Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers

In this note two results are established for energy functionals that are given by the integral of $W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$, the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand $W$ has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in $W^{1,BMO}(\Omega;\mathbb{R}^N)$, the subspace of the Sobolev space $W^{1,1}(\Omega;\mathbb{R}^N)$ for which the weak derivative $\nabla\mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$.Comment: 8 page

On the Uniqueness of Energy Minimizers in Finite Elasticity

The uniqueness of absolute minimizers of the energy of a compressible, hyperelastic body subject to a variety of dead-load boundary conditions in two and three dimensions is herein considered. Hypotheses under which a given solution of the corresponding equilibrium equations is the unique absolute minimizer of the energy are obtained. The hypotheses involve uniform polyconvexity and pointwise bounds on derivatives of the stored-energy density when evaluated on the given equilibrium solution. In particular, an elementary proof of the uniqueness result of Fritz John (Commun. Pure Appl. Math. 25:617–634, 1972) is obtained for uniformly polyconvex stored-energy densities.</p

Recommended Methods for Monitoring Skeletal Health in Astronauts to Distinguish Specific Effects of Prolonged Spaceflight

NASA uses areal bone mineral density (aBMD) by dual-energy X-ray absorptiometry (DXA) to monitor skeletal health in astronauts after typical 180-day spaceflights. The osteoporosis field and NASA, however, recognize the insufficiency of DXA aBMD as a sole surrogate for fracture risk. This is an even greater concern for NASA as it attempts to expand fracture risk assessment in astronauts, given the complicated nature of spaceflight-induced bone changes and the fact that multiple 1-year missions are planned. In the past decade, emerging analyses for additional surrogates have been tested in clinical trials; the potential use of these technologies to monitor the biomechanical integrity of the astronaut skeleton will be presented. OVERVIEW: An advisory panel of osteoporosis policy-makers provided NASA with an evidence-based assessment of astronaut biomedical and research data. The panel concluded that spaceflight and terrestrial bone loss have significant differences and certain factors may predispose astronauts to premature fractures. Based on these concerns, a proposed surveillance program is presented which a) uses Quantitative Computed Tomography (QCT) scans of the hip to monitor the recovery of spaceflight-induced deficits in trabecular BMD by 2 years after return, b) develops Finite Element Models [FEM] of QCT data to evaluate spaceflight effect on calculated hip bone strength and c) generates Trabecular Bone Score [TBS] from serial DXA scans of the lumbar spine to evaluate the effect of age, spaceflight and countermeasures on this novel index of bone microarchitecture. SIGNIFICANCE: DXA aBMD is a widely-applied, evidence-based predictor for fractures but not applicable as a fracture surrogate for premenopausal females and males <50 years. Its inability to detect structural parameters is a limitation for assessing changes in bone integrity with and without countermeasures. Collective use of aBMD, TBS, QCT, and FEM analysis for astronaut surveillance could accommodate NASA's aggressive schedule for risk definition and inform a NASA-developed model which assesses the probability of overloading bones during mechanically-loaded mission tasks and possibly for physical activities after return to Earth

What Happens to bone health during and after spaceflight?

Weightless conditions of space flight accelerate bone loss. There are no reports to date that address whether the bone that is lost during spaceflight could ever be recovered. Spaceinduced bone loss in astronauts is evaluated at the Johnson Space Center (JSC) by measurement of bone mineral density (BMD) by Dual-energy x-ray absorptiometry (DXA) scans. Astronauts are routinely scanned preflight and at various time points postflight (greater than or equal to Return+2 days). Two sets of BMD data were used to model spaceflight-induced loss and skeletal recovery in crewmembers following long-duration spaceflight missions (4-6 months). Group I was from astronauts (n=7) who were systematically scanned at multiple time points during the postflight period as part of a research protocol to investigate skeletal recovery. Group II came from a total of 49 sets of preflight and postflight data obtained by different protocols. These data were from 39 different crewmembers some of whom served on multiple flights. Changes in BMD (between pre- and postflight BMD) were plotted as a function of time (days-after-landing); plotted data were fitted to an exponential equation which enabled estimations of i) BMD change at day 0 after landing and ii) the number of days by which 50% of the lost bone is recovered (half-life). These fits were performed for BMD of the lumbar spine, trochanter, pelvis, femoral neck and calcaneus. There was consistency between the models for BMD recovery. Based upon the exponential model of BMD restoration, recovery following long-duration missions appears to be substantially complete in crewmembers within 36 months following return to Earth

Genome-wide association study using family-based cohorts identifies the WLS and CCDC170/ESR1 loci as associated with bone mineral density.

