Differentiable latent structure discovery for interpretable forecasting in clinical time series

Alexandre Kalimouttou; Anita Burgun; Francis Bach; Ivan Lerner; Jean Feydy

arxiv: 2604.27967 · v1 · submitted 2026-04-30 · 💻 cs.LG

Differentiable latent structure discovery for interpretable forecasting in clinical time series

Ivan Lerner , Jean Feydy , Alexandre Kalimouttou , Anita Burgun , Francis Bach This is my paper

Pith reviewed 2026-05-07 05:26 UTC · model grok-4.3

classification 💻 cs.LG

keywords gaussian processesstructure learningdirected acyclic graphsclinical time seriesforecastinginterpretabilitylatent pathwayselectronic health records

0 comments

The pith

A continuous-time Gaussian process learns sparse directed graphs of clinical variable dependencies to improve forecasting from irregular EHR data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces StructGP, a multi-task Gaussian process that combines process convolutions with differentiable structure learning to recover a sparse, ordered DAG of how variables such as blood pressure and creatinine influence one another over time. This structure is learned end-to-end under sparsity and acyclicity constraints, while still delivering full posterior uncertainty. The approach is tested on irregular electronic health records from septic shock patients, where it produces more accurate short-horizon forecasts than either independent per-variable models or unstructured kernels. An extension called LP-StructGP further adds shared latent pathways that capture common progression patterns across patients via subject-specific coupling filters. The central motivation is to obtain both better predictive performance and human-interpretable dependency graphs without first forcing the data onto a regular time grid.

Core claim

StructGP couples process convolutions with differentiable structure learning to uncover a sparse, ordered DAG of inter-variable dependencies in continuous-time multi-task Gaussian processes, while LP-StructGP adds latent pathways inferred via subject-specific coupling filters and softmax gating; both are trained with augmented Lagrangian methods under sparsity and acyclicity constraints using low-rank updates, and on a MIMIC-IV septic shock cohort they reduce 6-hour RMSE from 0.88 to 0.68, achieve superior calibration, and recover ground-truth graphs in simulations as cohort size grows.

What carries the argument

StructGP, a continuous-time multi-task Gaussian process that couples process convolutions with differentiable structure learning to produce a sparse ordered DAG of inter-variable dependencies under acyclicity and sparsity constraints.

If this is right

Short-horizon (6 h) forecasting RMSE drops from 0.88 to 0.68 on septic shock data with improved calibration (coverage 0.96 vs. 0.84).
Adding 15 extra inputs yields markedly lower error than unstructured kernels (0.63 vs. 3.02).
On the PhysioNet Challenge with 12k patients and 41 variables, competitive accuracy is achieved while retaining calibrated uncertainty.
In simulations the method recovers ground-truth graphs with Structural Hamming Distance approaching zero as cohort size grows.
Latent pathways capture cross-patient progression patterns via shared, temporally shifted trajectories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same differentiable DAG-learning machinery could be applied to other irregularly sampled multivariate time series such as financial or sensor data.
Recovered pathways might serve as a data-driven way to stratify patients into progression subtypes for targeted interventions.
Because the model outputs both a graph and full posterior trajectories, it could support what-if queries about the effect of changing one observed variable on future forecasts.

Load-bearing premise

The learned sparse DAG and latent pathways reflect genuine clinical dependencies rather than modeling artifacts or selection biases in the EHR data.

What would settle it

If the Structural Hamming Distance between the recovered DAG and a known ground-truth graph fails to approach zero as cohort size increases in controlled simulations, or if short-horizon RMSE on new irregular clinical data shows no improvement over independent-task baselines.

read the original abstract

Background: Timely, uncertainty-aware forecasting from irregular electronic health records (EHR) can support critical-care decisions, yet most approaches either impute to a grid or sacrifice interpretability. We introduce StructGP, a continuous-time multi-task Gaussian process that couples process convolutions with differentiable structure learning to uncover a sparse, ordered directed acyclic graph (DAG) of inter-variable dependencies while preserving principled uncertainty. We further propose LP-StructGP, which augments StructGP with latent pathways-shared, temporally shifted trajectories inferred via subject-specific coupling filters and a softmax gating mechanism-to capture cross-patient progression patterns. Both models are trained under sparsity and acyclicity constraints (augmented Lagrangian, Adam) using scalable low-rank updates. Results: In simulations, the approach reliably recovers ground-truth graphs (Structural Hamming Distance approaching 0 as cohorts grow) and pathway assignments (high Adjusted Rand Index). On a MIMIC-IV septic shock cohort (n=1,008; norepinephrine, creatinine, mean arterial pressure), StructGP improves short-horizon (6 h) forecasting over independent-task baselines (average RMSE 0.68 [95%CI: 0.63--0.74] vs. 0.88 [0.83-0.94]) and, with 15 additional inputs, markedly outperforms unstructured kernels (0.63 [0.58-0.69] vs. 3.02 [2.85-3.18]) with superior calibration (coverage 0.96 vs. 0.84). On the PhysioNet Challenge (12k patients, 41 variables), StructGP attains competitive accuracy (MAE 3.72e-2) relative to a state-of-the-art graph neural model while maintaining calibrated uncertainty. Conclusion: These results show that structured process convolutions with latent pathways deliver interpretable, scalable, and well-calibrated forecasting for irregular clinical time series.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

StructGP learns a sparse DAG inside a continuous-time GP for clinical forecasting and beats baselines on MIMIC-IV, but the interpretability claim lacks any check that the recovered edges reflect real physiology rather than EHR artifacts.

read the letter

The paper's core move is to embed differentiable DAG learning (via augmented Lagrangian) into a multi-task GP that uses process convolutions for irregular sampling. This lets the model infer a sparse, ordered graph of variable dependencies while keeping uncertainty calibration. They add LP-StructGP on top, which shares latent pathways across patients through subject-specific filters and softmax gating. Both are trained end-to-end with low-rank updates for scalability. On simulations the graph recovery is strong, with SHD dropping near zero as cohort size grows. On the MIMIC-IV septic shock set (n=1008) StructGP cuts 6-hour RMSE from 0.88 to 0.68 versus independent-task GPs and from 3.02 to 0.63 versus unstructured kernels, with better coverage. The PhysioNet run is competitive with a graph neural baseline while staying calibrated. That is the concrete advance: a single model that does structure discovery, forecasting, and uncertainty in one continuous-time framework without gridding the data. The soft spot is exactly where the stress-test points. The authors report no post-hoc inspection of the learned edges on real data—no check that norepinephrine points to MAP in the expected direction, no comparison against known clinical pathways, no sensitivity to treatment-policy confounders that are common in EHR. In observational data the optimizer can pick any of several DAGs that fit the predictive distribution equally well, and protocol-driven correlations plus MNAR missingness make artifactual graphs likely. Without that validation the “interpretable” label rests on simulation recovery alone. The latent-pathway component is also presented without ablation on how much it adds beyond the DAG. This work is aimed at people building decision-support tools for critical care who want both accuracy and some form of structure. A reader who cares about GP extensions or differentiable structure learning will find the technical integration useful even if the clinical story needs more evidence. It is coherent on its own terms and reports concrete numbers with intervals, so it deserves a serious referee who can press on the graph-validation gap and ask for ablations. I would send it out rather than desk-reject.

Referee Report

3 major / 2 minor

Summary. The manuscript presents StructGP, a continuous-time multi-task Gaussian process that couples process convolutions with differentiable structure learning to recover a sparse, ordered DAG of inter-variable dependencies under acyclicity and sparsity constraints (via augmented Lagrangian), enabling interpretable forecasting of irregular clinical time series. It further introduces LP-StructGP, which augments the model with latent pathways inferred through subject-specific coupling filters and softmax gating to capture cross-patient patterns. Simulations demonstrate reliable ground-truth graph recovery (SHD approaching 0) and pathway assignment (high ARI). On a MIMIC-IV septic shock cohort (n=1,008), StructGP reports improved 6-hour forecasting (RMSE 0.68 [0.63-0.74] vs. 0.88 [0.83-0.94] for independent-task baselines; 0.63 [0.58-0.69] vs. 3.02 [2.85-3.18] vs. unstructured kernels with 15 extra inputs) and better calibration (coverage 0.96 vs. 0.84), with competitive MAE (3.72e-2) on the PhysioNet Challenge (12k patients, 41 variables).

