Comparison of CD41 and CD62p cluster distributions within a clot. First level analysis is displayed in the images (a-c).

(a) shows the detailed analysis of the full samples. In this case, density (top) and curvature (bottom) distributions of all clusters for each cluster dimensions were compared at one time using a KS-/ WX-test (blue/red). The results indicate the dissimilarity of clusters for all cluster dimensions. As an indicator, an aggregated p-value of KS- and WX-test is determined using the weighting t-Norm-AND. The p-value (black dashed line) remains mostly below the critical p-value area (orange bar) disproving the similarity hypothesis. The corresponding values for (dis)similarity sim_M = 0.01/0.68 for the density and curvature distributions were determined respectively. A closer look at the KS-/WX-Test results on curvature comparison indicates that for cluster dimensions approx. 600 nm– 800 nm the distribution is above the critical p-value area (indicating similarity). (b) shows the aggregated p-value of density and curvature calculated with the weighting t-Norm-AND (blue) and the confidence interval (black dashed line). A sim_M = 0.36 is determined. The full-sample analysis was only, additionally performed, in order to show the full software capabilities (results are typically not used for a multilayer analysis). For such large samples, the fast bootstrap resampling is used. The graphs (c-d) clearly show a general dissimilarity of the samples. (d) depicts 100 curves–representing relative density of 100-resamples each including 2000 points (green)–used for the bootstrap based comparison of the cluster/curvature density distribution for both samples. In black, the averaged curve is represented. The detailed analysis of the bootstrapped samples (d) was performed as described in (a). (c) shows the statistical comparison of the cluster density (top) and curvature data (bottom), determined from the bootstrap results. For such detailed analysis (c), KS/WX- tests (blue/red) as well as the t-Norm-AND values (black) are plotted. Additionally, the boundaries of the confidence interval are displayed (magenta). The statistical comparison of the bootstrap derived data shows a sim_M = 0.21/0.76 and sim_L = 0.11/0.4 for cluster density and curvature comparison, respectively. The data on cluster density as well as curvature however, shows a general dissimilarity of the samples. A similarity for cluster curvatures for the dimension ranges of approx. 200 nm– 400 nm and approx. 600 nm– 800 nm is observed. (e-i) depicts the second level analysis. (e) shows the p-values determined by the mean-cross analysis of the average density (left)/curvature (right) values determined via bootstrapping. Herein, p-values of the mean-cross comparison (blue) and lower/upper confidential boundaries (black dashed line) are shown. The sim_M = 0.01 and 0.61 and sim_L = 0.005/0.1 for cluster density and curvature comparison are determined respectively. In general, the data emphasizes the dissimilarity hypothesis, however, the data for curvature comparison indicates a significant similarity for approx. 400 nm– 500 nm and >900 nm cluster density ranges. (h) shows the aggregated p-values for cluster curvature and density comparison (blue). The aggregation of the p-values results in sim_L = 0.24, indicating a general dissimilarity. (f) depicts the calculated K-/H-Ripley function values for the bootstrapped data (green) for all cluster dimensions. Using H-Ripley as the crucial dimension, representative for the largest difference (clustering caused) between the sample and complete spatial randomness, can be determined (for the two images the largest difference occurs for clusters sizes of 210nm). (g) depicts the comparison of the K-/H-Ripley function (K-function left, H-function Right) values at the second statistical level. The p-values of the cross comparison (red), mean-cross comparison (blue) and lower/upper confidential boundaries (black dashed line) are shown. In contrast to all the data presented on single molecule clustering, the cross-comparison on the global analysis via Ripley’s function indicates sample similarity (for clustering dimensions ranging between approx. 400 nm– 1 000 nm). Similar to the individual distributions, is the aggregation of the K-/H-Ripley functions results (i). The respective sim_M values for the Ripley’s functions comparison are 0.86 (K-/H-Ripley) and 0.55 (aggregated). The values are contrary to the previously shown results obtained on direct cluster comparison, thus a similarity is indicated. The varying result emphasizes the importance of a multilevel statistical analysis.

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