BACKGROUND: Osteoporosis is a common and debilitating bone disease that is characterised by a low bone mineral density (BMD), a highly heritable trait. Genome-wide association studies (GWAS) have proven to be very successful in identifying common genetic variants associated with BMD adjusted for age, gender and weight, however a large portion of the genetic variance for this trait remains unexplained. There is evidence to suggest significant genetic correlation between body size traits and BMD. It has also recently been suggested that unintended bias can be introduced as a result of adjusting a phenotype for a correlated trait. We performed a GWAS meta-analysis in two populations (total n = 6,696) using BMD data adjusted for only age and gender, in an attempt to identify genetic variants associated with BMD including those that may have potential pleiotropic effects on BMD and body size traits. RESULTS: We observed a single variant, rs2566752, associated with spine BMD at the genome-wide significance level in the meta-analysis (P = 3.36 × 10(-09)). Logistic regression analysis also revealed an association between rs2566752 and fracture rate in one of our study cohorts (P = 0.017, n = 5,654). This is an intronic variant located in the wntless Wnt ligand secretion mediator (WLS) gene (1p31.3), a known BMD locus which encodes an integral component of the Wnt ligand secretion pathway. Bioinformatics analyses of variants in moderate LD with rs2566752 produced strong evidence for a regulatory role for the variants rs72670452, rs17130567 and rs1430738. Expression quantitative trait locus (eQTL) analysis suggested that the variants rs12568456 and rs17130567 are associated with expression of the WLS gene in whole blood, cerebellum and temporal cortex brain tissue (P = 0.034-1.19 × 10(-23)). Gene-wide association testing using the VErsatile Gene-based Association Study 2 (VEGAS2) software revealed associations between the coiled-coil domain containing 170 (CCDC170) gene, located adjacent to the oestrogen receptor 1 (ESR1) gene, and BMD at the spine, femoral neck and total hip sites (P = 1.0 × 10(-06), 2.0 × 10(-06) and 2.0 × 10(-06) respectively). CONCLUSIONS: Genetic variation at the WLS and CCDC170/ESR1 loci were found to be significantly associated with BMD adjusted for only age and gender at the genome-wide level in this meta-analysis

Voluntary workplace genomic testing: wellness benefit or Pandora\u27s box?

Consumer interest in genetic and genomic testing is growing rapidly, with more than 26 million Americans having purchased direct-to-consumer genetic testing services. Capitalizing on the increasing comfort of consumers with genetic testing outside the clinical environment, commercial vendors are expanding their customer base by marketing genetic and genomic testing services, including testing for pharmacogenomic and pathogenic variants, to employers for inclusion in workplace wellness programs. We describe the appeal of voluntary workplace genomic testing (wGT) to employers and employees, how the ethical, legal, and social implications literature has approached the issue of genetic testing in the workplace in the past, and outline the relevant legal landscape. Given that we are in the early stages of development of the wGT market, now is the time to identify the critical interests and concerns of employees and employers, so that governance can develop and evolve along with the wGT market, rather than behind it, and be based on data, rather than speculative hopes and fears

Birth characteristics and childhood carcinomas

BACKGROUND: Carcinomas in children are rare and have not been well studied. METHODS: We conducted a population-based case–control study and examined associations between birth characteristics and childhood carcinomas diagnosed from 28 days to 14 years during 1980–2004 using pooled data from five states (NY, WA, MN, TX, and CA) that linked their birth and cancer registries. The pooled data set contained 57 966 controls and 475 carcinoma cases, including 159 thyroid and 126 malignant melanoma cases. We used unconditional logistic regression to calculate odds ratios (ORs) and 95% confidence intervals (CIs). RESULTS: White compared with ‘other' race was positively associated with melanoma (OR=3.22, 95% CI 1.33–8.33). Older maternal age increased the risk for melanoma (OR(per 5-year age increase)=1.20, 95% CI 1.00–1.44), whereas paternal age increased the risk for any carcinoma (OR=1.10(per 5-year age increase), 95% CI 1.01–1.20) and thyroid carcinoma (OR(per 5-year age increase)=1.16, 95% CI 1.01–1.33). Gestational age <37 vs 37–42 weeks increased the risk for thyroid carcinoma (OR=1.87, 95% CI 1.07–3.27). Plurality, birth weight, and birth order were not significantly associated with childhood carcinomas. CONCLUSION: This exploratory study indicates that some birth characteristics including older parental age and low gestational age may be related to childhood carcinoma aetiology