Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.

This paper proposes a hybrid data mining approach to quantitatively analyze product complexity of prefabricated construction components from product nonconforming quality performance data. The proposed model is constructed in three steps, which (1) measure product complexity by introducing a Bayesian-based nonconforming quality performance indicator; (2) score each type of product complexity by...

<p>A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class all finite simple graphs. A set <em>S</em> vertices graph <em>G</em> said ℘-set if <em>G</em>[<em>S</em>]∈ ℘. The maximum and minimum cardinalities are denoted by <em>M</em><sub>℘</sub>(<em>G</em>) <em>m</em>&l...

Multi-objective control systems for complex robots usually have to handle multiple prioritized tasks. Most existing hierarchical control techniques handle either strict task priorities by using null-space projectors or a sequence of quadratic programs; or non strict task priorities by using a weighting strategy. This paper proposes a novel approach to handle both strict and non-strict prioritie...

This paper generalizes the framework of Hierarchical Kernel Learning (HKL) and illustrates its utility in the domain of rule learning. HKL involves Multiple Kernel Learning over a set of given base kernels assumed to be embedded on a directed acyclic graph. This paper proposes a two-fold generalization of HKL: the first is employing a generic `1/`ρ block-norm regularizer (ρ ∈ (1, 2]) that allev...