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Building Ramanujan Graphs
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Related lectures (55)
Pseudo Randomness in Graphs
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Explores pseudo randomness in graphs using eigenvalues and polynomials, emphasizing the significance of bunched roots and common interlacers.
Isogenic Graphs: Spectral Analysis and Mathematical Applications
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Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.
Sparsest Cut: ARV Theorem
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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.
Convergence of Random Walks
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Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.
Ramanujan Graphs: Generating Functions and Expander Graphs
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Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.
Sparsest Cut and Concurrent Flow
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Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.
Statistical analysis of network data
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Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.
Diagonalization of Matrices
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Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.
Pseudorandomness: Expander Mixing Lemma
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Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.
Cheeger's Inequality
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Explores Cheeger's inequality and its implications in graph theory.
Sparsest Cut: Leighton-Rao Algorithm
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Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.
Graph Theory Fundamentals
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Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.
Linear Algebra: Vector Spaces and Linear Independence
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Covers vector spaces, operations, and linear independence with examples from polynomials and functions.
Polynomial Characteristic and Eigenvalues
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Covers the concept of polynomial characteristic of a matrix and its relation to eigenvalues.
Connectivity-Informed Brain Activity Interpretation
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Linear Algebra: Normal Equations and Symmetric Matrices
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Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.
Integration on H_pxH and Arithmetic
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Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.
Position Space Approach: Analyzing Banana Feynman Diagrams
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Presents the position space approach to banana Feynman diagrams and their differential equations.
Bellman Ford Algorithm
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Explores the Bellman Ford algorithm for finding the shortest path in graphs with negative edge weights.
Irreducibility Criteria in Rings
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Explores irreducibility criteria in rings, emphasizing linear and reducible polynomials.
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