L1 ⚛ L1-413 ⊙ Testnet

HMM Sequence Alignment and Profile Inference

Computational Biology · Computational genomics

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⬇ L1-413.md

# ⚛ L1 Principle — HMM Sequence Alignment and Profile Inference **ID:** `L1-413` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Computational genomics* > **🎯 Problem class:** statistical inverse · **🧮 Solution space:** HMM profile parameter matrix > **📡 Carrier:** N/A · **🌫 Noise:** multinomial > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555220 --- ## 🧠 1. Introduction **HMM Sequence Alignment and Profile Inference** is a **statistical inverse problem** whose unknown lives in **HMM profile parameter matrix** space, within the **Computational genomics** sub-domain of **Computational Biology**. Measurements consist of N/A via a **sequence emission probability** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · viterbi · alignment operator; O · baum welch · em training operator. Observations are corrupted by multinomial counting noise across categories. Existence of the recovered HMM_profile_parameter_matrix is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 500); sequence_divergence_too_high dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → S · viterbi · alignment → O · baum welch · em training → **y** (detector). ``` y = `O.baum_welch.em_training` `S.viterbi.alignment` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `S.viterbi.alignment` | S · viterbi · alignment operator | | `O.baum_welch.em_training` | O · baum welch · em training operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Computational genomics | | Carrier | N/A | | Problem class | statistical_inverse | | Solution space | HMM_profile_parameter_matrix | | Noise model | multinomial | | Integration axis | sequence_positions | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered HMM_profile_parameter_matrix is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 500); sequence_divergence_too_high dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | alignment_sensitivity_percent | | Secondary | specificity_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `statistical_inverse` · **Forward operator:** `sequence_emission_probability` **Center point:** | Parameter | Unit | Value | |---|---|---| | N sequences | — | 100 | | M model states | — | 200 | | L alignment length | — | 200 | | Sequence identity percent | — | 40 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N sequences | — | 5 – 10000 | | M model states | — | 10 – 2000 | | L alignment length | — | 20 – 5000 | | Sequence identity percent | — | 5 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 80 alignment_sensitivity_percent | Metric | Range | |---|---| | Alignment sensitivity percent | 30 – 100 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **alignment_sensitivity_percent**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf98f8579912e154da9fd2f93ff45db2c8a33fd2ce25458ca1bfa9cd3c29fc578` - **Chain tx hash:** `0xd95947e49ead7244913ccaea703b95ecdd11c9bbf6365b5a263ac302a158f87f` - **Chain block:** `41555220` --- ## File Mapping This bundle consists of: `L1-413.md`, `L1-413.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-413.md` | Source of truth — edit this | Human or LLM | | `L1-413.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-413`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-413.md).
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L2-413-001 HMM Sequence Alignment and Profile Inference — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_tx_hash": "0xd95947e49ead7244913ccaea703b95ecdd11c9bbf6365b5a263ac302a158f87f",
  "domain": "Computational Biology",
  "hardness_fn": {
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    "integration_axis": "sequence_positions",
    "noise_model": "multinomial",
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    "sensing_mechanism": "sequence_emission_probability",
    "solution_space": "HMM_profile_parameter_matrix",
    "sub_domain": "Computational genomics",
    "title": "HMM Sequence Alignment and Profile Inference"
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      "input_format": "measurement_only",
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        "sequence_identity_percent": 40
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      ],
      "M_model_states": [
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      "N_sequences": [
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      ],
      "sequence_identity_percent": [
        5,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Computational genomics",
  "title": "HMM Sequence Alignment and Profile Inference"
}

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