Worked Example Gallery
These examples are end-to-end demonstrations of the 8-phase workflow: each turns a plain-language idea into a calibrated mathematical model, includes rejected-lens rationales for why other perspectives were set aside, and closes with explicit falsification criteria. Rows are grouped by the primary lens demonstrated, following the fifteen lenses; most examples also compose secondary lenses.
Deterministic
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Epidemic Spread |
Deterministic (+ stochastic check) |
Epidemiology |
An SIR model exposes an R₀ threshold: whether an outbreak explodes or dies out is decided before any stochastic detail matters. |
| App Adoption Growth |
Deterministic (Bass diffusion archetype-first) |
Product growth |
A single well-chosen archetype (Bass ODE), calibrated on real signups and gated by BIC, answers ceiling and stall-timing questions. |
Stochastic
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Insurance Ruin Risk |
Stochastic |
Insurance / risk |
For rare-event solvency questions, deterministic averages are useless , ruin probability is a tail property that only a stochastic model can price. |
| Retail Inventory Under Uncertain Demand |
Stochastic (+ optimization, control) |
Retail operations |
Demand randomness converts a restocking question into an (s,Q) policy built from newsvendor logic plus safety stock. |
Optimization
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Coffee Shop Staffing |
Optimization (+ queueing) |
Service operations |
An Erlang-C wait cliff embedded in an ILP shows lenses composing: queueing computes the wait, optimization schedules the staff. |
Network
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Rumor Spread in a School |
Network |
Social dynamics |
Who-connects-to-whom changes the answer: contact structure, not just counts, decides how far a rumor travels and whether a public announcement stops it. |
Control
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Greenhouse Night Temperature |
Control |
Agriculture / building systems |
Keeping temperature above a setpoint against disturbances is a feedback problem , heater policy follows from the control view, not from prediction alone. |
Game theory
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Two Cafés Pricing War |
Game theory |
Economics / competition |
A 20% price cut looks profitable when rivals are frozen , game theory reveals the rival's response term that single-actor optimization cannot see. |
Causal inference
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Marketing Attribution |
Causal inference |
Digital marketing |
Users who see retargeting ads buying 3x more is selection, not effect , backdoor confounding must be adjusted before spending follows. |
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Sensor Placement |
Information theory |
Data center monitoring |
When you cannot measure everything, mutual information tells you which 3 sensor locations carry the most signal about overheating. |
Reliability
| Example |
Primary lens(es) |
Domain |
One-line takeaway |
| Delivery Fleet Preventive Maintenance |
Reliability |
Logistics |
Fixed-schedule versus run-to-failure becomes decidable once breakdown timing gets a Weibull hazard and costs go through renewal-reward analysis. |
Full texts live in /examples; each follows the standardized 8-phase report structure.