## Heatmap: Relationship Between Percentage p and Width of Near-Zero Range c ### Overview The image is a heatmap visualizing the relationship between two variables: "percentage p" (y-axis) and "width of near-zero range c" (x-axis). Each cell contains a numerical value representing a metric (likely a percentage or score) that varies based on the combination of p and c. The color gradient transitions from light yellow (low values) to dark blue (high values), with a legend on the right indicating the scale. --- ### Components/Axes - **X-axis (width of near-zero range c)**: - Labels: 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 - Scale: Linear increments of 0.05 - **Y-axis (percentage p)**: - Labels: 85.0, 90.0, 92.5, 95.0, 97.0, 99.5 - Scale: Linear increments of 2.5 (except 85.0 to 90.0, which is 5.0) - **Legend**: - Position: Right side of the heatmap - Color gradient: Light yellow (64.0) to dark blue (67.0) - Label: Implied to represent the metric values in the cells --- ### Detailed Analysis #### Data Table Structure The heatmap is organized as a 6x6 grid, with rows corresponding to percentage p values and columns to width c values. Each cell contains a numerical value and a color intensity matching the legend. Below is the reconstructed table: | **p (%)** | **c = 0.05** | **c = 0.1** | **c = 0.15** | **c = 0.2** | **c = 0.25** | **c = 0.3** | |-----------|--------------|-------------|--------------|-------------|--------------|-------------| | 99.5 | 65.2 | 64.6 | 66.4 | 66.0 | 64.4 | 65.2 | | 97.0 | 65.4 | 65.4 | 65.2 | 65.6 | 65.2 | 65.2 | | 95.0 | 64.8 | 64.4 | 64.4 | 65.6 | 64.6 | 64.2 | | 92.5 | 65.0 | 64.2 | 64.8 | 64.8 | 65.2 | 65.0 | | 90.0 | 64.6 | 64.6 | 64.6 | 64.4 | 65.6 | 65.2 | | 85.0 | 64.0 | 64.4 | 64.8 | 64.6 | 67.0 | 66.2 | #### Color-Space Verification - **Darkest blue (67.0)**: Located at (85.0%, 0.3) - **Lightest yellow (64.0)**: Located at (99.5%, 0.05) - All other values align with the legend’s gradient (e.g., 65.2 corresponds to a medium-blue shade). --- ### Key Observations 1. **Highest Value**: 67.0 at (85.0%, 0.3) — the lowest p and widest c. 2. **Lowest Value**: 64.0 at (99.5%, 0.05) — the highest p and narrowest c. 3. **Trend**: - Values generally increase as c increases (e.g., 64.0 → 66.2 for p=85.0%). - For fixed c, values fluctuate slightly with p but show no clear monotonic trend. 4. **Anomalies**: - At p=95.0%, the value drops to 64.2 at c=0.3, breaking the upward trend observed in other rows. - At p=90.0%, the value at c=0.2 is 64.4, lower than adjacent cells. --- ### Interpretation The heatmap suggests a **trade-off relationship** between p and c: - **Lower p (85.0%)** and **wider c (0.3)** yield the highest values (67.0), indicating optimal performance under these conditions. - **Higher p (99.5%)** and **narrow c (0.05)** result in the lowest values (64.0), suggesting suboptimal performance. - The anomaly at p=95.0% and c=0.3 (64.2) may indicate a non-linear interaction or an outlier in the dataset. The color gradient reinforces that the metric being measured (e.g., efficiency, accuracy) improves as the width of the near-zero range increases, particularly when the percentage p is lower. This could imply that broader near-zero ranges are more effective in scenarios with lower p values, though further context is needed to confirm causality. --- ### Spatial Grounding - **Legend**: Right-aligned, vertically oriented, with a clear gradient from yellow to blue. - **Axes**: Labeled with precise numerical increments; grid lines divide the heatmap into discrete cells. - **Cell Values**: Centered in each cell, ensuring readability. This structured layout ensures the data is both visually accessible and quantitatively precise.