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MCM/A题/数值分析检验/Prompt/4.md
2026-02-16 21:52:26 +08:00

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TASK: Output BASELINE_CONFIG_v1 as JSON only (parameters + scenario schedule).

INPUT DATA:

  • MODEL_SPEC parameter list (Prompt 1)
  • Scenario concept: 6-hour alternating profile with smooth transitions using: win(t;a,b,δ)=1/(1+exp(-(t-a)/δ)) - 1/(1+exp(-(t-b)/δ)) and L(t)=Σ L_j*win(t;a_j,b_j,δ), similarly for C(t), N(t)

METHODOLOGY:

  1. Choose δ = 20 seconds exactly.
  2. Define a 6-hour schedule with exactly 6 segments in seconds: Segment table fields: name, a_sec, b_sec, L_level, C_level, N_level, Ψ_level, T_a_C
  3. Use the example normalized levels: standby: L=0.10 C=0.10 N=0.20 streaming: L=0.70 C=0.40 N=0.60 gaming: L=0.90 C=0.90 N=0.50 navigation: L=0.80 C=0.60 N=0.80 Include exactly one “poor signal” hour where Ψ_level is lower than the rest.
  4. Freeze initial conditions: z0 in {1.00,0.75,0.50,0.25}; v_p0=0; w0=0; S0=1; T_b0=T_a(0)
  5. Freeze numerics: dt=1.0 second; t_max=24*3600 seconds; seed=20260201

DELIVERABLE: JSON object with keys:

  • params: {name:value} for every parameter in MODEL_SPEC
  • scenario: {delta_sec, segments:[...], win_definition_string}
  • initial_conditions: list of z0 values and fixed other inits
  • numerics: {dt, t_max, seed}

VALIDATION:

  • segments must cover [0,21600] seconds without gaps (allow overlaps only via smooth win)
  • all input levels must lie within required bounds (L,C,N,w in [0,1], Ψ in (0,1])

OUTPUT FORMAT: JSON only. No markdown.