02jnov19n2

02jnov19n2 - Harvard-MIT Division of Health Sciences and...

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Harvard-MIT Division of Health Sciences and Technology HST.508: Genomics and Computational Biology Net1: Last week's take home lessons Macroscopic continuous concentration rates (rbc) Cooperativity & Hill coefficients Bistability (oocyte cell division) Mesoscopic discrete molecular numbers Approximate & exact stochastic (low variance feedback) Chromosome Copy Number Control Flux balance optimization Universal stoichiometric matrix Genomic sequence comparisons (E.coli & H.pylori) 1
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Net2: Today's story & goals Biology to aid algorithms to aid biology Molecular & nano-computing Self-assembly Cellular network computing Genetic algorithms Neural nets 2
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3 Algorithm Running Time Given a size n problem, an algorithm runs O( f(n) ) time: O( f(n) ) : upper bound. ( Ω : lower θ: equal) 2500 150 6 300 30 3 30 20 10 10 6 4 2 2 3 2 10 10 10 1 ! 10 10 10 2 2 10 10 10 1 10 10 10 1 10 10 10 1 1000 100 10 1 > > > > > > = = = = n n n n n n n n Time n Polynomial { Exponential {
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Algorithm Complexity P = solutions in polynomial deterministic time. e.g. dynamic programming NP = (non-deterministic polynomial time) solutions checkable in deterministic polynomial time. e.g. RS A code breaking by factoring NP-complete = most complex subset of NP e.g. traveling all vertices with mileage < x NP-hard = optimization versions of above e.g. Minimum mileage for traveling all vertices Undecidable = no way even with unlimited time & space e.g. program halting problem NIST UCI ( http://hissa.ncsl.nist.gov/dads/HTML/npcomplete.html ), (http://www.ics.uci.edu/~eppstein/161/960312.html) 4
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How to deal with NP-complete and NP-hard Problems • Redefine the problem into Class P: – RNA structure Tertiary => Secondary – Alignment with arbitrary function=>constant • Worst-case exponential time: – Devise exhaustive search algorithms. – Exhaustive searching + Pruning. • Polynomial-time close-to-optimal solution: – Exhaustive searching + Heuristics (Chess) – Polynomial time approximation algorithms 5
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What can biology do for difficult computation problems • DNA computing – A molecule is a small processor, – Parallel computing for exhaustive searching. • Genetic algorithms – Heuristics for finding optimal solution, adaptation • Neural networks – Heuristics for finding optimal solution, learning,. .. 6
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Net2: Today's story & goals Biology to aid algorithms to aid biology Molecular nano-computing Self-assembly Cellular network computing Genetic algorithms Neural nets 7
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Electronic, optical & molecular nano-computing Steps: assembly > Input > memory > processor/math > output Potential biological sources: harvest design evolve A 30-fold improvement = 8 years of Moore’s law 8
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& self-assembly See Ebbesen et al., Extraordinary optical transmission through sub- wavelength hole arrays. Nature 391 , 667-669 (1998). Vlasov et al. (2001) On-chip natural assembly of silicon
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This note was uploaded on 01/24/2010 for the course HST. 508 taught by Professor Dr.georgechurch during the Fall '02 term at MIT.

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02jnov19n2 - Harvard-MIT Division of Health Sciences and...

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