WHY MATHEMATICS?

Why Mathematics? | CellCall Ligand-Receptor-TF Pathways: Rank Correlations, GSEA Activity Scores and Composite Communication Evidence

How CellCall connects extracellular ligand-receptor expression with receiver-side transcription-factor activity, and why every correlation, enrichment score and composite pathway claim needs its own interpretation.

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

Represent an L-R-TF axis from curated pathway knowledge
Use rank correlation to assess monotone regulatory association
Estimate TF and pathway activity from target-gene enrichment
Combine extracellular and intracellular evidence without hiding components

Chapter map

1. Sender-receiver pair
2. Ligand expression
3. Receptor expression
4. L-R-TF prior
5. Target regulon
6. Rank transformation
7. Spearman correlation
8. Correlation filter
9. Gene-set enrichment
10. TF activity score
11. L-R magnitude
12. Composite score
13. Pathway activity
14. Direction and visualization
15. Experimental comparison
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-receiver pair

The useful question is not only how to calculate, but what the calculation assumes. Cell types define the source and destination of the proposed signal.

A concrete situation

Cell A sends to cell B.

What the mathematics does not license

Mixed annotations blur the route. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Audit group identity. 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. Ligand expression

A small example makes the mechanism visible. The sender supplies an aggregated ligand value.

A concrete situation

Ligand L is high in A.

What the mathematics does not license

Transcript is not secreted protein. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Keep the evidence level. 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. Receptor expression

This is where modelling choices begin to affect evidence. The receiver supplies the receptor value.

A concrete situation

Receptor R is present in B.

What the mathematics does not license

Surface localization is unobserved. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Seek protein support. 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. L-R-TF prior

The central mathematical idea is concrete. Curated pathways connect a receptor to downstream TFs.

A concrete situation

R connects to TF1 and TF2.

What the mathematics does not license

Pathway maps are context-general. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Version the prior. 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. Target regulon

Here the geometry becomes operational. Each TF is represented by a target-gene set.

A concrete situation

TF1 has fifty targets.

What the mathematics does not license

Incorrect targets bias activity. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Report set provenance. 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. Rank transformation

This step deserves a careful pause. Expression values can be ordered without assuming equal intervals.

A concrete situation

Ranks replace raw magnitudes.

What the mathematics does not license

Ties and zeros matter. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

State the tie rule. 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. Spearman correlation

The useful question is not only how to calculate, but what the calculation assumes. Correlation is Pearson correlation of ranks.

A concrete situation

rho equals 0.6.

What the mathematics does not license

Association is not regulation. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Use significance and effect size. 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. Correlation filter

A small example makes the mechanism visible. Edges can require a P value and absolute rho threshold.

A concrete situation

P below 0.05 and |rho| above 0.1 pass.

What the mathematics does not license

Many tests inflate false positives. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Adjust or label exploratory. 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. Gene-set enrichment

This is where modelling choices begin to affect evidence. Targets concentrated near one end of a ranked list imply activity.

A concrete situation

TF1 targets enrich among up genes.

What the mathematics does not license

Gene sets overlap. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Show leading-edge genes. 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. TF activity score

The central mathematical idea is concrete. Enrichment and significance are summarized for each downstream TF.

A concrete situation

TF1 is active, TF2 is not.

What the mathematics does not license

Thresholding discards gradation. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Retain continuous scores. 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. L-R magnitude

Here the geometry becomes operational. Ligand and receptor expression form the extracellular component.

A concrete situation

A norm summarizes the pair.

What the mathematics does not license

Scaling and transcript length affect magnitude. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Publish the transform. 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. Composite score

This step deserves a careful pause. L-R magnitude is integrated with downstream TF activity.

A concrete situation

Strong expression and activity raise the score.

What the mathematics does not license

One layer can dominate. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Show component contributions. 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. Pathway activity

The useful question is not only how to calculate, but what the calculation assumes. Multiple axes are summarized within a pathway.

A concrete situation

JAK-STAT receives a high activity score.

