Concept

Subgraph isomorphism problem

Related lectures (29)

Explores group quotients and push-outs, discussing isomorphisms and surjectivity in different scenarios.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Statistical analysis of network data

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Networked Control Systems: Convergence Rate and Digraphs

Explores convergence rate in networked control systems and consensus in digraphs, emphasizing the challenges of computing Pess(A) and weight assignment.

Low Diameter Random Partitioning

Discusses Low Diameter Randomized Decomposition and graph partitioning for edge cuts and coloring.

Soft Graphs and Subgraphs

Covers soft graphs and induced subgraphs in graph theory.

Subgraphs vs Induced Subgraphs

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Categories: Functors, and Natural Transformations

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

Connected Components

Explores connected components in a decked space and the well-defined application of functions.

Mean field computation

Explores the computation of mean field and effective field in message passing algorithms.

Spin Model Exercises

Covers exercises on the spin model, independent set, matching, and increasing functions.

Abelianization of Fundamental Group

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

Whittaker Model: Properties and Analytic Continuation

Covers the properties of the Whittaker model and its analytic continuation.

Networked Control Systems: Consensus Algorithms in Digraphs

Explores consensus algorithms in digraphs, focusing on scenarios where the digraph is not strongly connected.

Introduction to Graph Theory

Covers the basics of graph theory, including network flows, degrees of vertices, walks, and subgraphs.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

Homotopical Algebra

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Isomorphism of Groups

Covers bijections between automorphisms and equivariant bijections in group isomorphisms.

Networks: Definitions

Covers the concept of networks, graphs, subgraphs, directed graphs, and indegree in network theory.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.