Heinz, G.: Wave Interference Networks - State of Research Historical Remarks Historical Remarks Time...

Heinz, G.:Heinz, G.: Wave Interference Networks - Wave Interference Networks - State of ResearchState of Research

Historical RemarksHistorical Remarks Time codes SpaceTime codes Space Integral TransformationsIntegral Transformations Application Acoustic CameraApplication Acoustic Camera Interference Projections & I.-IntegralsInterference Projections & I.-Integrals Properties: Properties:

– Self-I. (Zoom, Movement, Somato-t. Maps)Self-I. (Zoom, Movement, Somato-t. Maps)– Cross-I. (Spatio-Temporal Maps)Cross-I. (Spatio-Temporal Maps)– Holomorphic Maps (Lashleys Rats, I.-Overflow)…Holomorphic Maps (Lashleys Rats, I.-Overflow)…

Modelling the Brains Labyrinth, Fodele Beach Crete, 23.-Modelling the Brains Labyrinth, Fodele Beach Crete, 23.-27.9.200627.9.2006

www.gfai.de/~heinz [email protected]

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

mailto:[email protected]

26/09/06 © G. Heinz, www.gfai.de/~heinz 2

MotivationMotivation

Human brain has about Human brain has about 10101010 - 10 - 101111 neurons neurons Any neuron is typically connected with 1,000 to 10,000 Any neuron is typically connected with 1,000 to 10,000

others others Unthinkable amount of connectivityUnthinkable amount of connectivity Neurons communicate using time functions – small pulses Neurons communicate using time functions – small pulses

with geometrical wavelength in the range between 50µm with geometrical wavelength in the range between 50µm and 12mm*and 12mm*

Dependent of thickness, time functions flow slowly: µm/s Dependent of thickness, time functions flow slowly: µm/s … m/s… m/s

Excitements appear, Excitements appear, wherewhere lots of pulses meet lots of pulses meet To analyze a net, we have to ask only for possible places To analyze a net, we have to ask only for possible places

of of interferenceinterference of pulses (ionic, electric, molecular) of pulses (ionic, electric, molecular) Time functions can mathematically be expressed as Time functions can mathematically be expressed as

waveswaves

-> Wave interference network research on inhomogeneous -> Wave interference network research on inhomogeneous netsnets

*see www.gfai.de/~heinz/publications/papers/1994_IWK.pdf*see www.gfai.de/~heinz/publications/papers/1994_IWK.pdf


Great Interference IdeasGreat Interference Ideas


Great Ideas …Great Ideas …

ProjectionProjection: continuous time: continuous time interference integral appears interference integral appears

mirroredmirrored

ReconstructionReconstruction: inverse time: inverse time Interference integral appears Interference integral appears

non-mirrorednon-mirrored

dT

dT

dT

VorlageMirrored projection

Primary field

Secondary fieldInterference Projection

Vorlage

Interference Reconstruction

non-mirrored

Optical lense systems, Sonar Beamformíng with delay elements

Fink "Time Reversal Mirrors" Heinz "Acoustic Camera"

maximum delaymaximum delay

lenselense


Supersonic ArraysSupersonic Arrays

A, B, M – MethodsA, B, M – Methods Beam forming (ABF)Beam forming (ABF)


GPSGPS

The ultimative The ultimative space-time space-time solutionsolution


Radio TelescopesRadio Telescopes

Two directions:Two directions:– Superimposition of Superimposition of

I² (images) - VLAI² (images) - VLA– Superimposition of Superimposition of

time functions - time functions - SKASKA

Very Large Array (VLA)Very Large Array (VLA)

Superimposition of I² Superimposition of I² (images) to minimize (images) to minimize noisenoise


Square Square Kilometer Kilometer Array (SKA)Array (SKA)

Superimposition of Superimposition of time functionstime functions


WLAN-TransceiverWLAN-Transceiver

Digital filtersDigital filters TimingTiming Signal-ProcessingSignal-Processing


Outstanding ideas about interference, beyond:Outstanding ideas about interference, beyond:– Lloyd A. Jeffress 1947Lloyd A. Jeffress 1947 Place theory of sound Place theory of sound

localizationlocalization– David Bohm/Karl Pribram 1973 ff David Bohm/Karl Pribram 1973 ff Holomorphic Holomorphic

memorymemory– Shun Ichi Amari 1977Shun Ichi Amari 1977Cognition networksCognition networks– Mosche Abeles 1988 Mosche Abeles 1988 Synfire chainsSynfire chains– Wolf Singer 1988Wolf Singer 1988 Syncrozization in cats Syncrozization in cats

cortexcortex– Mark Konishi 1993Mark Konishi 1993 Place theory of sound localization Place theory of sound localization

