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Heinz, G.: Waves on Wires – Introduction to Interference Networks n What "Integrate and Fire" suggests n Interference Principle, I.- Networks n 1D-, 2D-, 3D- Projections n Interference Integrals n I.-Types: Self-I., Cross-I. n Self-I. (Zoom, Movement, Somato-t. Maps) n Cross-I. (Spatio-Temporal Maps) n Mixed S/C (Lashleys rats, I.-overflow) Author: Dr. Gerd Heinz, GFaI, Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B

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22/09/05Israel Lectures © G. Heinz, History n 1992 Introducing velocities and spikes into a (weighted) neural network I found a symmetry, a mirror property (in -> out map) (slide 9) n 1993 book "Neuronale Interferenzen": new principles and properties (zooming, movement, overflow, spatio-temp. maps) n Development of simulator 'PSI-Tools' for simulation of nets and for nerve- and acoustic experiments PSI-Tools n To demonstrate the qualities of the approach: acoustic images, acoustic movies ( , first in the world) , first in the world , first in the world n 1996 introduction of the term 'interference networks (IN)' characterizing the 'physical approach to neural networks (NN)' n Reason: Very different properties to weighted/pattern- NN's n 2004 International market entry with Acoustic Cameras n 2001, 2003, 2005 Awards for acoustic photo- and cinematography (www.acoustic-camera.com) www.acoustic-camera.com www.acoustic-camera.com n Extract:

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22/09/05Israel Lectures © G. Heinz, Abstraction Interference Networks n Term 'interference': superimposition of waves n Discrete 'waves on wires' n Spherical, 3-dimensional architecture Moving time functions (spikes) f(t- ) Moving time functions (spikes) f(t- ) –spike-duration (geom. pulse length) –refractory behaviour (pause) n Branch-delays (and -velocities) n Connectivity (spines, synapses) n Overlay operations (add, multiply…) n Computational problem: high number of branches branch

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22/09/05Israel Lectures © G. Heinz, Central Question: Relativity of Wave Length n Spikes move slowly through nerve system [2 µm/s … 120 m/s] n Spikes have a limited (geometric) size [µm … cm] n Velocity v, pulse duration T, grid g, geometrical wavelength s = v. T s gInterference network s >> gPool of neurons (NN.) s [µm] g [µm] Which proportion is truth? Which grid is addressed? Spines?Spines? Cell bodies?Cell bodies? Columns?Columns? It depends?It depends?

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22/09/05Israel Lectures © G. Heinz, What "Integrate and Fire" suggests The probability to excite a neuron is higher as more closed the partial impulses can reach it (Heinz, NI, 1993) random: no excitement synchronous: fire

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22/09/05Israel Lectures © G. Heinz, Projection Law (Heinz'93) n Waves need to be at the detecting place at the same time Self interference condition (all paths): … Self interference condition (all paths): … Self interference condition Self interference condition n Velocities and path length can be different, but delays can not n Applied into optics, GPS, acoustic camera, dig. filter theory n Different to classic approaches (Fermat, Huygens … Feynman)

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22/09/05Israel Lectures © G. Heinz, Classic Beam-Approach of Optics n Light way (beam) defined by a minimum of a path integral (Fermat, Huygens, Maupertuis, Newton, Euler, Lagrange, Hamilton, Leibniz, Jacobi, Helmholtz, Maxwell, Heisenberg, Schrödinger, Feynman) n Fermat: Minimum principle, shortest way of light n Huygens, Maupertuis: smallest action, wave theory q2q2q2q2 q1q1q1q1 q(t) Lagrange function = (T-V); T kinetic, V potential energy (compare H. Lübbig 1998, W. Kuhn 2001) water air min. path

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22/09/05Israel Lectures © G. Heinz, drawing: d. doebler The Forgotten Symmetry: First Inter-Medial Interference Circuit Tyto alba Sound localization model Sound localization model based on: Jeffres L. A.: A place theory of sound localization. J. Comp. Physiol. Psychol. 41 [1948]: symmetry line: mirror right left

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22/09/05Israel Lectures © G. Heinz, 1-dimensional Interference Projection (Heinz 1992) n Signals meet at locations with identical delays from source (self-interference) n (all other cases not drawn) n Specific neurons begin to communicate n Address relations between locations given by delays n Time codes location Single point observations look like density modulated signals or bursts?

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22/09/05Israel Lectures © G. Heinz, 3-dim. Interference Projection n Considered generating and detecting fields n Which properties exist between generating and detecting locations?

