Computational Modeling
Fall 2005
 

Today:

1) review and exam prep


Review
------

Python:

Dynamic typing.

Data structures (lists, tuples, dictionaries, heaps).

List comprehensions.

String and text processing.

Complex arithmetic.

Iterators and generators.
 

Graphs:

Graph representation.

Graph algorithms (shortest path, clique detection)

Small world graphs (Watts and Strogatz)

Scale-free networks.


Modeling:

Models and theories.

What makes a good (predictive, explanatory) model?

Kuhn: paradigm shifts, value judgement and theory choice.

Instrumentalism and realism

Epistemology

Reductionism and holism and emergence


Simulation:

continuous and discrete

deterministic and stochastic

equation-based and agent-based

time-stepping and event-based

Cellular automata (Wolfram), Turmites


Statistics:

Cumulative distributions, long-tailed distributions.

Zipf's law and the Pareto distribution.

Bayes's theorem.

Bayesian statistics.

	 hypothesis testing

	 parameter estimation, probability intervals

Bayesian epistemology.



Self-organized criticality:

Characteristics of critical systems

    Long-tailed distributions

    1/f noise
		 
Sand-pile model  (Bak, Tang, Wiesenfeld)

Other SOC systems (Gould and Tobochnik)


Fourier transform:

What is a signal?

Time domain, frequency domain.

Discrete FT, Fast FT.


Analysis of algorithms:

Order of growth of data structure operations.

Graph algorithms.

Fast Fourier Transform.

Heap implementation of priority queue.



Final Exam
----------

The exam will be Thursday, 4-7pm, in AC113.

I will be a little longer than the midterm, but should not
take 3 hours (except for part 4 below).


What would I put on the exam if I were me?

1) short/medium-answer questions about modeling and epistemology

2) algorithm implementation (graph, signal-processing, statistics)

3) analysis of algorithms

4) practical programming component
   (make sure you have a working Python environment with network)

5) Bayesian word problem