Download Day 3 - EE Sharif

Biomedical engineering Group
School of Electrical Engineering
Sharif University of Technology
Neural Representation
How World is Mapped onto the
Mind
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NEURAL SYSTEMS
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Amazingly profesion at solving problems
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Explanation: Representation
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Serving to relate the internal state of the animal to its environment
Can be manipulated internally without manipulating the actual, external,
represented object.
Penfild Observations
Transformation
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Seagulls and Shellfish
Bees and finding their ways
Rats and sense of direction
Exploiting representations
Updating
Manipulating
Relating
Explaining how neurobiological systems represent the world, and how they
use those representations, via transformations, to guide behavior
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NEURAL REPRESENTATION
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The main problem is to determine the exact
nature of the representation relation; that is, to
specify the relation between things ‘inside the
head’ and things ‘outside the head’.
We define
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The representational relationship
To see if it does the explanatory work that is needed
A,B,..
Decode
A close tie between neural representations as
understood by neuroscientists and codes as
understood by communications engineers
Codes in Engineering: Encode + …+ Decode
Stimulus
Encode/Decode : A procedure between 2
alphabets
Neural firings encode properties of external stimuli
Neural Modeling - Fall 1386
Encode
Morse
Encode
Neural
Firing
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REPRESENTATION
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Representation: one/more Neural
Firing
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90 degree orientation
Example: A neuron Firing for Face
orientation
Graded Representation: Firing more
or less strongly
Preferred Stimulus: One/More
Neurons
A Relation between Stimului and
Firing
Decoding: Inferring from Firing
Neural Modeling - Fall 1386
45 degree orientation
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Relevant Alphabets
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So many Different Alphabets
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Ex: Retinal Ganglion Cells
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Ex: An entire cortical area, like the primary visual cortex
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Color
spatial frequency
Intensity
spike trains of large populations of neurons
Relating neural responses (alphabet 1) and physical properties (alphabet
2)
Neural Alphabets:
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light intensities
certain retinal locations
spike trains of single neurons
average production rate of neural spikes (i.e., a rate code)
specific timings of neural spikes (i.e., a timing code)
population-wide groupings of neural spikes (population code)
synchrony of neural spikes across neurons (synchrony code)
Distances of Spikes in a Neural Loop
Number of Spikes in a Neural Loop
Of these possibilities, arguably the best evidence exists for a combination
of timing codes and population codes
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Physical properties
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Encoded by physicists and Neurons
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Only Encoded by neurons
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Displacement
Velocity
Acceleration
Wavelength
Temperature
Pressure
Mass, ..
Red
Hot
Square
Dangerous
Edible
Object
Conspecific
These latter ‘higher-order’ properties are inferred on the basis of (i.e., are the results of
transformations of) representations
For the time being we focus our attention on characterizing more basic physical properties,
where we believe successes can be more convincingly demonstrated
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Different Coding
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Engineering: Specified
Neurons: Discovered
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A lot of debate concerning what is
actually represented
what is represented depends in part
on how it is subsequently used
Have to know how the system works
in order to know what it represents.
we have a fairly comprehensive
understanding of what is actually
represented in the brain
Information encoded by a neural
population may be decoded in a
variety of ways
Neural Modeling - Fall 1386
How it Works
Obstacle
Representation
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The Single Neuron
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Synapse
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STRUCTURE
They have three distinct
parts:
 (1) Cell body,
 (2) Dendrites, and
 (3) the Axon
The particular type of
neuron that stimulates
muscle tissue is called a
motor neuron.
Dendrites receive impulses
and conduct them
toward the cell body.
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Myelinated Axons
The axon is a single long,
thin extension that
sends impulses to
another neuron.
They vary in length and
are surrounded by a
many-layered lipid and
protein covering called
the myelin sheath,
produced by the
schwann cells.
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Resting Potential
In a resting neuron
(one that is not
conducting an
impulse), there is a
difference in
electrical charges on the outside and inside of
the plasma membrane. The outside has a
positive charge and the inside has a negative
charge.
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Contribution of Active Transport
There are different numbers of potassium ions (K+)
and sodium ions (Na+) on either side of the
membrane. Even when a nerve cell is not
conducting an impulse, for each ATP molecule
that’s hydrolysed, it is actively transporting 3
molecules Na+ out of
the cell and 2 molecules
of K+ into the cell, at
the same time by
means of the
sodium-potassium pump.
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Contribution of facilitated diffusion
The sodium-potassium
pump creates a
concentration and
electrical gradient for
Na+ and K+, which
means that K+ tends to
diffuse (‘leak’) out of
the cell and Na+ tends
to diffuse in. BUT, the membrane is much more
permeable to K+, so K+ diffuses out along its
concentration gradient faster. Conversely, the electric field
causes both ions tend to come in.
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RESULTS IN:
a net positive charge
outside & a net negative charge
inside. Such a membrane is
POLARISED
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Action Potential
When the cell membranes
are stimulated, there is
a change in the
permeability of the
membrane to sodium
ions (Na+).
The membrane becomes
more permeable to Na+
and K+, therefore
sodium ions diffuse into the cell down a concentration
gradient. The entry of Na+ disturbs the resting
potential and causes the inside of the cell to become
more positive relative to the outside.
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All-or-None Principle
Throughout depolarisation, the Na+ continues
to rush inside until the action potential
reaches its peak and the sodium gates close.
If the depolarisation is not great enough to
reach threshold, then an action potential
and hence an impulse are not produced.
This is called the All-or-None Principle.
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Speed of Nerve Impulses
Impulses travel very rapidly along
neurones. The presence of a myelin
sheath greatly increases the velocity at
which impulses are conducted along the
axon of a neuron. In unmyelinated
fibres, the entire axon membrane is
exposed and impulse conduction is
slower.
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Speed of Nerve Impulses
Impulses travel very
rapidly along neurons.
The presence of a
myelin sheath greatly
increases the velocity at
which impulses are
conducted along the
axon of a neuron. In
unmyelinated fibres, the
entire axon membrane
is exposed and impulse
conduction is slower.
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Equivalent Model for Dendrites
and Axons
dx
Rdx
Cdx
i ( x, t )
v( x, t )
 C
x
t
v( x, t )
  Ri ( x, t )
x
 2 v ( x, t )
v( x, t )

RC
x 2
t
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Equivalent Model for an excited Neuron
dx
Rdx
v0(t)
Cdx
i ( x, t )
v( x, t )
 C
x
t
 2 v ( x, t )
v( x, t )

RC
x 2
t
v( x, t )
  Ri ( x, t )
x
v(0, t )  v0 (t )
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Transmission of Action
Potential/ Dendrite potential
 2v
v
 RC
2
x
t
 2V ( x, f )
 j 2fRCV ( x, f )
2
x
V ( x, f )  V0e
 2fRC x  j 2fRC x
e
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