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22/09/05Israel Lectures © G. Heinz, 3-dim. Interference Projection n Considered generating and detecting fields n Which properties exist between generating and detecting locations? n To find answers we arrange the spiking neurons n Mirrored projection appears as "interference integral" n Image conjunction!

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22/09/05Israel Lectures © G. Heinz, pixel grid = neurons grid Understanding the Wave Abstraction n Each neuron has different delays to source points n For didactic purposes we use some abstractions: –homogeneous velocity –equidistant neurons (as pixels of an image) n Detecting field is a bitmap of pixels (symbolizing neurons) pixel x y z neurone d- source points

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22/09/05Israel Lectures © G. Heinz, Understanding Gen.- and Det.- Masks n Each locations has its own time scheme, has its own mask Mask of a location Inverse Mask

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22/09/05Israel Lectures © G. Heinz, 2-dim. Wave Field Simulation If we consider all possible paths, any emission is on a circle of delay around any source: we call it 'wave' If we consider all possible paths, any emission is on a circle of delay around any source: we call it 'wave' n I² are composed of waves n Didactic suggestions: –homogeneous wave expansion –Linear superimposition (?!) Interference integral over the whole wave field: Wave field (pixels symbolize neurons) 30 channel simulation (Hz 1995)

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22/09/05Israel Lectures © G. Heinz, Quotation n "Your file gfai_30_.avi (GFaI-movie) reminds me of a trapped wave packet scattered inside a chamber. It also reminds me of ray tracing inside an inhomogeneous wave duct where one can compute the wave trajectories using Snell's law. So I understand that interference effects can be computed using geometry (the propagation path as a function of space and time) instead of wave mechanics. Feynman used the path integral approach to build up a sum of probabilities for quantum trajectories instead of using the Schrodinger wave equation." Glenn Takanishi, (Hawai)

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22/09/05Israel Lectures © G. Heinz, A Detailed Look to Interference of Discrete Waves n Excitement values becomes maximized at locations, where most waves meet n Not all, only some places have a chance to be excited n Timing codes the location of possibilities Image pixels seen as nerve cells with connections Homogeneous wave velocity and space for demonstration only (neuro-pile)

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22/09/05Israel Lectures © G. Heinz, Self- /Cross- Interference Relations Waves meet itself -> self-interference: wave i with i with i …Waves meet itself -> self-interference: wave i with i with i … Waves meet other waves -> cross-interference: wave i with i-1 …Waves meet other waves -> cross-interference: wave i with i-1 … (i, i, i, i) self-interference location (i, i, i, i) self-int. (i, 0, i-1, i) cross-int. location (1) (3) (2) (4) cross- interference distance

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22/09/05Israel Lectures © G. Heinz, 2-dim. Waves on Squids n Andrews squid-experiments (1995) show moving excitations between chromatophore-cells n Cells are connected via a nerve-like structure n Excitation and relaxation can produce waves n Time functions appear comparable to nerve n Although the mechanism is not exactly known, the effect needs a wave-interference description Circular wave

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22/09/05Israel Lectures © G. Heinz, Local Interaction n Waves delete in the refractoriness zone 'cleaning waves' 'cleaning waves''cleaning waves' n Analogy to frogs sciatic-nerve experiments (Ischias) frogs sciatic-nerve experiments frogs sciatic-nerve experiments n Refractory distance >> field size "cleaning" waves on squids (AP, 1995) Global, linear Local, non-linear "cleaning" waves in 2-dim. simulation

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22/09/05Israel Lectures © G. Heinz, Interference Integrals (Self-I., Visual Maps) n Long time-integration pulls up the energy of wave-hit-locations (self interference locations) n Source arrangement defines the maps n Maps can be conjunctive (g+h) Detecting fields Generating fields (g+h) time function plot

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Summary Chapter "Self Interference" Self interference increases the excitability of a neuron Self 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 movement of many spikes through any delaying space The term 'wave' abstracts a two- or higher dimensional movement of many spikes through any delaying space It is not possible to interpret anything, if we observe only one channel of a projection It is not possible to interpret anything, if we observe only one channel of a projection Timing defines the location: Only wave addressed neurons can learn Timing defines the location: Only wave addressed neurons can learn Self interference is very sensitive against any parameter drift, circuits need auto-control and regulation (-> Hebb's rule in a different light) Self interference is very sensitive against any parameter drift, circuits need auto-control and regulation (-> Hebb's rule in a different light) Local superimposition needs 'cleaning waves' before any neuron can be addressed Local superimposition needs 'cleaning waves' before any neuron can be addressed

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22/09/05Israel Lectures © G. Heinz, Cross-Interference n All channels with identical time functions n Cross interference distance: ds = v dt = v / f with f = 1/dt n "Spatio-temporal coding", temporal maps Huygens double split experiment for neurons (NI 1993): Heinz 1993 (i, i, i, … i) self- interference location (i, i+1, i-1 … ) cross-interference locations (around)

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22/09/05Israel Lectures © G. Heinz, Cross-Int. Integrals: "Spatio-Temporal Maps" n Cross interference defines all temporal maps n We consider identical, periodical fire on all channels n Cross interference is maximum for two channels -> which channel number has the auditory system? Only two? n We like 'harmony' in sound n 'Harmonies' address similar points

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22/09/05Israel Lectures © G. Heinz, Summary "Frequency Maps" n Cross interference defines all temporal maps n Increasing channel number (2…8) reduces cross interference intensity (due to over-conditioning) Heinz 1996 (i, i, i, … i) self- interference locations cross-interference locations around

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22/09/05Israel Lectures © G. Heinz, n Lashley was looking his life long for the locality of items learned (1920 … 1950) n Rats became teached a way through a labyrinth. He removed systematically small parts of the brain and proved the before learned Summary of his experiments: n The series of experiments... has discovered nothing directly of the real nature of the engram Interpretation: n Cross interferences look like self interferences (!) n "Tutographic" brain, if it is an interference system n We can not avoid the duality Self- and Cross- Interference Interaction Region of cross-interferences around Region of self-interference 3-channel Simulation

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22/09/05Israel Lectures © G. Heinz, 1-dim. Delay Shifter Modulates Wave Front n Variation of relative delay changes wave direction n Glia can modulate the velocity of nerves

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22/09/05Israel Lectures © G. Heinz, Delay Shift Moves Integrals n Variation of delay of one channel produces a moving interference integral (glia potential influences speed & location)

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22/09/05Israel Lectures © G. Heinz, 1-dim. Velocity Variation Modifies the Size n Variation of velocity (v, v' ) influences the size of a projection

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22/09/05Israel Lectures © G. Heinz, Velocity Variation Zooms Integrals n Variation of background velocity in the detecting field zooms the interference integrals (neuroglia) n Cross interferences appear for low velocities

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22/09/05Israel Lectures © G. Heinz, A Closer Look to Memory Density n As slower is the velocity in the detecting field, as smaller is the addressable region, as higher is the density and the addressable memory volume n If we ask "How do you do?", we get different answers: –Professor: (pause) "ohhhh" (pause) "don't know?" –Tennis profi: "Oh fine, I won the mastership!" n Who is who? v = 50 [mm/s] v = 10 [mm/s]

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22/09/05Israel Lectures © G. Heinz, Heinz 1993 Zooming & Movement for Pattern Matching n To recognize a person or face, we have to "scale" the image to the same size and position (zooming and movement) n Our eyes have no optical zoom n Adoption with electronic scaling? path: retina to visual cortex? n (Comparable task for somato-topic projections in Homunculus) + = ? + = match!

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22/09/05Israel Lectures © G. Heinz, Rule of Fire Rate n Cross interference pattern depends on channel number & refractory period n We increase the average fire rate (reduced cross- interference distance) n Field overflow occurs: Cross interference overflows the self-interf., loss of information! n Hypothesis: if pain is cross interference overflow, then this simple interference circuit models that behaviour ~ 7,5 ms ~ 5 ms ~ 4 ms ~ 1,5 ms

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22/09/05Israel Lectures © G. Heinz, n "Interference integral" = integration of time function of each location over time 1. Self-interference properties define –Somato-topic maps (mirrored projections) –Noise location (owl, dolphin) –Optical pictures, Acoustic Camera –Scaling (zoom, movement) 2. Cross-interference properties define –Frequency maps –Code and behavior maps –Pain? Summary: Spatio-Temporal Maps (Self- and Cross Interference Integrals)

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22/09/05Israel Lectures © G. Heinz, Analogy to Filter Theory n Neuron changes from a simple threshold gate to a digital filter circuit n Direct translation into digital filter structure is possible Distributed wire with delay Electrical node (!) Its a digital filter circuit!

