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Spark Core is the foundation of the overall project. It provides distributed task dispatching, scheduling, and basic I/O functionalities, exposed through an application programming interface (for Java, Python, Scala, .NET [16] and R) centered on the RDD abstraction (the Java API is available for other JVM languages, but is also usable for some other non-JVM languages that can connect to the ...
MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. [1] [2] [3]A MapReduce program is composed of a map procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a reduce method, which performs a summary ...
The action is called free (or semiregular or fixed-point free) if the statement that g⋅x = x for some x ∈ X already implies that g = e G. In other words, no non-trivial element of G fixes a point of X. This is a much stronger property than faithfulness. For example, the action of any group on itself by left multiplication is free.
A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and in fewer cases the transformations result in programs that semantically differ from the original in predictable ways.
For example, a bx run in the forward direction might transform input I into output O, while the same bx run backward would take as input versions of I and O and produce a new version of I as its output. Bidirectional model transformations are an important special case in which a model is input to such a program.
In computing, data transformation is the process of converting data from one format or structure into another format or structure. It is a fundamental aspect of most data integration [1] and data management tasks such as data wrangling, data warehousing, data integration and application integration.
Another class of simple examples comes from statistical estimation. The mean of a sample (a set of real numbers) is commonly used as a central tendency of the sample. It is equivariant under linear transformations of the real numbers, so for instance it is unaffected by the choice of units used to represent the numbers. By contrast, the mean is ...
The explicit form of a covariant transformation is best introduced with the transformation properties of the derivative of a function. Consider a scalar function f (like the temperature at a location in a space) defined on a set of points p, identifiable in a given coordinate system , =,, … (such a collection is called a manifold).