Significance. If the recovered DAGs and latent pathways prove robust and clinically meaningful rather than artifacts, the work could meaningfully advance uncertainty-aware, interpretable forecasting in critical care by marrying the principled uncertainty of Gaussian processes with scalable differentiable structure discovery. The reported predictive gains, especially the large margin when scaling inputs, and the simulation-based structure recovery provide a solid empirical foundation; however, the interpretability contribution hinges on real-data validation that is currently absent.

major comments (3)

[§4.2 (MIMIC-IV Experiments)] §4.2 (MIMIC-IV Experiments) and §5 (PhysioNet results): The central claim pairs forecasting gains with interpretability via the recovered sparse DAG and latent pathways, yet the real-data experiments report only aggregate RMSE, MAE, and calibration metrics with no post-hoc analysis, visualization, or validation of the learned graph structure. There is no assessment of whether recovered edges align with clinical physiology (e.g., norepinephrine → MAP directionality or creatinine feedback loops) or literature on septic shock. Simulations show SHD recovery under known ground truth, but this does not address the skeptic's concern that observational EHR artifacts (treatment policies, MNAR missingness, confounding) may drive the structure; without such checks the 'interpretable' qualifier is unsupported on the primary application data.
[Methods (Structure Learning subsection)] Methods (Structure Learning subsection): The model relies on two explicit free parameters—the DAG sparsity regularization strength and the acyclicity penalty parameter—optimized via augmented Lagrangian and Adam. No sensitivity analysis, ablation on penalty scheduling, or stability across random seeds is reported for the learned DAG on real data. This is load-bearing because multiple DAGs can yield similar predictive distributions under the same constraints; without demonstrating robustness the structure cannot be confidently interpreted as reflecting genuine dependencies.
[§3 (LP-StructGP Extension)] §3 (LP-StructGP Extension): The latent pathways component (subject-specific coupling filters + softmax gating) is presented as capturing cross-patient progression, yet no ablation isolates its contribution to the forecasting improvements versus base StructGP, nor is there analysis of whether the inferred pathways are consistent across patients or merely absorb residual variance. This weakens the claim that the full model delivers both structure discovery and improved calibration.

minor comments (2)

[Abstract] Abstract and §4.1: The phrase 'with 15 additional inputs' is used without listing or referencing the specific variables; a table or appendix listing them (and their preprocessing) would aid reproducibility.
[Figures] Figures (simulation and real-data DAG visualizations): Captions should explicitly state what error bars or variability measures represent (e.g., across random seeds or patients) and include legends for node/edge semantics.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which correctly identify gaps in validating the interpretability of the recovered structures on real clinical data. We address each point below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

Referee: §4.2 (MIMIC-IV Experiments) and §5 (PhysioNet results): The central claim pairs forecasting gains with interpretability via the recovered sparse DAG and latent pathways, yet the real-data experiments report only aggregate RMSE, MAE, and calibration metrics with no post-hoc analysis, visualization, or validation of the learned graph structure. There is no assessment of whether recovered edges align with clinical physiology (e.g., norepinephrine → MAP directionality or creatinine feedback loops) or literature on septic shock. Simulations show SHD recovery under known ground truth, but this does not address the skeptic's concern that observational EHR artifacts (treatment policies, MNAR missingness, confounding) may drive the structure; without such checks the 'interpretable' qualifier is unsupported on the primary application data.

Authors: We agree that post-hoc validation of the DAG on real data is essential to support the interpretability claim and that simulations alone do not fully address potential EHR artifacts. In the revised manuscript we will add a dedicated subsection with visualizations of the learned DAG from the MIMIC-IV septic shock cohort, highlighting key edges (including norepinephrine to MAP directionality and creatinine-related loops) and discussing their alignment with established septic shock physiology literature. We will explicitly note that the model captures predictive dependencies on observational data and discuss limitations arising from treatment policies and missingness, without claiming strict causality. While a full expert clinical panel review is outside the scope of this methodological contribution, the added analysis will provide concrete evidence that the structures reflect physiologically plausible relationships rather than pure artifacts. revision: yes
Referee: Methods (Structure Learning subsection): The model relies on two explicit free parameters—the DAG sparsity regularization strength and the acyclicity penalty parameter—optimized via augmented Lagrangian and Adam. No sensitivity analysis, ablation on penalty scheduling, or stability across random seeds is reported for the learned DAG on real data. This is load-bearing because multiple DAGs can yield similar predictive distributions under the same constraints; without demonstrating robustness the structure cannot be confidently interpreted as reflecting genuine dependencies.

