User:Johnsy/Advanced Modelling in Biology: Difference between revisions
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==Past Examination Papers== | ==Past Examination Papers== | ||
*[http://www.openwetware.org/images/5/55/Advanced_Biological_Modelling_2007.pdf 2007 Examination Paper (.pdf)] | |||
**[http://www.openwetware.org/images/8/8e/AMB_2007_answers_q1_q4.pdf 2007 Examination Answers Q1-4 (.pdf)] | |||
**[http://www.openwetware.org/images/0/0d/AMB_2007_answers_q5_a6.pdf 2007 Examination Answers Q5-6 (.pdf)] | |||
**Corrections: Q3 - graph incorrect, Q4 b) K must equal 1-(c/b) |
Revision as of 03:06, 19 May 2008
Advanced Modelling in Biology
Lecturer: Dr. Mauricio Barahona
Topics
- Optimization
- Introduction to optimization: definitions and concepts, standard formulation. Convexity. Combinatorial explosion and computationally hard problems.
- Least squares solution: pseudo-inverse; multivariable case. Applications: data fitting.
- Constrained optimization:
- Linear equality constraints: Lagrange multipliers
- Linear inequality constraints: Linear programming. Simplex algorithm. Applications.
- Gradient methods: steepest descent; dissipative gradient dynamics; improved gradient methods.
- Heuristic methods:
- Simulated annealing: Continuous version; relation to stochastic differential equations.
- Neural networks: General architectures; nonlinear units; back-propagation; applications and relation to least squares.
- Combinatorial optimization: ‘hard’ problems, enumeration, combinatorial explosion. Examples and formulation.
- Heuristic algorithms: simulated annealing (discrete version); evolutionary (genetic) algorithms. Applications.
- Discrete Systems
- Linear difference equations: general solution; auto-regressive models; relation to z-transform and Fourier analysis.
- Nonlinear maps: fixed points; stability; bifurcations. Poincaré section. Cobweb analysis. Examples: logistic map in population dynamics (period-doubling bifurcation and chaos); genetic populations.
- Control and optimization in maps. Applications: management of fisheries.
- Advanced Topics (Networks & Chaos)
- Networks in biology: graph theoretical concepts and properties; random graphs; deterministic, constructive graphs; small-worlds; scale-free graphs. Applications in biology, economics, sociology, engineering.
- Nonlinear control in biology: recurrence plots and embeddings; projection onto the stable manifolds; stabilization of unstable periodic orbits and anti-control. Applications to physiological monitoring.
Assignment
Past Examination Papers
- 2007 Examination Paper (.pdf)
- 2007 Examination Answers Q1-4 (.pdf)
- 2007 Examination Answers Q5-6 (.pdf)
- Corrections: Q3 - graph incorrect, Q4 b) K must equal 1-(c/b)