Search results
Results from the WOW.Com Content Network
A Euclidean isometry can be direct or indirect, depending on whether it preserves the handedness of figures. The direct Euclidean isometries form a subgroup, the special Euclidean group, often denoted SE(n) and E + (n), whose elements are called rigid motions or Euclidean motions. They comprise arbitrary combinations of translations and ...
The distance matrix can come from a number of different sources, including measured distance (for example from immunological studies) or morphometric analysis, various pairwise distance formulae (such as euclidean distance) applied to discrete morphological characters, or genetic distance from sequence, restriction fragment, or allozyme data.
Figure 6: Euclidean genetic distance between 51 worldwide human populations, calculated using 289,160 SNPs. [30] Dark red is the most similar pair and dark blue is the most distant pair. Euclidean distance is a formula brought about from Euclid's Elements, a 13 book set detailing the foundation of all euclidean mathematics.
For a clustering example, suppose that five taxa (to ) have been clustered by UPGMA based on a matrix of genetic distances.The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity).
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices.
A simple cladogram showing the evolutionary relationships between four species: A, B, C, and D. Here, Species A is the outgroup, and Species B, C, and D form the ingroup. In cladistics or phylogenetics, an outgroup [1] is a more distantly related group of organisms that serves as a reference group when determining the evolutionary relationships of the ingroup, the set of organisms under study ...
In the simplest case, shown in the first picture, we are given a finite set of points {, …} in the Euclidean plane.In this case, each point has a corresponding cell consisting of the points in the Euclidean plane for which is the nearest site: the distance to is less than or equal to the minimum distance to any other site .
The term sister group is used in phylogenetic analysis, however, only groups identified in the analysis are labeled as "sister groups".. An example is birds, whose commonly cited living sister group is the crocodiles, but that is true only when discussing extant organisms; [3] [4] when other, extinct groups are considered, the relationship between birds and crocodiles appears distant.