These projects aim to investigate the interconnectedness of network dynamics, epidemics, game theory, and flow in complex systems. The study will employ a combination of theoretical analysis, simulation, and data analysis to gain insights into how these various factors interact and influence the behavior of complex systems.
This project focuses on studying flow and capacity dynamics in graph networks, optimizing network performance, and exploring real-world applications of network flow and capacity. The project will develop algorithms and models for finding the shortest path and maximum flow between two nodes in the Los Angeles road network, search for social-optimum and Wardrop equilibrium, construct tolls, and create a perfect matching algorithm for solving a fundamental problem in graph theory.
The project aims to study the application of Markov chains and French De Groot dynamics in network graphs, analyzing network dynamics using the fundamental concepts of Markov chains such as transition matrices, stationary distributions, and random walks. The French De Groot dynamic will be examined as a model of opinion dynamics in a network, simulating the evolution of opinions among individuals over time. The study will investigate how different parameters affect the system's dynamics and use Python, NumPy, NetworkX, and Matplotlib libraries to implement and visualize the models.
The project's main objective is to simulate the 2009 pandemic in Sweden and evaluate the effectiveness of vaccination as a control measure. It includes sections on simulating epidemics on a random graph with and without vaccination, estimating the social structure of the Swedish population and disease-spread parameters, and optional simulations of pandemic spread using a random graph and simulated annealing to estimate optimal parameters. The project will implement simulation and optimization algorithms in a programming language and analyze the results to gain insights into disease spread and control measures. The project also explores the graph coloring technique for distributed learning in potential games, with two practical applications presented. Both applications define a set of possible states, and a node updates its color based on a probability distribution. The learning dynamics are the same in both applications, and a Nash equilibrium is found using the presented algorithm while investigating the effect of different parameters on learning dynamics and potential function quality.