Pith Number

pith:Q6KKKFK7

pith:2026:Q6KKKFK7VPGFNCUVXQNW3BV5DN

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Numerical Reliability of Logistic Gene Regulatory Network Models: Preventing Expression Shutdown and Robust Integration of Boolean-Derived ODE Systems

Ismail Belgacem

Logistic functions fix the smoothness, numerical stability, and zero-basal-rate flaws of Hill functions in gene regulatory network models.

arxiv:2605.01056 v2 · 2026-05-01 · q-bio.MN · math.DS

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4 Citations open

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Claims

C1strongest claim

Logistic functions f^± resolve all three structural flaws of Hill functions simultaneously: loss of global smoothness, silent complex-valued arithmetic corruption of ODE trajectories, and identically zero basal production rate that traps bistable models in off-states.

C2weakest assumption

That logistic functions with positive basal production accurately represent biological gene regulation at least as well as Hill functions for the systems considered, particularly that the non-zero basal rate does not distort dynamics in ways that invalidate the stability and escape-time results.

C3one line summary

Logistic functions replace Hill functions in gene regulatory network ODE models to ensure global smoothness, real-valued trajectories, positive basal production, and stable numerical integration across small and large networks.

Cited by

1 paper in Pith

Sustained Limit Cycles in the Logistic Two-Gene Genetic Oscillator: A Delay-Driven Hopf Bifurcation

Receipt and verification

First computed	2026-06-19T16:10:55.504194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8794a5155fabcc568a95bc1b6d86bd1b76ee15c7a2582a2e5f6990835d691ccf

Aliases

arxiv: 2605.01056 · arxiv_version: 2605.01056v2 · doi: 10.48550/arxiv.2605.01056 · pith_short_12: Q6KKKFK7VPGF · pith_short_16: Q6KKKFK7VPGFNCUV · pith_short_8: Q6KKKFK7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q6KKKFK7VPGFNCUVXQNW3BV5DN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8794a5155fabcc568a95bc1b6d86bd1b76ee15c7a2582a2e5f6990835d691ccf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b71ef78945f5e5943700ba4610837a1dcb2a0ef6de4e33c7892fde01b0a121e",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-bio.MN",
    "submitted_at": "2026-05-01T19:44:15Z",
    "title_canon_sha256": "f587f51d67d3e38ecc6e5c2846b7d86c5c6ef66449e14b353bfac210e991c3b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01056",
    "kind": "arxiv",
    "version": 2
  }
}