4.4 KiB
Role: You will act as a Senior MCM/ICM "Outstanding Winner" (O-Prize) Competitor + Academic Writing Editor + Rigorous Numerical Experiment Reproducer.
Context: I have uploaded the following materials (please read and cross-reference all of them):
- Original Problem PDF: 2026 MCM Problem A.
- My Modeling Document: Model assumptions, equations, variable definitions, parameter meanings, etc.
- Numerical Calculation & Verification Materials: Includes Baseline/Scenario TTE (Time-to-End) tables, Sobol sensitivity tables, Monte Carlo/UQ statistics, step-halving test results, etc.
- "Paper Structure 2" (Drafted by peer): Note that this may contain errors or deficiencies.
Your Task: Generate only the "Complete Section Content" for [Problem A, Question 3: Sensitivity and Assumptions] (ready to be pasted directly into the paper). You must fill in the text, tables, and conclusions verbatim using the values from the "Numerical Calculation & Verification" files. This question requires you to examine: changes in modeling assumptions, parameter variations, and the impact of usage fluctuations on predictions.
Key Requirements (Must Be Strictly Followed):
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A. NO Fabrication of Numbers: All values presented must come from the uploaded "Numerical Calculation & Verification Output." If a specific value cannot be found in the files, write "(Missing: Not found in output)" and specify which table or data section you need to complete it.
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B. "Structure 2" is for Reference Only: First, identify its unreasonable or unrigorous aspects (structural flaws, logic gaps, missing items, or inconsistencies with the problem statement). Then, provide your optimized structure and text for Question 3. Do not blindly copy the peer's heading hierarchy.
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C. Content Must Be "Reviewable": Every conclusion must be supported by verifiable numerical evidence (e.g., TTE, Sobol , MC Mean/Confidence Intervals, step-halving errors).
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D. Language & Format:
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Language: Chinese (as per original request; change this to "English" if you want the final output in English).
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Math: Use LaTeX for formulas.
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Tables: Use Markdown tables.
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Conclusions: Use clear subheadings and bullet points.
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E. Self-Consistency Check: At the end of the text, append a "Numerical Consistency Checklist" listing every key value used in the text (e.g., Baseline TTE, Scenario TTE, Sobol rankings, UQ Mean/CI) alongside its corresponding source table/field name to ensure readers can cross-check item by item.
Suggested Workflow (Output in this order):
【Phase 0: Data Digest】
- Extract and list the specific tables and key fields from the numerical output that you will use (e.g.,
TTE_TABLE,SCENARIO_TTE_TABLE,SOBOL_TABLE,UQ_SUMMARY,STEP_HALVING_TABLE). Organize these key values into a "Citation List" first.
【Phase 1: Structure Critique + Reconstruction】
- Critically review the issues in "Paper Structure 2" (focusing only on parts relevant to Question 3).
- Present your Optimized Section Structure for Question 3 (Suggested flow: 3.1 Baseline & Metrics, 3.2 Assumption Sensitivity, 3.3 Parameter Sensitivity (Local/Global), 3.4 Usage Fluctuations & Uncertainty (MC/UQ), 3.5 Numerical Stability & Robustness Evidence, 3.6 Summary: Drivers & Credibility Boundaries).
【Phase 2: Main Text for Question 3 (Final Submission Version)】
- Write the complete text for Question 3. Each subsection must follow the logic: "Method Evidence (Table/Value) Explanation (Physical Mechanism) Summary (Actionable Conclusion)."
- Mandatory Inclusion of Numerical Evidence:
- Different Initial Battery Levels / Baseline TTE results (including termination reasons, , etc.).
- TTE Rankings caused by Scenario Comparisons (Screen Brightness/CPU/Network/Signal/Temperature/Background processes).
- Global Parameter Sensitivity (Sobol and rankings; explain interaction terms).
- Usage Fluctuations (MC/UQ statistics: mean, std, quantiles, 95% CI, or key points on the survival curve).
- Numerical Verification Evidence (Step-halving error, monotonicity/non-negative checks) to support "Prediction Credibility & Stability."
Writing Goal: Make Question 3 read like an O-Prize Paper: clear structure, a complete chain of evidence, explaining why certain factors are the most sensitive, and clearly defining the conditions under which the model might fail or become unreliable.