In this paper we consider solving a sequence of weighted linear least squares problems where the only changes from one problem to the next are the weights and the right hand side (or data). We alternate between iterative and direct methods to solve the normal equations for the least squares problems. The direct method is the Cholesky factorization. For the iterative method we discuss a class of...

Craniosynostosis is a significant disorder affecting 1 in 2500 live births worldwide. Although a large body of work has focused on dural regulation and the contributions of molecular mediators such as fibroblast growth factor, bone morphogenetic protein, and transforming growth factor β, minimal attention has been directed toward osteoclast function in cranial suture biology. Receptor activator...

RANKL (receptor activator of NF-κB ligand) is a crucial cytokine for regulating diverse biological systems such as innate immunity, bone homeostasis and mammary gland differentiation, operating through activation of its cognate receptor RANK. In these normal physiological processes, RANKL signals through paracrine and/or heterotypic mechanisms where its expression and function is tightly contro...

Jaccard index similarity measure which applies the extension principle approach to obtain fuzzy maximum and fuzzy minimum has been proposed in ranking fuzzy numbers. However, the extension principle used is only applicable to normal fuzzy numbers and, therefore, fails to rank non-normal ones. Apart from that, the extension principle does not preserve the type of membership function of fuzzy num...

February 1, 2017 Version 3.0.0 Date 2016-09-16 Title Rank Product method for identifying differentially expressed genes with application in meta-analysis Author Francesco Del Carratore , Andris Janckevics Fangxin Hong , Ben Wittner , Rainer Breitling <r.breitling...

Classification of harmonic and semiharmonic graphs according to their cyclomatic number became of interest recently. All finite harmonic graphs with up to four independent cycles, as well as all finite semiharmonic graphs with at most one cycle were determined. Here, we determine all finite semiharmonic bicyclic graphs. Besides that, we present several methods to construct semiharmonic graphs f...

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In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.