Osteoporosis, a highly heritable disease, is characterized mainly by low bone-mineral density (BMD), poor bone geometry, and/or osteoporotic fractures (OF). Copy-number variation (CNV) has been shown to be associated with complex human diseases. The contribution of CNV to osteoporosis has not been determined yet. We conducted case-control genome-wide CNV analyses, using the Affymetrix 500K Array Set, in 700 elderly Chinese individuals comprising 350 cases with homogeneous hip OF and 350 matched controls. We constructed a genomic map containing 727 CNV regions in Chinese individuals. We found that CNV 4q13.2 was strongly associated with OF (p = 2.0 x 10(-4), Bonferroni-corrected p = 0.02, odds ratio = 1.73). Validation experiments using PCR and electrophoresis, as well as real-time PCR, further identified a deletion variant of UGT2B17 in CNV 4q13.2. Importantly, the association between CNV of UGT2B17 and OF was successfully replicated in an independent Chinese sample containing 399 cases with hip OF and 400 controls. We further examined this CNV's relevance to major risk factors for OF (i.e., hip BMD and femoral-neck bone geometry) in both Chinese (689 subjects) and white (1000 subjects) samples and found consistently significant results (p = 5.0 x 10(-4) -0.021). Because UGT2B17 encodes an enzyme catabolizing steroid hormones, we measured the concentrations of serum testosterone and estradiol for 236 young Chinese males and assessed their UGT2B17 copy number. Subjects without UGT2B17 had significantly higher concentrations of testosterone and estradiol. Our findings suggest the important contribution of CNV of UGT2B17 to the pathogenesis of osteoporosis.

An inverse source problem for a fractional diffusion equation is investigated. Under an assumption that the unknown source term is time independent, an analytical solution can be deduced based on the method of the eigenfunction expansion. Then, the uniqueness of the inverse problem is proved by analytic continuation and Laplace transform. Regularization schemes are considered to obtain the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed meshless method.

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity µ 4 is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed.

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We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations and kinematic transport equations for the molecular orientations. We prove the convergence of global strong solutions to single steady states as time tends to infinity as well as estimates on the convergence rate both in 2D for arbitrary regular initial data and in 3D for certain particular cases.