WHY MATHEMATICS?

Why Mathematics? | NicheNet Ligand-to-Target Reasoning: Weighted Networks, Propagation, Regulatory Potential and Activity Ranking

How NicheNet connects sender ligands to receiver target genes through an integrated knowledge graph, ranks explanatory candidates and keeps predictive activity separate from causality.

Why mathematics is important becomes easier to see when a real decision depends on it. This guide follows the mechanism from definitions and dimensions to a worked calculation, validation, practical learning and responsible use. It keeps factual evidence separate from interpretation and treats every illustrative scenario as an example rather than a promise of results.

Choose a reading route

Build a versioned ligand-receptor-signaling-regulatory network
Propagate influence from candidate ligands to possible targets
Score ligand activity against a defined receiver response gene set
Validate ranked hypotheses across donors and perturbations

Chapter map

1. Sender and receiver definition
2. Candidate ligands
3. Response gene set
4. Background universe
5. Ligand-receptor layer
6. Signaling layer
7. Regulatory layer
8. Integrated weighted graph
9. Network propagation
10. Ligand-target matrix
11. Pearson activity
12. AUROC
13. AUPR
14. Ligand ranking and ties
15. Ligand-target explanation
16. Governance and learning

Visit the How Mathematics Works hub for the wider series and its connections to education, reasoning, science, computing, design and careers.

1. Sender and receiver definition

The useful question is not only how to calculate, but what the calculation assumes. Cell groups are assigned roles for one biological contrast.

A concrete situation

Myeloid cells send and T cells receive.

What the mathematics does not license

Roles can reverse by pathway. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

State each contrast. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

2. Candidate ligands

A small example makes the mechanism visible. Expressed sender ligands and compatible receiver receptors define candidates.

A concrete situation

Twenty ligands pass filters.

What the mathematics does not license

Thresholds discard weak real signals. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Report all filters. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

3. Response gene set

This is where modelling choices begin to affect evidence. Receiver genes changing in the condition form a target set.

A concrete situation

Two hundred genes are differential.

What the mathematics does not license

Differential expression is not one ligand effect. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Preserve covariates. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

4. Background universe

The central mathematical idea is concrete. Eligible receiver genes define negatives or comparison genes.

A concrete situation

Eight thousand expressed genes form the universe.

What the mathematics does not license

An oversized universe inflates easy rankings. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Match detectability. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

Did You Know? In this chapter, the most important number is useful only together with its construction rule. Changing scaling, sample membership or validation design can change the numerical answer without changing the arithmetic.

5. Ligand-receptor layer

Here the geometry becomes operational. Curated edges connect extracellular ligands to receptors.

A concrete situation

Ligand L links receptor R.

What the mathematics does not license

Binding databases are incomplete. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Version sources. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

6. Signaling layer

This step deserves a careful pause. Directed intracellular edges carry influence from receptors.

A concrete situation

R activates kinase K.

What the mathematics does not license

Direction and context may be uncertain. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Retain evidence weights. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

7. Regulatory layer

The useful question is not only how to calculate, but what the calculation assumes. Transcription factors connect to target genes.

A concrete situation

TF T regulates gene G.

What the mathematics does not license

Regulatory edges can be cell-type specific. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Use context checks. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

8. Integrated weighted graph

A small example makes the mechanism visible. Evidence layers are combined into one network.

A concrete situation

Three databases support one edge.

What the mathematics does not license

Weight calibration affects paths. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Document integration. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

9. Network propagation

This is where modelling choices begin to affect evidence. Influence spreads from a ligand through weighted paths with decay or restart.

A concrete situation

Short supported routes dominate.

What the mathematics does not license

Hubs can acquire broad scores. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Compare degree-aware nulls. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

10. Ligand-target matrix

The central mathematical idea is concrete. Rows are ligands, columns targets and entries are regulatory potentials.

A concrete situation

L1 scores G1 higher than G2.

What the mathematics does not license

Scores are relative model outputs. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Avoid probability language. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

11. Pearson activity

Here the geometry becomes operational. Correlation compares predicted target scores with response labels or statistics.

A concrete situation

A ligand obtains r=0.32.

What the mathematics does not license

Linear association can miss useful ranking. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Report metric choice. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

12. AUROC

This step deserves a careful pause. The area under the ROC curve summarizes ranking of responsive above background genes.

A concrete situation

AUROC 0.72 exceeds random 0.5.

What the mathematics does not license

Class imbalance can hide low precision. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Add AUPR. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

13. AUPR

The useful question is not only how to calculate, but what the calculation assumes. Precision-recall area emphasizes recovery among rare positives.

A concrete situation

Early ranks contain many targets.

