Higher-order reverse automatic differentiation with emphasis on the third-order

It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian ( D3f(x)⋅d ) can be calculated at a cost proportional to that of a state-of-the-art method for calculating the Hessian matrix. We do this by first presenting a simple procedure for designing high order reverse methods and applying it to deduce several methods including a reverse method that calculates D3f(x)⋅d . We have implemented this method taking into account symmetry and sparsity, and successfully calculated this derivative for functions with a million variables. These results indicate that the use of third order information in a general nonlinear solver, such as Halley–Chebyshev methods, could be a practical alternative to Newton’s method. Furthermore, high-order sensitivity information is used in methods for robust aerodynamic design. An efficient high-order differentiation tool could facilitate the use of similar methods in the design of other mechanical structures

European experts consensus: BRCA/homologous recombination deficiency testing in first-line ovarian cancer

Background: Homologous recombination repair (HRR) enables fault-free repair of double-stranded DNA breaks. HRR deficiency is predicted to occur in around half of high-grade serous ovarian carcinomas. Ovarian cancers harbouring HRR deficiency typically exhibit sensitivity to poly-ADP ribose polymerase inhibitors (PARPi). Current guidelines recommend a range of approaches for genetic testing to identify predictors of sensitivity to PARPi in ovarian cancer and to identify genetic predisposition. Design: To establish a European-wide consensus for genetic testing (including the genetic care pathway), decision making and clinical management of patients with recently diagnosed advanced ovarian cancer, and the validity of biomarkers to predict the effectiveness of PARPi in the first-line setting. The collaborative European experts’ consensus group consisted of a steering committee (n = 14) and contributors (n = 84). A (modified) Delphi process was used to establish consensus statements based on a systematic literature search, conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-analyses guidelines. Results: A consensus was reached on 34 statements amongst 98 caregivers (including oncologists, pathologists, clinical geneticists, genetic researchers, and patient advocates). The statements concentrated on (i) the value of testing for BRCA1/2 mutations and HRR deficiency testing, including when and whom to test; (ii) the importance of developing new and better HRR deficiency tests; (iii) the importance of germline non-BRCA HRR and mismatch repair gene mutations for predicting familial risk, but not for predicting sensitivity to PARPi, in the first-line setting; (iv) who should be able to inform patients about genetic testing, and what training and education should these caregivers receive. Conclusion: These consensus recommendations, from a multidisciplinary panel of experts from across Europe, provide clear guidance on the use of BRCA and HRR deficiency testing for recently diagnosed patients with advanced ovarian cancer

Sea ice contribution to the airsea CO2 exchange in the Arctic and Southern Oceans

Although salt rejection from sea ice is a key process in deep-water formation in ice-covered seas, the concurrent rejection of CO2 and the subsequent effect on air–sea CO2 exchange have received little attention. We review the mechanisms by which sea ice directly and indirectly controls the air–sea CO2 exchange and use recent measurements of inorganic carbon compounds in bulk sea ice to estimate that oceanic CO2 uptake during the seasonal cycle of sea-ice growth and decay in ice-covered oceanic regions equals almost half of the net atmospheric CO2 uptake in ice-free polar seas. This sea-ice driven CO2 uptake has not been considered so far in estimates of global oceanic CO2 uptake. Net CO2 uptake in sea-ice–covered oceans can be driven by; (1) rejection during sea–ice formation and sinking of CO2-rich brine into intermediate and abyssal oceanic water masses, (2) blocking of air–sea CO2 exchange during winter, and (3) release of CO2-depleted melt water with excess total alkalinity during sea-ice decay and (4) biological CO2 drawdown during primary production in sea ice and surface oceanic waters

Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation

Portfolio optimization, Value-at-risk, Computational complexity, State–price density, G11,