Download Signal Analysis

LOOKING FOR QUANTUM
PROCESSES IN NETWORKS
OF HUMAN NEURONS ON
PRINTED CIRCUIT BOARD
R. Pizzi*, A. Fantasia*, F. Gelain°, D. Rossetti* & A. Vescovi°
*Dept of Information Technologies, University of Milan – Crema, Italy
° Stem Cells Research Institute, DIBIT S. Raffaele – Milano, Italy
Our Group
• The team: 3 physicists, 1 biologist, 1 electronic
engineer, 1 bioengineer, 3 computer scientists
• Virtual laboratory (3 IP videophones with
videocamera connection) between the Living
Networks Lab and the Stem Cells Research Institute
• The Stem Cells Research Institute is directed by
Prof. Angelo Vescovi, who has pioneered the field of
neural stem cells
• Recently he has described the capacity of neural
stem cells to give rise to skeletal muscle and
hemopoietic cells
The Stem Cells
• Stem cells are capable of both proliferation and
differentation into specialized cells, that serve as
a continuos source of new cells.
• Stem cells can be transplanted to create new
healthy tissues.
• Using human neural stem cells allows to
consider the possibility of really implantable
neural devices.
• Human neural stem cells can build real living
networks on artificial substrate
Objectives
• Comparing the activity of Artificial Networks
with living networks having the same
architecture
• Understanding learning processes in
biological neurons
• Developing computational functionalities on
living networks
• Looking for quantum processes in biological
neurons
Materials
• Artificials Neural Networks software (Kohonen and Hopfield
networks, Java source code)
• Quantum computing emulator (QuCalc on Mathematica®)
• Glass PCB with 100µm gold pads connected by thin
nickel/gold wires
• DAQ acquisition module with 2 digital 8 bit channel output
ports and 10 analog input ports
• Custom electronic circuit designed for maximum performance
voltage in cells stimulation
• Software (Delphi) interface for the input pattern set up and
data acquisition
The Experiments
Kohonen
Hopfield
The Experiments
• Kohonen networks
• Holographic Hopfieldlike networks
• Non locality basins
• Control basin (culture
medium)
The Kohonen Network
• Straightforward architecture
• Analogy with neurobiological (cortical)
structures
• Self-organization
X1
.
.
.
Xn
Input layer
Competitive layer
Classification of Simple Patterns
Kohonen network
Signal Analysis
QUALITATIVE ANALYSIS
Culture medium before stimulation
Channel 1
Channel 2
Channel 3
Signal Analysis
• The output corresponding to similar bitmaps take
similar values
Signal Analysis
Stimulation with the “0” bitmap
• The “0” bitmap is given by the electrical values
“11111111” but the neurons reply with low voltage
values
Signal Analysis
Culture medium stimulated with “0” bitmap
• The culture medium behaves as a conductor and
replays to the “0” with higher values
Signal Analysis
Neural cells after stimulation
• After the end of stimulation the cells keep signals
different both each others and from the signals before
the stimulation
Recurrence Quantification Analysis
•Non linear analysis tool
•Temporal series recostructed with delay-time
embedding
•Estimate of the distances between the series
vectors
•Representation by means of Recurrent Plots
• Unorganized signal
before the training
• Unorganized signal
(in evolution )during
the training
• Highly organized behavior during the presentation
of a “learnt” pattern
• Highly organized behaviour after the end of
stimulation
First Conclusions
•After the end of stimulation the cells were
healthy and alive.
•The cells reply to the presentation of organized
pattern with electrically specific signals.
•Similar bitmaps produce similar signals without
correlation with input voltages
•The cell seem to be able to keep information
after the end of stimulation.
