Search results
Results from the WOW.Com Content Network
The Robinson–Foulds or symmetric difference metric, often abbreviated as the RF distance, is a simple way to calculate the distance between phylogenetic trees. [1]It is defined as (A + B) where A is the number of partitions of data implied by the first tree but not the second tree and B is the number of partitions of data implied by the second tree but not the first tree (although some ...
For example, it maps the positive real numbers to the interval [−1, 1]. Thus the Cayley transform is used to adapt Legendre polynomials for use with functions on the positive real numbers with Legendre rational functions. As a real homography, points are described with projective coordinates, and the mapping is
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):
A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 ...
To see how this number arises, consider the real one-parameter map =.Here a is the bifurcation parameter, x is the variable. The values of a for which the period doubles (e.g. the largest value for a with no period-2 orbit, or the largest a with no period-4 orbit), are a 1, a 2 etc.
A BSP tree is traversed in a linear time, in an order determined by the particular function of the tree. Again using the example of rendering double-sided polygons using the painter's algorithm, to draw a polygon P correctly requires that all polygons behind the plane P lies in must be drawn first, then polygon P, then finally the polygons in ...
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.
As mentioned above, the logistic map itself is an ordinary quadratic function. An important question in terms of dynamical systems is how the behavior of the trajectory changes when the parameter r changes. Depending on the value of r, the behavior of the trajectory of the logistic map can be simple or complex.