User:Johnsy/Advanced Modelling in Biology: Difference between revisions
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(New page: =Advanced Modelling in Biology= '''Lecturer:''' Dr. Mauricio Barahona ==Topics== *'''Optimization''' **Introduction to optimization: definitions and concepts, standard formulation. Conve...) |
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=Advanced Modelling in Biology= | =Advanced Modelling in Biology= | ||
Spring 2008 Session | |||
'''Lecturer:''' Dr. Mauricio Barahona | '''Lecturer:''' Dr. Mauricio Barahona | ||
==Topics== | ==Topics== | ||
*'''Optimization''' | *[[User:Johnsy/Advanced Modelling in Biology/Optimization|'''Optimization''']] | ||
**Introduction to optimization: definitions and concepts, standard formulation. Convexity. Combinatorial explosion and computationally hard problems. | **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. | **Least squares solution: pseudo-inverse; multivariable case. Applications: data fitting. | ||
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**Heuristic algorithms: simulated annealing (discrete version); evolutionary (genetic) algorithms. Applications. | **Heuristic algorithms: simulated annealing (discrete version); evolutionary (genetic) algorithms. Applications. | ||
*'''Discrete Systems''' | *[[User:Johnsy/Advanced Modelling in Biology/Discrete Systems|'''Discrete Systems''']] | ||
**Linear difference equations: general solution; auto-regressive models; relation to z-transform and Fourier analysis. | **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. | **Nonlinear maps: fixed points; stability; bifurcations. Poincaré section. Cobweb analysis. Examples: logistic map in population dynamics (period-doubling bifurcation and chaos); genetic populations. | ||
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**Networks in biology: graph theoretical concepts and properties; random graphs; deterministic, constructive graphs; small-worlds; scale-free graphs. Applications in biology, economics, sociology, engineering. | **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. | **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. | ||
==Primer/Notes== | |||
*[http://openwetware.org/images/8/81/AMBPrimer.pdf AMB Primer (.pdf)] |
Latest revision as of 06:20, 10 August 2008
Advanced Modelling in Biology
Spring 2008 Session
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.