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Applications & Research Author: Dr. Gerd Heinz, GFaI, Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B

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22/09/05Israel Lectures © G. Heinz, Applied Interference Systems n Radar (electric waves) n Optics (electric waves) n Sonar (acoustic waves) n Acoustic cameras (ac. waves) n Digital filter theory (!) n Digital logic (computers) n Pattern- and Weight-Nets (Neuronal Networks) n Fuzzy logic n Global Positioning by Satellites n Cell phone carrier multiplex n Interferential bio-interaction (brain memory extension …) n Integral Transformations (!): convolution, correlation, FFT… … only the type of time function changes (floating/integer/binary)

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22/09/05Israel Lectures © G. Heinz, Bio-Neuro-Research n Data addressing –Refractoriness and bidirectional exchange –Geometrical wave length –Cleaning waves (non-linear superimposition) n Data processing –Temporal correspondence of arrangements –Data compression & segmentation –Interference learning, self-organisation n Spatial projectivity –High channel numbers? Field size contra channel number n Cross-interference properties (temporal selectivity) –Creating behaviour –Relations between net geometry and behaviour n Technical Applications –Wave cameras: acoustic, electric, ultrasonic –Mobile cell phone nets –Space-Time Filters

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22/09/05Israel Lectures © G. Heinz, Homepage microphone array (32 mics)data recordernotebook Vacuum cleaner Vacuum cleaner Vacuum cleaner Vacuum cleaner Sports car Sports car Sports car Sports car Needle printer Needle printer Needle printer Needle printer Application Acoustic Camera

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Conclusion We considered nerve nets to be discrete wave interference networks We considered nerve nets to be discrete wave interference networks An amazing amount of new questions, possibilities and directions appear An amazing amount of new questions, possibilities and directions appear Interdisciplinary co-operation can accelerate findings Interdisciplinary co-operation can accelerate findings Thanks for your attention! Author: Dr. Gerd Heinz, GFaI, Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B Hyperbolic projection 16-chnl. pulse waves

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22/09/05Israel Lectures © G. Heinz, Related Links Homepage Publication-Directory Historical Acoustic Camera Die Wahrheit triumphiert nie, ihre Gegner sterben nur ausDie Wahrheit triumphiert nie, ihre Gegner sterben nur aus Max Planck

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Thanks Thanks to Benny Hochner (Hebrew Univ. Jerusalem), Tamar Flash (Weizmann Inst. Rehovot) and Mosche Abeles (Bar-Ilan Univ. Ramat Gan) for invitation, talks and discussions. Thanks to my wife Gudrun. She helped me over years of missing acknowledgements without doubt. Israel Gerd Heinz Author: Dr. Gerd Heinz, GFaI, Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B

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More Theory n Add on's Author: Dr. Gerd Heinz, GFaI, Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B

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22/09/05Israel Lectures © G. Heinz, Interference Conditions in Detail n Generating Mask M, detecting (inverse) Mask M* M + M* = T all ways have the same delay" (Hz'93) n Cross interference: … plus /minus foregoer/follower"

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22/09/05Israel Lectures © G. Heinz, Understanding Bursts n Circuit (a) n Burst generation with low bias (b) n Code detection with high bias (c) n Data addressing possibility -> Example

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22/09/05Israel Lectures © G. Heinz, Summary: New Elementary Functions of Neuron n Code generation n Code detection n Data addressing n Neighborhood inhibition (for identical neurons) n Level generation (spike duration > refractoriness zone) Sources: NI 1993 NI 1993 SAMS 1994 SAMS 1994 BioNet 1996 BioNet 1996

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22/09/05Israel Lectures © G. Heinz, Inhomogenity and Over-Conditioning n A one-dimensional projection needs two channels n A two-dimensional projection needs three channels n (the system is called 'over-conditioned', if more channels match)... n For a n dimensional projection d we need n+1 channels d = n+1 n How to realize high dimensions? –Distorted, folded space –Diameter (velocity) variation of dendrites –Non-linear wiring -> Inhomogeneous delay-spaces

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22/09/05Israel Lectures © G. Heinz, Circuit Drawings n The way to draw circuits for space and time: intrinsic delay n Wires are not nodes!!! n General: limited velocity Distributed wires with delay

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22/09/05Israel Lectures © G. Heinz, Colored Interference Systems n Nerves diameter vary, different carrier mechanisms n Waves can meet

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22/09/05Israel Lectures © G. Heinz, Scene Representation and Information Reduction n Delay learning can compose single points, representing whole scenes n Example: 30 neurons "GH" can be represented using only 3 interference locations Source 16-chnl. destination

