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Quiz 3 2. Decision making in the honey bee model A)  Some'mes is exactly equivalent to the op'mal On optimal decision-making J. A. R. Marshall et al. 3
Figure 2. In the Usher–McClelland model of decision-making
diffusion model of decision making n the primate visual cortex, neural populations represent
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Figure 3. The expected dynamics of the Usher–McClelland
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is reached to the opEmal diffusion model of decision making.) Usher-­‐McClelland Model Leaky inhibitory integraEon Change in acEvaEon of a populaEon of neurons = input signal + noise – decay – inhibiEon from alternaEve populaEon Eqn 4.2 transforms Eqn 4.1 to decouple the Eqns and show the UM model approximates diffusion model & opEmal decision making when w = k & both are large How your brain makes decisions MoEon discriminaEon h[p://www.youtube.com/watch?v=hpvbZxDtXSY (1:40) Siegel et al FronEers in Human NeuroScience 5 (2011) h[p://www.economicswiki.com/economics-­‐tutorials/
pareto-­‐efficient-­‐pareto-­‐opEmal-­‐tutorial/ Bee decision-­‐making model Downloaded from rsif.royalsocietypublishing.org on 14 April 2009
On optimal decision-making
gradually increase their firing rate (Schall 2001;
Shadlen & Newsome 2001; Roitman & Shadlen 2002).
Detailed studies of their activity provide strong
evidence that the LIP neurons integrate input from the
corresponding MT neurons over time (Huk & Shadlen
2005; Hanks et al. 2006). Hence, as time progresses in the
task, the sensory evidence accumulated in the LIP
neurons becomes more and more accurate.
It has been observed that when the activity of the
LIP neurons exceeds a certain threshold, the decision is
made and an eye movement in the corresponding
direction is initiated (Schall 2001; Shadlen & Newsome
2001; Roitman & Shadlen 2002). This arrangement
of neural populations with decision thresholds lends
itself to representation through a simple model, as
described in §4.
J. A. R. Marshall et al.
3
excitation
inhibition
loss
Figure 2. In the Usher–McClelland model of decision-making
in the primate visual cortex, neural populations represent
accumulated evidence for each of the alternatives. These
populations y1 and y2 integrate noisy inputs I1 and I2, but leak
accumulated evidence at rate k. Each population also inhibits
the other in proportion to its own activation level, at rate w.
When wZk and both are large, the Usher–McClelland model
reduces to the diffusion model of decision-making (figure 3).
16
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4. THE USHER–MCCLELLAND MODEL
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The Usher–McClelland model represents decisionmaking using neural populations that act as mutually
inhibitory, leaky integrators of incoming evidence
(figure 2). In the moving-dots decision task described
above, these integrator populations would represent the
LIP neural populations corresponding to the different
possible eye movement decisions. Each population of
integrator neurons receives a noisy input signal that it
integrates, subject to some constant loss. Each population also inhibits the activation of the other to a
degree proportional to its own activation. So, as one
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0
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Figure 3. The expected dynamics of the Usher–McClelland
Ants: no direct switching Undecided Scouts choose y2 y2 commiCed scouts recruit new scouts y2 scouts decay from y2 Bee decision-­‐making model Undecided Scouts choose y2 y2 commiCed scouts recruit new scouts y2 scouts decay from y2 Y2 scouts directly switch to y1 InformaEon gathering, evaluaEon, deliberaEon, consensus, choice, implementaEon • 
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Bees commit all at once; waggle dances are broadcast in a crowded hive (only a few see it at at Eme) Ants go one at a Eme with no opportunity (usually) to assess mulEple nests; commit based on a quorum at one nest site How ants assess nest size: Ant lays a trail; leaves, returns, counts number of Emes it crosses its trail Ants show preferences, consistent rankings, transiEvity, weighing of all a[ributes Ants use a 'weighted addiEve Strategy' prefer bright, thick and narrow over dark thin and wide (with constant area) even though dark is most important Pra[ showed quorum sensing -­‐-­‐-­‐switch from tandem running to carrying (full commitment) once a (changeable) threshold # of ants have chosen to stay in a nest