Concept

Incidence structure

Related lectures (15)

Explores process unit modeling, balance equations, degrees of freedom, and flowsheet solving.

Explores the Ford Fulkerson algorithm, Max-Flow Min-Cut theorem, Incidence matrix, and network optimization complexity.

Process Models & Parameter Identification

Covers calibrating models using measurements, virtual sensors, data reconciliation, and parameter identification in process models.

The Transhipment Problem: Standard Form

Covers the linear optimization problem of the transhipment model.

The transhipment problem: Total unimodularity

Covers the transhipment problem, optimal solutions, and total unimodularity in matrices.

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

The Transhipment Problem: Total Unimodularity

Covers the transhipment problem, the incidence matrix, and total unimodularity.

Incidence Geometry & Elliptic Curves

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Bézout's Theorem and Cayley-Bacharach

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.

Graphs and Networks: Basics and Applications

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Network Flows Meets Simplex

Explores network flows, simplex method, linear programming, tree solutions, and dual solutions in optimization problems.

Network Flow Algorithms

Covers network flow algorithms, including Max Flow, Min Cut, and Negative Cost Cycle Algorithm, progressing from basic definitions to advanced algorithms like Bellman-Ford and Dijkstra's.

Matrix Tree Theorem

Explores the Matrix Tree Theorem and its application in calculating spanning trees in graphs.

Graphs and matrices

Explores graphs and matrices, including adjacency, degree, and Laplace matrices, Matrix-tree theorem, and spanning trees.

Hypergraphs and Link Prediction: Statistical Analysis of Network Data

Covers hypergraphs, complete hypergraphs, link prediction, and scoring methods in network data analysis.