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22/09/05Israel Lectures © G. Heinz, Overlays of I² n Axial (different generators and/or detectors on one 'bus') Radial (the delay geometry stays identical by add. of +/- ) Radial (the delay geometry stays identical by add. of +/- )

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22/09/05Israel Lectures © G. Heinz, Permutation and Decomposition of Scenes n Down: high dim. scenes can be decomposed to lower dimensions n Up: low dim. scenes can create higher dim. scenes using hyperbolic image overlays (without synchronization) n Examples: –Down: P1234 decomposes in P12, P23, P34, P41, P123, … P412 –Up: P12, P23, P34, P41 compose independent hyp. projections n Information reduction n A complex scene can be stored by (the position) of one neuron n "Complex neurons" n Neurons create behavior

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22/09/05Israel Lectures © G. Heinz, Projection contra Reconstruction n Natural time runs only in one direction: –Projection –Mirror property (!) n Computer time can run back –Reconstruction –Non-mirrored (!) –For technical purposes (AK) –Pseudo-wave-field problem n the direction of time axis defines the difference between them Reconstruction Projection

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22/09/05Israel Lectures © G. Heinz, Heinz Interference Transformation

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22/09/05Israel Lectures © G. Heinz, n We have to live with a small number of channels n Any time-function recorded by a sensor (microphone, electrode) has lost the wave-field information n In reconstruction it produces a new wave field (secondary wave field) n This is complete different to the original wave field n But we have to work with! Secondary Wave Field Original Wave Field Recording Sensor Emission Understanding Primary and Secondary Wave Fields x z y

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22/09/05Israel Lectures © G. Heinz, Source wave-frontwave-back Virtual Waves (I.-Reconstruction) pos. direction of time Orig. WF P pos. time Sec. WF n Recording channels come out of the sensors -> spherical waves n Time flow shows waves with wave- front direction to the center! (Hz'96) Example of secondary wave field with inverted waves

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22/09/05Israel Lectures © G. Heinz, Time across Space n Projection: continuous time n interference integral appears mirrored n Reconstruction: inverse time n Interference integral appears non-mirrored dT template Mirrored projection Primary field Secondary field Interference Projection f(t-T) template Interference Reconstruction f(t+T) Inverse time n Optical lense systems, Sonar n Nerve systems (!) n Beamformíng with delay elements n Fink "Time Reversal Mirrors" n Acoustic Camera Max. delay

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22/09/05Israel Lectures © G. Heinz, Calculation n Interference- Transformation (HIT) n "Interference Projection" published in BioNet96 n First acoustic image 1994 used the Interference- Transformation (HIT) as "reconstruction" (not published)

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Bio-Models Author: Dr. Gerd Heinz, GFaI, Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B

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22/09/05Israel Lectures © G. Heinz, Heinz93 Source: Heinz, Neuronale Interferenzen 1993 A Wave Model for Penfields Homunculus... n A hyperbola defines a fixed delay difference to two points F, F' n Different hyperbolas define different delay differences a/a', c/c' n Pulses meet at different locations, see drawing n (Self-I. location is defined by wave front direction)

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22/09/05Israel Lectures © G. Heinz, Thumb Experiment n Waves can be inspected with NLG n We find moving body projections n Orthogonal arrangements? Interpretation: Arrangement: Result:

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22/09/05Israel Lectures © G. Heinz, Homunculus and the Thumb Experiment n Motion moves projections dependent of position, see thumb experiment n Ganglion spinale creates a hyperbolic projection into medulla spinalis n So the movement is compensated, thumb position (up/down) does not influence homunculus position n -> Nerve system needs 'normalized' or scaled maps – free of body distortions n Penfield's "Homunculus" seems to be a scaled projection n Shift of somato-topic maps can be compensated –Sensory maps –Motor maps

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22/09/05Israel Lectures © G. Heinz, Visual Cortex n Waves define the direction of self interference location n Supposed, nerve bundles have comparable delays n Self interference location appear, where wave direction and screen have identical orientation n Scale-normalization of images needs zooming and movement n Visual cortex as a normalized wave field screen? Heinz 1993

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22/09/05Israel Lectures © G. Heinz, Interference Circuit Examples n To detect scenes or frequencies or codes, to control bodies, to create behaviour…

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22/09/05Israel Lectures © G. Heinz, Bi-directional: Singers Synchronization? n Using micro-electrodes, Wolf Singer found 1986 a deep tone in cats cortex n Has he found an interferential wave projection? n To "hold" a projection for some time (learn phase), we need a repetition? observation

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