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
- 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.
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?
- 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.
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?