Transcript Mathematical Modelling of the Immune System Response to Cancer

Mechanisms of Simple
Perceptual Decision
Making Processes
Xueying Wang
SAMSI/NCSU
CMMSC, NCTU, December 30, 2009
Outline
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History of two-alternative decision making
research
 Drift-diffusion models (DDMs)
 The reduced two-variable models (RTVM)
Analytical study on DDMs
Theoretical reduction of the RTVM to a DDM
Numerical investigation on the RTVM
Experimental data fitting
Summary and discussion
DDMs
DDMs
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Free response tasks
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Force response tasks
Directional Discrimination Tasks
Mazurek et al. ,Cereb Cortex 13, 2003
Biological background
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MT (middle temporal area)
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LIP (lateral intraparietal area)
Decision processes
Mazurek et al., Cereb. Cortex 13, 2003
The spiking neuronal network model
Wang, X.J., Neuron,36,2002
The RTVM
Wong and Wang, J. Neurosci. 26, 2006
The RTVM
Analysis of DDMs on the force response tasks
Analysis of DDMs on the force response tasks
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Drift rate and diffusion
coefficient are only functions
of time
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Drift rate and diffusion coefficient
are only functions of the spatial
variable
Analysis of DDMs on the free response tasks
Case I: Drift rate and diffusion coefficient are only functions of time
Analysis of DDMs on the free response tasks
Case I: Drift rate and diffusion coefficient are only functions of time
Analysis of DDMs on the free response tasks
Case II: Drift rate and diffusion coefficient are only spatially dependent.
Simulation of binary decision making process by the RTVM
Dynamics of this model
Dynamics of this model with weak noise
The features of the dynamics of this model
We show that the stochastic solution
and the deterministic counterpart
remain close when the amplitude of
noise is weak enough.
The analysis on the RTVM
Reduction to a 1-dimensional DDM
The original model vs. the simplified model
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the correct response
probability
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Mean reaction time
black dots -- monte carlo simulation of the original model over 50,000 trials
red curves – the analytical results of the simplified model
Reduction to a 1-dimensional DDM
U' = f(U)
V =   f(u)du
Effect of the starting point and the coherence
level on the performance
coh=0
coh=30
Accuracy
Mean reaction time
Numerical investigation on the RTVM
The transition pdf
coh=0
coh=30
Numerical investigation on the RTVM
The correct response probability (CP)
coh
noise
decision threshold
Numerical investigation on the RTVM
Mean reaction time
coh
noise
decision threshold
Experimental data fitting
Quantile probability plot
Experimental data fitting
Summary
We uncovered mechanisms underlying the simple
perceptual decision making processes by investigating
DDMs and the RTVM.
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We gave a detailed analysis of DDMs.
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Force response tasks
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Free response tasks
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We found precise conditions on parameters for when
the biophysical-based two-dimensional model can be
rigorously reduced to a one-dimensional DDM.
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We provided precise estimates on the parameter
values so that the biophysical-based model can be
controlled to reproduce the psychological
experimental data.
Discussion and future research
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Apply asymptotic analysis to study the RTVM in the
case of weak noise, which may characterize the
stochastic dynamics of the whole system without the
reduction to the unstable manifold.
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The dynamics of neural activity governed by the
properties of the individual neurons, network
architecture and synaptic plasticity
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The mechanisms of multiple-choice decision making
processes
Thanks
Questions?