Bone homeostasis is regulated by a delicate balance between osteoblastic bone formation and osteoclastic bone resorption. Osteoclastogenesis is controlled by the ratio of receptor activator of NFB ligand (RANKL) relative to its decoy receptor, osteoprotegerin (OPG). The source of OPG has historically been attributed to osteoblasts (OBs). While activated lymphocytes play established roles in pat...

Deconvolution refers to the problem of estimating the unknown input to an LTI system when the output signal and system response are known. In practice, the available output signal is also noisy. For some systems, the deconvolution problem is quite straight forward; however, for systems that are non-invertible or nearly non-invertible (e.g. narrow-band or with frequency response nulls), the prob...

We investigate magnetic properties of defective graphene, using a modified Hubbard model of the pi electrons of the carbon atoms. Spin interaction between pi elections and dangling sp2 bond has been taken into consideration. Mean field approximation is employed in our calculation, in order to deal with very large fragment of graphene. Magnetism of graphene with different types of defects will b...

We introduce the concept of a bounded below set in a lattice. This can be used to give a generalization of Rota's broken circuit theorem to any nite lattice. We then show how this result can be used to compute and combinatorially explain the Mobius function in various examples including non-crossing set partitions, shu e posets, and integer partitions in dominance order. Next we present a gene...