Background: There is an ongoing research for breast cancer diagnostic tools that are cheaper, more accurate and more convenient than mammography. Methods: In this study, we employed surface-enhanced Raman scattering (SERS) for analysing urine from n = 53 breast cancer patients and n = 22 controls, with the aim of discriminating between the two groups using multivariate data analysis techniques such as principal component analysis—linear discriminant analysis (PCA-LDA). The SERS spectra were acquired using silver nanoparticles synthesized by reduction with hydroxylamine hydrochloride, which were additionally activated with Ca²⁺ 10⁻⁴ M. Results: The addition of Ca(NO₃)₂ 10⁻⁴ M promoted the specific adsorption to the metal surface of the anionic purine metabolites such as uric acid, xanthine and hypoxanthine. Moreover, the SERS spectra of urine were acquired without any filtering or processing step for removing protein traces and other contaminants. Using PCA-LDA, the SERS spectra of urine from breast cancer patients were classified with a sensitivity of 81%, a specificity of 95% and an overall accuracy of 88%. Conclusion: The results of this preliminary study contribute to the translation of SERS in the clinical setting and highlight the potential of SERS as a novel screening strategy for breast cancer.

Numerical schemes for advection-dominated transport problems are are evaluated in a comparative study. Explicit and implicit finite difference methods are analyzed together with a global random walk algorithm in the frame of a splitting procedure. The efficiency of the methods with respect to the control of the numerical diffusion is investigated numerically on one-dimensional problems with constant coefficients and two-dimensional problems with variable coefficients consisting of realizations of space-random functions.

In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique for some associated dynamical systems. Furthermore, we investigate through numerical simulations the empirical rate of convergence of these iterative schemes toward a local minimum of the loss function, with some suitable choices of the underlying hyper-parameters. We validate the convergence of these optimizers using the results of the accuracy and of the loss function on the MNIST, MNIST-Fashion and CIFAR 10 classification datasets.