•High increase of self-organization in stimulate
cells
The Classical Hopfield network
1. Fully interconnected network
2. Hebb-like learning
3. Isomorphic to general quantum equations
Classification of Simple Patterns
Hopfield
network
The Experiment
• Network training with 50 sequences of all the
possibile “1” and “0” patterns (frequency 40 Hz)
• Presentation of the “1” pattern, 50 lectures
• Presentation of the “0” pattern, 50 lectures
• Presentation of the “1” pattern affected by
noise, 50 lectures
• Presentation of the “0” pattern affected by
noise, 50 lectures
Signal Analysis
During the training
0,08000
0,06000
0,04000
0,02000
-0,04000
46
41
36
31
26
21
16
11
-0,02000
6
1
0,00000
Signal Analysis
0,08000
• 50 presentations of
pattern “0”
0,06000
0,04000
0,02000
49
45
41
37
33
29
25
21
17
9
13
-0,02000
5
1
0,00000
-0,04000
-0,06000
0,04000
-0,04000
-0,06000
49
45
41
37
33
29
25
21
17
9
13
-0,02000
5
0,00000
1
• 50 presentations
of pattern “0”
affected by noise
0,02000
Signal Analysis
0,04000
• 50 presentations of
pattern “1”
0,02000
46
41
36
31
26
21
16
11
-0,02000
6
1
0,00000
-0,04000
-0,06000
0,04000
-0,04000
-0,06000
46
41
36
31
26
21
16
11
-0,02000
6
0,00000
1
• 50 presentations of
pattern “1” affected
by noise
0,02000
Recurrence Quantification Analysis
• Plot after presentation of pattern “0”
Channel 1
Channel 3
Recurrence Quantification Analysis
• Plot after presentation of pattern “1”
Channel 1
Channel 3
Preliminary Results
• The network answers in a selective way to
different patterns
• Similar patterns give rise to similar answers
Preliminary Results
• Organized behavior with respect to
presentation of different patterns
• High determinism of signals depending on the
neuron channel and the presented pattern
Preliminary Results
• The living network can “codify” the
patterns
• The distribution of the 50 + 50 outputs to
compare quantum and classical behaviour is
underway
• “On-the-fly” analysis shows irregularities in
the reply to the same pattern: a quantum
effect ?
Quantum Network
• We are developing an artificial quantum neural
network to see if it could be a better model for
the behaviour of real cells.
• Neurons are represented by qu-bits.
• Unitary evolution is achieved by a sequence of
local 2-qubit unitary evolutions acting on
randomly choosen couples of neurons.
Quantum Network
• After k 2-qubit unitary evolutions the state of
the network is a classical state obtained after a
“wave collapse” of the global quantum state.
• Learning in this model is achieved by
modifying the complex parameters that
regulate quantum interaction between
neurons.
• The model enables the possibility of quantum
tunneling between different energy levels.
Quantum Network
Unitary Evolutions on
the 2 qubit space
generates
entangled global state
Dynamics:
Random choice
of two qubits
Unitary evolution
k times
Wave collapse
Quantum tunneling in neural
networks
• Classical Boltzmann machines introduce thermal
noise to avoid system to be trapped in local minima
• The path climbs the slope of the energy gap
between 2 minima
• Quantum tunneling in quantum networks allows to
reach the minima passing through the energy gap
• This method allows faster computation in finding
global minimum
• The computation is robust against noise and
decoherence
Quantum tunneling in the quantum
neural network
Energy level
Classical stochastic
networks
Quantum
Tunneling
Configurations
space
Testing quantum non-local
correlations in neurons
• We tried to test if EPR-like correlations may exist
in neurons
• EPR correlations between two systems A,B are
of the kind
|0A0B>+|1A1B>
i.e. the whole system is in a superposition of two
state |0A0B> , |1A1B>
• In every state the two systems A,B present
statistical correlations.
Non Locality Experiment
• Two dishes electrically connected
• Then separated and electrically insulated
• 50 electrical stimulations (40 Hz)
• 50 light stimulations with 466 nm LED (near UV band)
The Measures
• Signals crosscorrelation before
stimulations:
• Signals crosscorrelation after
electrical stimulation:
• Signals coherence after electrical
stimulation:
• Signal crosscorrelation after LED
stimulation:
0.304
0.184
0.47
-0.484
• Signals coherence after
LED stimulation:
0.80
Experimental results
• The best correlations between systems A,B have
been obtained with light stimulation directed only
to system A.
• This doesn’t necessarily mean that EPR
correlations are present in neurons.
• It could be explained by some kind of
communication between separated neurons.
• More experiments are needed to formulate
theoretical explanations.
Considerations
•LED stimulations should not affect the signals
•The “multipower” of stem cells (even
potential retinal cells) could be a reason for
reaction
•Reaction to LED stimulation cannot be caused
by electrical interference between basins
•The extremely low energy could have avoided
dechoerence processes
Future Developments
• Accurate analysis of signals (non linear
analysis, ANN analysis)
• Further experiments to validate the
previous ones
• Accomplishment of the quantum formalism
for the network training
• More complex living networks to perform
more complex tasks