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This facet of word2vec has been exploited in a variety of other contexts. For example, word2vec has been used to map a vector space of words in one language to a vector space constructed from another language. Relationships between translated words in both spaces can be used to assist with machine translation of new words. [27]
A spreadsheet's concatenate ("&") function is used to assemble a complex text string—in this example, XML code for an SVG "circle" element. In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end.
Vector field reconstruction has several applications, and many different approaches. Some mathematicians have not only used radial basis functions and polynomials to reconstruct a vector field, but they have also used Lyapunov exponents and singular value decomposition . [ 2 ]
Each character in the string key set is represented via individual bits, which are used to traverse the trie over a string key. The implementations for these types of trie use vectorized CPU instructions to find the first set bit in a fixed-length key input (e.g. GCC 's __builtin_clz() intrinsic function ).
A (,)-tensor field is a differential -form, a (,)-tensor field is a vector field, and a (,)-tensor field is -vector field. While differential forms are widely studied as such in differential geometry and differential topology , multivector fields are often encountered as tensor fields of type ( 0 , k ) {\displaystyle (0,k)} , except in the ...
Beltrami fields with a constant proportionality factor are a distinct category of vector fields that act as eigenfunctions of the curl operator. In essence, they are functions that map points in a three-dimensional space, either in R 3 {\displaystyle \mathbb {R} ^{3}} (Euclidean space) or on a flat torus T 3 {\displaystyle \mathbb {T} ^{3 ...
Interchanging the vector field v and ∇ operator, we arrive at the cross product of a vector field with curl of a vector field: = () , where ∇ F is the Feynman subscript notation, which considers only the variation due to the vector field F (i.e., in this case, v is treated as being constant in space).
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .