# Technical Data Extraction: Coverage Ratio vs. $n_s$ ## 1. Image Overview This image is a line graph with error bars comparing two experimental datasets. It illustrates the relationship between a sample size or parameter denoted as $n_s$ and a "Coverage Ratio." ## 2. Component Isolation ### Header/Title * No explicit title is present within the image frame. ### Main Chart Area * **X-Axis Label:** $n_s$ * **X-Axis Markers (Categorical/Log-spaced):** 500, 750, 1000, 2000, 3000, 6000, 8000. Note: The spacing on the x-axis is not linear; it appears to be treated as categorical or semi-logarithmic. * **Y-Axis Label:** Coverage Ratio * **Y-Axis Markers:** 0.84, 0.86, 0.88, 0.90, 0.92, 0.94, 0.96, 0.98, 1.00. ### Legend * **Location:** Bottom right [approximate coordinates: x=0.85, y=0.20]. * **Title:** Experiment * **Series 1:** Blue circle ($\bullet$) - Experiment 1 * **Series 2:** Orange circle ($\bullet$) - Experiment 2 --- ## 3. Trend Verification and Data Extraction ### Trend Analysis * **Experiment 1 (Blue):** Shows a steep upward slope from $n_s = 500$ to $n_s = 2000$, after which the growth rate decelerates significantly, approaching an asymptote near 1.00. * **Experiment 2 (Orange):** Starts at a higher coverage ratio than Experiment 1 at $n_s = 500$. It follows a similar upward trajectory but with a less steep initial slope. It is surpassed by Experiment 1 at $n_s = 2000$, then converges toward the same asymptote near 1.00. ### Data Table (Estimated Values) Values are extracted based on visual alignment with axis markers. Error bars indicate standard deviation or confidence intervals. | $n_s$ (X-axis) | Experiment 1 (Blue) | Experiment 2 (Orange) | | :--- | :--- | :--- | | **500** | ~0.852 | ~0.883 | | **750** | ~0.916 | ~0.947 | | **1000** | ~0.969 | ~0.970 | | **2000** | ~0.990 | ~0.986 | | **3000** | ~0.992 | ~0.991 | | **6000** | ~0.996 | ~0.995 | | **8000** | ~0.997 | ~0.996 | --- ## 4. Detailed Observations * **Crossover Point:** A significant crossover occurs between $n_s = 1000$ and $n_s = 2000$. At $n_s = 1000$, the two experiments are nearly identical. By $n_s = 2000$, Experiment 1 (Blue) achieves a higher coverage ratio than Experiment 2 (Orange). * **Error Bars:** * Experiment 1 (Blue) has larger error bars at lower $n_s$ values (500, 750), suggesting higher variance in results for smaller sample sizes. * Experiment 2 (Orange) has relatively consistent error bar sizes until $n_s = 2000$. * For both series, error bars become extremely small as $n_s$ reaches 6000 and 8000, indicating high precision and convergence as the coverage ratio nears 1.00. * **Saturation:** Both experiments show "saturation" behavior, where increasing $n_s$ beyond 3000 yields diminishing returns in the Coverage Ratio, as both are already >0.99.

# Technical Document Analysis of Coverage Ratio vs. n_s ## Figure Description The image is a line graph comparing the **Coverage Ratio** across varying values of **n_s** for two experimental conditions (Experiment 1 and Experiment 2). The graph includes error bars for data points, a legend, and labeled axes. --- ### Key Components 1. **Axes**: - **X-axis**: Labeled **n_s**, with markers at 500, 750, 1000, 2000, 3000, 6000, and 8000. - **Y-axis**: Labeled **Coverage Ratio**, with markers at 0.84, 0.86, 0.88, 0.90, 0.92, 0.94, 0.96, 0.98, and 1.00. 2. **Legend**: - Located in the **bottom-right corner**. - **Experiment 1**: Blue line and data points. - **Experiment 2**: Orange line and data points. 3. **Data Points**: - Error bars are present for all data points, indicating variability in measurements. --- ### Data Extraction #### Experiment 1 (Blue) | n_s | Coverage Ratio | Error Bar Range (Approximate) | |-------|----------------|-------------------------------| | 500 | 0.855 | ±0.015 | | 750 | 0.918 | ±0.010 | | 1000 | 0.965 | ±0.005 | | 2000 | 0.988 | ±0.003 | | 3000 | 0.992 | ±0.002 | | 6000 | 0.997 | ±0.001 | | 8000 | 0.998 | ±0.001 | #### Experiment 2 (Orange) | n_s | Coverage Ratio | Error Bar Range (Approximate) | |-------|----------------|-------------------------------| | 500 | 0.882 | ±0.015 | | 750 | 0.945 | ±0.010 | | 1000 | 0.970 | ±0.005 | | 2000 | 0.985 | ±0.003 | | 3000 | 0.990 | ±0.002 | | 6000 | 0.996 | ±0.001 | | 8000 | 0.997 | ±0.001 | --- ### Trends and Observations 1. **General Trend**: - Both experiments show an **increasing Coverage Ratio** as **n_s** increases. - Coverage Ratio approaches **1.00** asymptotically for both experiments. 2. **Convergence**: - At **n_s = 2000**, the Coverage Ratios for both experiments are nearly identical (~0.985–0.988). - Beyond **n_s = 2000**, the lines converge further, with minimal divergence. 3. **Initial Disparity**: - At **n_s = 500**, Experiment 2 starts with a higher Coverage Ratio (0.882 vs. 0.855 for Experiment 1). - By **n_s = 750**, the gap narrows (0.945 vs. 0.918). 4. **Error Bar Behavior**: - Error bars decrease in magnitude as **n_s** increases, indicating improved precision in measurements for larger **n_s** values. --- ### Spatial Grounding - **Legend Placement**: Bottom-right corner (coordinates: [x=0.85, y=0.15] relative to the figure). - **Data Point Colors**: - Blue (Experiment 1) matches the legend. - Orange (Experiment 2) matches the legend. --- ### Component Isolation 1. **Header**: None. 2. **Main Chart**: - Two lines (blue and orange) with error bars. - Axes labeled and scaled. 3. **Footer**: None. --- ### Final Notes - The graph confirms that **higher n_s values** lead to **higher Coverage Ratios**, with both experiments converging near **1.00**. - Experimental conditions (1 and 2) show similar performance at large **n_s**, but Experiment 2 starts with a slight advantage at lower **n_s**.