Authors: We acknowledge that robustness to the sparsity and acyclicity penalties is critical for confident interpretation. Although internal development runs showed stable core structures, these checks were not reported. In the revision we will add a sensitivity analysis subsection that varies both penalty strengths over a grid, reports edge overlap and SHD relative to a reference DAG on the MIMIC-IV data, and includes stability metrics (e.g., edge agreement) across five random seeds. This will demonstrate that the primary dependencies remain consistent and address the concern that multiple DAGs could produce similar forecasts. revision: yes
Referee: §3 (LP-StructGP Extension): The latent pathways component (subject-specific coupling filters + softmax gating) is presented as capturing cross-patient progression, yet no ablation isolates its contribution to the forecasting improvements versus base StructGP, nor is there analysis of whether the inferred pathways are consistent across patients or merely absorb residual variance. This weakens the claim that the full model delivers both structure discovery and improved calibration.

Authors: We agree that an explicit ablation is required to isolate the latent pathways' contribution. In the revised manuscript we will add an ablation study directly comparing StructGP and LP-StructGP on the MIMIC-IV 6-hour forecasting task, reporting differences in RMSE, calibration coverage, and MAE. We will further analyze pathway consistency by computing adjusted Rand index on the softmax gating assignments across patients and include visualizations of representative subject-specific coupling filters to illustrate whether they capture systematic temporal shifts or primarily residual variance. These additions will clarify the incremental value of the LP extension. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results and model definition remain independent.

full rationale

The paper defines StructGP via process convolutions coupled to differentiable DAG learning under standard augmented-Lagrangian acyclicity and sparsity penalties. Forecasting performance (RMSE, MAE, calibration) is obtained by direct comparison against independent-task GPs and unstructured kernels on held-out MIMIC-IV and PhysioNet data; these metrics are not algebraically forced by the same fitted parameters that define the model. Graph recovery is assessed via SHD and ARI on simulations with known ground truth, again an external measurement rather than a self-referential identity. No equation equates a claimed prediction to a quantity defined by the model itself, and no load-bearing step reduces to a self-citation whose content is unverified. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

The central claim rests on standard Gaussian-process modeling assumptions for irregular data plus the effectiveness of differentiable optimization for recovering clinically meaningful structure. Free parameters include regularization strengths for sparsity and acyclicity. New entities (latent pathways and coupling filters) are introduced without external falsifiable evidence beyond improved fit on the reported cohorts.

free parameters (2)

DAG sparsity regularization strength
Controls the degree of sparsity in the learned graph during augmented-Lagrangian optimization.
Acyclicity penalty parameter
Enforces the directed-acyclic-graph constraint in the structure-learning objective.

axioms (2)

domain assumption Clinical variables can be represented as coupled continuous-time Gaussian processes linked by process convolutions.
Core modeling choice that enables handling of irregular sampling without imputation.
domain assumption Inter-variable dependencies form a sparse directed acyclic graph that can be recovered differentiably.
Assumed to deliver both interpretability and improved forecasting.

invented entities (2)

latent pathways no independent evidence
purpose: Shared, temporally shifted trajectories that capture cross-patient progression patterns.
Introduced in LP-StructGP to improve performance on common disease trajectories.
subject-specific coupling filters no independent evidence
purpose: Infer latent pathways via softmax gating mechanism.
Component of the LP-StructGP extension for patient-specific modulation.

pith-pipeline@v0.9.0 · 5660 in / 1803 out tokens · 84103 ms · 2026-05-07T05:26:39.715143+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

write newline

" write newline " cite write " FUNCTION editor.postfix editor num.names #1 > "( )" "( )" if FUNCTION editor.trans.postfix editor num.names #1 > "( )" "( )" if FUNCTION trans.postfix translator num.names #1 > "( )" "( )" if FUNCTION authors.editors.reflist.apa5 'field := 'dot := field num.names 'numnames := numnames 'format.num.names := format.num.names na...

work page
[2]

sn-aps.bst

FUNCTION identify.aps.version "sn-aps.bst" " [2024/07/19 v1.1 APS bibliography style]" * top ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year eprint archive archivePrefix primaryClass adsurl adsnote version lab...

work page 2024
[3]

write newline

" write newline "" before.all 'output.state := FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION n.separate 't := "" #0 'numnames := t empty not t #-1 #1 subs...

work page
[4]

sn-basic.bst

FUNCTION identify.basic.version "sn-basic.bst" " [2024/07/19 v1.1 bibliography style]" * top ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year archivePrefix primaryClass adsurl adsnote version lab...

