Simulation and Self-Organization

Teaching

Simulation and self-organization covers computational topics related to economics, ecology, and evolution. Techniques covered include differential equations, stochastic methods, and multi-agent simulations.

  • Mathematical models of competition, evolution, and economic activities
  • Ontogeny and phylogeny
  • Pattern formation and communication in biological systems
  • Multi-agent and intelligent agent modelling and analysis
  • Techniques for large-scale simulation
  • Applications of self-organization to the creation of structures
  • Applications of computational science to testing biological, social, and economic theories
  • Organic computing

Materials

Questions

Lecture 1

  • Given a collection of samples from a real-world distribution, describe how you would generate additional samples with a similar distribution.
  • What is the relationship between the median and the mean of a typical income distribution.
  • What is the Lorenz curve?
  • What is the Gini coefficient?
  • Name a reasonably good parametric approximation to income distributions.
  • Describe possible sources of income inequality in an economy in which all workers are treated identically.
  • Explain how competition in an economy can amplify inequality.

Lecture 2

  • What is the purpose of an auction?

  • What is a common value auction? What is a private value auction?

  • What is an English / Dutch / first price sealed bid / second price sealed bid auction?

  • What other auction is a Dutch auction equivalent to? Why?

  • What other auction is an English auction equivalent to? Why?

  • What are revenue and efficiency of auctions?

  • Explain common assumptions in auction theory: independence, risk neutrality, no budget constraints, symmetry, rationality

  • Explain how you simulate auctions in a discrete event simulation. How do you represent strategies? What kinds of strategies are possible?

  • What is the Nash equilibrium?

  • What is a repeated auction and how does it differ from a simple auction?

Lecture 3

  • Explain and discuss the paper “Markets as a substitute for rationality”.
  • Explain how markets select for efficiency. Describe a simple simulation demonstrating this phenomenon.
  • Explain how private investment selects for efficiency and how bad investors are punished by the market.
  • Explain attacks that public investment schemes may be subject to.

Lecture 4

  • What is a cellular automaton?
  • How are 1D, 1-NN cellular automata numbered?
  • What is Rule 110 and what is special about it?
  • What is the 2D parity cellular automaton?
  • What are the rules for Conway’s game of life?
  • What is the “gossip model”? What does it model?
  • How does the gossip model relate to diffusion and relaxation models?
  • What is the Greenberg-Hastings cellular automaton?
  • What is the “majority model”?
  • What is Schelling’s model of segregation and what does it show? Why is it important?

Lecture 5

  • Generally, what is a cellular automaton? How does it differ from other kinds of computational models?
  • What classes of cellular automata do we distinguish?
  • What is Hashlife?
  • What is WireWorld?
  • What is Langton’s Ant?
  • What are self-replicating loops? What is Evoloop?
  • What is LargerThanLife?
  • How can you implement Conway’s Life and its generalizations using FFT?
  • What is a lattice gas cellular automaton?

Lecture 6

  • Describe how differential equations can be used to model bacterial population growth.
  • Describe the relationship between differential equation models and the underlying discrete, stochastic processes.
  • What is logistic growth?
  • For a 1D first order differential equation, what are the criteria for stability of solutions?
  • Given systems of first order equations, what are the nullclines?
  • What is a limit cycle?
  • What are the equations for the harmonic oscillator?
  • What are the equations for a real physical pendulum? What does the phase space look like?
  • What does the phase space for the Lotka-Volterra equations look like?
  • Describe the FitzHugh-Nagumo and the van der Pol models.
  • What is a chaotic solution to a differential equation?
  • Given examples of differential equations with chaotic behavior.
  • What is the logistic map?
  • What is the minimum dimensionality for a chaotic solution of a differential equation? difference equation?

Lecture 7

  • Describe the structure of epidemic disease models using differential equations.
  • What are the SIR, SIS, SIR-with-birth models?
  • What is a hypercycle model?
  • What is a delay differential equation? What properties do such equations commonly have?
  • What is a diffusion model? How is it expressed as a partial differential equation?
  • How do diffusion models relate to random walks?
  • What is the relationship between the diffusion equation and the Poisson equation?

Lecture 8

  • What is morphogenesis?
  • What are the first stages of the morphogenesis of higher animals?
  • What are the first stages of the embryogenesis of Drosophila?
  • What patterns in the Drosophila embryo are laid down maternally?
  • What is a reaction-diffusion network?
  • Explain how reaction-diffusion reactions create equally sized segments.
  • What is a Turing system?
  • What is a Gray-Scott system?
  • How can you quickly explore the parameter space of systems like Gray Scott systems?

Lecture 9

  • What is a social network, and what are its components?
  • What are examples of social networks? (Not just the electronic kind.)
  • What is the relationship between social networks and graphs?
  • What is the star graph? hypercube graph? line graph? wheel graph? barbell graph? complete graph? empty graph?
  • What are walks, trails, and paths?
  • What are closed walks, cycles, and tours?
  • What is are geodesics, the geodesic distance, the diameter of a graph, and the eccentricity of a node?
  • When is a graph connected? What are cut-points and bridges?
  • What does it mean for two graphs to be isomorphic? What is subgraph isomorphism? What is the complexity of solving these problems?
  • What is a tree? a bipartite graph? a complement of a graph? a clique?
  • What idea does the notion of “centrality” try to capture in a social network?
  • What measures of centrality are there?
  • What is structural balance?
  • What is a cohesive subgroup? How can they be defined?
  • What is the clustering coefficient of a node/graph?

Lecture 10

  • What is a random binomial graph?
  • What is the Erdös-Renyi model?
  • What is the model of randomly citing scientists?
  • How is the Barabasi-Albert model generated?
  • What is the key property of the Barabasi-Albert model?
  • What kind of graphs is the Barabasi-Albert model supposed to generate?
  • What is a power law?
  • Does the Erdös-Renyi model follow a power law?
  • How is the Watts-Strogatz graph generated?
  • What is a small world graph?

Lecture 11

  • What is the difference between correlation and causation?
  • Define causation.
  • Give an example where correlation between two variables exists, even though there is no causal relationship.
  • Describe the steps for developing a frequentist statistical test.
  • What is the difference between a Bayesian probability of a hypothesis and a frequentist p-value?
  • What is a confidence interval?
  • What is 95% confidence interval for the binomial distribution? Where does this occur frequently?
  • What is the t-test used for?
  • What assumptions does the t-test rely on?
  • What happens when the assumptions of the t-test are violated?
  • What is the null hypothesis in a two-sided t-test?
  • What is the difference between a one-sample and a two-sample t-test?
  • What is the Mann-Whitney U Test?
  • Since the U Test is non-parametric, why don’t we always use it?
  • Explain the parts of a box plot.
  • How are the notches in a box plot computed? What do they mean?
  • Explain the concept of publication bias and how it affects the interpretation of published results.
  • What are bootstrap methods? When are they used?
  • What is a permutation test? When is it used?
  • What is cross-validation and when is it used?