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Unformatted text preview: 01/24/2007: Lecture 2 Evo l u t iona ry P rocess:
What is (or, what will we mean by) an "evolutionary process?" The word "evolution" comes up a lot in science and engineering (e.g. RLC circuit with sources.) From a vector x whose entries are capacitor voltages and inductor currents we can generically wri te an ODE: Dxt=Axt+Et Dxt=dxdt E(t) is a vector of functions dependent on sources This equation governs the t ime"evolution" of state variables (ie, entr ies in x(t)) If you have nonlinear stuff, get: Dx(t)=f(x(t),E(t) ) > which is a nonlinear ODE. Dynam ical Systems Theory studies things like this. In Newtonian physics, sim ilarly, for a system of N part icles let: x i = position of particle i pi = momentum of particle i then (mi = mass of pt. i) Dxit=1mipi(t) Dpit= fi(t) < net force on particle I (can depend on {xj, pj} and our "exogenous" forces.) z=xp= 2Ndimensional vector, get Dzt=F(xt, Et) E(t) are exogeneous forces Talk about this equation governing the time"evolution" of particles, positions, p's. In quantum mechanics, have PDEs (eg Shrodinger Equation) governing time"evolution" of the wave function of a quantum system Missing from this is any explicit role for randomness. B io I deas an d B io Evo l u t io n:
"What is life?" Tough one > (see, Shrodinger's Book of the same title) For now, living things are made up of cells (one cell or many) Prokaryotic organisms: cells don't have nuclei (inside cell is water + some key functional molecules, structures) Eukaryotic: cells have nuclei (cells w/ cells inside) Lynn Margulis: prokaryotics became eukaryotics by parasiticms and or symbiosis Concentrate on eukaryotic: ...
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 Spring '07
 DELCHAMPS
 Algorithms, Force, z=xp= 2Ndimensional vector, Dynam ical Systems, key functional molecules

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