work page 2024
[5]

write newline

" write newline "" before.all 'output.state := FUNCTION add.period duplicate empty 'skip "." * add.blank if FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION ...

work page
[6]

write newline

" write newline "" before.all 'output.state := FUNCTION output.doi doi empty skip "doi:" doi * "" * output if FUNCTION format.archive archivePrefix empty "" archivePrefix ":" * if FUNCTION format.primaryClass primaryClass empty "" " [" primaryClass * "] " * if FUNCTION format.eprint eprint empty "" archive empty " https://arxiv.org/abs/" eprint * " " * " ...

work page
[7]

write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTION find.integer 't := #0 'int := int not t empty not and t #1 #1 substring 's :=...

work page
[8]

write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTION find.integer 't := #0 'int := int not t empty not and t #1 #1 substring 's :=...

work page
[9]

sn-nature.bst

FUNCTION identify.nature.version "sn-nature.bst" " [2024/07/19 v1.1 bibliography style]" * top ENTRY address archive author booktitle chapter edition editor eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url doi volume year archivePrefix primaryClass eid adsurl adsnote version l...

work page 2024
[10]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

work page
[11]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize ":" * " " *...

work page
[12]

sn-vancouver-num.bst

FUNCTION identify.vancouver.version "sn-vancouver-num.bst" " [2024/07/19 v1.1 Vancouver bibliography style]" * top ENTRY address assignee author booktitle chapter cartographer day edition editor howpublished institution inventor journal key keywords month note number organization pages part publisher school series title type volume word year eprint doi ur...

work page 2024
[13]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize ":" * " " *...

work page

[1] [1]

write newline

" write newline " cite write " FUNCTION editor.postfix editor num.names #1 > "( )" "( )" if FUNCTION editor.trans.postfix editor num.names #1 > "( )" "( )" if FUNCTION trans.postfix translator num.names #1 > "( )" "( )" if FUNCTION authors.editors.reflist.apa5 'field := 'dot := field num.names 'numnames := numnames 'format.num.names := format.num.names na...

work page

[2] [2]

sn-aps.bst

FUNCTION identify.aps.version "sn-aps.bst" " [2024/07/19 v1.1 APS bibliography style]" * top ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year eprint archive archivePrefix primaryClass adsurl adsnote version lab...

work page 2024

[3] [3]

write newline

" write newline "" before.all 'output.state := FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION n.separate 't := "" #0 'numnames := t empty not t #-1 #1 subs...

work page

[4] [4]

sn-basic.bst

FUNCTION identify.basic.version "sn-basic.bst" " [2024/07/19 v1.1 bibliography style]" * top ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year archivePrefix primaryClass adsurl adsnote version lab...

work page 2024

[5] [5]

write newline

" write newline "" before.all 'output.state := FUNCTION add.period duplicate empty 'skip "." * add.blank if FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION ...

work page

[6] [6]

write newline

" write newline "" before.all 'output.state := FUNCTION output.doi doi empty skip "doi:" doi * "" * output if FUNCTION format.archive archivePrefix empty "" archivePrefix ":" * if FUNCTION format.primaryClass primaryClass empty "" " [" primaryClass * "] " * if FUNCTION format.eprint eprint empty "" archive empty " https://arxiv.org/abs/" eprint * " " * " ...

work page

[7] [7]

write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTION find.integer 't := #0 'int := int not t empty not and t #1 #1 substring 's :=...

work page

[8] [8]

write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTION find.integer 't := #0 'int := int not t empty not and t #1 #1 substring 's :=...

work page

[9] [9]

sn-nature.bst

FUNCTION identify.nature.version "sn-nature.bst" " [2024/07/19 v1.1 bibliography style]" * top ENTRY address archive author booktitle chapter edition editor eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url doi volume year archivePrefix primaryClass eid adsurl adsnote version l...

work page 2024

[10] [10]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

work page

[11] [11]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize ":" * " " *...

work page

[12] [12]

sn-vancouver-num.bst

FUNCTION identify.vancouver.version "sn-vancouver-num.bst" " [2024/07/19 v1.1 Vancouver bibliography style]" * top ENTRY address assignee author booktitle chapter cartographer day edition editor howpublished institution inventor journal key keywords month note number organization pages part publisher school series title type volume word year eprint doi ur...

work page 2024

[13] [13]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize ":" * " " *...

work page