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 
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 
	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 
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 
don't =care= about R!!! (what?) 
mitochondrial DNA 
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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