Instructor: Peter Mucha

Course on canvas.dartmouth.edu.⇗

Syllabus

Course Schedule: Note future topics listed here are tentative and will likely move around as time permits. An "R" in the schedule means we will have class in the Thursday X-hour. Similarly, a "T" means we will have class in the corresponding Tuesday time.
Week Topics

1

MWF

A Very Brief History of Population Dynamics
See (eventually) Bacaër chapters 1–6, 16, 21 and 22

  • Monday 9/16: Fibonacci sequence (chap. 1) and geometric growth (chap. 3)
  • Wednesday 9/18: Halley's life table (chap. 2) and continued discussion on geometric growth (chap. 3)
  • Friday 9/20: Leslie matrix, eigenvectors, and Perron–Frobenius theorem (chap. 21)

2

MWF
  • Monday 9/23: Malthus (chap. 5) and logistic equation (chap. 6), with brief introduction to disease models (chap. 4)

Cellular Automata
See Sayama chapters 11 and 19.
If you are using PyCX, see also chapter 10.

  • Wednesday 9/25: Cellular Automata, PyCX, NetLogo, and the majority opinion model ("Voting" in NetLogo)
  • Friday 9/27: "Fire" model and percolation. Stochastic Cellular Automata "Voting random" example

3

MWF

Percolation
See Sayama chapter 12 (but not 12.3 yet) and Bacaër chapter 22.

  • Monday 9/30: Branching Process and Renormalization Group estimates for the percolation threshold
  • Wednesday 10/2: Cobweb diagram of Renormalization Group to interpret Finite-Size Effects, BehaviorSpace experiments
  • Friday 10/4: Analyze BehaviorSpace data and introduce a stochastic variant of the Fire model

4

MWF

Agent Based Models
See Sayama chapter 19

  • Monday 10/7: Survey of popular Agent-Based Models

Mean Field Approximation
See Sayama section 12.3, Bacaër chapter 16 and Kermack & McKendrick (1927).

  • Wednesday 10/9: Majority/Voting and Voting Random models
  • Friday 10/11: Fire model and SIR

5

WRF

Networks
See Kolaczyk & Csárdi chapters 1–5; Sayama chapters 15–17; Easley & Kleinberg sections 13.4, 14.3 & 14.6; and Holme, Porter & Sayama (2019) Links to an external site..

No class on Monday 10/14

  • Wednesday 10/16: Motivation and Introduction to Networks (K&C chapters 1–2)
  • Thursday 10/17: Visualization and Descriptive Analysis (K&C 3, 4.1–4.3; Sayama 15.1–15.5, 17.2–17.4)
  • Friday 10/18: Graph Partitioning (K&C 4.4)

6

MWR

Random Graph Models

  • Monday 10/21: Erdős–Rényi and the Giant Component model
  • Wednesday 10/23: Percolation on ER random graphs, and "Explosive Percolation"
  • Thursday 10/24: Preferential Attachment, Small World, and Configuration models

No class on Friday 10/25

7

MWF

Network Dynamics and Mean Field Approximations
See Sayama chapter 18 and Porter & Gleeson.

  • Monday 10/28: Dynamics on Networks, Diffusion on Networks, and Mean-Field Approximation
  • Wednesday 10/30: MF on z-Regular Random Graphs (SI and SIS)
  • Friday 11/1: Friendship Paradox and Homogeneous MF

8

MWF

Heterogeneous Mean Field, Pair Approximation, and Approximate Master Equations

  • Monday 11/4: Heterogeneous MF for SIS
  • Wednesday 11/6: Finish HMF for SIS and Network Simulations of SIR
  • Friday 11/8: Pair Approximation for SIS and SIR

9

MWRF
  • Monday 11/11: Pair Approximation for Voter Model and Co-evolving Voter Model (see Durrett et al., 2012)

Wednesday, Thursday and Friday:  Course project presentations

10

MT

 Monday and Tuesday: Course project presentations