WHY MATHEMATICS?

Why Mathematics? | LIANA Consensus Cell Communication: Method-Resource Separation, Rank Conversion and Robust Rank Aggregation

How LIANA compares cell-communication methods and prior resources on equal footing, converts incompatible outputs into ranks and builds consensus without mistaking agreement for truth.

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

Separate the interaction resource from the scoring method
Map incompatible method outputs into a common ordered table
Aggregate repeated high ranks with an explicit null model
Use disagreement and external data as evidence about robustness

Chapter map

1. Annotated expression input
2. Interaction resource
3. Scoring method
4. Method-resource grid
5. Common interaction key
6. Score direction
7. Rank conversion
8. Missing ranks
9. Candidate universe
10. Robust rank aggregation
11. Consensus magnitude
12. Consensus specificity
13. Resource sensitivity
14. Method sensitivity
15. Orthogonal validation
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. Annotated expression input

The central mathematical idea is concrete. One cell-by-gene matrix and labels enter all methods.

A concrete situation

Six cell types share one dataset.

What the mathematics does not license

Preprocessing can favor some scorers. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Version the common input. 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. Interaction resource

Here the geometry becomes operational. A catalogue defines possible ligand-receptor pairs.

A concrete situation

Resource A contains two thousand edges.

What the mathematics does not license

Coverage varies by pathway and tissue. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Report eligible edges. 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. Scoring method

This step deserves a careful pause. An algorithm assigns magnitude or specificity to every eligible pair.

A concrete situation

One method uses products and another ranks means.

What the mathematics does not license

Outputs answer different questions. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Name each estimand. 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. Method-resource grid

The useful question is not only how to calculate, but what the calculation assumes. Every selected method can be paired with every resource.

A concrete situation

Seven methods cross sixteen resources.

What the mathematics does not license

Some combinations require adaptations. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Record compatibility rules. 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. Common interaction key

A small example makes the mechanism visible. Ligand, receptor, sender and receiver identify a row.

A concrete situation

L-R from A to B is one key.

What the mathematics does not license

Complex naming and direction can mismatch. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Harmonize identifiers. 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. Score direction

This is where modelling choices begin to affect evidence. Higher or lower raw values may indicate stronger evidence.

A concrete situation

A p value reverses a magnitude score.

What the mathematics does not license

Wrong direction inverts the ranking. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Test monotonicity. 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. Rank conversion

The central mathematical idea is concrete. Raw method outputs become ordered positions or percentiles.

A concrete situation

The best item receives rank one.

What the mathematics does not license

Ranks discard effect-size gaps. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Keep original 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. Missing ranks

Here the geometry becomes operational. A method may omit interactions after filtering.

A concrete situation

One complex is absent from two lists.

What the mathematics does not license

Treating missing as worst or unavailable changes consensus. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Declare the 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.

9. Candidate universe

This step deserves a careful pause. The set of items eligible for aggregation defines the null.

A concrete situation

Ten thousand common keys remain.

What the mathematics does not license

Pre-filtering can improve ranks artificially. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Freeze before testing. 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. Robust rank aggregation

The useful question is not only how to calculate, but what the calculation assumes. Order statistics measure repeated top placement.

A concrete situation

One edge ranks in the top one percent five times.

What the mathematics does not license

Correlated methods violate independence ideals. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Interpret as stability. 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. Consensus magnitude

A small example makes the mechanism visible. Method-specific magnitude ranks can be combined separately.

A concrete situation

High-expression evidence aligns across tools.

What the mathematics does not license

Magnitude is not specificity. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Keep two consensus axes. 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. Consensus specificity

This is where modelling choices begin to affect evidence. Specificity or probability-like ranks form another summary.

A concrete situation

One pair is cell-type restricted.

What the mathematics does not license

Different nulls remain underneath. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Show method 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. Resource sensitivity

The central mathematical idea is concrete. Rankings are rerun across prior catalogues.

A concrete situation

An edge vanishes under a smaller resource.

