This is the read-me file for the dynamics/Mathematica directory which is
associated with the "Learning Dynamical Systems" tutorial.

Contexts/Packages 

All packages and notebooks used in the tutorial are referenced
with respect to the default startup path (which includes a
path to the Packages directory that comes with Mathematica)
augmented with a path to the parent directory of the Dynamics
directory. If you are on a machine in the computer science
department at Brown, augment your path by adding the following 
command to your Mathematica initialization file (~/init.m). 

        PrependTo[$Path,"/u/tld/programming/Mathematica/"] 

On a personal computer, you will have to copy the necessary
files and, for example on a MacIntosh, add the following
command to your initialization file,

        PrependTo[$Path,"HD:Mathematica"]

and create the directory HD:Mathematica:Dynamics with the
subdirectories Exercises and Packages corresponding to

        HD:Mathematica:Dynamics:Exercises: 
        HD:Mathematica:Dynamics:Packages: 

The remainder of this discussion is implementation
independent and so, for example, the expression
Dynamics`Packages` refers to the subdirectory of the
Dynamics directory whether you are using a Unix, MacIntosh,
or MS-DOS machine.

Packages found in Dynamics`Packages` are in a raw ASCII format, 
not in the portable Mathematica notebook format. Files found in
Dynamics`Exercises` and ending in .m are in the standard notebook
format while those ending in .txt are not.  The code in the noteboks
found in Dynamics`Exercises` makes use of the following standard
packages.

DiscreteMath`Combinatorica`     

        Constructing, manipulating, and displaying graphs.

Statistics`ContinuousDistributions`

        See Page 585 in Mathematica.

Code in Dynamics`Packages` is in the form of Mathematica
packages with associated contexts.  Currently the
Dynamics directory is organized with two subdirectories
Exercises and Packages containing exercises and supporting
packages, respectively. For the time being, there is also a
directory Old for versions of code that are or are becoming
obsolete. Here are some of the more stable packages.

Dynamics`Packages`MarkovProcesses`                      

        Representing Markov processes and finite state 
        machines.  Depends on DiscreteMath`Combinatorica`.

Dynamics`Packages`MarkovExamples`                      

        Examples of Markov processes specified as temporal
        Bayesian networks. 

Dynamics`Packages`BayesianNetworks`                     

        Representing Bayesian networks and factored joint 
        distributions.  Depends on DiscreteMath`Combinatorica`.

Dynamics`Packages`TemporalBayesianNetworks`             

        Representing two-stage temporal Bayesian networks. 
        Depends on Dynamics`Packages`MarkovProcesses`,  
        Dynamics`Packages`BayesianNetworks`, and 
        DiscreteMath`Combinatorica`.

Dynamics`Packages`NearestNeighbors`     

        Simple procedures for finding k nearest neighbors.

Dynamics`Packages`CooperandHerskovits`     

        Implementation of Cooper and Herskovits [1992].

Here are the current plans for notebooks. Some of these are 
yet to be created (tentative authors indicated on the right).

Dynamics`Exercises`BayesianNetworks`
Dynamics`Exercises`CooperandHerskovits`

Dynamics`Exercises`LogisticFunction`  
Dynamics`Exercises`LorenzEquations`  
Dynamics`Exercises`CellularAutomata`
Dynamics`Exercises`TimeSeries` 

Dynamics`Exercises`DelayCoordinateEmbedding`            
Dynamics`Exercises`LearningHiddenMarkovModels`          <hs>
Dynamics`Exercises`MachineReconstruction`               <sml>

Dynamics`Exercises`DiscreteFourierTransform`            <hs>
Dynamics`Exercises`GibbsSampling`                       <tld>
Dynamics`Exercises`SingularValueDecomposition`          <sml>

Here is some more information on standard Mathematica packages and
functions that have proved useful in implementing the exercises for
this tutorial.

Packages`DiscreteMath`Combinatorica`

  ShowGraph[g_Graph]

  ShowGraph[g_Graph,Directed]

  ShowLabeledGraph[g_Graph]

  ShowLabeledGraph[g_Graph,labels_List]

  ChangeVertices[g_Graph,vertices_List]

  Vertices[g_Graph]

  ChangeEdges[g_Graph,edges_List]

  Edges[g_Graph]

  IsomorphicQ[g_Graph,h_Graph]

  ToAdjacencyLists[g_Graph]

  FromAdjacencyLists[edges_List,vertices_List]

  See ``Implementing Discrete Mathematics: Combinatorics and Graph 
  Theory with Mathematica'' by Steven Skiena, Addison Wesley, 1990.

Packages`Statistics`ContinuousDistributions`

  See Page 585 in Mathematica.

  NormalDistribution[m,s] returns a normal (Gaussian)
  distribution with mean s and standard deviation s.

  PDF[dist,x] returns the probability density function at x.

  CDF[dist,x] returns the cumulative distribution function at x.

  Random[dist] returns a pseudorandom number with the specified distribution.

Packages`Statistics`DiscreteDistributions`

  See Page 589 in Mathematica

  BernoulliDistribution returns the discrete Bernoulli distribution with
  mean p.

  BinomialDistribution[n,p] returns the binomial distribution for n
  trials with probability p.

Packages`Statistics`LinearRegression`

Packages`Statistics`MovingAverage`

Packages`DiscreteMath`ComputationalGeometry`

Here are few built-in functions that turned out to be useful.

  SingularValues[m] gives the singular value decomposition (SVD) for a
  numerical matrix m. The result is a list {u,w,v} where w is the list
  of nonzero singular values, and m can be written as
  
        Conjugate[Transpose[u]].DiagonalMatrix[w].v
  
  See page 665 in Mathematica, Second Edition, by Wolfram for a 
  description. See also SingularValues[m, Tolerance -> t]. 
  
  Fourier[data]
  InverseFourier[data]
  
  See page 679 in Mathematica, Second Edition, by Wolfram for examples
  illustrating how the Fourier transform can be used in analyzing and
  smoothing data.