Pith Number

pith:6MI7ZK5G

pith:2026:6MI7ZK5GVNSIBUVEVT67TDEZ55

not attested not anchored not stored refs resolved

Multi-resolution Spatial Graphical Regression Models for Hierarchical Spatial Transcriptomics Data

Aaron M. Udager, Allison M. May, Evan T. Keller, Liying Chen, Satwik Acharyya, Veerabhadran Baladandayuthapani

Bayesian model allows gene networks to vary across hierarchical spatial domains in tumors.

arxiv:2605.16804 v1 · 2026-05-16 · stat.AP

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The proposed model allows precision matrices to vary across hierarchically structured spatial domains, capturing both local and global organization within the tumor.

C2weakest assumption

The assumption that spatial proximity and pathological gradients provide a reliable basis for borrowing strength in the edge selection strategy, as described in the spatially structured edge selection component of the model.

C3one line summary

mSGR is a Bayesian framework that infers spatially varying gene regulatory networks from multi-resolution hierarchical spatial transcriptomics data using Gaussian process priors and variational Bayes inference.

References

14 extracted · 14 resolved · 0 Pith anchors

[1] The term exp(−agp(||sk||2 2 +||tk||2

[2] Notably, whena gp = 0, the modified squared exponential kernel becomes a standard exponential kernel

[3] The primary barrier to implementing GPs lies in their significant computational and 38 numerical challenges 2013

[4] Updateωk ii: ωk ii∼Gamma   Nk 2 +aω, 1 2 E  Yi(Sk)− ∑ j̸=i Hk ij·˜vk ij·I(zk ij >0)  2 +bω  . 43

[5] Update Λ ij: E−Λijl=E−Λij { −1 2 (Λij−Zij)T (Λij−Zij)− 1 2σ2 Λi (Λij−mΛi,prior )TU−1(Λij−mΛi,prior ) } Λij∼N   ( I+ 1 σ2 Λi U−1 )−1( EZij + 1 σ2 Λi U−1mΛi,prior ) , ( I+ 1 σ2 Λi U−1 )−1 

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:23.081751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f311fcaba6ab6480d2a4acfdf98c99ef77bec815195bff90570fa796fe562cec

Aliases

arxiv: 2605.16804 · arxiv_version: 2605.16804v1 · doi: 10.48550/arxiv.2605.16804 · pith_short_12: 6MI7ZK5GVNSI · pith_short_16: 6MI7ZK5GVNSIBUVE · pith_short_8: 6MI7ZK5G

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6MI7ZK5GVNSIBUVEVT67TDEZ55 \
  | 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: f311fcaba6ab6480d2a4acfdf98c99ef77bec815195bff90570fa796fe562cec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e82e538254ca87dd5a88a488599692aa54067ba6dbcc0b8e8f5fd71f3e9722f2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "stat.AP",
    "submitted_at": "2026-05-16T04:17:07Z",
    "title_canon_sha256": "3aaba8e0e4c2732baa4353452755fe7f4d85e99d1fdad22f8bc960b5fc2537cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16804",
    "kind": "arxiv",
    "version": 1
  }
}