First, we attach a cubical complex to the object of interest, then we associate an algebraic structure on which a number of simplifying operations preserving the topology but not necessarily the geometric nature of the complex are possible. This is a unifying dimension independent approach. We ...
Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds - Schwartz, Ziegler - 2003 () Citation Context ...al order on IRn and hence the cubes, and whether this can be transferred consistently to the cubical complex. 3. Construction of a cubical ...
Google algorithms are highly complex systems designed to retrieve data from its search index and deliver the most relevant search engine results for user queries. These search ranking factors enable algorithms to evaluate and rank web pages on SERPs. Initially, Google introduced just a few... ...
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We construct a cubical CW-complex CK( M) whose rational cohomology algebra contains Vassiliev invariants of knots in the 3-manifold M. We construct CK( R 3) by attaching cells to CK( R 3) for every degenerate 1-singular and 2-singular knot, and we show that π 1( CK( R 3))=1 ...
A cubical complex K on vertex set V is a collection of subsets of V , partially ordered by inclusion, satisfying the following properties: 1. K has a minimal element ∅. 2. For all v ∈ V , the singleton {v} ∈ K. 3. For any nonempty F ∈ K, the interval [∅, F ] = ...
It gives an example test which produces a (surprisingly complex) composition of squares in the universe. The file quotient.cub contains an example of a computation from an equivalence class. The relation R over Nat is to have the same parity, and the map is Nat/R -> Bool which returns ...
Some ideas: Implement post types (e.g., link posts, image posts) Generate images for posts using AI image generation (e.g., Stable Diffusion) Add the ability for real users to create posts and comments, and observe AI reactions Implement more complex user interactions and relationships...
Here ℓ is a length function on G obtained from the combinatorial distance function on the complex X. 机译:我们证明,如果G是一个离散组,它允许对有限维CAT(0)多维数据集X进行度量上适当的作用,则G是微弱的。我们通过构造均匀有界的希尔伯特空间表示π z 来做到这一点,其数量z ℓ(g)是矩阵系数。
by constructing a family of balanced spheres that simultaneously minimize all face numbers as a function of the dimension of the complex and its number of vertices.In the second part; we study the family of cubical pseudomanifolds. We... I. Novik,S Klee - University of Washington 被引量: ...