Topology in Complex Networks: Insights from Topological Data Analysis

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Dynamic Programming: Shortest Paths Algorithms

Explores dynamic programming strategies for finding shortest paths in networks with various algorithms and complexities.

Network clustering

Explores network clustering, spectral clustering, k-means algorithm, eigenvalue properties, block model estimation, and structural similarity measurement.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Interlacing Families and Ramanujan Graphs

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Networked Control Systems: Opportunities

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Graph Models and Brain Connectomics

Explores graph theory in brain connectomics, MRI applications, network analysis relevance, and individual fingerprinting.

Spectral Clustering: Theory and Applications

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Handling Networks: Graph Theory

Explores graph theory concepts, centrality measures, and real-world network properties, providing insights into handling diverse types of networks.

Graph Theory: Girth and Independence

Covers girth, independence, probability, union bound, sets, and hypergraph recoloring.