What the mathematics does not license

Baseline equals positive prevalence. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Report prevalence. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

14. Ligand ranking and ties

A small example makes the mechanism visible. Activity values order candidates for follow-up.

A concrete situation

Three ligands form a stable top set.

What the mathematics does not license

Small score gaps may be noise. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Bootstrap donors. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

15. Ligand-target explanation

This is where modelling choices begin to affect evidence. Top regulatory-potential edges explain a ranked ligand.

A concrete situation

L1 links ten response genes.

What the mathematics does not license

A path is not experimental causality. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Prioritize perturbations. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

16. Governance and learning

The central mathematical idea is concrete. Version groups, filters, contrasts, networks, propagation and metrics.

A concrete situation

A student traces one weighted path.

What the mathematics does not license

A rank is a testable hypothesis. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Write a NicheNet evidence card. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

A seven-day practice lab

Day 1: define the decision, observation unit, X variables and Y or reference condition.
Day 2: reproduce the smallest worked example and check every dimension, unit and sign.
Day 3: build a transparent baseline and write what it assumes.
Day 4: fit the main method inside a training-only pipeline; record every parameter.
Day 5: challenge one assumption with a deliberately difficult dataset or operating regime.
Day 6: compare validation metrics with the practical workload created by errors.
Day 7: present one supported conclusion, one unresolved uncertainty and one safe next experiment.

Questions for a student, parent or mentor

Which part of the model is a mathematical definition, and which part is a choice?
What small calculation would catch a sign, scale or dimension error?
What evidence comes from training, validation and the untouched test?
What benign condition could look like a fault or prediction failure?
How would the answer change for another response, asset, school project or time period?
What should a human review before acting on the score?

A method-specific audit before deployment

NicheNet links a sender-side ligand to receiver-side target genes through a prior knowledge graph. The graph integrates ligand-receptor interactions, intracellular signaling connections and transcriptional regulation. Instead of stopping at a ligand-receptor edge, the method asks which expressed ligands best explain a receiver gene set. The output is a ranked regulatory-potential model, not a measurement of molecule counts moving between cells.

The prior graph is weighted by combining evidence from several databases. Network propagation spreads influence from ligands through signaling and gene-regulatory paths. Parameters control how strongly long paths decay, how sources restart the walk and how different evidence layers contribute. A ligand-target score is high when the integrated network provides strong, well-supported routes from that ligand to that target under the trained model.

Ligand activity is evaluated against an observed receiver gene set. The predicted ligand-target ranking can be compared with responsive versus background genes using Pearson correlation, AUROC or precision-recall measures. These summaries answer different questions. AUROC considers ranking across thresholds, while AUPR is more sensitive when responsive genes are rare. Neither score makes the ligand causal; both depend on the background universe and differential-expression choices.

NicheNet can prioritize ligand-receptor and ligand-target links for follow-up, yet the ranking inherits the incompleteness and context mismatch of prior knowledge. Expressed genes may not yield active proteins, and a receiver program may have several causes. Strong use therefore reports candidate-ligand filters, gene-set construction, network version, activity metric and robustness across donors, while reserving causal language for perturbation or direct biochemical evidence.

Frequently asked questions

What is NicheNet?

NicheNet predicts active ligands and their target genes by combining sender-receiver expression with prior ligand-receptor, signaling and gene-regulatory networks.

What is regulatory potential?

It is a network-derived score that ranks how strongly a candidate ligand is connected to a possible target through weighted prior paths.

How is ligand activity measured?

Predicted target scores are compared with an observed receiver response gene set using ranking or association metrics such as AUROC, AUPR or Pearson correlation.

Why does the background gene set matter?

Every activity metric contrasts responsive genes with a declared universe; changing eligible genes changes prevalence and the ranking problem.

What does a high ligand rank mean?

Under the chosen expression filters, prior network and response set, the ligand has a target profile that best matches the observed receiver programme.

Does NicheNet prove a ligand caused the programme?

No. It prioritizes hypotheses. Perturbation, receptor activity, protein measurements, timing and replication are needed for causal claims.

Primary source and fact-check note

Robin Browaeys, Wouter Saelens and Yvan Saeys, “NicheNet: modeling intercellular communication by linking ligands to target genes,” Nature Methods 17, 159–162 (2020), DOI 10.1038/s41592-019-0667-5. Definitions and core claims in this article were checked against this primary publication. Calculations shown here were independently recomputed. Examples are educational illustrations; they are not reported industrial performance results.

Useful next reading

Keep the options open. Mathematics education supports clearer questions, transferable problem-solving skills and informed choices across science, engineering, computing, AI, statistics, design and many other careers. It does not guarantee intelligence, income, admission or employment; those outcomes depend on far more than one subject or model.

