Pith Number

pith:TALNI6PB

pith:2026:TALNI6PBWZ3FROFZJGLHBZWWSD

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Circula-based multivariate distributions on the flat torus, with applications in structural biology

Alix Lh\'eritier, Fr\'ed\'eric Cazals, Guillaume Carri\`ere

A low-rank latent variable model yields the first closed-form normalized distributions on the flat torus that carry explicit covariance structure.

arxiv:2605.12577 v1 · 2026-05-12 · stat.AP

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\pithnumber{TALNI6PBWZ3FROFZJGLHBZWWSD}

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Claims

C1strongest claim

using a low rank covariance structure to define circulae based on a latent variable model, we design the first closed-form normalized distribution on the flat torus T^d--with covariance structure. ... we propose the first models for joint distributions of torsion angles (backbone and side-chains) for neighboring amino-acids in proteins.

C2weakest assumption

That the low-rank covariance structure in the latent variable model adequately captures the true dependencies among torsion angles on the flat torus without significant loss of fidelity or introduction of artifacts for protein data.

C3one line summary

Presents the first closed-form normalized distributions on the flat torus with covariance structure via circula and latent models, then applies them to model joint torsion angles in proteins with SOTA likelihood and sparsity.

References

52 extracted · 52 resolved · 0 Pith anchors

[1] Roger B Nelsen.An introduction to copulas. Springer, 2006 2006

[2] Fonctions de répartition à n dimensions et leurs marges 1959

[3] The estimation method of inference functions for margins for multivariate models 1996

[4] Computing a nearest correlation matrix with factor structure.SIAM Journal on Matrix Analysis and Applications, 31(5):2603–2622, 2010 2010

[5] Vine copula based modeling.Annual Review of Statistics and Its Application, 9(1):453–477, 2022 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:01.600357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9816d479e1b67658b8b9499670e6d690d3ed2be5c0a86cdf498a91a38dffb175

Aliases

arxiv: 2605.12577 · arxiv_version: 2605.12577v1 · doi: 10.48550/arxiv.2605.12577 · pith_short_12: TALNI6PBWZ3F · pith_short_16: TALNI6PBWZ3FROFZ · pith_short_8: TALNI6PB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TALNI6PBWZ3FROFZJGLHBZWWSD \
  | 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: 9816d479e1b67658b8b9499670e6d690d3ed2be5c0a86cdf498a91a38dffb175

Canonical record JSON

{
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    "abstract_canon_sha256": "4e7c5477a07fd7d2b5901534a0506ad257149c136f03a90603f3a451a2033784",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.AP",
    "submitted_at": "2026-05-12T13:15:22Z",
    "title_canon_sha256": "5837fff43e3aaa9d37f25d8a26e6592fc5a327a28f5dadb77182ce42645cd01b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12577",
    "kind": "arxiv",
    "version": 1
  }
}