What the mathematics does not license

Shared genes create dependence. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Avoid independent-edge 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.

14. Direction and visualization

A small example makes the mechanism visible. Circos and Sankey views encode model direction and magnitude.

A concrete situation

One route appears thick.

What the mathematics does not license

Graphics can hide denominators. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Link every edge to a table. 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. Experimental comparison

This is where modelling choices begin to affect evidence. Predictions can be checked with perturbation or measured response.

A concrete situation

Blocking R reduces target activity.

What the mathematics does not license

One validation does not validate all axes. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Define claim scope. 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 expression, priors, correlations, gene sets, enrichment and scores.

A concrete situation

A student traces one L-R-TF path.

What the mathematics does not license

Composite evidence needs decomposed reporting. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Write a CellCall audit 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

CellCall extends a ligand-receptor edge into an L-R-TF axis. Curated pathway knowledge links each receptor to downstream transcription factors. The method combines sender ligand expression, receiver receptor expression and receiver-side TF activity, so the score asks for both an extracellular candidate and an intracellular response pattern. This is a richer question than co-expression alone, but it also inherits uncertainty from every link in the axis.

TF activity is not read directly from one TF transcript. CellCall uses the expression behaviour of downstream target genes, gene-set enrichment analysis and significance filtering to construct activity evidence. Spearman rank correlation is used when building or filtering regulatory relationships because it measures monotone association without assuming a linear scale. A statistically significant correlation remains association; it does not prove that the TF caused the target change.

The communication score combines an L-R expression magnitude with the activity scores of TFs connected to that pair. Scaling, transcript-length adjustment, target-set definition and the number of eligible TFs can all alter the result. A high score may arise from strong ligand-receptor expression, strong downstream activity or both. Keeping those components visible prevents a composite number from hiding which layer actually supplied the evidence.

CellCall also calculates pathway activity so results can be summarized above individual pairs. Pathway enrichment is useful for organizing many axes, but overlapping genes make pathway scores dependent. The honest conclusion is a prioritized route from sender to receiver response, not a filmed molecular journey. Perturbing the ligand or receptor, measuring proteins and checking independent samples remain essential for causal claims.

Frequently asked questions

What is CellCall?

CellCall is a toolkit that links sender ligand and receiver receptor expression with downstream transcription-factor activity through curated L-R-TF pathway axes.

Why include transcription factors?

Receiver-side TF activity provides evidence closer to an intracellular response than ligand-receptor co-expression alone.

What does Spearman correlation measure?

It measures the strength of a monotone association between ranked variables. It does not require a linear relationship and does not establish causation.

How is TF activity estimated?

CellCall uses downstream target-gene behaviour, gene-set enrichment analysis and significance rules rather than assuming TF messenger RNA equals TF activity.

What is a composite communication score?

It combines ligand-receptor expression magnitude with activity evidence from downstream TFs associated with that pair.

Does a high CellCall score prove the whole pathway occurred?

No. It prioritizes a knowledge-constrained route; protein state, timing, spatial contact and perturbation evidence are still required.

Primary source and fact-check note

Yang Zhang, Tianyuan Liu, Xuesong Hu et al., “CellCall: integrating paired ligand-receptor and transcription factor activities for cell-cell communication,” Nucleic Acids Research 49(15), 8520–8534 (2021), DOI 10.1093/nar/gkab638. 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

Axis audit

Version every ligand-receptor-TF connection.

Expression audit

Keep sender ligand and receiver receptor components.

Correlation audit

Report rho, P value, multiplicity and sample unit.

Regulon audit

Document target sets and leading-edge genes.

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.

Activity audit

Retain continuous enrichment before thresholds.

Composite audit

Expose weights and component contributions.

Pathway audit

Account for overlapping genes and axes.

Final claim

A scored route is a prioritized hypothesis, not a filmed pathway.