(2)(2)– Andrew Packard 1995Andrew Packard 1995 Waves on SquidsWaves on Squids

The alternative: State machines f(t-1), f(t-2),…f(t-n)The alternative: State machines f(t-1), f(t-2),…f(t-n)– Boole 1854, Augusta Ada 1858Boole 1854, Augusta Ada 1858– McCulloch/Pitts 1943 (!)McCulloch/Pitts 1943 (!)– Neural (Pattern-) NetworksNeural (Pattern-) Networks– Medwedjev, Moore, Mealy 1955Medwedjev, Moore, Mealy 1955– Fairchild TTL 1968, Intel 4004 1971Fairchild TTL 1968, Intel 4004 1971

Historical Remarks: First Interference Historical Remarks: First Interference SystemsSystems


The Idea: Time codes SpaceThe Idea: Time codes Space

Well known relations between Well known relations between f(x) f(x) andand f(t) f(t) about about velocityvelocity

Timing defines interference locationTiming defines interference location Different timing -> different interference locationDifferent timing -> different interference location

location x

Timing f(t-T)Timing f(t-T)

intensity f(x)intensity f(x)


Time Function or Wave?Time Function or Wave?

Identity: time function is a Identity: time function is a wavewave

Independent of any circuit Independent of any circuit structur structur (local coupled): (local coupled): only delay defines location(!)only delay defines location(!)

Global models allowed, but do Global models allowed, but do not model eating waves not model eating waves (nonlinear superimposition)(nonlinear superimposition)

Delay distanceDelay distance (Fig.: constant velocity)(Fig.: constant velocity)

f(t)f(t) f(t-f(t-))


Weights or Delays?Weights or Delays?

Nerve NetNerve Net

DifferenceDifference: :

Jeffress rule interpreted by weights Jeffress rule interpreted by weights and and delays -> Interference networksdelays -> Interference networks

Mirrored maps Mirrored maps

Hebbs rule interpreted by Hebbs rule interpreted by patternspatterns and and weightsweights

Non-mirrored maps Non-mirrored maps


Waves Generate ImagesWaves Generate Imagestime-integration over a location in a wavefield time-integration over a location in a wavefield

produces the Interference Integral (I²) – called produces the Interference Integral (I²) – called "image""image"Vorlage Zeitfunktionen Bild demodemo


Second Remark: Intellectual Power of Second Remark: Intellectual Power of MankindMankind

Signal theory is built on Signal theory is built on interference of two multiplied (or interference of two multiplied (or added) channelsadded) channels: field theory, filter-t., integral transformations, : field theory, filter-t., integral transformations, modulations…modulations…– Fourier-TransformationFourier-Transformation– Laplace-TransformationLaplace-Transformation– Z-Transformation (Discrete LT)Z-Transformation (Discrete LT)– Wavelet-TransformationWavelet-Transformation– Hilbert-TransformationHilbert-Transformation– Gabor-TransformationGabor-Transformation– Auto correlationAuto correlation– Cross correlationCross correlation– ConvolutionConvolution– Area calculation (g=1)Area calculation (g=1)– Frequency modulation (FM, PM, QM)Frequency modulation (FM, PM, QM)– Amplitude modulation (AM, SM)Amplitude modulation (AM, SM)

But: We discuss But: We discuss nn channels (n >> 2), not only two: channels (n >> 2), not only two:

Pyramidal cell has on average 7400 synapses?Pyramidal cell has on average 7400 synapses?

b

a

dtgtxKtz )()()(

b

an

nngnxKkz )()()(

continuous:

discrete:


Complex Numbers in Interference Complex Numbers in Interference SystemsSystems

ImIm

ReRe

= = vt = v/f vt = v/f

ddsensorsensor sensorsensor

Problems for d > Problems for d > ::

0°< 0°< < 360° < 360°

0°< 0°< < 360° < 360°


Complex Numbers and Interference Complex Numbers and Interference SystemsSystems

Wavelengths Wavelengths can be shorter as the arrangement of can be shorter as the arrangement of sensors dsensors d

Complex numbers range between 0…360°Complex numbers range between 0…360° A 'phase' is multivalent: wave number is very importantA 'phase' is multivalent: wave number is very important Avoid to use complex numbers for d > Avoid to use complex numbers for d >

– Integral transformations not allowed (!)Integral transformations not allowed (!)– No FFT, no Laplace, no Gabor, no Wavelet!No FFT, no Laplace, no Gabor, no Wavelet!– Only time domain calculations possibleOnly time domain calculations possible

Forget Field Theory!Forget Field Theory!??

-> Work in time domain-> Work in time domain

Can we really imagine?Can we really imagine?

Quantum physics: Heisenbergs uncertainty relation Quantum physics: Heisenbergs uncertainty relation failed?failed?


