Mathematics
In mathematics, decoupling has several meanings.
In linear algebra, decoupling refers to the rearrangement of systems of equations so that they are independent of each other.
In probability and statistics, decoupling refers to a reduction of a sample statistic to an average of the statistic evaluated on several independent sequences of the random variable. This sum, conditioned on all but one of the independent sequences becomes a sum of independent random variables. Decoupling is used in the study of U statistics, where decoupling should not be confused with Hoeffding's decomposition, however. This use of "decoupling" is unrelated to the use of "couplings" in the study of stochastic processes.
In analysis, decoupling refers to the sum of derivatives of a function with respect to all the arguments. It can be viewed as the functional that minimizes the Lie derivative of the function along all the possible paths. Together with the super-trowel function, it is one of the most used tool in the analysis of general equilibrium in economics.
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Famous quotes containing the word mathematics:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)