This repository contains my assignments in the course Dynamics, Networks and Computation:
- Ex1 - This assignment explores the robustness and structure of networks through node removal experiments, MCMC sampling, and edge-swapping methods. I analyzed both real and synthetic networks, implemented sampling techniques for the configuration model, and studied uniformity and convergence. Key topics include random vs. targeted attacks, phase transitions, power-law degree sequences, and Markov Chain-based graph sampling.
- Ex2 - This assignments explores dynamic behaviors in biological systems through computational simulations and analysis. It covers bacterial population growth using stochastic models, simulates feed-forward gene regulatory networks with and without noise, and implements Hill functions for soft logic gates. The final section models gene regulation in the lac operon and demonstrates how biological systems can mimic a NAND gate. All simulations and analyses are implemented in Python using numerical methods.
- Ex3 - This assignments explores memory, regulation, and evolutionary models in biological networks. It begins with implementing Hopfield networks to store and retrieve binary image patterns, including analysis of stochastic updates and local connectivity. It then simulates optimal regulation under noisy environmental sensing, evaluating when regulatory strategies are beneficial. Finally, it examines protein interaction networks and models their evolution using duplication-mutation mechanisms to analyze structural properties and compare to null models.
- Ex4 - This assignment models emergent dynamics in two classic systems. It extends Rule-184 traffic cellular automata with speed-limits, look-ahead cooperation, and crash removal to map the fundamental flow diagram ϕ(ρ). It then solves the Gray-Scott reaction–diffusion PDE on a 2-D grid, reproducing and perturbing spot/stripe patterns. All simulations are Numba-accelerated; outputs include flow-density plots and time-lapse pattern movies.