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Here are equivalent characterizations of real trees which can be used as definitions: 1) (similar to trees as graphs) A real tree is a geodesic metric space which contains no subset homeomorphic to a circle. [1] 2) A real tree is a connected metric space (,) which has the four points condition [2] (see figure):
The nodes in the first tree are univariate random variables. The edges are constraints or conditional constraints explained as follows. Recall that an edge in a tree is an unordered set of two nodes. Each edge in a vine is associated with a constraint set, being the set of variables (nodes in first tree) reachable by the set membership relation ...
The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, [ 1 ] it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle , in a configuration traditionally used to depict the Pythagorean theorem .
If, however, the similarity function satisfies the triangle inequality then it is possible to use the result of each comparison to prune the set of candidates to be examined. The first article on metric trees, as well as the first use of the term "metric tree", published in the open literature was by Jeffrey Uhlmann in 1991. [2]
function knn_search is input: t, the target point for the query k, the number of nearest neighbors of t to search for Q, max-first priority queue containing at most k points B, a node, or ball, in the tree output: Q, containing the k nearest neighbors from within B if distance(t, B.pivot) - B.radius ≥ distance(t, Q.first) then return Q ...
The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.
Brownian trees are mathematical models of dendritic structures associated with the physical process known as diffusion-limited aggregation. A Brownian tree is built with these steps: first, a "seed" is placed somewhere on the screen. Then, a particle is placed in a random position of the screen, and moved randomly until it bumps against the seed.
Borderline tree is a term used in forestry. It is a concept that comes from variable radius plots, or point sampling. It happens when a tree cannot be easily determined as in or out when using a prism or angle gauge .