA and the Keck Foundation Background and Disclaimer Cognitive Mechanics Fractional Order Mechanics Reasons for FC in ID: 638346
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Slide1
Scaling Laws in Cognitive Science
Christopher KelloCognitive and Information SciencesThanks to NSF, DARPA, and the Keck FoundationSlide2
Background and Disclaimer
Cognitive Mechanics…
Fractional Order Mechanics?Slide3
Reasons for FC in Cogsci
Intrinsic FluctuationsCritical BranchingLévy-like ForagingContinuous-Time Random WalksSlide4
Intrinsic Fluctuations
Neural activity is intrinsic and ever-presentSleep, “wakeful rest”Behavioral activity also has intrinsic expressionsPostural sway, gait, any repetition Slide5
Lowen
& Teich
(1996),
JASA
Allan Factor
Analyses Show Scaling Law
Clustering
Intrinsic Fluctuations In Spike TrainsSlide6
Intrinsic Fluctuations in LFPs
Beggs &
Plenz
(2003),
J Neuroscience
Bursts of LFP Activity in
Rat Somatosensory Slice PreparationsSlide7
Mazzoni
et al. (2007), PLoS One
Burst Sizes Follow a 3/2 Inverse
Scaling
Law
Intrinsic Fluctuations in LFPs
Intact Leech Ganglia
Dissociated Rat HippocampusSlide8
Intrinsic Fluctuations in SpeechSlide9
Intrinsic Fluctuations in SpeechSlide10
Intrinsic Fluctuations in Speech
Log f
Log S(f)
S(f) ~ 1/f
αSlide11
Scaling Laws in Brain and Behavior
How can we model and simulate the pervasiveness of these scaling laws?Clustering in spike trainsBurst distributions in local field potentialsFluctuations in repeated measures of behavior Slide12
Critical Branching
Critical branching is a critical point between damped and runaway spike propagation
Damped Runaway
pre
postSlide13
Spiking Network Model
LeakyIntegrate&Fire
Neuron
Source
Sink
ReservoirSlide14
Critical Branching AlgorithmSlide15
Critical Branching Tuning
Tuning ON Tuning OFFSlide16
Spike TrainsSlide17
Allan Factor ResultsSlide18
Neuronal BurstsSlide19
Neuronal Avalanche ResultsSlide20
Simple Response SeriesSlide21
1/f Noise in Simple ResponsesSlide22
Memory Capacity of Spike DynamicsSlide23
Critical Branching and FC
The critical branching algorithm produces pervasive scaling laws in its activity. FC might serve to:Analyze and better understand the algorithmFormalize the capacity for spike computationRefine and optimize the algorithmSlide24
Lévy-like Foraging
Animal Foraging
Memory Foraging
Slide25
Lévy-like Visual SearchSlide26
Lévy-like Visual SearchSlide27
Lévy-like Foraging GamesSlide28
“Optimizing” Search with Levy Walks
Lévy walks with μ ~ 2 are maximally efficient under certain assumptionsHow can these results be generalized and applied to more challenging search problems? Slide29
Continuous-Time Random Walks
In general, the CTRW probability density obeys
Mean
waiting time:
Jump
length variance:Slide30
Human-Robot Search Teams
Wait times correspond to times for vertical movements
Tradeoff between sensor
accuracy and scope
Human-controlled and algorithm-controlled search agents in virtual environmentsSlide31
Conclusions
Neural and behavioral activities generally exhibit scaling lawsFractional calculus is a mathematics suited to scaling law phenomenaTherefore, cognitive mechanics may be usefully formalized as fractional order mechanicsSlide32
Collaborators
Gregory AndersonBrandon BeltzBryan KersterJeff RodnyJanelle SzaryMarty MayberryTheo Rhodes
John Beggs
Stefano Carpin
YangQuan
Chen
Jay Holden
Guy Van Orden