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Calculus. In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, [1] The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself.
Evolution of the lifelogging lanyard camera. From left to right: Mann (1998); Microsoft (2004); Mann, Fung, Lo (2006); Memoto (2013) A lifelog is a personal record of one's daily life in a varying amount of detail, for a variety of purposes. The record contains a comprehensive dataset of a human's activities. The data could be used to increase ...
Write-ahead logging. In computer science, write-ahead logging ( WAL) is a family of techniques for providing atomicity and durability (two of the ACID properties) in database systems. [1] A write ahead log is an append-only auxiliary disk-resident structure used for crash and transaction recovery. The changes are first recorded in the log ...
A logarithmically convex function f is a convex function since it is the composite of the increasing convex function and the function , which is by definition convex. However, being logarithmically convex is a strictly stronger property than being convex. For example, the squaring function is convex, but its logarithm is not.
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, [1] [2] in the context of constructive quantum field theory. Similar results were ...
LogSumExp. The LogSumExp (LSE) (also called RealSoftMax [1] or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms. [2] It is defined as the logarithm of the sum of the exponentials of the arguments:
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer.