\n ## Chart: Average Success Probability vs. Saturation Parameter ### Overview The image presents two charts, side-by-side, displaying the relationship between Average Success Probability and a saturation parameter (denoted as 𝜚²). Both charts include a reference line representing the "no noise" condition. The charts are labeled "CIM-SFC" and "CIM-CFC" respectively. Both charts have the same y-axis scale and x-axis scale. ### Components/Axes * **X-axis:** Labeled "𝜚² (saturation parameter)". The scale is logarithmic, ranging from 10⁻⁸ to 10⁰. * **Y-axis:** Labeled "Average Success Probability (N=100)". The scale ranges from 0.0 to 1.0. * **Legend (Top-Left of each chart):** * "no noise" - Represented by a dotted gray line. * **Data Series:** A single blue line representing the Average Success Probability for a given saturation parameter. ### Detailed Analysis **Chart 1: CIM-SFC** The blue line in the CIM-SFC chart initially remains relatively flat, hovering around 0.55, from approximately 10⁻⁸ to 10⁻³ on the x-axis. Around 10⁻³ the line begins to descend sharply. * **Approximate Data Points:** * 𝜚² = 10⁻⁸: Average Success Probability ≈ 0.56 * 𝜚² = 10⁻⁷: Average Success Probability ≈ 0.56 * 𝜚² = 10⁻⁶: Average Success Probability ≈ 0.56 * 𝜚² = 10⁻⁵: Average Success Probability ≈ 0.55 * 𝜚² = 10⁻⁴: Average Success Probability ≈ 0.54 * 𝜚² = 10⁻³: Average Success Probability ≈ 0.48 * 𝜚² = 10⁻²: Average Success Probability ≈ 0.35 * 𝜚² = 10⁻¹: Average Success Probability ≈ 0.12 * 𝜚² = 10⁰: Average Success Probability ≈ 0.03 The dotted gray "no noise" line is positioned horizontally at approximately 0.58. **Chart 2: CIM-CFC** The blue line in the CIM-CFC chart is initially flat, around 0.65, from approximately 10⁻⁸ to 10⁻³ on the x-axis. Around 10⁻³ the line begins to descend sharply. * **Approximate Data Points:** * 𝜚² = 10⁻⁸: Average Success Probability ≈ 0.66 * 𝜚² = 10⁻⁷: Average Success Probability ≈ 0.66 * 𝜚² = 10⁻⁶: Average Success Probability ≈ 0.66 * 𝜚² = 10⁻⁵: Average Success Probability ≈ 0.65 * 𝜚² = 10⁻⁴: Average Success Probability ≈ 0.64 * 𝜚² = 10⁻³: Average Success Probability ≈ 0.55 * 𝜚² = 10⁻²: Average Success Probability ≈ 0.35 * 𝜚² = 10⁻¹: Average Success Probability ≈ 0.12 * 𝜚² = 10⁰: Average Success Probability ≈ 0.03 The dotted gray "no noise" line is positioned horizontally at approximately 0.58. ### Key Observations * Both charts exhibit a similar trend: a relatively stable Average Success Probability at low saturation parameters, followed by a rapid decline as the saturation parameter increases. * The "no noise" line provides a baseline for comparison. The Average Success Probability drops below this baseline as the saturation parameter increases, indicating a degradation in performance due to the saturation effect. * The CIM-CFC chart maintains a higher Average Success Probability than the CIM-SFC chart for most of the saturation parameter range. ### Interpretation The charts demonstrate the impact of the saturation parameter (𝜚²) on the Average Success Probability of two different methods, CIM-SFC and CIM-CFC. The saturation parameter appears to introduce noise or instability, leading to a decrease in success probability. The "no noise" line represents the theoretical maximum success probability in the absence of this saturation effect. The fact that both charts show a similar trend suggests that the saturation effect is a fundamental limitation of the underlying process. The difference in initial success probability between CIM-SFC and CIM-CFC indicates that CIM-CFC is more robust to the saturation effect, maintaining a higher success rate for a wider range of saturation parameters. The sharp decline in success probability at higher saturation parameters suggests a critical threshold beyond which the methods become unreliable. The logarithmic scale of the x-axis highlights the sensitivity of the success probability to changes in the saturation parameter at lower values.