Heinz, G.: Waves on Wires – Introduction to Interference Networks n What "Integrate and Fire"...

Heinz, G.:Heinz, G.: Waves on Wires – Waves on Wires – Introduction to Interference NetworksIntroduction to Interference Networks

What "Integrate and Fire" suggests What "Integrate and Fire" suggests Interference Principle, I.- NetworksInterference Principle, I.- Networks 1D-, 2D-, 3D- Projections1D-, 2D-, 3D- Projections Interference IntegralsInterference Integrals I.-Types: Self-I., Cross-I.I.-Types: Self-I., Cross-I. Self-I. (Zoom, Movement, Somato-t. Maps)Self-I. (Zoom, Movement, Somato-t. Maps) Cross-I. (Spatio-Temporal Maps)Cross-I. (Spatio-Temporal Maps) Mixed S/C (Lashleys rats, I.-overflow)Mixed S/C (Lashleys rats, I.-overflow)

AuthorAuthor:: Dr. Gerd Heinz, GFaI, 12489 BerlinDr. Gerd Heinz, GFaI, 12489 BerlinAlbert-Einstein-Str. 16, Floor 5, Room 12BAlbert-Einstein-Str. 16, Floor 5, Room 12B

www.gfai.de/~heinz www.acoustic-camera.com [email protected]

http://www.gfai.de/~heinz

http://www.acoustic-camera.com/

mailto:[email protected]

22/09/05 Israel Lectures © G. Heinz, www.gfai.de/~heinz 2

HistoryHistory 1992 Introducing velocities and spikes into a (weighted) neural 1992 Introducing velocities and spikes into a (weighted) neural

network I found a symmetry, a network I found a symmetry, a mirror propertymirror property (in -> out map) (in -> out map)

http://www.gfai.de/~heinz/historic/index.htm (slide 9)http://www.gfai.de/~heinz/historic/index.htm (slide 9) 1993 book "Neuronale Interferenzen": new principles and 1993 book "Neuronale Interferenzen": new principles and

properties (zooming, movement, overflow, spatio-temp. maps) properties (zooming, movement, overflow, spatio-temp. maps)

http://http://www.gfai.de/~heinz/publications/NI/index.htmwww.gfai.de/~heinz/publications/NI/index.htm 1994 - 98 Development of simulator '1994 - 98 Development of simulator 'PSI-ToolsPSI-Tools' for simulation ' for simulation

of nets and for nerve- and acoustic experimentsof nets and for nerve- and acoustic experiments To demonstrate the qualities of the approach: acoustic To demonstrate the qualities of the approach: acoustic

images, acoustic movies (images, acoustic movies (1994-96, first in the world1994-96, first in the world)) 1996 introduction of the term 1996 introduction of the term 'interference networks (IN)' 'interference networks (IN)'

characterizing the characterizing the 'physical approach to neural networks (NN)''physical approach to neural networks (NN)' Reason: Very different properties to weighted/pattern- NN'sReason: Very different properties to weighted/pattern- NN's 2004 International market entry with Acoustic Cameras2004 International market entry with Acoustic Cameras 2001, 2003, 2005 Awards for acoustic photo- and 2001, 2003, 2005 Awards for acoustic photo- and

cinematography (www.acoustic-camera.com)cinematography (www.acoustic-camera.com) Extract: http://de.wikipedia.org/wiki/InterferenznetzwerkExtract: http://de.wikipedia.org/wiki/Interferenznetzwerk

http://www.gfai.de/~heinz/publications/NI/index.htm

http://www.gfai.de/~heinz/publications/NI/index.htm

http://www.gfai.de/~heinz/historic/hardware/psi.hlp


Abstraction “Interference Networks”Abstraction “Interference Networks”

Term 'interference': superimposition of wavesTerm 'interference': superimposition of waves Discrete Discrete 'waves on wires''waves on wires' Spherical, Spherical, 3-dimensional architecture3-dimensional architecture Moving time functions (spikes) f(t-Moving time functions (spikes) f(t-))

– spike-duration (geom. pulse length)spike-duration (geom. pulse length)– refractory behaviour (pause)refractory behaviour (pause)

Branch-delays (and -velocities)Branch-delays (and -velocities) Connectivity (spines, synapses)Connectivity (spines, synapses) Overlay operations (add, multiply…)Overlay operations (add, multiply…)

Computational problem: Computational problem: high number of brancheshigh number of branches

branchbranch


Central Question: Relativity of Wave Central Question: Relativity of Wave LengthLength Spikes move slowly through nerve system [2 µm/s … 120 Spikes move slowly through nerve system [2 µm/s … 120

m/s]m/s] Spikes have a limited (geometric) size [µm … cm]Spikes have a limited (geometric) size [µm … cm] Velocity v, pulse duration T, grid g, geometrical wavelength s Velocity v, pulse duration T, grid g, geometrical wavelength s

= v = v .. T T

s s g g Interference networkInterference network

s >> gs >> g Pool of neurons (NN.)Pool of neurons (NN.)

s [µm]s [µm]

g [µm] g [µm]

Which proportion is Which proportion is truth?truth?

