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Venn diagram of information theoretic measures for three variables , , and , represented by the lower left, lower right, and upper circles, respectively.The ...
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
To illustrate the processes, consider the case of dissolving a weak acid, HA, in water. The pH can be calculated using an ICE table. The pH can be calculated using an ICE table. Note that in this example, we are assuming that the acid is not very weak, and that the concentration is not very dilute, so that the concentration of [OH − ] ions ...
Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article. In terms of a communication channel in which the output Y {\displaystyle Y} is a noisy version of the input X {\displaystyle X} , these relations ...
This formula can be verified by counting how many times each region in the Venn diagram figure is included in the right-hand side of the formula. In this case, when removing the contributions of over-counted elements, the number of elements in the mutual intersection of the three sets has been subtracted too often, so must be added back in to ...
The law of water balance states that the inflows to any water system or area is equal to its outflows plus change in storage during a time interval. [ 2 ] [ 3 ] In hydrology , a water balance equation can be used to describe the flow of water in and out of a system.
Venn diagram of information theoretic measures for three variables x, y, and z, represented by the lower left, lower right, and upper circles, respectively. The interaction information is represented by gray region, and it is the only one that can be negative.
Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms. [1] During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution, [10] [11] but Gelenbe's G-network model showed this not to be the case. [12]