discrete-heat-kernels-simplicial

Apply heat kernel smoothing on k-simplices using the Hodge Laplacian.

2|Updated Feb 12, 2026

Search Tags:#higher-order #brain-networks #simplicial #heat-kernel #hodge-laplacian #topological-signal-processing

Ready to run

npx skills add https://github.com/hiyenwong/ai_collection --skill discrete-heat-kernels-simplicial

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: discrete-heat-kernels-simplicial
Source: https://github.com/hiyenwong/ai_collection/tree/main/collection/skills/discrete-heat-kernels-simplicial
Command: npx skills add https://github.com/hiyenwong/ai_collection --skill discrete-heat-kernels-simplicial

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Discrete heat kernel smoothing on simplicial complexes extends classical signal processing to higher-dimensional structures, enabling denoising and analysis of signals on k-simplices beyond vertices and edges, with potential applications in functional brain networks.

Core Features & Use Cases

Simplicial complex construction and allocation of higher-order structures
Hodge Laplacian based diffusion for smoothing signals on k-simplices
Boundary operators and efficient sparse computation
Applications to higher-order network analysis and brain connectivity

Quick Start

Load your simplicial dataset and apply heat kernel smoothing on a chosen k to begin processing.

Frequently Asked Questions about discrete-heat-kernels-simplicial

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I apply heat kernel smoothing to signals on simplicial complexes?▼

Heat kernel smoothing on simplicial complexes applies diffusion across k-simplices using the Hodge Laplacian to denoise higher-order signals. You load your dataset, select a dimension k, and the process regularizes signals beyond standard vertices and edges.

What is topological signal processing for higher-order brain networks?▼

Topological signal processing for higher-order brain networks extends data analysis beyond pairwise connections by representing data as simplicial complexes. It uses Hodge Laplacian diffusion to smooth and analyze signals across these multi-node structures.

Do I need Python and gudhi to compute the Hodge Laplacian for higher-order network analysis?▼

Yes, computing the Hodge Laplacian for higher-order network analysis requires a Python environment with numpy, scipy, gudhi, networkx, and nibabel. These dependencies are essential for constructing simplicial complexes and building boundary operators.

What's the best way to denoise signals on k-simplices rather than just graph vertices?▼

To denoise signals on k-simplices rather than just graph vertices, apply discrete heat kernel diffusion over a constructed simplicial complex. This approach leverages boundary operators and the Hodge Laplacian to regularize higher-order topological signals.

When should I use simplicial complex construction for functional brain connectivity data?▼

Use simplicial complex construction for functional brain connectivity data when you need to model and smooth higher-order interactions beyond standard edges. It enables Hodge Laplacian based diffusion to denoise signals across multi-node structures.

How does heat kernel diffusion on the Hodge Laplacian handle sparse computation?▼

Heat kernel diffusion on the Hodge Laplacian handles sparse computation by utilizing efficient boundary operators. This allows the smoothing process to scale when applying diffusion-based regularization across chosen dimensions of the simplicial complex.