Which grid is addressed?Which grid is addressed?• Spines?Spines?• Cell bodies?Cell bodies?• Columns?Columns?• It depends?It depends?


What "Integrate and Fire" suggestsWhat "Integrate and Fire" suggests

„„The probability to excite a neuron is higher as more The probability to excite a neuron is higher as more closed the partial impulses can reach it“ closed the partial impulses can reach it“ (Heinz, NI, 1993)(Heinz, NI, 1993)

random: no excitement synchronous: random: no excitement synchronous: firefire


Projection Law Projection Law (Heinz'93)(Heinz'93) Waves need to be at the detecting place at the same Waves need to be at the detecting place at the same

timetime

Self interference conditionSelf interference condition (all paths): (all paths): … …

Velocities and path length can be different, but delays Velocities and path length can be different, but delays can notcan not

Applied into optics, GPS, acoustic camera, dig. filter Applied into optics, GPS, acoustic camera, dig. filter theorytheory

Different to classic approaches (Fermat, Huygens … Different to classic approaches (Fermat, Huygens … Feynman) Feynman)

http://www.gfai.de/~heinz/publications/papers/1994_SAMS.pdf



Classic Beam-Approach of OpticsClassic Beam-Approach of Optics

Light way (beam) defined by a Light way (beam) defined by a minimum of a path minimum of a path integralintegral (Fermat, Huygens, Maupertuis, Newton, Euler, (Fermat, Huygens, Maupertuis, Newton, Euler, Lagrange, Hamilton, Leibniz, Jacobi, Helmholtz, Maxwell, Lagrange, Hamilton, Leibniz, Jacobi, Helmholtz, Maxwell, Heisenberg, Schrödinger, Feynman)Heisenberg, Schrödinger, Feynman)

Fermat: Minimum principle, shortest way of lightFermat: Minimum principle, shortest way of light Huygens, Huygens, Maupertuis: smallest action, waveMaupertuis: smallest action, wave theory theory

dtqqLdsmvSq

q

q

q

)',( 2

1

2

1

qq22

qq11

q(t)q(t)

Lagrange function = (T-V); T kinetic, V potential energyLagrange function = (T-V); T kinetic, V potential energy

(compare H. Lübbig 1998, W. Kuhn 2001)(compare H. Lübbig 1998, W. Kuhn 2001)

waterwater

airair

min. pathmin. path


drawing: d. doebler

The Forgotten Symmetry:The Forgotten Symmetry:First Inter-Medial Interference CircuitFirst Inter-Medial Interference Circuit

Tyto albaTyto alba

Sound localization model based on: Jeffres L. A.: A place theory of sound localization. J. Comp. Physiol. Psychol. 41 [1948]: 35-39

symmetry line: mirror symmetry line: mirror right

left

http://www.gfai.de/~heinz/historic/intro/intro.htm


1-dimensional Interference 1-dimensional Interference Projection Projection ((Heinz 1992)Heinz 1992)

Signals meet at Signals meet at locations with identical locations with identical delays from source delays from source (self-interference)(self-interference)

(all other cases not (all other cases not drawn)drawn)

Specific neurons begin Specific neurons begin to communicateto communicate

Address relations Address relations between locations between locations given by delaysgiven by delays

Time codes locationTime codes locationSingle point observations Single point observations look like density look like density modulated signals or modulated signals or bursts?bursts?


3-dim. Interference Projection3-dim. Interference Projection

Considered Considered generating and generating and detecting fieldsdetecting fields

Which properties Which properties exist between exist between generating and generating and detecting detecting locations?locations?


3-dim. Interference Projection3-dim. Interference Projection

Considered Considered generating and generating and detecting fieldsdetecting fields

Which properties Which properties exist between exist between generating and generating and detecting detecting locations?locations?

To find answers To find answers we arrange the we arrange the spiking neuronsspiking neurons

Mirrored Mirrored projection projection appears as appears as "interference "interference integral" integral"

Image Image conjunction!conjunction!


pixel grid = pixel grid = neurons neurons gridgrid

Understanding the Wave AbstractionUnderstanding the Wave Abstraction Each neuron has different delays to source pointsEach neuron has different delays to source points For didactic purposes we use some abstractions: For didactic purposes we use some abstractions:

– homogeneous velocityhomogeneous velocity– equidistant neurons (as pixels of an image)equidistant neurons (as pixels of an image)

Detecting field is a bitmap of pixels (symbolizing Detecting field is a bitmap of pixels (symbolizing neurons)neurons)

pixelpixel

x

y

z

neuroneneurone

33

2211

3d- source 3d- source pointspoints


Understanding Gen.- and Det.- MasksUnderstanding Gen.- and Det.- Masks Each locations has its own time scheme, has its own mask Each locations has its own time scheme, has its own mask

Mask of a locationMask of a location

Inverse MaskInverse Mask


2-dim. Wave Field Simulation2-dim. Wave Field Simulation If we consider all possible paths, any emission is If we consider all possible paths, any emission is

on a circle of delay on a circle of delay around any source: we call around any source: we call it 'wave'it 'wave'

I² are composed of waves I² are composed of waves Didactic suggestions: Didactic suggestions:

– homogeneous wave expansionhomogeneous wave expansion– Linear superimposition (?!)Linear superimposition (?!)

Interference integral over Interference integral over the whole wave field:the whole wave field:

Wave fieldWave field(pixels symbolize neurons)(pixels symbolize neurons)

30 channel simulation (Hz 1995)30 channel simulation (Hz 1995)


QuotationQuotation

"Your "Your file gfai_30_.avi (file gfai_30_.avi (GFaI-movie) reminds me of a GFaI-movie) reminds me of a trapped wave packet scattered inside a chamber. It also trapped wave packet scattered inside a chamber. It also reminds me of ray tracing inside an inhomogeneous reminds me of ray tracing inside an inhomogeneous wave duct where one can compute the wave wave duct where one can compute the wave trajectories using Snell's law. trajectories using Snell's law. So I understand that So I understand that interference effects can be computed using geometry interference effects can be computed using geometry (the propagation path as a function of space and time) (the propagation path as a function of space and time) instead of wave mechanics.instead of wave mechanics. Feynman used the path Feynman used the path integral approach to build up a sum of probabilities for integral approach to build up a sum of probabilities for quantum trajectories instead of using the Schrodinger quantum trajectories instead of using the Schrodinger wave equation." wave equation."

Glenn Takanishi, Glenn Takanishi, www.neuralmachines.comwww.neuralmachines.com (Hawai) (Hawai)

http://www.neuralmachines.com/


A Detailed Look to Interference of Discrete A Detailed Look to Interference of Discrete WavesWaves

Excitement values becomes Excitement values becomes maximized at locations, where maximized at locations, where most waves meet most waves meet

Not all, only some placesNot all, only some places have a chance to be excitedhave a chance to be excited

Timing codes the location of Timing codes the location of possibilitiespossibilities

Image pixels Image pixels seen as seen as

nerve cells nerve cells with with

connectionsconnections

Homogeneous wave velocity and space Homogeneous wave velocity and space for demonstration only (neuro-pile)for demonstration only (neuro-pile)


Self- /Cross- Interference RelationsSelf- /Cross- Interference Relations

• Waves meet itself -> Waves meet itself -> self-interferenceself-interference: wave i with i with i …: wave i with i with i …

• Waves meet other waves -> Waves meet other waves -> cross-interferencecross-interference: wave i with : wave i with i-1 …i-1 …

(i, i, i, i) (i, i, i, i)

self-interference self-interference locationlocation

(i, i, i, i)(i, i, i, i)

self-int.self-int.

(i, 0, i-1, i) (i, 0, i-1, i)

cross-int. locationcross-int. location

(1)(1)

(3)(3)

(2)(2)

(4)(4)

cross-cross-interference interference

distancedistance


2-dim. Waves on Squids2-dim. Waves on Squids

Andrews squid-experiments (1995) show moving Andrews squid-experiments (1995) show moving excitations between chromatophore-cellsexcitations between chromatophore-cells

Cells are connected via a nerve-like structureCells are connected via a nerve-like structure Excitation and relaxation can produce wavesExcitation and relaxation can produce waves Time functions appear Time functions appear

comparable to nervecomparable to nerve Although the mechanism is Although the mechanism is

not exactly known, the effect not exactly known, the effect needs a wave-interference needs a wave-interference descriptiondescription

http://http://www.gfai.de/~heinz/historic/biomodel/squids/squids.htmwww.gfai.de/~heinz/historic/biomodel/squids/squids.htm

Circular waveCircular wave

http://www.gfai.de/~heinz/historic/biomodel/squids/squids.htm



Local InteractionLocal Interaction

Waves delete in the Waves delete in the refractoriness zone refractoriness zone 'cleaning waves''cleaning waves'

Analogy to Analogy to frogs sciatic-nerve experiments frogs sciatic-nerve experiments (Ischias)(Ischias)

Refractory distance >> field Refractory distance >> field size size

http://http://www.gfai.de/~heinz/historic/biomodel/squids/squids.htmwww.gfai.de/~heinz/historic/biomodel/squids/squids.htm

"cleaning" waves on squids (AP, 1995)"cleaning" waves on squids (AP, 1995)

Global,Global,linearlinear

Local, Local, non-linearnon-linear

"cleaning" waves in 2-dim. simulation"cleaning" waves in 2-dim. simulation

http://www.gfai.de/~heinz/publications/papers/2004_BICS.pdf

http://www.gfai.de/~heinz/publications/NI/KA06.pdf




Interference Integrals (Interference Integrals (SelfSelf-I-I., Visual., Visual Maps)Maps)