What the mathematics does not license

Absence may mean missing knowledge. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Distinguish unavailable from negative. 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. Method sensitivity

Here the geometry becomes operational. Rank overlap and correlation reveal model dependence.

A concrete situation

Two methods disagree on a pathway.

What the mathematics does not license

Low agreement is informative. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Investigate assumptions. 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. Orthogonal validation

This step deserves a careful pause. Spatial, protein and activity data test separate requirements.

A concrete situation

A receptor protein supports one edge.

What the mathematics does not license

Colocalization alone is not signaling. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Triangulate evidence. 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 useful question is not only how to calculate, but what the calculation assumes. Version inputs, resources, methods, transformations and aggregation.

A concrete situation

A student aggregates four short rankings.

What the mathematics does not license

Consensus is stability, not truth. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Write a LIANA consensus 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

LIANA separates two choices that are often entangled: the resource that lists possible ligand-receptor relationships and the method that scores them. This creates a controlled comparison. The same expression data can be paired with different resources and the same resource can be evaluated by several methods. If rankings change, the disagreement becomes visible evidence about model dependence rather than an invisible software difference.

Different methods return quantities with incompatible scales: means, products, specificity values, test statistics, probabilities or ranks. LIANA translates these outputs into a common interaction table and uses ranks for consensus. Rank conversion preserves order while giving up unsupported numerical comparability. A score of ten from one method is never assumed to mean the same thing as ten from another.

The consensus uses robust rank aggregation to ask whether an interaction is repeatedly placed near the top more often than expected under random orderings. An item that ranks highly in several methods receives stronger consensus evidence than one that wins a single method and disappears elsewhere. The null depends on the candidate universe and complete or missing rankings, so filtering before aggregation is part of the statistical design.

The primary comparison found that both prior resources and scoring methods substantially influence predicted communication. Consensus is therefore a stability summary, not a vote that makes an interaction true. Spatial colocalization, receptor protein abundance, cytokine activity, perturbations and independent samples remain external evidence. For students, this is a powerful lesson in ensemble reasoning: aggregation helps only when the inputs, ranks and failure modes are documented.

Frequently asked questions

What is LIANA?

LIANA is a common interface for running and comparing multiple cell-cell communication methods and interaction resources, with consensus ranking across methods.

Why separate methods and resources?

A resource controls which interactions are eligible, while a method controls how eligible interactions are scored. Separating them reveals both sources of variation.

Why use ranks?

Ranks preserve order when raw outputs have incompatible units, ranges and directions, avoiding false arithmetic across unrelated scores.

What is robust rank aggregation?

It evaluates whether an item appears unusually near the top across several ranked lists relative to random orderings.

Does consensus guarantee a true interaction?

No. Shared databases, preprocessing and assumptions can make methods agree for the same wrong reason.

How should LIANA results be validated?

Compare with spatial colocalization, receptor protein abundance, cytokine or target activity, perturbations and independent samples while preserving method-level results.

Primary source and fact-check note

Daniel Dimitrov, Dénes Türei, Martin Garrido-Rodriguez et al., “Comparison of methods and resources for cell-cell communication inference from single-cell RNA-Seq data,” Nature Communications 13, 3224 (2022), DOI 10.1038/s41467-022-30755-0. 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

Input audit

Give every method the same documented expression input.

Resource audit

Separate unavailable interactions from negative evidence.

Direction audit

Confirm whether high or low raw output is favorable.

Rank audit

Keep raw scores beside converted ranks.

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.

Universe audit

Freeze candidate keys before aggregation.

Dependence audit

Recognize correlated methods and shared databases.

Validation audit

Test consensus with independent modalities and samples.

Final claim

Consensus measures stability, not truth.

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: Annotated expression input

Begin with this mechanism: One cell-by-gene matrix and labels enter all methods. Recreate the concrete case: Six cell types share one dataset. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Preprocessing can favor some scorers. Complete the transfer step: Version the common input. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 2: Interaction resource

Begin with this mechanism: A catalogue defines possible ligand-receptor pairs. Recreate the concrete case: Resource A contains two thousand edges. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Coverage varies by pathway and tissue. Complete the transfer step: Report eligible edges. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 3: Scoring method

Begin with this mechanism: An algorithm assigns magnitude or specificity to every eligible pair. Recreate the concrete case: One method uses products and another ranks means. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Outputs answer different questions. Complete the transfer step: Name each estimand. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 4: Method-resource grid

Begin with this mechanism: Every selected method can be paired with every resource. Recreate the concrete case: Seven methods cross sixteen resources. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Some combinations require adaptations. Complete the transfer step: Record compatibility rules. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

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: Common interaction key

Begin with this mechanism: Ligand, receptor, sender and receiver identify a row. Recreate the concrete case: L-R from A to B is one key. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Complex naming and direction can mismatch. Complete the transfer step: Harmonize identifiers. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 6: Score direction

Begin with this mechanism: Higher or lower raw values may indicate stronger evidence. Recreate the concrete case: A p value reverses a magnitude score. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Wrong direction inverts the ranking. Complete the transfer step: Test monotonicity. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 7: Rank conversion

Begin with this mechanism: Raw method outputs become ordered positions or percentiles. Recreate the concrete case: The best item receives rank one. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Ranks discard effect-size gaps. Complete the transfer step: Keep original scores. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 8: Missing ranks

Begin with this mechanism: A method may omit interactions after filtering. Recreate the concrete case: One complex is absent from two lists. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Treating missing as worst or unavailable changes consensus. Complete the transfer step: Declare the rule. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

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: Candidate universe

Begin with this mechanism: The set of items eligible for aggregation defines the null. Recreate the concrete case: Ten thousand common keys remain. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Pre-filtering can improve ranks artificially. Complete the transfer step: Freeze before testing. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 10: Robust rank aggregation

Begin with this mechanism: Order statistics measure repeated top placement. Recreate the concrete case: One edge ranks in the top one percent five times. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Correlated methods violate independence ideals. Complete the transfer step: Interpret as stability. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 11: Consensus magnitude

Begin with this mechanism: Method-specific magnitude ranks can be combined separately. Recreate the concrete case: High-expression evidence aligns across tools. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Magnitude is not specificity. Complete the transfer step: Keep two consensus axes. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 12: Consensus specificity

Begin with this mechanism: Specificity or probability-like ranks form another summary. Recreate the concrete case: One pair is cell-type restricted. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Different nulls remain underneath. Complete the transfer step: Show method contributions. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

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: Resource sensitivity

Begin with this mechanism: Rankings are rerun across prior catalogues. Recreate the concrete case: An edge vanishes under a smaller resource. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Absence may mean missing knowledge. Complete the transfer step: Distinguish unavailable from negative. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 14: Method sensitivity

Begin with this mechanism: Rank overlap and correlation reveal model dependence. Recreate the concrete case: Two methods disagree on a pathway. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Low agreement is informative. Complete the transfer step: Investigate assumptions. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 15: Orthogonal validation

Begin with this mechanism: Spatial, protein and activity data test separate requirements. Recreate the concrete case: A receptor protein supports one edge. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Colocalization alone is not signaling. Complete the transfer step: Triangulate evidence. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.

Workshop 16: Governance and learning

Begin with this mechanism: Version inputs, resources, methods, transformations and aggregation. Recreate the concrete case: A student aggregates four short rankings. Write candidate keys, resource indicators, raw scores, score directions, ranks, percentiles, missing-list rules and aggregate probabilities with dimensions, direction and normalization. Calculate the smallest non-trivial example by hand, then reproduce it in code. Challenge this limitation: Consensus is stability, not truth. Complete the transfer step: Write a LIANA consensus card. Change exactly one annotation, threshold, subunit, permutation block, resource, score direction, candidate universe, specificity denominator, propagation setting, prize-cost scale or forest penalty. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, model output, null evidence, interpretation and decision on separate notebook lines. Reserve complete donors, tissues, conditions or interaction families outside tuning when testing transfer.