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