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WINNERLESS COMPETITION PRINCIPLE IN NEUROSCIENCE Mikhail Rabinovich INLS University of California, San Diego. ’. competition stimulus Winnerless without + dependent = Competition WINNER clique Principle. Hierarchy of the Models.
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WINNERLESS COMPETITION PRINCIPLE IN NEUROSCIENCE Mikhail Rabinovich INLS University of California, San Diego ’
competition stimulus Winnerless without + dependent = CompetitionWINNER clique Principle
Hierarchy of the Models • Network with realistic H-H model neurons & random inhibitory & excitatory connections • Network with FitzHugh-Nagumo spiking neurons • Lotka-Volterra type model to describe the spiking rate of the Principal Neurons (PNs)
is the strength of inhibition in i by j is the strength of excitation in i by k is the excitation from the other neural ensembles is an external action Stimulus dependent Rate Model Is the firing rate of neuron i
Canonical L-V model (N>3) A heteroclinic sequence consists of finitely many saddle equilibria and finitely many separatrices connecting these equilibria. The heteroclinic sequence can serve as an attracting set if every saddle point has only one unstable direction. The condition for this is: i+1 i Necessary condition for stability:
Then the heteroclinic contour is a global attractor if A noise transfer the heteroclinic contour to a stable limit cycle with the same order of a sequential switching Consider the matrix Canonical Lotka-Volterra model Rigorous results (N=3)
WLC Principle & SHS (rate model) Geometrical image of the switching activity in the phase space is the orbit in the vicinity of the heteroclinic sequence
WLC Principle & SHS (H-H neurons) Geometrical image of the switching activity in the phase space is the orbit in the vicinity of the heteroclinic contour
The main questions: • How does sensory information transform into behavior in a robust and reproducible way? • Do neural systems generate new information based on their sensory inputs? • Can transient dynamics be reproducible?
WLC can generate an irregular but reproducible sequence Model assumptions • All connections are inhibitory • The SRCs are asymmetrically connected • There is 30% connectivity among the neurons • The hunting neuron excites allSCHs at variable strength
Projection of the strange attractorfrom the 6D phase space of the statocyst network
Weak reciprocal excitation stabilizes WLCdynamics:Birth of the stable limit cycle in the vicinity of the former heteroclinic sequence
Conductance-based model for “Winner take all” and “Winnerless” competition Winner take all Winnerless
Motor output dynamics Firing rates of 4 different tail motorneurons at different burst episodes In spite of the irregularity the sequence is preserved
Spatio-temporal coding in the Antennal Lobe of Locust(space = odor space) Lessons from the experiments: The key role of the inhibition Nonsymmetric connections No direct connection between PNs
input output 1 1 0 2 1 1 8 2 0 9 Time 8 9 0 Transformation of the identity input Into spatio-temporal output based on the intrinsic sequential dynamics of the neural ensemble 0 1 0 1 0 1 0 0 0 1 1 Winnerless Competition Principle & New Dynamical Object: Stable Heteroclinic Sequence WLC & SHS
Transient dynamics of the bee antennal lobe activity during post-stimulus relaxation
Low dimensional projection of Trajectories Representing PN Population Response over Time
Reproducible sequences in complex networks Inequalities for reproducibility:
Neuron Reproducibility of the heteroclinic sequence
Stable manifolds of the saddle points keep the divergent directions in check in the vicinity of a heteroclinic sequence
WLC in complex neural ensembles Complex network = many elements + + disordered connections Most important phenomena in complex systems on the edge of reproducibility are: (i) clustering, and (ii) competition
Rate model of the Random network QIs the step function
TWO REGIMES: A) B)
WLC networks cooperation: * synchronization(i) electrical connections, (ii) synaptic connections; (iii) ultra-subharmonic synchronization ** competition
Competition between learned sequences: on line decision making