Circus Circuits Keith L. Downing The Norwegian University of - PowerPoint PPT Presentation

Circus Circuits Keith L. Downing The Norwegian University of Science and Technology (NTNU) Trondheim, Norway keithd@idi.ntnu.no March 18, 2010 Keith L. Downing Circus Circuits

Auditory Localization in Barn Owls On Far Coincidence Detectors: Right Only fire on 2 coincident inputs From A Left Ear B C Delay Lines D E From Right Ear On Far Left Keith L. Downing Circus Circuits

Motion Detectors Riechard Detector (1961) Based on the fly's visual system. T3 Neurons thresholded to 45% line T2 fire only on moving left to multiple, simultaneous inputs right T1 Delay Delay Delay Keith L. Downing Circus Circuits

Temporal Differentiation via Delayed Inhibition Passage through the intermediate Excite neuron, B, delays the A(T) signal, which B inverts. Inhibit A B dA/dt A(T+d) - A(T ) dA/dt B A T T+d Time Keith L. Downing Circus Circuits

Temporal Differentiation via Habituation Excite B habituates to the A(T) input, so it only fires when A(T+d) exceeds A(T). A B dA/dt A(T+d) - A(T ) dA/dt Habituation B A T T+d Time Keith L. Downing Circus Circuits

Temporal Differentiation via Synaptic Depression Synapes from A to dA/dt become Excite temporarily depressed by A activation A dA/dt A(T+d) - A(T ) Synaptic Depression dA/dt A T T+d Time Tripp, B. and Eliasmith, C. (2010), Population Models of Temporal Differentiation, Neural Computation , 22, pp. 621-659. Keith L. Downing Circus Circuits

Higher-Order Derivatives Delay B dA/dt C A d2A/dt2 Habituation C B dA/dt d2A/dt2 A Synaptic Depression d2A/dt2 A dA/dt Keith L. Downing Circus Circuits

Central Pattern Generators for 4-Legged Movement Phase Differences 1/4 3/4 0 1/2 t2 t4 Walking: Left Rear, Left Front, Right Rear, Right Front t1 t3 Ian Stewart (1998), Life’s Other Secret , Ch. 9. Keith L. Downing Circus Circuits

General Gait Generator AL2 AR2 AL1 AR1 Auxiliary Neuron Intra-loop connection with delay d1 Left Right Front Front Inter-loop connection with delay d2 Left Right Rear Rear Q: Do you need different circuits for different gaits? A. NO! Just double the circuit size + adjust 2 delays. Keith L. Downing Circus Circuits

Walking -vs- Jumping Walk Jump d1 = 1/4 d1 = 1/4 d2 = 1/2 d2 = 0 3/4 1/4 3/4 3/4 1/2 0 1/2 1/2 1/4 3/4 1/4 1/4 0 1/2 0 0 Keith L. Downing Circus Circuits

Pacing -vs- Trotting Pace Trot d1 = 0 d1 = 1/2 d2 = 1/2 d2 = 1/2 0 1/2 1/2 0 0 1/2 0 1/2 0 1/2 1/2 0 0 1/2 0 1/2 Keith L. Downing Circus Circuits

Adjustable Delays via Variable Oscillatory Inputs p1 Right Front mV S1 time Shorter delay when Delay S2 is active p2 S2 Right Rear Keith L. Downing Circus Circuits

Achieving Delays via Leaky Integration and Firing Delay Neuron's Membrane Potential Firing Threshold Input from Input Oscillator from Leg Neuron Leak Integration of 2 inputs (one big, one small) suffices to achieve firing threshold. Due to leak current, many small inputs over a longer time period cannot reach threshold. So weak oscillations alone cannot trigger the neuron. Keith L. Downing Circus Circuits

Cricket Phonotaxis Biorobotics Aids Biology Barbara Webb(2001), Biorobotics: Methods and Applications. Ch. 1 Using cricket robot driven by a simple neural net to give a synthetic explanation for how female crickets show a preference for particular syllable durations and frequencies in mating calls. Sound Wave Peak Syllable Syllable Duration Period Time Bug Off! Keith L. Downing Circus Circuits

Anatomy Determines Preferred Syllable Wavelength Left Ear Right Ear 2d Sound d Source R L Peak Peak Trough Distance (d) between the ears on the legs should be 1/4 of syllable wavelength. This maximizes the pressure differences on the two sides of the ear, giving the loudest possible sensation. Keith L. Downing Circus Circuits

Bang the Drum Time = P / 4 P = Syllable Period Time = P / 2 Reflected Peak meets Incoming Trough P = Syllable period At time 0, the first peak hits the left ear, causing it to vibrate and create internal wave K. At time P/4, K meets the right ear drum, causing it to vibrate and send wave K* back toward the left ear drum. At time P/2, K* meets the incoming trough → maximum pressure difference → The cricket rocks. Keith L. Downing Circus Circuits

Preferred Syllable Duration Neural mechanisms of this preference not yet known, but ANN work provides sufficiency argument for a 4-neuron mechanism. Use leaky integrate-and-fire models; motor neurons have larger time constants (i.e. are slower integrators) than auditory neurons. Synapses from auditory to motor neurons can habituate due to weak auditory firing. Move Move Right Left Motor MNL MNR Neurons Excite Inhibit Auditory ANL ANR Neurons Right Eardrum Left Eardrum Keith L. Downing Circus Circuits

Cricket Top 10 Hits More Charge Fires! builds builds up Robot up MNL Decays Moves Left ANL Auditory input from the left side of the robot. Due to the slower motor time constants, MNL takes awhile to build up enough charge. During each syllable, the synapse habituates due to constant activity. Between syllables, the synapse recovers. Keith L. Downing Circus Circuits

Zero Points Charge builds MNL up Decays No Movement Habituation ANL The syllables are so long that the synapse habituates considerably. Thus MNL ’s leak current exceeds its input even when ANL is spiking. The synapse may or may not recover between syllables, depending upon the rest time. But enough charge leaks out that MNL must start anew at each syllable and never builds up enough charge to fire. Keith L. Downing Circus Circuits

Brain Clocks Wright (Sept, 2002). Times of our Lives. Scientific American Collections of cortical neurons with diverse firing patterns enable recording and reuse of specific time intervals. A Time Signatures B T1 T2 T3 T4 A 0 1 1 0 B 1 1 1 0 C C 0 1 0 1 D 1 0 0 1 T3 is the time when D A and B are firing T1 T2 T3 T4 Keith L. Downing Circus Circuits

Corticostriatal Interaction Cortical neurons oscillate at 10-40 Hz (beta + gamma bands). Temporal-context detectors in the striatum (entry to basal ganglia). STN → SNr resets cortical oscillators via simultaneous inhibition. For example, when a dance instructor says, ”Begin.” Salient event (e.g. Instructor says, ”Now Jump”) → SNc sends dopamine to striatum → Temporal context learned. Cerebral Cortex Excite C B Inhibit Dopamine A D STN Striatum S SNr SNc Keith L. Downing Circus Circuits

Temporal Context Learning C C B B A A D D Hebbian Learning S S Jump Jump Coincident acitivity of B and D is learned by S, which just happens to be on when B and D are. In the future, when Instructor says ”Begin”, all oscillators reset. Then, when B and D both become active, S detects it (i.e. time interval T1) and triggers jumping. Keith L. Downing Circus Circuits