# Dynamics and Cognitive Models | MS in CogSci

#### Lecture 1 | Introduction

• “Freud was inspired by the theory of thermodynamics and used the term psychodynamics to describe the processes of the mind as flows of psychological energy (libido or psi) in an organically complex brain.” [Psychodynamics – Wikipedia]

#### Lecture 2 | Linear models

• What is a linear model?
• If the derivative of a model with respect to time is a linear equation for time, we call the model linear.
• “Linear” in this context means the “linear” of linear partial differential equations.
• Example: Malthusian Theory of Population
• 데이터의 개수가 아니라, 데이터의 quality가 연구에 결정적이다.
• The Newton’s cooling law
$$\frac{dT}{dt}=-k(T(t)-T_{env})$$ $$T(t)=(T(0)-T_{env})e^{kt}+T_{env}$$
• nls function in R [more]
• NLS = Nonlinear Least Square
• “We then apply the nls() function of R to get the more accurate values along with the confidence intervals.”
• McClelland, J. L. (1979). On the time relations of mental processes: an examination of systems of processes in cascade. Psychological review86(4), 287.
• Computational optimization techniques | Mathematical optimization | Wikipedia [LINK]
##### Assignments
• Read and understand the logistic differential equation.
• Logistic differential equation | Wikipedia [LINK]
• Look for where the logistic function is used.
• Neural network, population model, item response theory, growth of cancer cells (medicine), logistic regression
• Applications. Logistic function. Wikipedia. [LINK]
• Read the following paper up to page 27.
• Van Geert, P. (1991). A dynamic systems model of cognitive and language growth. Psychological review98(1), 3.
• Read the following book from page 4 to 8.
• Strogatz, S. H. (2018). Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press. [LINK]
• Read the following paper and think about the fault of fitting to means.
• Myung, I. J., Kim, C., & Pitt, M. A. (2000). Toward an explanation of the power law artifact: Insights from response surface analysis. Memory & Cognition28(5), 832-840. [LINK]
• Read the following articles and understand population growth rate.
• Population growth rate | Wikipedia [LINK]
• Population growth rate | Naver 지식백과 [LINK]
• The law relating response time to practice trials had been considered the power function. The following paper says that the law had been accepted as the power function because the law was fitted to means. Instead, the paper says that the law may follow the exponential if the law are not fitted to the means.
• Heathcote, A., Brown, S., & Mewhort, D. J. K. (2000). The power law repealed: The case for an exponential law of practice. Psychonomic bulletin & review7(2), 185-207. [LINK]
• Think about cognitive phenomena that follow similarly to the Newton’s cooling law and show your thought for 2 minutes.

#### Summer challenge: Understanding the diffusion model

• Ratcliff, R. (1978). A theory of memory retrieval. Psychological review85(2), 59.
• Ratcliff, R., & Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychonomic bulletin & review9(3), 438-481.

#### Lecture 11 (5/14/2019) |

##### Assignments
• Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: theory and data for two-choice decision tasks. Neural computation20(4), 873-922. [PDF]
• Blough, D. S. (2011). A random-walk model of accuracy and reaction time applied to three experiments on pigeon visual discrimination. Journal of Experimental Psychology: Animal Behavior Processes37(2), 133.  [PDF]

#### Lecture 12 (5/21/2019) |

• Tavares, G., Perona, P., & Rangel, A. (2017). The attentional drift diffusion model of simple perceptual decision-making. Frontiers in neuroscience11, 468. [PDF]