Search results
Results from the WOW.Com Content Network
An embedding, or a smooth embedding, is defined to be an immersion that is an embedding in the topological sense mentioned above (i.e. homeomorphism onto its image). [ 4 ] In other words, the domain of an embedding is diffeomorphic to its image, and in particular the image of an embedding must be a submanifold .
A smooth embedding is an injective immersion f : M → N that is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding – that is, for any point x ∈ M there is a neighbourhood, U ⊆ M, of x such that f : U → N is an embedding, and conversely a local embedding is an ...
In natural language processing, a word embedding is a representation of a word. The embedding is used in text analysis.Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning. [1]
For example, if X and Y are smooth over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. [1] If is regularly embedded into a regular scheme, then B is a complete intersection ring. [2]
An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
The Nash embedding theorem is a global theorem in the sense that the whole manifold is embedded into R n. A local embedding theorem is much simpler and can be proved using the implicit function theorem of advanced calculus in a coordinate neighborhood of the manifold. The proof of the global embedding theorem relies on Nash's implicit function ...
Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus.