Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more effective by reducing noise and data overfit. The relevance of features in a classification procedure is linked to the fact that misclassifications costs are frequently asymmetric, since false positive and false negative cases may have very different consequences. However, off-the-shelf Feature Selection procedures seldom take into account such cost-sensitivity of errors. In this paper we propose a mathematical-optimization-based Feature Selection procedure embedded in one of the most popular classification procedures, namely, Support Vector Machines, accommodating asymmetric misclassification costs. The key idea is to replace the traditional margin maximization by minimizing the number of features selected, but imposing upper bounds on the false positive and negative rates. The problem is written as an integer linear problem plus a quadratic convex problem for Support Vector Machines with both linear and radial kernels. The reported numerical experience demonstrates the usefulness of the proposed Feature Selection procedure. Indeed, our results on benchmark data sets show that a substantial decrease of the number of features is obtained, whilst the desired trade-off between false positive and false negative rates is achieved.

This paper studies the Cauchy problem for a helical vortex filament evolving by the 3D incompressible Navier-Stokes equations. We prove global-in-time well-posedness and smoothing of solutions with initial vorticity concentrated on a helix. We provide a local-in-time well-posedness result for vortex filaments periodic in one spatial direction, and show that solutions with helical initial data preserve this symmetry. We follow the approach of [4], where the analogue local-in-time result has been obtained for closed vortex filaments in $\mathbb{R}^3$. Next, we apply local energy weak solutions theory with a novel estimate for helical functions in non-helical domains to uniquely extend the solutions globally in time. This is the first global-in-time well-posedness result for a vortex filament without size restriction and without vanishing swirl assumptions.

The increase in congestion in surface traffic, airborne pollution, and other environmental issues have motivated the transit authorities to promote public transit worldwide. In big cities and large metropolitan areas, adding new rapid transit lines attracts more commuters to the public system, as they frequently allow saving travel time as compared to the private mode (car) that faces high congestion. In addition, the travel time has less variability with respect to preset schedules, and rapid lines are more efficient than slow modes operated by buses. When a new rapid transit line is constructed, it partially replaces the traffic of existing slow transit lines. As a consequence, some of the slow-mode lines have to be either canceled or their routes modified to collaborate properly with the new rapid transit line. This process is usually carried out in a sequential way, thus leading to suboptimal solutions. In this paper, we consider an integrated model for simultaneously designing rapid and redesigning slow networks. The aim of the model is community-oriented, that is, to maximize the demand covered (or captured) by both modes. We present a mathematical programming formulation that is solved by using a specially improved Benders decomposition. For this purpose, we include a partial decomposition to speed up the computation. The computational experiments are done on a case study based on real data obtained from a survey of mobility among transportation zones in the city of Seville.