## Heatmap: Scores for Different η_A and Plus Values
### Overview
The image is a heatmap visualizing scores across varying values of η_A (x-axis) and "Plus Multipliers" (y-axis). Scores are represented by color intensity (light blue to dark blue) and numerical values embedded in each cell. The color scale ranges from 30 (lightest) to 80 (darkest).
### Components/Axes
- **X-axis (η_A Values)**:
- Labels: `5.00E-05`, `2.00E-04`, `4.00E-04`, `6.00E-04`
- Title: "η_A Values"
- **Y-axis (Plus Multipliers)**:
- Labels: `5`, `10`, `20`, `40`
- Title: "Plus Multipliers"
- **Legend**:
- Position: Right of the heatmap
- Scale: `30` (light blue) to `80` (dark blue)
- Label: "Score"
### Detailed Analysis
#### η_A = 5.00E-05
- **Multiplier 5**: Score = 29.49 (light blue)
- **Multiplier 10**: Score = 40.93 (medium blue)
- **Multiplier 20**: Score = 29.36 (light blue)
- **Multiplier 40**: Score = 29.67 (light blue)
#### η_A = 2.00E-04
- **Multiplier 5**: Score = 42.90 (medium blue)
- **Multiplier 10**: Score = 48.50 (medium blue)
- **Multiplier 20**: Score = 56.40 (dark blue)
- **Multiplier 40**: Score = 62.03 (dark blue)
#### η_A = 4.00E-04
- **Multiplier 5**: Score = 46.39 (medium blue)
- **Multiplier 10**: Score = 67.90 (dark blue)
- **Multiplier 20**: Score = 64.86 (dark blue)
- **Multiplier 40**: Score = 51.84 (medium blue)
#### η_A = 6.00E-04
- **Multiplier 5**: Score = 45.71 (medium blue)
- **Multiplier 10**: Score = 52.69 (medium blue)
- **Multiplier 20**: Score = 62.63 (dark blue)
- **Multiplier 40**: Score = 50.43 (medium blue)
### Key Observations
1. **Highest Scores**:
- Occur at η_A = 4.00E-04 and Multiplier = 10 (67.90).
- Second-highest at η_A = 2.00E-04 and Multiplier = 40 (62.03).
2. **Lowest Scores**:
- Cluster in the η_A = 5.00E-05 row (scores 29.36–40.93).
3. **Trends**:
- Scores generally increase with higher η_A values, especially in higher multiplier rows (e.g., Multiplier = 40: 29.67 → 62.03 → 51.84 → 50.43).
- Multiplier has a stronger influence on scores than η_A in most cases (e.g., Multiplier = 40 scores range from 29.67 to 62.03).
4. **Anomalies**:
- η_A = 5.00E-05 shows inconsistent performance (e.g., Multiplier = 20 score = 29.36, lower than Multiplier = 5 at 29.49).
- η_A = 4.00E-04 and Multiplier = 40 (51.84) underperforms compared to lower η_A values at the same multiplier.
### Interpretation
The heatmap demonstrates that **both η_A and Plus Multipliers significantly impact scores**, with higher values of both parameters generally yielding better results. However, the relationship is non-linear:
- **Multiplier Dominance**: Increasing the multiplier from 5 to 40 often results in larger score improvements than increasing η_A (e.g., η_A = 2.00E-04: 42.90 → 62.03 for Multiplier = 5 → 40).
- **Diminishing Returns**: At higher η_A values (e.g., 6.00E-04), score improvements plateau or decline in some cases (e.g., Multiplier = 40: 62.63 → 50.43).
- **Optimal Parameters**: The combination of η_A = 4.00E-04 and Multiplier = 10 maximizes scores (67.90), suggesting a balance between η_A and multiplier magnitude is critical.
The color gradient confirms these trends, with darker blues (higher scores) concentrated in the middle-to-right η_A values and higher multiplier rows. This visualization highlights the importance of tuning both parameters to achieve optimal performance.
