# Technical Document Extraction: Evolution Analysis of σₘ, Norm Differences, and T Distributions
## Image Structure
The image contains **16 subplots** organized into **4 main sections** (Window Sizes = 1, 5, 10, m) with **3 subplots per section**:
1. Evolution of σₘ (top row)
2. Evolution of ||p^(m) - p^(1)||₁ (middle row)
3. Distribution of T (bottom row)
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## Key Labels and Axis Titles
### Common Elements
- **X-axis**: "Generation m" (all subplots)
- **Y-axis (σₘ plots)**: "σₘ" (range: 0.0–1.0)
- **Y-axis (norm plots)**: "||p^(m) - p^(1)||₁" (range: 0.0–2.0)
- **Y-axis (T distributions)**: "Count" (range: 0–30)
- **X-axis (T distributions)**: "Generation m" (range: 0–500)
### Section-Specific Labels
- **Window Size = 1**
- σₘ: "Evolution of σₘ"
- Norm: "Evolution of ||p^(m) - p^(1)||₁"
- T Distribution: "Distribution of T"
- **Window Size = 5**
- σₘ: "Evolution of σₘ"
- Norm: "Evolution of ||p^(m) - p^(1)||₁"
- T Distribution: "Distribution of T"
- **Window Size = 10**
- σₘ: "Evolution of σₘ"
- Norm: "Evolution of ||p^(m) - p^(1)||₁"
- T Distribution: "Distribution of T"
- **Window Size = m**
- σₘ: "Evolution of σₘ"
- Norm: "Evolution of ||p^(m) - p^(1)||₁"
- T Distribution: "Distribution of T"
### Legends
- **σₘ plots**: Red line labeled "Mean = X" (X varies by window size)
- **Norm plots**: Red line labeled "Mean = X" (X varies by window size)
- **T Distributions**: Red vertical line labeled "Mean = X" (X varies by window size)
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## Key Trends and Data Points
### 1. Evolution of σₘ
- **Window Size = 1**
- σₘ stabilizes at **~0.95** after an initial sharp rise (0–50 generations).
- Red line confirms mean ≈ 0.95.
- **Window Size = 5**
- σₘ increases gradually from **~0.2 to ~0.8** over 500 generations.
- Red line confirms mean ≈ 0.8.
- **Window Size = 10**
- σₘ rises steadily from **~0.3 to ~0.9** over 500 generations.
- Red line confirms mean ≈ 0.9.
- **Window Size = m**
- σₘ fluctuates between **~0.4 and ~0.6** with high variance.
- Red line confirms mean ≈ 0.5.
### 2. Evolution of ||p^(m) - p^(1)||₁
- **Window Size = 1**
- Norm drops sharply from **~2.0 to ~0.0** within 50 generations.
- Red line confirms mean ≈ 0.0.
- **Window Size = 5**
- Norm decreases gradually from **~2.0 to ~0.5** over 500 generations.
- Red line confirms mean ≈ 0.5.
- **Window Size = 10**
- Norm decreases from **~2.0 to ~0.3** over 500 generations.
- Red line confirms mean ≈ 0.3.
- **Window Size = m**
- Norm stabilizes at **~0.1** after an initial drop.
- Red line confirms mean ≈ 0.1.
### 3. Distribution of T
- **Window Size = 1**
- T values cluster tightly around **mean = 17**.
- Histogram shows a narrow peak at low T values.
- **Window Size = 5**
- T values spread between **~50 and ~250**, with mean = 95.
- Histogram shows a bimodal distribution.
- **Window Size = 10**
- T values spread between **~100 and ~400**, with mean = 216.
- Histogram shows a multimodal distribution.
- **Window Size = m**
- T values cluster tightly around **mean = 98**.
- Histogram shows a single peak at low T values.
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## Spatial Grounding and Color Verification
- **Legend Placement**: Top-right corner of each subplot.
- **Color Consistency**:
- Red lines in σₘ and norm plots match "Mean = X" labels.
- Green bars in T distributions match "Mean = X" labels.
- No mismatches detected between legend colors and data points.
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## Component Isolation
### Header
- Title: "Window Size = X" (X = 1, 5, 10, m)
- Subtitle: "Evolution of σₘ" or "Evolution of ||p^(m) - p^(1)||₁" or "Distribution of T"
### Main Chart
- **σₘ Plots**: Line charts with red trend lines.
- **Norm Plots**: Line charts with red trend lines.
- **T Distributions**: Bar charts with red vertical mean lines.
### Footer
- No explicit footer elements; all data is contained within subplots.
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## Data Table Reconstruction (Hypothetical)
| Window Size | σₘ Mean | ||p^(m) - p^(1)||₁ Mean | T Mean |
|-------------|---------|--------------------------|--------|
| 1 | 0.95 | 0.0 | 17 |
| 5 | 0.8 | 0.5 | 95 |
| 10 | 0.9 | 0.3 | 216 |
| m | 0.5 | 0.1 | 98 |
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## Conclusion
The image demonstrates how window size impacts:
1. **σₘ stability** (smaller windows stabilize faster).
2. **Norm convergence** (larger windows reduce differences between p^(m) and p^(1)).
3. **T distribution spread** (larger windows increase variability in T values).
