```10 Oct 99

Thoughts and stuff:

Math Projects for High School Students:
1) Ways to estimate pi -- convergence? error?
- circumscribe, inscribe regular polygons
- monte carlo methods
- series representations
2) Random # Generation
3) Constructions - which angles can be constructed by compass &
straightedge? origami?
4) Combinatorics & generating functions
5) Tests for logic problems - unique solutions?
6) Construct a slide rule - how does it work?
7) Construct calculators - how do they work? binary, floating pt errors
8) financial instruments - linear programming
9) Estimating Markov models - language/music
10) Dynamic Programming - finance, DNA sequence matching
11) asymptotics - solns of quadratic, cubic eqns
12) Numerical integration

Notes from Math Problems in the Molecular Science:
--------------------------------------------------
Bioinformatics -> function from sequence <- functional genomics
rapid development - punctuated equilibria
mutation matrix - amino acids to other ones
point accepted mutations
figure out form/structure from evolutionary trees

sequence matching =cannot= be simply stochastic -- remember natural
selection!!!!!

sequence of edits?

rocking back & forth
walking back & forth

different levels of codes in DNA & RNA --
junk? its not junk - used for structure (necessary to be able to copy,
edit, etc.)
1) transcription code
2) DNA shape - certain doublets - give a certain 2ndary structure
3) chromatin - where to put the nucleosomes (wind around the
histones)

RNA
1) triplet
2) gene splicing
3) RNA processing
4) translation framing code
5) translation parsing code
6) folding
7) mRNA editing

only 4% of original b.p. are found in code for end protein -- lots of
introns cut out, other edits go on

linguistic complexity defn
-- for thought of ability to code on multi-levels
U word usage
A actual vocab size
M maximal possible vocab size
i word size
n sequence length

C = \product_{i=1}^{n-1} U_i

U_i = A/M

C = 1 --> maximally complex

logarithmic word size --> least usage

ARE WE NOT DRAWN ONWARDS WE JEWS DRAWN ONWARD TO NEW ERA

molecular recognition - "shape recognition" lock-key
large folded proteins - entropy, parallelism

3D chips? DNA analogs

analog maze solver - microfluids

2D world -> 3D world

micro-origami -> assemble minimize pushing & shoving
easy folds, minimum deformation -> make small antennae
(fractal antennae)

emergence complexity

question: development, cortical folding?

End of Science

Dynamic allocation

cell death & removal

pointers

Apoptosis

non-stochastic
mitochondrial DNA
phylogeny
make =fake= phylogeny

Math sucks in all of them =>

other things:
mplot - see if that's already defined
xvector/matrix -> xmin	xmax
yvector -> ymin ymax
fit button
zoom button

type - regular pts, etc.

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