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• There’s also a geometric realization functor for simplicial complexes.
• Simplicial sets are a topos of presheaves, so from a category-theoretic viewpoint they’re more tractable than simplicial complexes.
• We merge all points determined to be equivalent, joining their subsimplices into a single simplicial complex.
• There is a bijection between simplicial complexes and squarefree monomial ideals.
• We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions.
• The maximal dimension of its simplices (which may be infinite) is called the dimension of a simplicial complex .
• A simplicial complex is called locally finite if each of its vertices belongs to only finitely many simplices.
• The resulting simplicial complex is called the nerve of the family (cf.
• It is called the geometric realization (or body, or geometric simplicial complex) of , and is denoted by .
• We introduce the uniform face ideal of a simplicial complex with respect to an ordered proper vertex colouring of the complex.
• From this, we give the graded Betti numbers in terms of the face-vector of the underlying simplicial complex.
• These kinds of simplicial complexes also have corresponding geometric realizations as topological spaces.
• You probably already know of many examples of simplicial complexes.
• Triangular meshes (as commonly used in computer graphics) are just 2d simplicial complexes; as are Delaunay triangulations.
• Splits a simplicial complex into its connected components.
• This module implements the basic structure of finite simplicial complexes.
• To define a simplicial complex, specify its facets: the maximal subsets (with respect to inclusion) of the vertex set belonging to \(K\).
• In this case, when producing the internal representation of the simplicial complex, omit those that are not.
• The keys must be the vertices for the simplicial complex, and the values should be distinct sortable objects, for example integers.
• For a simplicial complex embedded in a k-dimensional space, the k-faces are sometimes referred to as its cells.
• See also the discussion at Polytope of simplicial complexes as subspaces of Euclidean space made up of subsets, each of which is a simplex.
• The word ‘polyhedron’ is used here as it is often used by algebraic topologists, as a space described by a simplicial complex.
• Given a space and an open cover, the nerve of the cover is a simplicial complex (see Čech methods and the discussion there).
• R\subseteq X\times Y , there are two simplicial complexes that encode information on the relation.
• To get from a simplicial complex to a fairly small simplicial set, you pick a total order on the set of vertices.
• Homology is defined on a region called a simplicial complex or just a complex.
• A simplicial complex is a region that is built by gluing smaller regions together.
• A simplicial complex is the union of all of the simplexes, including the faces of the simplexes.
• The homology of a simplicial complex at each dimension is a group called the homology group.
• We simulate the SCM over the simplicial complexes obtained from the four data sets as described in Methods.
• , the dynamics of the SCM on the RSC is very similar to the one observed on the real-world simplicial complexes.

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위키데이터

• ID : Q994399

Spacy 패턴 목록

• [{'LOWER': 'simplicial'}, {'LEMMA': 'complex'}]
• [{'LOWER': 'simplicial'}, {'LEMMA': 'complex'}]