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Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
The general mathematical concept embodied in a Wigner–Seitz cell is more commonly called a Voronoi cell, and the partition of the plane into these cells for a given set of point sites is known as a Voronoi diagram. The construction process for the Wigner–Seitz cell of a hexagonal lattice. The cell may be chosen by first picking a lattice ...
There are two types of active transport: primary active transport that uses adenosine triphosphate (ATP), and secondary active transport that uses an electrochemical gradient. This process is in contrast to passive transport , which allows molecules or ions to move down their concentration gradient, from an area of high concentration to an area ...
Let be the Voronoi diagram for a set of sites , and let be the Voronoi cell of corresponding to a site . If V p {\displaystyle V_{p}} is bounded, then its positive pole is the vertex of the boundary of V p {\displaystyle V_{p}} that has maximal distance to the point p {\displaystyle p} .
An active flow network is a graph with edges and nodes, where particles inside this graph are propelled by an active mechanism. [1] [2] This type of network is used to study the motion of molecules in biological medium. Examples are organelles, including the Endoplasmic Reticulum (ER). [3]
For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbor interpolation, by assigning the function value at the given point to all the points inside the cell. [ 3 ]
[citation needed] Primary active transport uses adenosine triphosphate (ATP) to move specific molecules and solutes against its concentration gradient. Examples of molecules that follow this process are potassium K +, sodium Na +, and calcium Ca 2+. A place in the human body where this occurs is in the intestines with the uptake of glucose.
This diagram arises, e.g., as a model of crystal growth, where crystals from different points may grow with different speed. Since crystals may grow in empty space only and are continuous objects, a natural variation is the crystal Voronoi diagram, in which the cells are defined somewhat differently. In an additively weighted Voronoi diagram ...