Computational Biology-ID: Information‑Field Greedy Algorithms

This repository contains the official implementation of the algorithms described in:

Validation of the Real-Imaginary Duality Principle in Core Challenges of Computational Biology: From Sequencing by Hybridization to RNA Inverse Folding Hongkui Liu, Kai Huang (2026)

The work introduces a unified Real‑Imaginary Duality Principle that solves two NP‑hard problems – Sequencing by Hybridization (SBH) and RNA inverse folding – exactly and in linear time, without training data or parameter tuning.

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🔬 Core Algorithm Entry Point

The sole entry point for the exact, linear‑time SBH assembler is:

SBH/sbh_greedy_assembler.py

This script implements the information‑field greedy algorithm as described in Section 2.1 of the paper:

• Virtual space: De Bruijn graph topology (legal overlaps)
• Real space: observed k‑mer multiplicities ("fuel")
• Dynamics: at each step, choose the legitimate successor with the highest remaining fuel
• Automatically discards isolated error k‑mers

All other SBH scripts in the SBH/ directory are supplementary validation or extended variants (lookahead, full GL dynamics, error‑position scans, complexity benchmarks). They are not required to reproduce the core linear‑time results.

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📁 Repository Structure

ComputationalBiology-ID/
├── SBH/                                   # DNA assembly (SBH) algorithms
│   ├── sbh_greedy_assembler.py            # ★ CORE ALGORITHM ★ (linear-time greedy)
│   ├── sbh_lookahead_greedy.py            # Lookahead variant (diffusion term)
│   ├── sbh_full_gl_dynamics.py            # Full GL dynamics with backtracking
│   ├── sbh_error_scan.py                  # Error rate vs. coverage scan (Table 1)
│   ├── sbh_error_position_scan.py         # 0.1% error-position determinism (seeds)
│   ├── complexity_race.py                 # Linear vs. exponential runtime (Fig. 1)
│   └── ... (logs, test outputs)
├── RNA_inverse_folding/                   # RNA secondary structure design
│   ├── rna_inverse_folding.py             # Free-energy gradient flow solver
│   └── Eterna100_Solved_Log.txt           # 96/99 puzzles solved (97.0%)
└── README.md                              # Updated documentation

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🧬 SBH: Linear‑Time DNA Assembly

Run the core algorithm

cd SBH
python sbh_greedy_assembler.py

Expected output (perfect spectrum, 5000 bp, k=11)

Assembled 5000 bp in 4.8 seconds
Coverage: 100.00%
Reconstruction matches reference exactly.

Reproduce main results from the paper

Experiment	Script	Paper reference
Error‑position determinism (0.1% error)	sbh_error_position_scan.py	Section 2.2, Table 1
Graceful degradation (2% error → 83.5% coverage)	sbh_lookahead_greedy.py	Section 2.2, Table 1
Complexity comparison (greedy vs. backtracking)	complexity_race.py	Section 2.3, Fig. 1
Full GL dynamics (backtracking + 2‑step lookahead)	sbh_full_gl_dynamics.py	Supplementary

All scripts automatically simulate a random 5,000 bp genome, inject errors (if applicable), run the assembler, and report coverage, reconstructed length, and longest match.

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🧬 RNA Inverse Folding: Eterna100 Benchmark

cd RNA_inverse_folding
python rna_inverse_folding.py

The solver achieves 97.0% success rate (96/99 puzzles) in 10 seconds total (25.5 ms per puzzle) – surpassing all known fully automated algorithms.

• No pre‑training, no deep learning, no sequence databases.
• Uses only a simplified Turner‑like energy model and a free‑energy gradient flow.
• Unsolved puzzles (Still Life, The Turtle, Snowflake Necklace) are likely undesignable (see Section 2.6 and [5]).

See Eterna100_Solved_Log.txt for the complete list of solved puzzles.

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License

This project is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0).

You are free to share and adapt the material under the following terms:

• Attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
• NonCommercial – You may not use the material for commercial purposes.
• ShareAlike – If you remix, transform, or build upon the material, you must distribute your contributions under the same license.

For commercial use, please contact the authors.

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🧪 Reproducibility

• Random seeds are fixed where needed (e.g., sbh_error_position_scan.py uses seeds 0‑9).
• All experiments run on a single CPU core; no GPU required.
• Python dependencies: torch (only for supplementary scripts), matplotlib, numpy, difflib (standard library).

Install required packages:

pip install torch matplotlib numpy   # optional for supplementary scripts

For core SBH and RNA folding, only the Python standard library is needed.

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