Spatial averaging and apparent acceleration in inhomogeneous spaces

As an alternative to dark energy that explains the observed acceleration of the universe, it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre–Tolman–Bondi (LTB) solution of Einstein’s field equations. To test this possibility, it is necessary to solve the null geodesics. In this paper we first give a detailed derivation of a fully analytical set of differential equations for the radial null geodesics as functions of the redshift in LTB models. As an application we use these equaions to show that a positive averaged acceleration a _D obtained in LTB models through spatial averaging can be incompatible with cosmological observations. We provide examples of LTB models with positive a _D which fail to reproduce the observed luminosity distance D _L (z). Since the apparent cosmic acceleration a ^FLRW is obtained from fitting the observed luminosity distance to a FLRW model we conclude that in general a positive a _D in LTB models does not imply a positive a ^FLRW .     

Dipeptidyl Peptidase 3 Activity as a Promising Biomarker of Bone Fragility in Postmenopausal Women

The dipeptidyl peptidase 3 (Dpp3) is a ubiquitous zinc-dependent aminopeptidase, participating in the activation or degradation of signaling peptides and in the Keap1–Nrf2 antioxidant pathway. The absence of Dpp3 in the Dpp3 knockout mouse model causes increased osteoclast activity, altered osteogenic function, sustained oxidative stress in the bone tissue, and bone loss. We aimed to assess the association of Dpp3 activity with bone fragility in postmenopausal osteoporosis and the impact of denosumab on enzymatic activity. We conducted a two-phase study including 69 postmenopausal women with severe osteoporosis and 36 postmenopausal women without osteometabolic conditions, as controls (cross-sectional phase). Subjects with severe osteoporosis were assessed at baseline and 14 days after the first denosumab administration (prospective phase). The results showed significant reduction in serum Dpp3 activity (expressed as nmoles of formed product/mg proteins/min) in patients vs. controls (0.791 ± 0.232 vs. 1.195 ± 0.338; p < 0.001), and significant association with bone mass at the femoral neck (r = 0.28, p = 0.02) in patients prior to treatment. We found a negative correlation between C-terminal telopeptide (CTX) or N-terminal pro-peptide of type 1 procollagen (P1NP) levels and Dpp3 activity (respectively, r = −0.29, p = 0.012; and r = −0.2572, p = 0.033). Dpp3 activity did not change after denosumab injection. Our findings support a critical role played by Dpp3 in bone homeostasis as a potential bone protective factor. Additional clinical studies in larger cohorts might explore the implementation of Dpp3 assessment as a biomarker of bone health status.     

Cones of lines having high contact with general hypersurfaces and applications

Given a smooth hypersurface $X\subset {\mathbb{P}}^{n+1}$ of degree $d⩾2$, we study the cones $V_p^h\subset {\mathbb{P}}^{n+1}$ swept out by lines having contact order $h⩾2$ at a point $p\in X$. In particular, we prove that if X is general, then for any $p\in X$ and $2⩽h⩽\min \{n+1,d\}$, the cone $V_p^h$ has dimension exactly $n+2-h$. Moreover, when X is a very general hypersurface of degree $d⩾2n+2$, we describe the relation between the cones $V_p^h$ and the degree of irrationality of k-dimensional subvarieties of X passing through a general point of X. As an application, we give some bounds on the least degree of irrationality of k-dimensional subvarieties of X passing through a general point of X, and we prove that the connecting gonality of X satisfies $d-⌊\frac{\sqrt{16n+25}-3}{2}⌋⩽conn.gon(X)⩽d-⌊\frac{\sqrt{8n+1}+1}{2}⌋$.