Modeling Decisions A Mathematical Model of the Neuronal Decision Making Process

Modeling Decisions
A Mathematical Model of the Neuronal
Decision Making Process
Tricia Sun and Erinna Woo, 2012
Introduction
• Decision making is an invaluable characteristic
of the mind
Psychological
Mathematical
&
Biological
Decision
Neuroscience
Decision
Neuroscience
• Has only existed for about 20 years
• Cross-disciplinary field
▫ Neuroscience
▫ Mathematics
Computer Programming
Biology
• Goal: to capture the process of decision making by
analyzing the behavior of neuronal circuits
• Gain understanding of psychiatric disorders for
future treatment
Aspects of the model
Mathematical
Biological
• Helps predict level of neural activity
• Shows relationship between electrical
activity and decisions
• Shows how mind functions in a decision
process
• Represents a neural network
A Decision
Reward
Decision
Risk
Consequence
• One neural population
represents one
alternative or choice
• One population must
“win”
▫ Cross a firing rate or
activity threshold
▫ Gains activity from
external or internal
stimuli
▫ Intra-neural population
interactions
The “Competition”
Excitatory signal
• Brings population closer to
threshold
Inhibitory signal
• Brings population farther from
threshold
• Populations excite themselves while trying to inhibit the
other
• Activity level increases as “evidence” for the choice is
accumulated
Simple Forced
Decision Task: Model Description
• Basics of decision making
• 2 separate equations representing 2 different
neuron population (2 decisions)
Mathematical
Description
•
E: activity level within populations 1 or 2
t: time
S: external stimuli
axy: activity from signals, where x is the pop. “sending” activity and y is
the pop. “receiving” activity
c: maximum activity level
b: a transition point, from where activity is low to where activity is high.
Simple Forced
Decision Task Model- Finite
•
Model Behavior
•
Initial Conditions
• Miniscule differences between the two initial
conditions can change decision
Inhibition Rates
• When one population sends stronger inhibitory
signals to the other:
With no difference in strength
With slight difference in strength
Adding Variables
• Biased visual evidence
More evidence favoring one
side alters decision
Disparity , decision time
• Initial conditions have more
weight
Control the end decision more
Biased visual evidence is trivial
when initial conditions counter
the bias
Adding Noise
• Realistic addition of “confusing” visual stimuli
• Harder to make a decision, decision time increases
▫ Depends on amplitude of noise
Which Direction?
Decisions with Noise
• If all other parameters remain unbiased, mind randomly
decides
▫ 50% chance correct
▫ More noise decreases probability of a correct decision
Noise Continued
Increasing noise increases
confusion, as indicated by black
plots on the right.
If noise never ceases, a
decision is never made.
Steady States
and Stability
• There are 3 steady states
▫ Negative rate of change near steady state  stable
▫ Positive rate of change near steady state unstable
Steady States and Stability
E[2]
E[1]
E[0]
Example
These are the Sprouse twins.
Who is the boy on the right, Dylan or Cole?
• Dylan = blue and Cole = red line.
• Dylan and Cole are identical, so it is extremely
difficult to decide who is who
Let’s add evidence: Cole has shorter hair.
Your brain can now decide that the boy on the
right is Cole based on the visual evidence.
Biological Example
A polar bear is eating a seal.
Another polar bear approaches.
Fight or Flight?
• Initial Conditions:
▫ previous attacks with serious injuries
• External Stimuli/Evidence:
▫ aggressive opponent
▫ risk of not having a meal
Fight vs. flight
Initial conditions
(experience) + evidence for
flight (aggressive opponent)
outweigh the evidence for
fight (not having a meal)
Summary
• Simple model with two alternatives
▫ two differential equations modeling activity of two
neural populations within the brain, where each
population represents one alternative in a decision
• A decision  “competition” between the two
populations
▫ A population must pass an activity threshold to be
“chosen”
• Model reflects reality & aids in the
comprehension of psychiatric disorders
Bibliography
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The Kavli Foundation (interviewer) & Lee, D., Salzman, C., & Wang, X-J.
(Interviewees). (2011). The
Neuroscience of Decision Making [Interview transcript]. Retrieved from The Kavli Foundation
Web site: http://www.kavlifoundation.org/science-spotlights/neuroscience-of-decisionmaking
Kong-Fatt Wong, Xiao-Jing Wang. J Neurosci. 2006 January 25; 26(4): 1314–1328.
doi: 10.1523/JNEUROSCI.3733-05.2006
Meurs, Rinie Van. Polar bear eating a seal. HowStuffWorks “Polar Bear Diet.” HowStuffWorks, 10 Sept. 2010.
Web. 02 Aug. 2012. <http://static.ddmcdn.com/gif/polar-bear-3.jpg>.
“Polar Bear.” What Do Polar Bears Eat? Woondu, 2008. Web. 02 Aug. 2012. <http://woondu.com/what-dopolar-bears-eat/>.
“Polar Bear Hunting.” Polar Bear | Bear Hunting Blog. N.p., 3 June 2011. Web. 2 Aug. 2012.
<http://www.bearhunting.us/category/bear-hunting-type/polar-bear/>.
Tanzer, Myles. Dylan and Cole Sprouse. Digital image. There's A New Set of Twins on
Camhttp://easybib.com/cite/form/imagepus. NYU Local, 7 June 2010. Web.
01 Aug. 2012.
<http://nyulocal.com/entertainment/2010/06/07/theres-a-n ew-set-of-twins-on-campus/>.
Two-alternative forced choice. (2012). In Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Twoalternative_forced_choice
Wang, X-J. (2006). Introduction to computational neuroscience. Retrieved from
wang.medicine.yale.edu/pdf_pub/introduction-chapter.xjwang.pdf