First ApplicationFirst Applicationwww.acoustic-camera.comwww.acoustic-camera.com

microphone array (32 mics) data recorder notebook

• Vacuum cleaner

• Sports car

• Needle printer

Examples:

Start NoiseImage

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


WorldwideWorldwide

Distributors: Germany, France, Great Britain, Spain, Netherlands, Sweden, Distributors: Germany, France, Great Britain, Spain, Netherlands, Sweden, Austria, Italy, Switzerland, China, India, South-Korea, Taiwan, Japan, Austria, Italy, Switzerland, China, India, South-Korea, Taiwan, Japan, Singapore, Australia, Newsealand, USA, Mexico, Brasilia, Argentina, Singapore, Australia, Newsealand, USA, Mexico, Brasilia, Argentina, Chile, South-Africa Chile, South-Africa

System price ~ 100.000,- €System price ~ 100.000,- €

Used for car development worldwideUsed for car development worldwide


Nomination of Acoustic Camera for Nomination of Acoustic Camera for German Future Award 2005German Future Award 2005

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

http://www.deutscher-zukunftspreis.dehttp://www.deutscher-zukunftspreis.de

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

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

http://www.deutscher-zukunftspreis.de/


Properties of Interference SystemsProperties of Interference Systems


Relativity of Wave LengthRelativity of Wave Length Spikes move slowly through nerve system [2 µm/s … 120 m/s]Spikes move slowly through nerve system [2 µm/s … 120 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 = v Velocity v, pulse duration T, grid g, geometrical wavelength s = v .. T T

s s < g g Interference networkInterference network

s >> gs >> g Weighted Nets (NN.)Weighted Nets (NN.)

s [µm]s [µm]

g [µm] g [µm]

Information processing:Information processing:Which grid is Which grid is

addressed?addressed?• Spines?Spines?• Cell body?Cell body?• Columns?Columns?• It depends!It depends!


Calculation of Waves: MaskCalculation of Waves: Mask Each locations has its own time scheme -> mask algorithmEach locations has its own time scheme -> mask algorithm

Mask of a locationMask of a location

Inverse MaskInverse Mask

Excitement conditionExcitement condition


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

The probability to excite a neuron is higher as more closed The probability to excite a neuron is higher as more closed the partial impulses can reach itthe partial impulses can reach it

random: no excitement synchronous: firerandom: no excitement synchronous: fire


Projection LawProjection Law Waves need to be at the detecting place at the same timeWaves need to be at the detecting place at the same time

Self interference conditionSelf interference condition (all paths): (all paths): 11 = = 22 = … = = … = nn

Velocities and path length can be different, but delays can notVelocities and path length can be different, but delays can not … … Optics, GPS, acoustic camera, dig. filter theoryOptics, GPS, acoustic camera, dig. filter theory Different to Fermat, Huygens … Feynman - trajectories Different to Fermat, Huygens … Feynman - trajectories

Source NI 1993


drawing: d. doebler

Sound Localization Model:Sound Localization Model:First Inter-Medial Interference CircuitFirst Inter-Medial Interference Circuit

Tyto albaTyto alba

Konishis model (1993) basing 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


Interference ProjectionInterference Projection

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

(all other cases not drawn)(all other cases not drawn) Specific neurons begin to Specific neurons begin to

communicatecommunicate Address relations between Address relations between

locations given by delayslocations given by delays Delays code locationsDelays code locationsFig.: Title page of "Neuronale Interferenzen", Fig.: Title page of "Neuronale Interferenzen",

Heinz, 1993Heinz, 1993

Single point observations Single point observations look like density look like density modulated signals or modulated signals or bursts? They say nothing bursts? They say nothing about destinations!about destinations!


Long Axons: Interference ProjectionLong Axons: Interference Projection

Considered Considered generating and generating and detecting fieldsdetecting fields

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


Long Axons: Interference ProjectionLong Axons: Interference Projection

Spiking neurons Spiking neurons have been arrrangedhave been arrranged

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

Image conjunction!Image conjunction!– Which difference Which difference

between Hearing between Hearing and Seeing? and Seeing?

– Ideas?Ideas?


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)

Neuronal basic Neuronal basic functions?!functions?!

Data addressing Data addressing possibility ->possibility ->

ExampleExample


New Elementary Functions of NeuronsNew Elementary Functions of Neurons

Code generation Code generation Code detection Code detection Data addressing Data addressing Neighborhood inhibition (identical neurons) Neighborhood inhibition (identical neurons) Level generation (spike duration > pause)Level generation (spike duration > pause)

details:details:

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


Waves on SquidsWaves on Squids

Andrews squid-experiments (1995) show moving excitations Andrews squid-experiments (1995) show moving excitations between chromatophore-cellsbetween 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 wave

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



Local InteractionLocal Interaction

Waves delete in the refractoriness Waves delete in the refractoriness zone: "cleaning" waveszone: "cleaning" waves

