Search

Obtaining lightweight and accurate approximations of Hessian applies in inverse problems governed by partial differential equations (PDEs) is an essential task to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The $\mathcal{O}(N^{3})$ computational complexity of dense linear algebraic routines such as that needed for sampling from Gaussian proposal distributions and Newton solves by direct linear methods, can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. We demonstrate the use of HODLR approximation by efficiently generating Hessian approximations that allow fast generation of samples from a Gaussianized posterior proposal distribution. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss-Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global low-rank approximations, for large-scale problems by studying the data-misfit Hessian associated to inverse problems governed by the Stokes flow model on the Humboldt glacier and Greenland ice sheets., 28 pages, 12 figures, submitted to Inverse Problems

Background Accumulating evidence links COVID‐19 incidence and outcomes with vitamin D status. We investigated if an interaction existed between vitamin D levels and social deprivation in those with and without COVID‐19 infection. Methods Upper or lower respiratory tract samples from 104 patients were tested for SARS‐CoV‐2 RNA in accordance with Public Health England criteria (January‐May 2020) using RT‐PCR. The latest serum total 25‐hydroxyvitamin D(25‐OHD) levels, quantified by LC‐MS/MS, was obtained for each patient (September 2019‐April 2020). Index of Multiple Deprivation (IMD) was generated for each patient. Univariate and logistic regression analyses examined associations between age, gender, 25‐OHD, IMD score and SARS‐CoV‐2 result in the total cohort and subgroups. Results In the total cohort, a positive SARS‐CoV‐2 test was significantly associated with lower 25‐OHD levels and higher IMD. A positive test was associated with higher IMD in the male subgroup and with lower 25‐OHD levels in those aged >72 years. Low 25‐OHD and IMD quintile 5 were separately associated with positive COVID‐19 outcome in the cohort. Patients in IMD quintile 5 with vitamin D levels ≤ 34.4 nmol/L were most likely to have a positive COVID‐19 outcome, even more so if aged >72 years (OR: 19.07, 95%CI: 1.71‐212.25; P = .016). Conclusions In this cohort, combined low vitamin D levels and higher social deprivation were most associated with COVID‐19 infection. In older age, this combination was even more significant. Our data support the recommendations for normalising vitamin D levels in those with deficient / insufficient levels and in groups at high risk for deficiency.

CD6 is a type I T‐cell surface receptor that modulates antigen receptor signalling. Its activity is regulated by binding of its membrane proximal domain (domain 3) to a cell surface ligand, CD166. CD6 monoclonal antibodies (mAbs) specific for the membrane distal domain (domain 1) perturb CD6 function including itolizumab (Alzumab™), which has reached the clinic for treatment of autoimmune disease. We characterized molecular and functional properties of several CD6 mAbs including itolizumab to define potential mechanisms of action. Epitope mapping using the crystal structure of CD6 to design mutants identified two distinct binding sites on different faces of domain 1, one containing residue R77, crucial for MT605 and T12.1 binding and the other, E63, which is crucial for itolizumab and MEM98. Analysis of binding kinetics revealed that itolizumab has a lower affinity compared with other CD6 domain 1 mAbs. We compared potential agonistic (triggering) and antagonistic (blocking) properties of CD6 mAbs in assays where the mechanism of action was well defined. CD6 domain 1 and 3 mAbs were equally effective in triggering interleukin‐2 production by a cell line expressing a chimeric antigen receptor containing the extracellular region of CD6. CD6 domain 1 mAbs hindered binding of multivalent immobilized CD166 but were inferior compared with blocking by soluble CD166 or a CD6 domain 3 mAb. Characterization of CD6 mAbs provides an insight into how their functional effects in vivo may be interpreted and their therapeutic use optimized.

AIM Although "late onset hypogonadism", a condition that includes low testosterone and symptoms, is common in men over the age of 40 years, diagnosis is not clear cut amongst non-specialists. It is the aim of this review to provide an up to date picture of how this state should be diagnosed and managed. METHODS We aim to describe how primary and secondary hypogonadism should be excluded before the diagnosis of late onset hypogonadism is reached. As laboratory testosterone measurements are essential the current pitfalls such as inappropriate sample collection and the use of population derived reference ranges are expanded. We review current evidence to determine associations between late onset hypogonadism and morbidity/mortality and benefits following testosterone replacement therapy. RESULTS A review of the current evidence shows that late onset hypogonadism is associated with a worse metabolic state and increased mortality. Longitudinal studies have suggested that significant reductions in both symptoms and mortality are seen, especially in patients with type 2 diabetes. DISCUSSION This review highlights the importance of diagnosing late onset hypogonadism due to its association with morbidity/mortality and benefits following testosterone replacement. Thus, after making recommendations to ensure correct diagnosis we speculate whether the time has come to move away from population derived testosterone levels towards evidence based action limits.

Objective: Sex hormone binding globulin (SHBG) is a marker of insulin resistance. Given established links between BMI and socioeconomic disadvantage, we investigated how SHBG varies by index of multiple deprivation (IMD). Research Design and Methods: Using laboratory data from a Midlands UK population of mixed ethnicity, we examined the relation between blood concentrations of SHBG and IMD in 1160 women aged between 17 and 71 years. Women with a serum SHBG >250 nmol/L were excluded. Results: Mean age was 28.7 (95% confidence interval (CI) 28.2-29.1) years. 48.2% of women were of Caucasian origin, 15.5% of Southern Asian ethnicity and 2.6% were of African or other origin (33.7% were of unknown origin). SHBG increased with age (Spearman’s ρ=0.195; p

Previous studies have shown that patients who present at first or a later presentation with a cluster of new basal cell carcinoma (BCC) comprise a subgroup, termed multiple presentation phenotype (MPP), that is at increased risk of developing further lesions. In this study, we examined the hypothesis that patients who develop multiple clusters are a high-risk subgroup. We found, in a total group of 926 BCC patients, 32 patients with 2-5 BCC clusters (multiple cluster MPP) and 113 cases with only one cluster (single cluster MPP). Multiple cluster MPP cases had mean of 11.3 BCC compared with 3.7 in single cluster MPP cases during similar follow-up. Ultraviolet (UV) exposure in these groups was similar. We determined whether the multiple cluster MPP was associated with characteristics associated with sensitivity to UV or glutathione S-transferase (GST) GSTT1, GSTM1, cytochrome P450 (CYP) CYP2D6, tumour necrosis factor (TNF)-alpha and vitamin D receptor (VDR) genotypes previously associated with BCC presentational phenotypes. While the frequencies of blue eyes and male gender were greater in multiple cluster than single cluster cases, these differences were not significant. In multiple cluster cases, mean age at first presentation with single tumours occurred earlier and the frequencies of CYP2D6 extensive metabolizer (EM) (94.4%) and GSTT1 null (41.2%) were significantly greater (P = 0.028 and P = 0.004) than in single cluster cases (67.1% and 14.3%, respectively). The odds ratios for the individual associations of CYP2D6 EM and GSTT1 null with the multiple cluster MPP were relatively larger; 15.5 and 7.39, respectively. TNF-alpha and VDR genotypes were not associated with multiple cluster MPP. We propose that the MPP is not the consequence of excessive UV exposure but rather reflects the presence of a distinct BCC subgroup which is defined by combinations of risk genes.