In this course we will try to answer some of the most pressing questions of life, which will ultimately be: “Why do we die?”
It turns out that in order to answer such a question, we will have to dive into the way as to how Biological systems are organized: what makes them ‘tick’? Why are they so special, when compared to other physical-chemical systems, like the ocean, rocks, or the moon and the stars? Why is it that there are these astonishing scaling laws that seem to hold over almost 25 (!) orders of magnitude in body mass (i.e., from single-cell organisms, with a mass of a few picograms, all the way up to the 30 m long Blue Whale of 160 tons …).
We will see that all Biological systems share three basic principles (‘Newton’s Laws’ for biological systems ….) that we can formulate quantitatively, and on the basis of which we can build a true scientific theory of complex systems that answers the above questions. In a nutshell: “Complex biological systems are characterized by branching fractal networks that have optimized the total energy transfer throughout the network to ‘feed’ the body”.
The theory has been developed by Geoffrey West and his colleagues from the Santa Fé institute of Complex Systems (New Mexico, USA). The work has been published in many papers in Nature, Science, PNAS, etc., and in the course we will introduce and discuss several of their most important papers.
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- Lecture 1: Classical scaling laws (V~R3 and A~R2) to biomechanics, biodynamics
- Lecture 2: Elasticity and Poisseuille flow; introduction Navier-Stokes equations.
- Lecture 3: Fractal geometry
- Lecture 4: The fractal network theory: why do the power laws have exponents ±n/4? Introduction to the three ground principles for scaling in biological distributive networks: the model of West et al. (Santa Fé institute): applied to the heart and blood circulation system, and the lungs
- Lecture 5: Application of the network theory to plants and trees.
- Lecture 6: Application of allometry to growth and death and the crucial role of fractal geometry in biological scaling.
- Lecture 7: Application of allometry to other systems: cities and forests
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Bachelor level:
- 2nd or 3rd year Science (biophysics profile)
- 2nd or 3rd year Physics
- 2nd or 3rd year Mathematics (with Physics minor)
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Basic mathematics, in particular geometric series, basic integrals and differential equations
Basic first-year mechanics
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Homework (exercises): 30%
Written Exam: 70%
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