Welcome to Aya's Blog.
Physics student at NUS, interested in computational physics, crystal structure prediction and density functional theory.
Atomistic modelling of electronic materials under nonequilibrium conditions
Statistical ensembles, nonequilibrium phenomena, density functional theory, the Kohn–Sham approach and periodic systems.
Physics and Technology
How quantum dots, nanowires, carbon nanotubes and graphene connect microscopic structure to electronic states and functional devices.
Central Limit Theorem: MGFs, Proof, and Random Walks
The central limit theorem, its assumptions and MGF proof, with normal approximations, random walks, moment calculations, and worked exercises.
Complex Systems Helpsheet: Probability and Network Formulas
A formula sheet covering the CLT, stable distributions, power laws, BA and ER networks, graph matrices, connectivity, and network metrics.
Network Basics: Graphs, Matrices, Projections, and Connectivity
Graph types, adjacency matrices, bipartite projections, directed components, degrees and two-step neighbors, with worked network examples.
Network Metrics: Centrality, PageRank, Clustering, and Communities
Network distances, centrality, PageRank, cores, clustering, modularity, and BFS complexity, with conditions and a worked four-node example.
Network Models: Preferential Attachment, BA, and Erdős–Rényi
Derive the Barabási–Albert degree distribution through continuum and master equations, then compare preferential attachment with Erdős–Rényi networks.
NetworkX: Graph Construction, Algorithms, and Reproducible Checks
Build and inspect NetworkX graphs, manage attributes, choose algorithms with the right preconditions, and reproduce network-metric calculations.
Complex Systems Practice: Eight Problems and Worked Solutions
Eight worked problems on normal approximations, power laws, Cauchy sums, preferential attachment, graph connectivity, centrality, and BFS complexity.
