Codes on graphs: Models for elementary algebraic topology and statistical physics
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Abstract (arXiv)
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic (n,k) group codes and their information sets; normal realizations of homology and cohomology spaces; dual and hybrid models; and connections with system-theoretic concepts such as observability, controllability, and input/output realizations.
Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). First posted on arXiv 20 Jul 2017.
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Citing papers per year: 2022: 1; 2023: 2; 2024: 1; 2025: 0; 2026: 1.
5 papers.
- 2022Mappings for Marginal Probabilities with Applications to Models in Statistical Physicscited by 1
- 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learningcited by 1
- 2023The Exact Determinant of a Specific Class of Sparse Positive Definite Matricescited by 0
- 2024Topology-Aware Exploration of Energy-Based Models Equilibrium: Toric QC-LDPC Codes and Hyperbolic MET QC-LDPC Codescited by 0
- 2026Accelerated Random-Sweep Gibbs Sampling for Gaussian Graphical Models via Dual Normal Factor Graphscited by 0
- 2026Accelerated Random-Sweep Gibbs Sampling for Gaussian Graphical Models via Dual Normal Factor Graphs30 Jul 2026
- 2024Topology-Aware Exploration of Energy-Based Models Equilibrium: Toric QC-LDPC Codes and Hyperbolic MET QC-LDPC Codes26 Jan 2024
- 2023The Exact Determinant of a Specific Class of Sparse Positive Definite Matrices11 Nov 2023
- 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning28 Jul 2023
- 2022Mappings for Marginal Probabilities with Applications to Models in Statistical Physics10 Aug 2022