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-receiver pair

Begin with this mechanism: Cell types define the source and destination of the proposed signal. Recreate the concrete case: Cell A sends to cell B. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Mixed annotations blur the route. Complete the transfer step: Audit group identity. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 2: Ligand expression

Begin with this mechanism: The sender supplies an aggregated ligand value. Recreate the concrete case: Ligand L is high in A. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Transcript is not secreted protein. Complete the transfer step: Keep the evidence level. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 3: Receptor expression

Begin with this mechanism: The receiver supplies the receptor value. Recreate the concrete case: Receptor R is present in B. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Surface localization is unobserved. Complete the transfer step: Seek protein support. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 4: L-R-TF prior

Begin with this mechanism: Curated pathways connect a receptor to downstream TFs. Recreate the concrete case: R connects to TF1 and TF2. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Pathway maps are context-general. Complete the transfer step: Version the prior. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

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: Target regulon

Begin with this mechanism: Each TF is represented by a target-gene set. Recreate the concrete case: TF1 has fifty targets. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Incorrect targets bias activity. Complete the transfer step: Report set provenance. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 6: Rank transformation

Begin with this mechanism: Expression values can be ordered without assuming equal intervals. Recreate the concrete case: Ranks replace raw magnitudes. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Ties and zeros matter. Complete the transfer step: State the tie rule. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 7: Spearman correlation

Begin with this mechanism: Correlation is Pearson correlation of ranks. Recreate the concrete case: rho equals 0.6. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Association is not regulation. Complete the transfer step: Use significance and effect size. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 8: Correlation filter

Begin with this mechanism: Edges can require a P value and absolute rho threshold. Recreate the concrete case: P below 0.05 and |rho| above 0.1 pass. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Many tests inflate false positives. Complete the transfer step: Adjust or label exploratory. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

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: Gene-set enrichment

Begin with this mechanism: Targets concentrated near one end of a ranked list imply activity. Recreate the concrete case: TF1 targets enrich among up genes. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Gene sets overlap. Complete the transfer step: Show leading-edge genes. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 10: TF activity score

Begin with this mechanism: Enrichment and significance are summarized for each downstream TF. Recreate the concrete case: TF1 is active, TF2 is not. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Thresholding discards gradation. Complete the transfer step: Retain continuous scores. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 11: L-R magnitude

Begin with this mechanism: Ligand and receptor expression form the extracellular component. Recreate the concrete case: A norm summarizes the pair. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Scaling and transcript length affect magnitude. Complete the transfer step: Publish the transform. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 12: Composite score

Begin with this mechanism: L-R magnitude is integrated with downstream TF activity. Recreate the concrete case: Strong expression and activity raise the score. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: One layer can dominate. Complete the transfer step: Show component contributions. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

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: Pathway activity

Begin with this mechanism: Multiple axes are summarized within a pathway. Recreate the concrete case: JAK-STAT receives a high activity score. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Shared genes create dependence. Complete the transfer step: Avoid independent-edge language. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 14: Direction and visualization

Begin with this mechanism: Circos and Sankey views encode model direction and magnitude. Recreate the concrete case: One route appears thick. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Graphics can hide denominators. Complete the transfer step: Link every edge to a table. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 15: Experimental comparison

Begin with this mechanism: Predictions can be checked with perturbation or measured response. Recreate the concrete case: Blocking R reduces target activity. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: One validation does not validate all axes. Complete the transfer step: Define claim scope. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.

Workshop 16: Governance and learning

Begin with this mechanism: Version expression, priors, correlations, gene sets, enrichment and scores. Recreate the concrete case: A student traces one L-R-TF path. Write ligand-receptor magnitudes, ranks, Spearman coefficients, target sets, enrichment values, TF activities and composite scores with direction, units and denominators. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short script. Challenge this limitation: Composite evidence needs decomposed reporting. Complete the transfer step: Write a CellCall audit card. Change exactly one annotation, normalization, comparison panel, required subunit, target set, correlation threshold, permutation block, random seed, score cutoff or multiplicity family. Explain which mathematical object changes, which interpretation survives and which claim must weaken. Keep observation, transformation, null evidence, summary label and biological conclusion on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing whether the reasoning transfers.