Interestingly, he found that no minimising total order of subsets of existed for his problem, contrasting with both the Kruskal–Katona theorem and Theorem 1.4. A second motivation concerns vertex-isoperimetric problems for graphs. The vertex boundary of a set of vertices of a graph is the set ...
Spleen size, total number of splenocytes and individual subsets in WT and nude rats.doi:10.1371/JOURNAL.PONE.0059602.G005Gu LijuanXiong XiaoxingWei DingtaiGao XuwenKrams SheriZhao HengPLOS ONE
graded collateral connections (CC) according to the angiographic visibility: CC0: no continuous connection between donor and recipient artery, CC1: continuous, thread-like connections ( ≥0.4 mm), and CC2: continuous, small side branch-like size of the collateral throughout its course (>1 mm)...
i, Forest plot of HRs (center points) and 95% CIs (error bars) of multivariate Cox proportional hazard models with age, TmS (high versus low), chemotherapy (yes versus no), Oncotype Dx risk classification (high versus intermediate versus low) as predictors for DFS in METABRIC (see details...
How many solutions exist of the equation x_1 + x_2 + x_3 + x_4 + x_5 = 12, where each x_i is a positive integer? How many numbers greater than one thousand can be made using the digits 1, 0, 3, 4, and 5 without repetition? How...
The AbC™ Total Antibody Compensation Bead Kit provides a consistent, accurate, and simple-to-use technique for the setting of flow cytometry compensation when using fluorochrome-conjugated mouse, rat, hamster, or rabbit antibodies with any laser in flow cytometry.• Broadest multispecies ...
A complete metric measure space that fulfills the doubling property is proper, meaning that all closed and bounded subsets are compact, see [2, Proposition 3.1]. Following the concept of Heinonen and Koskela [23], we call a Borel function\(g: {\mathcal {X}}\rightarrow [0, \infty ]\...
A cycle is a closed walk with no repeated vertices. If any vertex in the graph is reachable from any other vertex, the graph is said to be connected. Every graph can be viewed as a matrix through the use of its adjacency matrix. The adjacency matrix of a network with graph G is ...
Since v is an arbitrary vertex, every vertex of G is in a γt-set with one of its neighbors, the condition holds for all subsets S with |S|=1. Next assume that S={u,v}. Without loss of generality, we many assume that two pebbles are placed on u and one pebble is placed on ...
It provides an accurate measurement of the VCW and it allows, through the use of subsets of the markers placed on the thorax, the measurement of separate compartments, such as the rib cage, abdomen, or smaller components (9). Being based on the direct measure- ment of chest wall volumes,...