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

A C B E D

From Left Ear From Right Ear

On Far Right On Far Left

Coincidence Detectors: Only fire on 2 coincident inputs Delay Lines Keith L. Downing Circus Circuits

Motion Detectors

Delay Delay Delay 45% line moving left to right

T1 T2 T3 Based on the fly's visual system. Riechard Detector (1961) Neurons thresholded to fire only on multiple, simultaneous inputs Keith L. Downing Circus Circuits

Temporal Differentiation via Delayed Inhibition

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

Temporal Differentiation via Habituation

A dA/dt Excite B habituates to the A(T) input, so it

• nly fires when A(T+d) exceeds A(T).

A(T+d) - A(T) Time A T+d T dA/dt B

Habituation

B Keith L. Downing Circus Circuits

Temporal Differentiation via Synaptic Depression

A dA/dt Excite Synapes from A to dA/dt become temporarily depressed by A activation A(T+d) - A(T) Time A T+d T dA/dt

Synaptic Depression

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

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

Central Pattern Generators for 4-Legged Movement

1/2 3/4 1/4 Phase Differences t1 t3 t4 t2 Walking: Left Rear, Left Front, Right Rear, Right Front

Ian Stewart (1998), Life’s Other Secret, Ch. 9.

Keith L. Downing Circus Circuits

General Gait Generator

Inter-loop connection with delay d2 Intra-loop connection with delay d1 Auxiliary Neuron Left Front Left Rear Right Front Right Rear AL2 AL1 AR2 AR1

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

1/4 3/4 1/2 3/4 1/2 1/4 Walk d1 = 1/4 d2 = 1/2 1/4 1/4 3/4 1/2 3/4 1/2 Jump d1 = 1/4 d2 = 0

Keith L. Downing Circus Circuits

Pacing -vs- Trotting

1/2 1/2 1/2 1/2 Pace d1 = 0 d2 = 1/2 1/2 1/2 1/2 1/2 Trot d1 = 1/2 d2 = 1/2

Keith L. Downing Circus Circuits

Adjustable Delays via Variable Oscillatory Inputs

Right Front Right Rear S1 Delay p1 mV time p2 S2 Shorter delay when S2 is active

Keith L. Downing Circus Circuits

Achieving Delays via Leaky Integration and Firing

Input from Leg Neuron Firing Threshold Input from Oscillator Delay Neuron's Membrane Potential 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.

Time Syllable Duration Syllable Period Sound Wave Peak

Bug Off!

Keith L. Downing Circus Circuits

Anatomy Determines Preferred Syllable Wavelength

Right Ear Left Ear L R d 2d Peak Peak Trough Sound Source

Distance (d) between the ears on the legs should be 1/4

• f syllable wavelength.

This maximizes the pressure differences on the two sides

• f the ear, giving the loudest possible sensation.

Keith L. Downing Circus Circuits

Bang the Drum

Reflected Peak meets Incoming Trough Time = P / 4 Time = P / 2 P = Syllable Period

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.

ANR ANL

Right Eardrum Left Eardrum

MNR

Auditory Neurons Motor Neurons

MNL

Move Left Move Right

Excite Inhibit

Keith L. Downing Circus Circuits

Cricket Top 10 Hits

ANL MNL Robot Moves Left Charge builds up

Decays More builds up Fires!

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

ANL MNL No Movement Charge builds up

Decays Habituation

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.

D C A B T1 T2 T3 T4 1 1 1 1 1 1 1 1 1 A B C D T1 T2 T3 T4 Time Signatures T3 is the time when A and B are firing 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.

D C A B S SNc SNr STN Excite Inhibit Dopamine Cerebral Cortex Striatum

Keith L. Downing Circus Circuits

Temporal Context Learning

D C A B S D C A B S Hebbian Learning Jump Jump

Coincident acitivity of B and D is learned by S, which just happens to be

• n 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