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:
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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.