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README.md

@@ -502,7 +502,7 @@ the definition for the mitochondrion is fully contained within the melanosome me
 
 # [Example 9](https://gist.githubusercontent.com/richardtjornhammar/e84056e0b10f8d550258a1e8944ee375/raw/e44e7226b6cb8ca486ff539ccfa775be981a549c/example9.py): Impetuous [deterministic DBSCAN](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for dbscan)
 
-[DBSCAN](https://en.wikipedia.org/wiki/DBSCAN) is a clustering algorithm that can be seen as a way of rejecting points, from any cluster, that are positioned in low dense regions of a point cloud. This introduces holes and may result in a larger segment, that would otherwise be connected via a non dense link to become disconnected and form two segments, or clusters. The rejection criterion is simple. The central concern is to evaluate a distance matrix <img src="https://render.githubusercontent.com/render/math?math=D_{ij}">  with an applied cutoff <img src="https://render.githubusercontent.com/render/math?math=\epsilon"> this turns the distances into true or false values depending on if a pair distance between point i and j is within the distance cutoff. This new binary Neighbour matrix <img src="https://render.githubusercontent.com/render/math?math=N_{ij}=D_{ij}\ge\epsilon"> tells you wether or not two points are neighbours (including itself). The DBSCAN criterion states that a point is not part of any cluster if it has fewer than `minPts` neighbors. Once you've calculated the distance matrix you can immediately evaluate the number of neighbors each point has and the rejection criterion, via <img src="https://render.githubusercontent.com/render/math?math=R_i=(\sum_{j} N_{ij}\ge\epsilon)-1 < minPts">. If the rejection vector R value of a point is True then all the pairwise distances in the distance matrix of that point is set to a value larger than epsilon. This ensures that a distance matrix search will reject those points as neighbours of any other for the choosen epsilon. By tracing out all points that are neighbors and assessing the [connectivity](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for connectivity) you can find all the clusters.
+[DBSCAN](https://en.wikipedia.org/wiki/DBSCAN) is a clustering algorithm that can be seen as a way of rejecting points, from any cluster, that are positioned in low dense regions of a point cloud. This introduces holes and may result in a larger segment, that would otherwise be connected via a non dense link to become disconnected and form two segments, or clusters. The rejection criterion is simple. The central concern is to evaluate a distance matrix <img src="https://render.githubusercontent.com/render/math?math=D_{ij}">  with an applied cutoff <img src="https://render.githubusercontent.com/render/math?math=\epsilon"> this turns the distances into true or false values depending on if a pair distance between point i and j is within the distance cutoff. This new binary Neighbour matrix <img src="https://render.githubusercontent.com/render/math?math=N_{ij}=D_{ij}\le\epsilon"> tells you wether or not two points are neighbours (including itself). The DBSCAN criterion states that a point is not part of any cluster if it has fewer than `minPts` neighbors. Once you've calculated the distance matrix you can immediately evaluate the number of neighbors each point has and the rejection criterion, via <img src="https://render.githubusercontent.com/render/math?math=R_i=(\sum_{j} N_{ij}\le\epsilon)-1 < minPts">. If the rejection vector R value of a point is True then all the pairwise distances in the distance matrix of that point is set to a value larger than epsilon. This ensures that a distance matrix search will reject those points as neighbours of any other for the choosen epsilon. By tracing out all points that are neighbors and assessing the [connectivity](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for connectivity) you can find all the clusters.
 
 In this [example](https://gist.githubusercontent.com/richardtjornhammar/e84056e0b10f8d550258a1e8944ee375/raw/e44e7226b6cb8ca486ff539ccfa775be981a549c/example9.py) we do exactly this for two gaussian point clouds. The dbscan search is just a single line `dbscan ( data_frame = point_cloud_df , eps=0.45 , minPts=4 )`, while the last lines are there to plot the [results](https://bl.ocks.org/richardtjornhammar/raw/0cc0ff037e88c76a9d65387155674fd1/?raw=true) ( has [graph revision dates](https://gist.github.com/richardtjornhammar/0cc0ff037e88c76a9d65387155674fd1/revisions) )
 
@@ -722,7 +722,7 @@ It is readily viewable below and we can see that the UMAP and Distance Geometry
 
 # Example 14: Connectivity, hierarchies and linkages
 
-In the `impetuous.clustering` module you will find several codes for assessing if distance matrices are connected at some distance or not. `connectivity` and `connectedness` are two methods for establishing the number of clusters in the binary Neighbour matrix. The Neighbour matrix is just the pairwise distance matrix of your systems with an applied cutoff (<img src="https://render.githubusercontent.com/render/math?math=N_{ij}=D_{ij}\ge\epsilon">) and is related to the adjacency matrix from graph theory by adding a unit dirac delta function to it (<img src="https://render.githubusercontent.com/render/math?math=A_{ij}=N_{ij} - \delta_1(|i-j|)">).
+In the `impetuous.clustering` module you will find several codes for assessing if distance matrices are connected at some distance or not. `connectivity` and `connectedness` are two methods for establishing the number of clusters in the binary Neighbour matrix. The Neighbour matrix is just the pairwise distance matrix of your systems with an applied cutoff (<img src="https://render.githubusercontent.com/render/math?math=N_{ij}=D_{ij}\le\epsilon">) and is related to the adjacency matrix from graph theory by adding a unit dirac delta function to it (<img src="https://render.githubusercontent.com/render/math?math=A_{ij}=N_{ij} - \delta_1(|i-j|)">).
 
 "Connection" algorithms, such as the two mentioned, evaluate every distance and add them to the same cluster if there is any true overlap for a specific distance cutoff evaluation. "Link" algorithms try to determine the number of clusters for all unique distances by reducing and ignoring some connections to already linked constituents of the system in accord with a chosen heuristic.