Weekly/Biweekly assignments of the course Physical Models of Living Systems. The course aims to teach understanding and explaining the basic concepts and the use of advanced techniques in modeling living systems.
The solutions of the exercises are carried out in the pdf file PMoLS.pdf and in the notebooks present in this repository. Below is a list of the assignments, each accompanied by a brief description, with a link to the corresponding notebook.
- hw01: Consumer Resource Model with 1 species and 1 abiotic resource; comparison between the Quasi Stationary Approximation (QSA) and the full solution
- hw02: Spatial scaling of the SAD
- hw03: Simulation of the Lotka-Volterra equations
- hw04: Modelling ecological interactions through random matrices and analysis of the food web
-
hw05, 06: Simulation of the Generalized Consumer Resource Model in the case
$m=p=5$ ; comparison of the analytical and the numerical solutions, simulation of the QSA -
hw07: Analytical calculation of the avalanche duration probability
$P_>(t)$ if$\lambda_i = \lambda$ for all$t$ and all neurons; simulation of independent heterogeneous Poisson processes - hw08: Study of the stability of the excitatory-inhibitory two neurons system plus simulation both in the stable regime and in the limit cycle regime
- hw09: Hopfield Networks, creation of a network that learns some binary patterns and evolution setting another pattern as initial condition
- hw10: Simulation of the stochastic dynamics of the two stage model, using the Gillespie algorithm