Long time-integration pulls up Long time-integration pulls up the energy of wave-hit-the energy of wave-hit-locations (self interference locations (self interference locations)locations)

Source arrangement defines Source arrangement defines the mapsthe maps

Maps can be conjunctive Maps can be conjunctive (g+h)(g+h)

Detecting fieldsDetecting fields

Generating fields (g+h)Generating fields (g+h)

time function plottime function plot

Summary Chapter "Self Summary Chapter "Self Interference"Interference"

• Self interference increases the excitability of a neuronSelf interference increases the excitability of a neuron• Self interference properties define 'mirrored projections'Self interference properties define 'mirrored projections'• The term 'wave' abstracts a two- or higher dimensional The term 'wave' abstracts a two- or higher dimensional

movement of many spikes through any delaying spacemovement of many spikes through any delaying space• It is not possible to interpret anything, if we observe only It is not possible to interpret anything, if we observe only

one channel of a projectionone channel of a projection• Timing defines the location: Only wave addressed neurons Timing defines the location: Only wave addressed neurons

can learncan learn• Self interference is very sensitive against any parameter Self interference is very sensitive against any parameter

drift, circuits need auto-control and regulation drift, circuits need auto-control and regulation (-> Hebb's rule in a different light)(-> Hebb's rule in a different light)

• Local superimposition needs 'cleaning waves' before any Local superimposition needs 'cleaning waves' before any neuron can be addressedneuron can be addressed


CrossCross-Interference-Interference

All channels with identical time All channels with identical time functionsfunctions

Cross interference distance: Cross interference distance: ds = v dt = v / f ds = v dt = v / f with f = 1/dtwith f = 1/dt

"Spatio-temporal coding", temporal "Spatio-temporal coding", temporal mapsmaps

Huygens double split Huygens double split experiment for neurons (NI 1993):experiment for neurons (NI 1993):

Heinz 1993

Heinz 1993

(i, i, i, … i) self-(i, i, i, … i) self-interference interference

locationlocation

(i, i+1, i-1 … ) (i, i+1, i-1 … ) cross-interference cross-interference locations (around)locations (around)


Cross-Int. Integrals: "Spatio-Temporal Cross-Int. Integrals: "Spatio-Temporal Maps"Maps" Cross interference defines all temporal mapsCross interference defines all temporal maps We consider identical, periodical fire on all channelsWe consider identical, periodical fire on all channels Cross interference is maximum for two channels Cross interference is maximum for two channels

-> which channel number has the-> which channel number has the auditory system? Only two? auditory system? Only two?

We like 'harmony' in soundWe like 'harmony' in sound 'Harmonies' address similar points'Harmonies' address similar points


Summary "Frequency Maps"Summary "Frequency Maps" Cross interference defines all temporal mapsCross interference defines all temporal maps Increasing channel number (2…8) reduces cross interference Increasing channel number (2…8) reduces cross interference

intensity (due to over-conditioning)intensity (due to over-conditioning)

Heinz 1996

(i, i, i, … i) self-(i, i, i, … i) self-interference interference

locationslocations

cross-interference cross-interference locations aroundlocations around


LashleyLashley was looking his life long for the locality of items was looking his life long for the locality of items learned (1920 … 1950) learned (1920 … 1950)

Rats became teached a way through a labyrinth. He Rats became teached a way through a labyrinth. He removed systematically small parts of the brain and removed systematically small parts of the brain and proved the before learnedproved the before learned

Summary of his experiments: Summary of his experiments: The series of experiments ... The series of experiments ...

“has discovered nothing “has discovered nothing directly of the real nature directly of the real nature of the engram“of the engram“

Interpretation: Interpretation: Cross interferences look like Cross interferences look like

self interferences (!)self interferences (!) "Tutographic" brain, if it "Tutographic" brain, if it

is an interference systemis an interference system We can not avoid the dualityWe can not avoid the duality

Self- and Cross- Interference InteractionSelf- and Cross- Interference Interaction

Region of cross-interferences aroundRegion of cross-interferences around

Region of self-interferenceRegion of self-interference

3-channel Simulation3-channel Simulation


1-dim. Delay Shifter Modulates Wave 1-dim. Delay Shifter Modulates Wave FrontFront

Variation of relative delay changes wave directionVariation of relative delay changes wave direction Glia can modulate the velocity of nervesGlia can modulate the velocity of nerves

http://www.gfai.de/~heinz/publications/NI/KA04.pdfhttp://www.gfai.de/~heinz/publications/NI/KA04.pdf



Delay Shift Moves IntegralsDelay Shift Moves Integrals

Variation of delay of one channel produces a moving Variation of delay of one channel produces a moving interference integral (glia potential influences speed & interference integral (glia potential influences speed & location)location)