Extended laboratory: topic-specific validation and responsible use

Contrast audit

Define sender, receiver and receiver response precisely.

Universe audit

Match background genes to detectable candidates.

Network audit

Version every database, edge direction and weight.

Propagation audit

Test hub bias and decay parameters.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Metric audit

Report correlation, AUROC, AUPR and baselines.

Stability audit

Bootstrap donors and alternative gene sets.

Causality audit

Reserve causal claims for perturbation evidence.

Final claim

Ligand activity is a model-based explanatory rank.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Sender and receiver definition

Start from this mechanism: Cell groups are assigned roles for one biological contrast. Recreate the small case: Myeloid cells send and T cells receive. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Roles can reverse by pathway. Complete the transfer task: State each contrast. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 2: Candidate ligands

Start from this mechanism: Expressed sender ligands and compatible receiver receptors define candidates. Recreate the small case: Twenty ligands pass filters. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Thresholds discard weak real signals. Complete the transfer task: Report all filters. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 3: Response gene set

Start from this mechanism: Receiver genes changing in the condition form a target set. Recreate the small case: Two hundred genes are differential. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Differential expression is not one ligand effect. Complete the transfer task: Preserve covariates. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 4: Background universe

Start from this mechanism: Eligible receiver genes define negatives or comparison genes. Recreate the small case: Eight thousand expressed genes form the universe. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: An oversized universe inflates easy rankings. Complete the transfer task: Match detectability. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 5: Ligand-receptor layer

Start from this mechanism: Curated edges connect extracellular ligands to receptors. Recreate the small case: Ligand L links receptor R. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Binding databases are incomplete. Complete the transfer task: Version sources. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 6: Signaling layer

Start from this mechanism: Directed intracellular edges carry influence from receptors. Recreate the small case: R activates kinase K. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Direction and context may be uncertain. Complete the transfer task: Retain evidence weights. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 7: Regulatory layer

Start from this mechanism: Transcription factors connect to target genes. Recreate the small case: TF T regulates gene G. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Regulatory edges can be cell-type specific. Complete the transfer task: Use context checks. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 8: Integrated weighted graph

Start from this mechanism: Evidence layers are combined into one network. Recreate the small case: Three databases support one edge. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Weight calibration affects paths. Complete the transfer task: Document integration. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 9: Network propagation

Start from this mechanism: Influence spreads from a ligand through weighted paths with decay or restart. Recreate the small case: Short supported routes dominate. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Hubs can acquire broad scores. Complete the transfer task: Compare degree-aware nulls. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 10: Ligand-target matrix

Start from this mechanism: Rows are ligands, columns targets and entries are regulatory potentials. Recreate the small case: L1 scores G1 higher than G2. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Scores are relative model outputs. Complete the transfer task: Avoid probability language. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 11: Pearson activity

Start from this mechanism: Correlation compares predicted target scores with response labels or statistics. Recreate the small case: A ligand obtains r=0.32. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Linear association can miss useful ranking. Complete the transfer task: Report metric choice. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 12: AUROC

Start from this mechanism: The area under the ROC curve summarizes ranking of responsive above background genes. Recreate the small case: AUROC 0.72 exceeds random 0.5. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Class imbalance can hide low precision. Complete the transfer task: Add AUPR. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 13: AUPR

Start from this mechanism: Precision-recall area emphasizes recovery among rare positives. Recreate the small case: Early ranks contain many targets. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Baseline equals positive prevalence. Complete the transfer task: Report prevalence. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 14: Ligand ranking and ties

Start from this mechanism: Activity values order candidates for follow-up. Recreate the small case: Three ligands form a stable top set. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: Small score gaps may be noise. Complete the transfer task: Bootstrap donors. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 15: Ligand-target explanation

Start from this mechanism: Top regulatory-potential edges explain a ranked ligand. Recreate the small case: L1 links ten response genes. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: A path is not experimental causality. Complete the transfer task: Prioritize perturbations. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.

Workshop 16: Governance and learning

Start from this mechanism: Version groups, filters, contrasts, networks, propagation and metrics. Recreate the small case: A student traces one weighted path. Write nodes, directed edges, evidence weights, propagated scores, target labels, ranks, AUROC, precision, recall and donor-level estimates with dimensions, units and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation directly: A rank is a testable hypothesis. Complete the transfer task: Write a NicheNet evidence card. Change exactly one distance, marginal, regularization, atlas weight, background universe, propagation setting, tensor rank, missing-value rule or random seed. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, assumption, model output, statistical evidence, biological interpretation and practical decision on separate notebook lines. When the question concerns transfer, reserve complete donors, tissues, sections, contexts or marker genes outside tuning.