Sentence examples for a partition of v from inspiring English sources

Let {V1,…,V l } be a partition of V and a1 ,…,al a set of non-negative integers.

It is easy to see that (V_{ij}) is a partition of V, that is, (V=bigcup_{i=1}^{n}bigcup_{j=1}^{m}V_{ij}).

Let K be an integer no less than 2. According to Definition 1, a K-VDP is a partition of V into K nonempty subsets such that each node is in exact one subset.

Let (V_1,...,V_p) be a partition of V into p subsets called clusters (i.e. (V=V_1 cup V_2 cup... cup V_p) and (V_l cap V_k = emptyset) for all (l,k in {1,...,p})).

We show that, under this model, the original coloring problem gives rise to a new coloring version (called Probabilistic Min Coloring) where the objective becomes to determine a partition of V into independent sets S1,S2,…,Sk, that minimizes the quantity ∑i= 1kf(Si), where, for any independent set Si,i= 1,…,k, f(Si)= 1-∏vj∈Si 1-pj).

Proof Consider the Theorem 1, it is obviously that the controller K which could render the inequality (14) hold, if inequality (7) hold with A Z, B Z, C Z, D Z. Introduce a partition of V and its inverse W : = V - 1. From W V = I, [ W 11 W 12 ] V = [ I 0 ] and lead to (17).

Consider a partitioning of V, the vertex set of G, into non-overlapping pools P={ P1,…, P n }.

Output: A partitioning of V into pools P={ P1, P2,···, P n },, which maximizes the following objective function: Randomly partition the vertex set V of the graph G into n different pools.

The introduction of v0 divides the rectangle V into three areas:  A′ and A′′ is a set of vectors incomparable with IΓ ∪ , Figure 1 A space  V  of incomparable vectors bounded by coordinates vectors w 1, w2 ∈ I Γ. Figure 2 A partition of space  V  when a new vector  γ is introduced.

More formally, a separated graph is a pair ( E, C ), where E is a graph, C = ⊔ v ∈ E 0 C v, and, for each v ∈ E 0, C v is a partition of s - 1 ( v ) (into pairwise disjoint nonempty subsets).

The modularity score of a network is defined as follows [ 16]: consider a network with its set of nodes V and set of edges E, the Q score is defined as a function of a partition P of V, (1) Q (P ) = ∑ i (e ii − a i 2 ) where e ii is the fraction of edges in community i (over all edges in the network) and a i is the fraction of edges that are incident on a node in community i.