专题：Topological and Geometric Data Analysis

This cluster of papers focuses on the application of topological data analysis in various scientific and engineering domains. It covers topics such as persistent homology, shape analysis, statistical topology, machine learning, and spatial data.
最新文献
Experimental Discovery of a Universal Continuous Topological Void in Random 3‑SAT

preprint Full Text OpenAlex

Technical Addendum to "A Conditional Proof that P ≠ NP": Detailed Proof Plan for the 1RSB Extension

preprint Full Text OpenAlex

Addendum 8: Exponential Backtracking from the Persistent Topological Void

preprint Full Text OpenAlex

Addendum 7 v2: Rigorous Persistent Second Betti Number β₂ > 0 from 1‑RSB Clustering (Explicit hollow‑triangle construction and FKCK verification)

preprint Full Text OpenAlex

Addendum 7: Persistent Second Betti Number \(\beta_2 > 0\) from 1RSB Clustering

preprint Full Text OpenAlex

Addendum 8 v2: Rigorous Exponential Backtracking from the Persistent Topological Void (Size–width trade‑off for the 1‑RSB solution space)

preprint Full Text OpenAlex

The Anti-Drift Cognitive Control Loop (ADCCL): A Geometric Foundation for Hallucination-Free AI

article Full Text OpenAlex

Experimental Detection of the Overlap Gap Property in Random 3‑SAT and a Novel Graph‑Theoretic Complexity Metric

preprint Full Text OpenAlex

Experimental Evidence of a Topological Obstruction Separating P and NP: Connections to Geometric Complexity Theory, the Padding Barrier, and Algebraic Multiplicity Gaps

preprint Full Text OpenAlex

Quaternionic Funnel Structure of the Syracuse Map

preprint Full Text OpenAlex

近5年高被引文献
Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation

article Full Text OpenAlex 483 FWCI92.8362

On the singularities of a Riemannian manifold

article Full Text OpenAlex 319 FWCI24.9096

What Are Higher-Order Networks?

article Full Text OpenAlex 307 FWCI46.6622

AMBIOSOLAR. Análisis del despliegue de la energía solar en el sureste de la Península ibérica

preprint Full Text OpenAlex 267 FWCI0

Harmonic analysis on the Heisenberg group

book-chapter Full Text OpenAlex 232 FWCI0

Non-invertible higher-categorical symmetries

article Full Text OpenAlex 216 FWCI112.0871

Topological data analysis in biomedicine: A review

review Full Text OpenAlex 156 FWCI21.6339

Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud

article Full Text OpenAlex 130 FWCI17.9499

Fractal photonic topological insulators

article Full Text OpenAlex 122 FWCI17.5845

Liouville Quantum Gravity as a Mating of Trees

book-chapter Full Text OpenAlex 122 FWCI0