1. Population vector algorithm
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3. Response of a M1 neuron to mechanical perturbations in different contexts
Each panel illustrates wrist position, the instantaneous firing rate
and a raster display of the response of the neuron in individual trials.
Evarts and Fromm, 1978

4. The monkeys are trained to operate the arm for a self-feeding
task using a joystick
2. Their own arms were then restrained and the prosthetic arm
was controlled with populations of motor cortex single- and
multi-unit spiking activity.
Velliste et al., 2008

7. Endpoint trajectory variability
Semi-transparent coloured regions represent trajectory standard deviation
(over all sessions) around average trajectories (grey lines) to each target.
Velliste et al., 2008

8. Spike occurrences for each unit, grouped by major tuning component
(red, x; green, y; blue, z; purple, gripper)
Distribution of the four-dimensional preferred directions of the
116 units used. Arrow direction indicates x, y, z components,
colour indicates gripper component (blue, negative; purple,
zero; red, positive).

9. Spike rasters of a single unit during six movements in each of 8 directions.
This unit (with {x,y,z} components of its preferred direction, fired maximally
in the backward-up-right direction (B,U,R) and fired least in the
forward-downleft direction (F,D,L).
Velliste et al., 2008

11. Keeping the gripper closed during retrieval.
Gripper aperture as continuously varying colour from blue (closed) to purple
(part-way open) to red (open).
Velliste et al., 2008

12. Population vector algorithm

13. Population vector algorithm:
relies on the directional tuning of each unit, characterized by a single
preferred direction in which the unit fires maximally.
is a vector sum of the preferred directions of the units in the recorded
population, weighted by the firing rates of the units.
Discharge rate versus movement
direction.
Tuning function in three-dimensional
Cartesian coordinate frame.
The solid vertical lines denote
the preferred direction (PD) of each cell.
The vector sum of all cells defines a
population vector.

14. Vector sum of all cells defines a population vector
Mean hand trajectory is shown in the central panel for movements
to each of eight spatial targets. The large black arrow denotes the
preferred direction (PD) of the neuron.

15. Population vector algorithm:
Population vector, P, which points in the predicted direction of movement:
The ith contribution, Ci, to the population output is represented as a unit
vector pointing in its preferred direction, and weighted by some function
of its firing rate, Wi = f (D).
D is the cell’s discharge rate, bo is its mean discharge rate, mx, my and
mz are the x, y and z components of a unit vector pointing in the direction
of movement, and bx, by and bz are regression coefficients.
Schwartz et al., 2001

16. Population vector algorithm:
For an assembly (Hebb 1949) or population of motor neurons {1 ≤ i ≤ N}
with momentary firing rate νi the weighted vector sum, the so-called
population vector n:
encodes the direction e of movement resulting from an assembly of motor
neurons while ν, the length of the population vector n, is proportional to
the instantaneous speed of the drawing motion.
each neuron with label i its preferred direction ei - a unit vector.
Hemmen and Schwartz, 2008

17. M - a unit vector in the movement direction (consisting of mx, my and mz).
B - a vector pointing in the cell’s preferred direction (the direction where the
cell fires maximally).
This linear relation can also be expressed in terms of a cosine-tuning equation:
where θ is defined as the angle between
the preferred and movement directions.
Each dot denotes the preferred direction of an individual neuron.

19. Direction vector algorithm

20. Bayesian maximum likelihood method
to reconstruct positions, based on the following formula:
P(x|n) is the probability of the rat occupying bin x given the cell activity
in the window
P(x) is the mean probability of the rat occupying position x.
fi(x) is the probability of the cell i firing in map bin x, which equates with
the average firing rate of the cell in that bin.
ni is the number of spikes from cell i in the sliding window,
and τ is the size of the sliding window.
C(τ, n) is a normalization factor calculated so that the sum of the
probabilities for each bin = 1.

21. Huxter et al., 2008

22. …plasticity vector algorithm

23. Thank you for your attention