1-dim. Velocity Variation Modifies the Size1-dim. Velocity Variation Modifies the Size

Variation of velocity (Variation of velocity (v, v' v, v' ) influences the size of a ) influences the size of a projectionprojection

http://www.gfai.de/~heinz/publications/NI/KA04.pdfhttp://www.gfai.de/~heinz/publications/NI/KA04.pdf



Velocity Variation Zooms IntegralsVelocity Variation Zooms Integrals Variation of background velocity in the detecting field Variation of background velocity in the detecting field

zooms the interference integrals (neuroglia)zooms the interference integrals (neuroglia) Cross interferences appear for low velocitiesCross interferences appear for low velocities


A Closer Look to Memory DensityA Closer Look to Memory Density

As slower is the velocity in the detecting field, as As slower is the velocity in the detecting field, as smaller is the addressable region, as higher is the smaller is the addressable region, as higher is the density and the addressable memory volumedensity and the addressable memory volume

If we ask "How do you do?", we get different answers:If we ask "How do you do?", we get different answers:– Professor: (pause) "ohhhh" (pause) "don't know?"Professor: (pause) "ohhhh" (pause) "don't know?"– Tennis profi: "Oh fine, I won the mastership!"Tennis profi: "Oh fine, I won the mastership!"

Who is who?Who is who?

v = 50 [mm/s]v = 50 [mm/s]v = 10 [mm/s]v = 10 [mm/s]

22/09/05 Israel Lectures © G. Heinz, www.gfai.de/~heinz 31Heinz 1993

Zooming & Movement for Pattern Zooming & Movement for Pattern MatchingMatching

To recognize a person or face, we have to "scale" the To recognize a person or face, we have to "scale" the image to the same size and position (zooming and image to the same size and position (zooming and movement)movement)

Our eyes have no optical zoomOur eyes have no optical zoom Adoption with electronic scaling? path: Adoption with electronic scaling? path: retina to visual retina to visual

cortexcortex?? (Comparable task for somato-topic projections in (Comparable task for somato-topic projections in

Homunculus)Homunculus)

++ == ??

++ == match!match!


Rule of Fire RateRule of Fire Rate

Cross interference Cross interference pattern depends on pattern depends on channel number & channel number & refractory periodrefractory period

We increase the We increase the average fire rate average fire rate (reduced cross-(reduced cross-interference distance) interference distance)

Field overflow occurs: Field overflow occurs: Cross interference Cross interference overflows the self-overflows the self-interf.,interf.,loss of information!loss of information!

Hypothesis: if pain is Hypothesis: if pain is cross interference cross interference overflow, then this overflow, then this simple interference simple interference circuit models that circuit models that behaviourbehaviour

~ 7,5 ms~ 7,5 ms

~ 5 ms~ 5 ms

~ 4 ms~ 4 ms

~ 1,5 ms~ 1,5 ms


"Interference integral" = integration of time "Interference integral" = integration of time function of each location over timefunction of each location over time

1.1. Self-interference properties defineSelf-interference properties define– Somato-topic maps (mirrored projections)Somato-topic maps (mirrored projections)– Noise location (owl, dolphin) Noise location (owl, dolphin) – Optical pictures, Acoustic CameraOptical pictures, Acoustic Camera– Scaling (zoom, movement)Scaling (zoom, movement)

2.2. Cross-interference properties define Cross-interference properties define – Frequency maps Frequency maps – Code and behavior mapsCode and behavior maps– Pain?Pain?

Summary: Spatio-Temporal Maps Summary: Spatio-Temporal Maps (Self- and Cross Interference Integrals)(Self- and Cross Interference Integrals)


Analogy to Filter TheoryAnalogy to Filter Theory

Neuron changes from a simple Neuron changes from a simple threshold gate to a digital filter threshold gate to a digital filter circuitcircuit

Direct translation into digital Direct translation into digital filter structure is possiblefilter structure is possible

Distributed wire with delayDistributed wire with delay Electrical node (!)Electrical node (!)

It’s a digital filter circuit!It’s a digital filter circuit!

Applications & ResearchApplications & Research







Applied Interference SystemsApplied Interference Systems Radar (electric waves)Radar (electric waves) Optics (electric waves)Optics (electric waves) Sonar (acoustic waves)Sonar (acoustic waves) Acoustic cameras (ac. waves)Acoustic cameras (ac. waves) Digital filter theory (!)Digital filter theory (!) Digital logic (computers)Digital logic (computers) Pattern- and Weight-NetsPattern- and Weight-Nets

(Neuronal Networks)(Neuronal Networks) Fuzzy logicFuzzy logic Global Positioning by SatellitesGlobal Positioning by Satellites Cell phone carrier multiplexCell phone carrier multiplex Interferential bio-interaction (brain memory extension …)Interferential bio-interaction (brain memory extension …) Integral Transformations (!): convolution, correlation, FFT…Integral Transformations (!): convolution, correlation, FFT…

… … only the type of time function changes only the type of time function changes (floating/integer/binary)(floating/integer/binary)


Bio-Neuro-ResearchBio-Neuro-Research Data addressing Data addressing

– Refractoriness and bidirectional exchangeRefractoriness and bidirectional exchange– Geometrical wave lengthGeometrical wave length– Cleaning waves (non-linear superimposition)Cleaning waves (non-linear superimposition)

Data processing Data processing

– Temporal correspondence of arrangementsTemporal correspondence of arrangements– Data compression & segmentationData compression & segmentation– Interference learning, self-organisationInterference learning, self-organisation

Spatial projectivitySpatial projectivity

– High channel numbers? Field size contra channel numberHigh channel numbers? Field size contra channel number Cross-interference properties (temporal selectivity)Cross-interference properties (temporal selectivity)

– Creating behaviourCreating behaviour– Relations between net geometry and behaviourRelations between net geometry and behaviour

Technical Applications Technical Applications

– Wave cameras: acoustic, electric, ultrasonicWave cameras: acoustic, electric, ultrasonic– Mobile cell phone netsMobile cell phone nets– Space-Time FiltersSpace-Time Filters


Homepage Homepage http://www.acoustic-camera.com/http://www.acoustic-camera.com/

microphone array (32 mics) data recorder notebook

• Vacuum cleanerVacuum cleaner

• Sports carSports car

• Needle printerNeedle printer

Application Acoustic CameraApplication Acoustic Camera


ConclusionConclusion

We considered nerve nets to be discrete wave We considered nerve nets to be discrete wave interference networksinterference networks

An amazing amount of new questions, An amazing amount of new questions, possibilities and directions appearpossibilities and directions appear

Interdisciplinary co-operation can accelerate Interdisciplinary co-operation can accelerate findingsfindings

Thanks for your attention!Thanks for your attention!


[email protected] www.gfai.de/~heinz www.acoustic-camera.com

Hyperbolic projection

16-chnl. pulse waves





Related LinksRelated Links

HomepageHomepage

http://www.gfai.de/~heinz/http://www.gfai.de/~heinz/

Publication-DirectoryPublication-Directory

http://www.gfai.de/~heinz/publications/index.htmhttp://www.gfai.de/~heinz/publications/index.htm

HistoricalHistorical

http://www.gfai.de/~heinz/historic/index.htmhttp://www.gfai.de/~heinz/historic/index.htm

Acoustic CameraAcoustic Camera

http://www.acoustic-camera.comhttp://www.acoustic-camera.com

„„Die Wahrheit triumphiert Die Wahrheit triumphiert nie, ihre Gegner sterben nur nie, ihre Gegner sterben nur

ausaus““

Max PlanckMax Planck

http://www.gfai.de/~heinz/

http://www.gfai.de/~heinz/publications/index.htm

http://www.gfai.de/~heinz/historic/index.htm


ThanksThanks

Thanks to Benny Hochner (Hebrew Univ. Jerusalem), Tamar Thanks to Benny Hochner (Hebrew Univ. Jerusalem), Tamar Flash (Weizmann Inst. Rehovot) and Mosche Abeles (Bar-Ilan Flash (Weizmann Inst. Rehovot) and Mosche Abeles (Bar-Ilan Univ. Ramat Gan) for invitation, talks and discussions. Univ. Ramat Gan) for invitation, talks and discussions.

Thanks to my wife Gudrun. She helped me over years of Thanks to my wife Gudrun. She helped me over years of missing acknowledgements without doubt.missing acknowledgements without doubt.

Israel 27.9.-6.10.2005Israel 27.9.-6.10.2005

Gerd HeinzGerd Heinz






More TheoryMore Theory

Add on'sAdd on's







Interference Conditions in DetailInterference Conditions in Detail

Generating Mask M, detecting (inverse) Mask M* M + Generating Mask M, detecting (inverse) Mask M* M + M* = TM* = T„all ways have the same delay" (Hz'93)„all ways have the same delay" (Hz'93)

Cross interference: Cross interference: „… plus /minus foregoer/follower"„… plus /minus foregoer/follower"


Understanding BurstsUnderstanding Bursts

Circuit (a)Circuit (a)

Burst generation Burst generation with low bias (b)with low bias (b)

Code detection Code detection with high bias (c)with high bias (c)

Data addressing Data addressing possibility ->possibility ->

ExampleExample


Summary: New Elementary Functions of Summary: New Elementary Functions of NeuronNeuron Code generation Code generation Code detection Code detection Data addressing Data addressing Neighborhood inhibition (for identical neurons) Neighborhood inhibition (for identical neurons) Level generation (spike duration > refractoriness zone)Level generation (spike duration > refractoriness zone)

http://www.gfai.de/~heinz/historic/biomodel/models.htm#burstshttp://www.gfai.de/~heinz/historic/biomodel/models.htm#bursts

http://www.gfai.de/~heinz/publications/papers/2002_NF.pdfhttp://www.gfai.de/~heinz/publications/papers/2002_NF.pdf

Sources:Sources:

• NI 1993NI 1993

• SAMS 1994SAMS 1994

• BioNet 1996BioNet 1996

http://www.gfai.de/~heinz/historic/biomodel/models.htm#bursts

http://www.gfai.de/~heinz/publications/papers/2002_NF.pdf


Inhomogenity and Over-ConditioningInhomogenity and Over-Conditioning

A one-dimensional projection needs two channelsA one-dimensional projection needs two channels A two-dimensional projection needs three channelsA two-dimensional projection needs three channels (the system is called 'over-conditioned', if more channels (the system is called 'over-conditioned', if more channels

match)match)

. . .. . . For a n dimensional projection d we need n+1 channelsFor a n dimensional projection d we need n+1 channels

d = n+1d = n+1

How to realize high dimensions?How to realize high dimensions?– Distorted, folded spaceDistorted, folded space– Diameter (velocity) variation of dendritesDiameter (velocity) variation of dendrites– Non-linear wiringNon-linear wiring

-> Inhomogeneous delay-spaces-> Inhomogeneous delay-spaces

http://www.gfai.de/~heinz/publications/papers/2002_NF.pdfhttp://www.gfai.de/~heinz/publications/papers/2002_NF.pdf

http://www.gfai.de/~heinz/publications/papers/2002_NF.pdf


Circuit DrawingsCircuit Drawings

The way to draw circuits for The way to draw circuits for space and time: intrinsic space and time: intrinsic delaydelay

Wires are not nodesWires are not nodes!!!!!! General: limited velocityGeneral: limited velocity

Distributed wires with delayDistributed wires with delay


Colored Interference SystemsColored Interference Systems Nerves diameter vary, different carrier mechanismsNerves diameter vary, different carrier mechanisms Waves can meetWaves can meet


Scene Representation andScene Representation andInformation ReductionInformation Reduction Delay learning can compose single Delay learning can compose single

points, representing whole scenespoints, representing whole scenes Example: 30 neurons "GH" can be Example: 30 neurons "GH" can be

represented using only 3 represented using only 3 interference locations interference locations

Source 16-chnl. destination


Overlays of I²Overlays of I²

Axial (different generators and/or detectors on one Axial (different generators and/or detectors on one 'bus')'bus')

Radial (the delay geometry stays identical by add. of +/- Radial (the delay geometry stays identical by add. of +/- ))

http://www.gfai.de/~heinz/publications/papers/1994_SAMS.pdfhttp://www.gfai.de/~heinz/publications/papers/1994_SAMS.pdf



Permutation and Decomposition of ScenesPermutation and Decomposition of Scenes Down: high dim. scenes can be decomposed to lower Down: high dim. scenes can be decomposed to lower

dimensionsdimensions Up: low dim. scenes can create higher dim. scenes using Up: low dim. scenes can create higher dim. scenes using

hyperbolic image overlays (without synchronization)hyperbolic image overlays (without synchronization) Examples: Examples:

– Down: P1234 decomposes in P12, P23, P34, P41, P123, Down: P1234 decomposes in P12, P23, P34, P41, P123, … P412… P412

– Up: P12, P23, P34, P41 compose independent hyp. Up: P12, P23, P34, P41 compose independent hyp. projectionsprojections

Information reductionInformation reduction A complex scene canA complex scene can

be stored by (the be stored by (the position) of one position) of one neuronneuron

"Complex neurons""Complex neurons" Neurons create Neurons create

behaviorbehavior


Projection contra ReconstructionProjection contra Reconstruction

Natural time runs only in one Natural time runs only in one direction:direction:– ProjectionProjection– Mirror property (!)Mirror property (!)

Computer time can run back Computer time can run back – ReconstructionReconstruction– Non-mirrored (!)Non-mirrored (!)– For technical purposes (AK)For technical purposes (AK)– Pseudo-wave-field problemPseudo-wave-field problem

the direction of time axis the direction of time axis defines the difference between defines the difference between themthem

ReconstructionReconstruction

ProjectionProjection


Heinz Interference TransformationHeinz Interference Transformation


We have to live with a We have to live with a small number of small number of channelschannels

Any time-function Any time-function recorded by a sensor recorded by a sensor (microphone, (microphone, electrode) has lost the electrode) has lost the wave-field informationwave-field information

In reconstruction it In reconstruction it produces a new wave produces a new wave field (secondary wave field (secondary wave field)field)

This is complete This is complete different to the original different to the original wave fieldwave field

But we have to work But we have to work with!with!

Secondary Wave FieldSecondary Wave Field

Original Wave FieldOriginal Wave Field

Recording Sensor

Emission

Understanding Primary and Secondary Wave Understanding Primary and Secondary Wave FieldsFields

x

z

y


SourceSource

wave-frontwave-front

wave-backwave-back

Virtual Waves (I.-Reconstruction) Virtual Waves (I.-Reconstruction)

332211pos. direction of timepos. direction of time

Orig. WFOrig. WF

P‘

3322

11pos. timepos. time

Sec. WFSec. WF Recording Recording

channels come out channels come out of the sensors -> of the sensors -> spherical wavesspherical waves

Time flow shows Time flow shows waves with wave-waves with wave-front direction to front direction to the center! the center! (Hz'96)(Hz'96)

Example of secondary wave field Example of secondary wave field with inverted waveswith inverted waves


Time across SpaceTime across Space

ProjectionProjection: continuous time: continuous time interference integral interference integral

appears appears mirroredmirrored

ReconstructionReconstruction: inverse : inverse timetime

Interference integral Interference integral appears appears non-mirrorednon-mirrored

dT

dT

dT

templateMirrored projection

Primary field

Secondary fieldInterference Projection f(t-T)

template

Interference Reconstruction f(t+T)

Inverse time

Optical lense systems, SonarOptical lense systems, Sonar Nerve systems (!)Nerve systems (!) Beamformíng with delay elementsBeamformíng with delay elements

Fink "Time Reversal Mirrors"Fink "Time Reversal Mirrors" Acoustic CameraAcoustic Camera

Max. delayMax. delay


CalculationCalculation

Interference- Interference- Transformation (HIT)Transformation (HIT)

"Interference Projection" "Interference Projection" published in BioNet‘96published in BioNet‘96

First acoustic image First acoustic image 1994 used the 1994 used the Interference-Interference-Transformation (HIT) as Transformation (HIT) as "reconstruction" (not "reconstruction" (not published)published)

http://www.gfai.de/~heinz/publications/papers/http://www.gfai.de/~heinz/publications/papers/1996_Bionet.pdf1996_Bionet.pdf

Bio-ModelsBio-Models







Heinz93 Source: Heinz, Neuronale Interferenzen 1993

A Wave Model for Penfields Homunculus...A Wave Model for Penfields Homunculus... A hyperbola defines a fixed delay difference to two A hyperbola defines a fixed delay difference to two

points F, F' points F, F' Different hyperbolas define different delay differences Different hyperbolas define different delay differences

a/a', c/c'a/a', c/c' Pulses meet at different locations, see drawingPulses meet at different locations, see drawing (Self-I. location is defined by wave front direction)(Self-I. location is defined by wave front direction)


Thumb ExperimentThumb Experiment Waves can be inspected with Waves can be inspected with

NLGNLG We find moving body projectionsWe find moving body projections Orthogonal arrangements?Orthogonal arrangements?

Interpretation:Interpretation:

Arrangement:Arrangement: Result:Result:


Homunculus and the Thumb ExperimentHomunculus and the Thumb Experiment Motion moves projections Motion moves projections

dependent of position, see thumb dependent of position, see thumb experimentexperiment

Ganglion spinale creates a Ganglion spinale creates a hyperbolic projection into hyperbolic projection into medulla spinalismedulla spinalis

So the movement is So the movement is compensated, thumb position compensated, thumb position (up/down) does not influence (up/down) does not influence homunculus positionhomunculus position

-> Nerve system needs -> Nerve system needs 'normalized' or scaled maps – 'normalized' or scaled maps – free of body distortionsfree of body distortions

Penfield's "Homunculus" seems Penfield's "Homunculus" seems to be a scaled projectionto be a scaled projection

Shift of somato-topic maps can Shift of somato-topic maps can be compensatedbe compensated– Sensory mapsSensory maps– Motor mapsMotor maps


Visual CortexVisual Cortex

Waves define the direction Waves define the direction of self interference locationof self interference location

Supposed, nerve bundles Supposed, nerve bundles have comparable delayshave comparable delays

Self interference location Self interference location appear, where wave appear, where wave direction and screen have direction and screen have identical orientationidentical orientation

Scale-normalization of Scale-normalization of images needs zooming and images needs zooming and movementmovement

Visual cortex as a Visual cortex as a normalized wave field normalized wave field screen?screen?

Heinz 1993


Interference Circuit ExamplesInterference Circuit Examples

To detect scenes or To detect scenes or frequencies or codes, to frequencies or codes, to control bodies, to create control bodies, to create behaviour…behaviour…


Bi-directional: Singers Synchronization?Bi-directional: Singers Synchronization? Using micro-electrodes, Using micro-electrodes,

Wolf Singer found 1986 Wolf Singer found 1986 a deep tone in cats a deep tone in cats cortexcortex

Has he found an Has he found an interferential wave interferential wave projection?projection?

To "hold" a projection To "hold" a projection for some time (learn for some time (learn phase), we need a phase), we need a repetition?repetition?

observationobservation

Heinz, G.: Waves on Wires – Introduction to Interference Networks n What "Integrate and Fire"...

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