WHY MATHEMATICS?

Why Mathematics? | scDiffCom Differential Communication: Cell-Label and Condition-Label Permutations, Empirical P Values and FDR

How scDiffCom separates within-condition cell-type specificity from between-condition change, then turns two randomization questions into transparent empirical evidence and guarded regulation labels.

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 balanced ligand-receptor scores with geometric means
Shuffle cell labels to test sender-receiver specificity
Shuffle condition labels to test differential communication
Adjust empirical tails and interpret UP, DOWN, FLAT and NSC carefully

Chapter map

1. Candidate universe
2. Emitter mean
3. Receiver mean
4. Geometric score
5. Expression fraction
6. Observed difference
7. Log fold change
8. Cell-label null
9. Specificity tail
10. Condition-label null
11. Two-sided differential tail
12. Benjamini-Hochberg
13. Detection gates
14. Differential gate
15. Regulation labels
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. Candidate universe

A small example makes the mechanism visible. m cell types and l ligand-receptor entries create m squared times l candidates.

A concrete situation

Ten types and 500 pairs make 50,000 candidates.

What the mathematics does not license

The resource controls multiplicity. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Freeze the universe. 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. Emitter mean

This is where modelling choices begin to affect evidence. Ligand expression is averaged within emitter cells and condition.

A concrete situation

Condition A mean is four.

What the mathematics does not license

Cells are not donors. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Report sample structure. 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. Receiver mean

The central mathematical idea is concrete. Receptor expression is averaged within receiver cells and condition.

A concrete situation

Receiver mean is nine.

What the mathematics does not license

Rare populations give unstable means. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Use uncertainty 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.

4. Geometric score

Here the geometry becomes operational. The square root of the partner product balances both sides.

A concrete situation

sqrt(4 times 9) equals six.

What the mathematics does not license

Zero creates log-ratio problems. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

State zero handling. 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. Expression fraction

This step deserves a careful pause. Detected-cell fractions describe prevalence beyond the mean.

A concrete situation

Half the emitters express L.

What the mathematics does not license

Thresholds depend on preprocessing. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Publish fractions. 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. Observed difference

The useful question is not only how to calculate, but what the calculation assumes. Condition B score minus condition A score is the differential statistic.

A concrete situation

Eight minus six equals two.

What the mathematics does not license

Absolute change ignores baseline scale. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Also report fold change. 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. Log fold change

A small example makes the mechanism visible. The log score ratio gives symmetric relative change.

A concrete situation

log(8/6) is positive.

What the mathematics does not license

Small denominators inflate ratios. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Keep raw 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.

8. Cell-label null

This is where modelling choices begin to affect evidence. Cell types are permuted to test pair specificity.

A concrete situation

Labels are shuffled 10,000 times.

What the mathematics does not license

Donor structure may break exchangeability. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Block when possible. 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. Specificity tail

The central mathematical idea is concrete. Observed within-condition score is compared with its cell-label null.

A concrete situation

Few null scores exceed the observed.

What the mathematics does not license

Finite permutations limit resolution. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Report counts and P. 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. Condition-label null

Here the geometry becomes operational. Condition labels are exchanged to test score change.

A concrete situation

Treatment and control labels shuffle.

What the mathematics does not license

Paired designs require paired exchange. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Respect the design. 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. Two-sided differential tail

This step deserves a careful pause. Absolute randomized differences are compared with the observed absolute difference.

A concrete situation

Both increases and decreases count.

What the mathematics does not license

The tail does not give direction. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Use observed sign. 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. Benjamini-Hochberg

The useful question is not only how to calculate, but what the calculation assumes. Ordered P values are scaled by family size and rank.

A concrete situation

One tail survives FDR control.

What the mathematics does not license

Dependence and family definition matter. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Name the tested family. 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. Detection gates

A small example makes the mechanism visible. Expression, specificity and score-quantile rules define detected interactions.

A concrete situation

A specific but tiny score is filtered.

What the mathematics does not license

A gate changes recall. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Run threshold sensitivity. 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. Differential gate

This is where modelling choices begin to affect evidence. Adjusted P and fold-change thresholds define reliable change.

A concrete situation

A 1.5-fold rule is applied.

What the mathematics does not license

Thresholds create boundary cases. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Show continuous values. 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. Regulation labels

The central mathematical idea is concrete. UP, DOWN, FLAT and NSC summarize combined outcomes.

A concrete situation

One edge is UP.

What the mathematics does not license

Labels compress several decisions. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Link labels to columns. 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

Here the geometry becomes operational. Version counts, labels, permutations, seeds, tails, FDR and gates.

A concrete situation

A student shuffles a six-cell toy dataset.

What the mathematics does not license

Exchangeability is the key assumption. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Write a scDiffCom 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

scDiffCom defines a candidate cell-cell interaction by an emitter cell type, a receiver cell type and a ligand-receptor interaction. Within each condition it computes a communication score as the geometric mean of average ligand expression in emitters and average receptor expression in receivers. The geometric mean balances the two partners and reduces domination by one very large value. Expression fractions are retained because the same mean can arise from many modest cells or a few extreme cells.

The first permutation test shuffles cell-type labels. It asks whether a score is unusually specific to the stated emitter-receiver pair relative to randomized group assignments. The second test shuffles condition labels and compares the observed score difference with its null distribution. These are different null questions. A signal can be specific within both conditions yet show no reliable change, or it can change while failing the chosen detection filters.

Empirical one-sided specificity tails and a two-sided differential tail are adjusted for multiple testing with the Benjamini-Hochberg procedure. Detection additionally uses expression criteria and a score quantile rule; differential calls combine adjusted significance with a fold-change threshold. Consequently, the familiar UP, DOWN, FLAT and NSC labels are products of several gates. They are useful summaries, not raw observations.

Exchangeability is the central assumption. Cells are not independent biological replicates, and unrestricted label shuffling can be misleading when donors, tissues or batches structure the data. The original tool is designed for cell-level analyses, so replicate-aware sensitivity checks remain important. A responsible report publishes the score, fractions, null scheme, number of permutations, empirical tails, adjusted values, fold change and category together.

Frequently asked questions

What is scDiffCom?

scDiffCom is a framework for detecting and comparing expression-supported cell-cell interactions between two conditions using ligand-receptor scores and permutation tests.

What is the default communication score?

It is the geometric mean of average ligand expression in emitter cells and average receptor expression in receiver cells, using normalized non-log counts.

Why are there two permutation tests?

Cell-label permutations ask whether an interaction is specific to a cell-type pair; condition-label permutations ask whether its score changes between conditions.

What is an empirical P value?

It is the proportion of randomized statistics at least as extreme as the observed statistic, with finite-permutation resolution and an explicitly defined tail.

Why adjust P values?

Thousands of candidate cell-pair and ligand-receptor combinations are tested. Benjamini-Hochberg adjustment controls the expected false-discovery proportion under its assumptions.

Do UP and DOWN mean causal activation or inhibition?

No. They describe score direction after detection, significance and fold-change rules; they do not establish the molecular cause of the change.

Primary source and fact-check note

Cyril Lagger, Elena Ursu, Aurélien Equey et al., “scDiffCom: a tool for differential analysis of cell-cell interactions provides a mouse atlas of aging changes in intercellular communication,” Nature Aging 3, 1446–1461 (2023), DOI 10.1038/s43587-023-00514-x. 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

Universe audit

Freeze cell types, LRIs and candidate family.

Score audit

Keep group means, fractions, geometric scores and zeros.

Specificity audit

Document cell-label exchangeability and blocks.

Differential audit

Document condition-label exchangeability and pairing.

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.

Tail audit

Report permutation count, exceedances and sidedness.

Multiplicity audit

Name the Benjamini-Hochberg family.

Gate audit

Publish sensitivity to score and fold-change thresholds.

Final claim

A regulation label summarizes rules; it is not causal proof.

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: Candidate universe

Begin with this mechanism: m cell types and l ligand-receptor entries create m squared times l candidates. Recreate the concrete case: Ten types and 500 pairs make 50,000 candidates. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: The resource controls multiplicity. Complete the transfer step: Freeze the universe. 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: Emitter mean

Begin with this mechanism: Ligand expression is averaged within emitter cells and condition. Recreate the concrete case: Condition A mean is four. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Cells are not donors. Complete the transfer step: Report sample structure. 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: Receiver mean

Begin with this mechanism: Receptor expression is averaged within receiver cells and condition. Recreate the concrete case: Receiver mean is nine. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Rare populations give unstable means. Complete the transfer step: Use uncertainty checks. 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: Geometric score

Begin with this mechanism: The square root of the partner product balances both sides. Recreate the concrete case: sqrt(4 times 9) equals six. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Zero creates log-ratio problems. Complete the transfer step: State zero handling. 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: Expression fraction

Begin with this mechanism: Detected-cell fractions describe prevalence beyond the mean. Recreate the concrete case: Half the emitters express L. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Thresholds depend on preprocessing. Complete the transfer step: Publish fractions. 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: Observed difference

Begin with this mechanism: Condition B score minus condition A score is the differential statistic. Recreate the concrete case: Eight minus six equals two. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Absolute change ignores baseline scale. Complete the transfer step: Also report fold change. 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: Log fold change

Begin with this mechanism: The log score ratio gives symmetric relative change. Recreate the concrete case: log(8/6) is positive. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Small denominators inflate ratios. Complete the transfer step: Keep raw 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 8: Cell-label null

Begin with this mechanism: Cell types are permuted to test pair specificity. Recreate the concrete case: Labels are shuffled 10,000 times. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Donor structure may break exchangeability. Complete the transfer step: Block when possible. 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: Specificity tail

Begin with this mechanism: Observed within-condition score is compared with its cell-label null. Recreate the concrete case: Few null scores exceed the observed. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Finite permutations limit resolution. Complete the transfer step: Report counts and P. 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: Condition-label null

Begin with this mechanism: Condition labels are exchanged to test score change. Recreate the concrete case: Treatment and control labels shuffle. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Paired designs require paired exchange. Complete the transfer step: Respect the design. 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: Two-sided differential tail

Begin with this mechanism: Absolute randomized differences are compared with the observed absolute difference. Recreate the concrete case: Both increases and decreases count. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: The tail does not give direction. Complete the transfer step: Use observed sign. 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: Benjamini-Hochberg

Begin with this mechanism: Ordered P values are scaled by family size and rank. Recreate the concrete case: One tail survives FDR control. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Dependence and family definition matter. Complete the transfer step: Name the tested family. 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: Detection gates

Begin with this mechanism: Expression, specificity and score-quantile rules define detected interactions. Recreate the concrete case: A specific but tiny score is filtered. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: A gate changes recall. Complete the transfer step: Run threshold sensitivity. 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: Differential gate

Begin with this mechanism: Adjusted P and fold-change thresholds define reliable change. Recreate the concrete case: A 1.5-fold rule is applied. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Thresholds create boundary cases. Complete the transfer step: Show continuous values. 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: Regulation labels

Begin with this mechanism: UP, DOWN, FLAT and NSC summarize combined outcomes. Recreate the concrete case: One edge is UP. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Labels compress several decisions. Complete the transfer step: Link labels to columns. 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 counts, labels, permutations, seeds, tails, FDR and gates. Recreate the concrete case: A student shuffles a six-cell toy dataset. Write group means, expression fractions, geometric scores, score differences, log fold changes, null exceedances, empirical tails and adjusted values 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: Exchangeability is the key assumption. Complete the transfer step: Write a scDiffCom 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.