I add a tag to the publisher @physreve.bsky.social

Thanks to everyone who supported this work 🙏
Exploring high-dimensional geometry continues to reveal new insights into complex systems 🌌

Y. Horiike and S. Fujishiro, Orthogonal projections of hypercubes, Phys. Rev. E 112, 045304 (2025)

📕 Phys. Rev. E →
doi.org/10.1103/v291...

📘 Open-access links:
🧮 arXiv preprint (full text) → doi.org/10.48550/arX...
📗 Nagoya Univ. Repository → hdl.handle.net/2237/0002013...

🎨 Supplementary materials:
🖼️ Poster → doi.org/10.5281/zeno...
🎤 Slides → doi.org/10.5281/zeno...

We explore the mathematical properties of these hypercube projections:
✅ Density of hypercubic vertices
✅ Error bounds
These let us analyze large discrete systems more intuitively 📊

By projecting these spaces, we can:
🔹 Spot hidden patterns in complex data
🔹 Study geometry of energy landscapes
🔹 Connect abstract math to real-world phenomena
This bridges fields from statistical physics to systems biology — and helps us “see” high-dimensional worlds 🔍

High-dimensional binary spaces describe systems with many “on/off” states — like gene networks, spin systems, or neural models 💡
But visualizing them is tough 😅
Our work proposes a projection method that maps these giant spaces into 2D or 3D while keeping their structure intact