A brief overview of quantum computing
or, Can we compute faster in a multiverse?
Tom Carter
http:/cogs.csustan.edu/~ tom/quantum
. . .
. June, 2001
1
Our general topics:
Hilbert space and quantum mechanics Tensor products Quantum bits (qubits) Entangled
A Little Probability
. . Coding and Information Theory Fall, 2004
Tom Carter http:/astarte.csustan.edu/~ tom/ October, 2004
1
Some probability background
There are two notions of the probability of an event happening. The two general notions are: 1. A fr
Nonlinear Systems
(. . . and chaos) a brief introduction
Tom Carter Computer Science CSU Stanislaus http:/csustan.csustan.edu/~ tom/Lecture-Notes/Nonlinear-Systems/Nonlinear-Systems.pdf November 7, 2011
1
Our general topics:
What are nonlinear systems? A
Making Sense
Tom Carter
http:/astarte.csustan.edu/~ tom/SFI-CSSS
April 2, 2009
1
Making Sense
Introduction / theme / structure 3
Language and meaning Language and meaning (ex) . . . . . . . . . . . . . . .
6 7
Theories, models and simulation Theories, mod
The Logistic Flow
(Continuous)
Tom Carter
http:/astarte.csustan.edu/ tom/SFI-CSSS
Complex Systems Summer School
June, 2008
1
Logistic ow . . .
We all know that the discrete logistic map
Pn+1 = rPn(1 Pn)
exhibits interesting behavior of various sorts
for v
A brief survey of linear algebra
Tom Carter
http:/astarte.csustan.edu/~ tom/linear-algebra
Santa Fe Institute Complex Systems Summer School
June, 2001
1
Our general topics:
Why linear algebra Vector spaces (ex) Examples of vector spaces (ex) Subspaces (e
Some Fractals and Fractal Dimensions
The Cantor set:
we take a line segment, and remove the middle third. For each remaining piece, we again remove the middle third, and continue indefinitely.
To calculate the fractal / Hausdorff /
capacity / box-counti
What is Interdisciplinary?
Discipline (and punish? :-)
Physics Chemistry
Biology
Mathematics
Economics
Psychology
Etc.
Or . . .
Physics Chemistry Biology Social Sciences
Etc. q
Or . . .
Mathematics
Real World
But is this really . . .
Mathematics
Real Worl
An introduction to information theory and entropy
Tom Carter
http:/astarte.csustan.edu/~ tom/SFI-CSSS Complex Systems Summer School Santa Fe
June, 2007
1
Contents
Measuring complexity Some probability ideas Basics of information theory Some entropy theory
Some Fractals and Fractal Dimensions
The Cantor set:
we take a line segment, and remove the middle third. For each remaining piece, we again remove the middle third, and continue indefinitely.
To calculate the fractal / Hausdorff /
capacity / box-counting
Some Fractals and Fractal Dimensions
The Cantor set: we take a line segment,
and remove the middle third. For each remaining piece, we again remove the middle third, and continue indefinitely.
To calculate the fractal / Hausdorff /
capacity / box-counti
The Logistic Flow
(continuous)
Tom Carter
Complex Systems Summer School
June, 2009
1
Discrete logistic map
We all know that the discrete logistic map Pn+1 = rPn (1 - Pn ) exhibits interesting behavior of various sorts for various values of the parameter r
Econ 102
(Random walks
and high nance)
Tom Carter
http:/astarte.csustan.edu/ tom/SFI-CSSS
Fall, 2008
1
Our general topics:
Financial Modeling
Some random (variable) background
What is a random walk?
Some Intuitive Derivations
2
Financial Modeling
Lets u
Entropy, Power Laws, and Economics
Tom Carter
Complex Systems Summer School SFI, 2007
http:/astarte.csustan.edu/~ tom/
Santa Fe June, 2007
1
Contents
Mathematics of Information Some entropy theory A Maximum Entropy Principle Application: Economics I Fit t
A very brief introduction to differentiable manifolds
Tom Carter
http:/cogs.csustan.edu/~ tom/diff-manifolds
Santa Fe Institute Complex Systems Summer School
June, 2001
1
Our general topics:
Why differentiable manifolds 3
Topological spaces
4
Examples of
A very brief introduction to differentiable manifolds
Tom Carter
http:/cogs.csustan.edu/~ tom/diff-manifolds
Santa Fe Institute Complex Systems Summer School
June, 2001
1
Our general topics:
Why differentiable manifolds Topological spaces (ex) Examples o
Introduction to theory of computation
Tom Carter
http:/astarte.csustan.edu/~ tom/SFI-CSSS
Complex Systems Summer School
June, 2005
1
Our general topics:
Symbols, strings and languages Finite automata Regular expressions and languages Markov models Contex
Clustering in Networks
(Spectral Clustering with the Graph Laplacian . . . a brief introduction)
Tom Carter Computer Science CSU Stanislaus http:/csustan.csustan.edu/~ tom/Clustering March 2, 2011
1
Our general topics:
What is Clustering? 3
An Example
8
S
What shape is a circle?
Complex Systems Summer School,
Santa Fe Institute
Tom Carter
http:/astarte.csustan.edu/~ tom/SFI-CSSS June 24, 2006
1
How do we define a circle?
We usually define a circle as C = cfw_x | |x| = 1 (i.e., the set of all vectors x of l