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  2. Set splitting problem - Wikipedia

    en.wikipedia.org/wiki/Set_splitting_problem

    In computational complexity theory, the set splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S 1, S 2 such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S 1 or S 2.

  3. Split graph - Wikipedia

    en.wikipedia.org/wiki/Split_graph

    A split graph may have more than one partition into a clique and an independent set; for instance, the path a–b–c is a split graph, the vertices of which can be partitioned in three different ways: the clique {a, b} and the independent set {c} the clique {b, c} and the independent set {a} the clique {b} and the independent set {a, c}

  4. Solovay model - Wikipedia

    en.wikipedia.org/wiki/Solovay_model

    ZF stands for Zermelo–Fraenkel set theory, and DC for the axiom of dependent choice.. Solovay's theorem is as follows. Assuming the existence of an inaccessible cardinal, there is an inner model of ZF + DC of a suitable forcing extension V[G] such that every set of reals is Lebesgue measurable, has the perfect set property, and has the Baire property.

  5. Linear separability - Wikipedia

    en.wikipedia.org/wiki/Linear_separability

    Suppose some data points, each belonging to one of two sets, are given and we wish to create a model that will decide which set a new data point will be in. In the case of support vector machines , a data point is viewed as a p -dimensional vector (a list of p numbers), and we want to know whether we can separate such points with a ( p − 1 ...

  6. Bipartite network projection - Wikipedia

    en.wikipedia.org/wiki/Bipartite_network_projection

    The values of these weights depend on the degrees of the two sets of nodes in the original bipartite network. For example, in a co-authorship network, [ 4 ] the number of observed co-authorships depends on (1) the number of papers each author wrote and (2) the number of authors on each paper.

  7. Graph partition - Wikipedia

    en.wikipedia.org/wiki/Graph_partition

    The linear combination of the smallest two eigenvectors leads to [1 1 1 1 1]' having an eigen value = 0. Figure 2: The graph G = (5,5) illustrates that the Fiedler vector in red bisects the graph into two communities, one with vertices {1,2,3} with positive entries in the vector space, and the other community has vertices {4,5} with negative ...

  8. Dichotomy - Wikipedia

    en.wikipedia.org/wiki/Dichotomy

    In this image, the universal set U (the entire rectangle) is dichotomized into the two sets A (in pink) and its complement A c (in grey). A dichotomy / d aɪ ˈ k ɒ t ə m i / is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be

  9. Narrowing of algebraic value sets - Wikipedia

    en.wikipedia.org/wiki/Narrowing_of_algebraic...

    Narrowing is based on value sets that allow multiple values to be packaged and considered as a single value. This allows the inverses of functions to always be considered as functions. To achieve this value sets must record the context to which a value belongs. A variable may only take on a single value in each possible world. The value sets ...