Alpha-waves in EEG? Dreams?Alpha-waves in EEG? Dreams? Local couplingLocal coupling

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

gh NI 1993




SelfSelf-Interference Integrals (-Interference Integrals (VisualVisual Maps) Maps)

Self interference of waves (i, i, i)Self interference of waves (i, i, i) Source arrangement defines mapSource arrangement defines map Conjunctive, spatial mapsConjunctive, spatial maps

Detecting fieldsDetecting fields

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

time function plottime function plot


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

• Waves meet itself -> "Waves meet itself -> "SelfSelf-"interference: wave -"interference: wave ii with with ii with with ii … …

• Waves meet other waves -> "Waves meet other waves -> "CrossCross"-interference: wave "-interference: wave ii with with i-1i-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


CrossCross Interference Integrals - Interference Integrals - temporaltemporal Maps Maps Increasing channel number (2…8) reduces cross interference Increasing channel number (2…8) reduces cross interference

intensity if we consider over-conditioning effectsintensity if we consider over-conditioning effects

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

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

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 holomorphy!We can not avoid the holomorphy!

Holomorphic MemoryHolomorphic Memory

Region of cross-interferences aroundRegion of cross-interferences around

Region of self-interferenceRegion of self-interference

3-channel Simulation3-channel Simulation


Delay Shift Moves Interference Integrals (I²)Delay Shift Moves Interference Integrals (I²)

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


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

interference integrals (neuroglia)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 As slowerslower is the velocity in the detecting field, as smaller is the is the velocity in the detecting field, as smaller is the addressable region, as addressable region, as higherhigher must be the density and the must be the density and the addressable memory volumeaddressable memory volume

wavelength [µm] = velocity [µm/ms] * duration [ms]wavelength [µm] = velocity [µm/ms] * duration [ms]

v = 50 µm/msv = 50 µm/ms v = 10 µm/msv = 10 µm/ms


Rule of Fire RateRule of Fire Rate

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

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

Field overflow occurs: Field overflow occurs: Cross interference Cross interference overflows the self-interf.,overflows the self-interf.,level generation!level generation!

Hypothesis: if pain is cross Hypothesis: if pain is cross interference overflow, then interference overflow, then this simple interference this 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


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 (!)

digital filter circuitdigital filter circuit


Over-Conditioned NetworksOver-Conditioned Networks

Using high numbers of channels the Using high numbers of channels the delays on different paths do not delays on different paths do not match, resulting in blurred match, resulting in blurred excitements far away from axisexcitements far away from axis

Example: four channels project on a Example: four channels project on a two- dimensional layer, see bottom two- dimensional layer, see bottom imageimage

Four channels do not match on a 2-dim. field (max. 3)numb_channels = space_dimension +1

n= d + 1 or d = n - 1 High space dimensions for high

channel numbers necessary Nerves need folded, inhomogeneous

networks (!)

cleanclean blurredblurred


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


SummarySummary Little time shifts have dramatic influence on locations Little time shifts have dramatic influence on locations

of interference, supposed we have small pulsesof interference, supposed we have small pulses To analyze nerve networks we introduce the term To analyze nerve networks we introduce the term

Interference NetworkInterference Network as a as a physicalphysical oriented approach oriented approach to neurocomputingto neurocomputing

We introduced We introduced interference integralsinterference integrals to visit locations to visit locations of interferenceof interference

Investigating the influence of small delays we find a lot Investigating the influence of small delays we find a lot of new effects: movement, zooming, conjugation, of new effects: movement, zooming, conjugation, permutation, overflow, new neuronal basic functionspermutation, overflow, new neuronal basic functions

Analyzing projections we find over-condition effects Analyzing projections we find over-condition effects regarding n-dimensional, inhomogeneous delay spacesregarding n-dimensional, inhomogeneous delay spaces

It is not possible to ignore small delays – pattern It is not possible to ignore small delays – pattern simulations (NN) deliver wrong resultssimulations (NN) deliver wrong results

It is not allowed, to use complex numbers to model It is not allowed, to use complex numbers to model interference systemsinterference systems

We have to re-think We have to re-think neural network researchneural network research completelycompletely

And we have to re-think And we have to re-think field theoryfield theory into time domain into time domain


FutureFuture

IN-research will be included in the "BMBF- Informations- IN-research will be included in the "BMBF- Informations- und Kommunikationstechnologien Programm (IKT2020)"und Kommunikationstechnologien Programm (IKT2020)"

We try to start a pilot project (until now 13 proposals)We try to start a pilot project (until now 13 proposals)

Find 1 GB more on Find 1 GB more on www.gfai.de/~heinzwww.gfai.de/~heinz

Thanks for your attention.Thanks for your attention.

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

Heinz, G.: Wave Interference Networks - State of Research Historical Remarks Historical Remarks Time...

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