Novel Mathematical Model of Breast Cancer Diagnostics Using an Associative Pattern Classification.

Breast cancer is a disease that has emerged as the second leading cause of cancer deaths in women worldwide. The annual mortality rate is estimated to continue growing. Cancer detection at an early stage could significantly reduce breast cancer death rates long-term. Many investigators have studied different breast diagnostic approaches, such as mammography, magnetic resonance imaging, ultrasound, computerized tomography, positron emission tomography and biopsy. However, these techniques have limitations, such as being expensive, time consuming and not suitable for women of all ages. Proposing techniques that support the effective medical diagnosis of this disease has undoubtedly become a priority for the government, for health institutions and for civil society in general. In this paper, an associative pattern classifier (APC) was used for the diagnosis of breast cancer. The rate of efficiency obtained on the Wisconsin breast cancer database was 97.31%. The APC's performance was compared with the performance of a support vector machine (SVM) model, back-propagation neural networks, C4.5, naive Bayes, k-nearest neighbor (k-NN) and minimum distance classifiers. According to our results, the APC performed best. The algorithm of the APC was written and executed in a JAVA platform, as well as the experimental and comparativeness between algorithms.

Transversal aberrations at arbitrary Hartmann-plane distances: application in the least-squares fitting of Hartmann data.

In a previous work, we introduced the concept of transversal aberrations {U,V} calculated at arbitrary Hartmann-plane distances z=r [Appl. Opt.55, 2160 (2016)APOPAI1559-128X10.1364/AO.55.002160]. These transversal aberrations can be used to estimate the wave aberration function W, as well as the classical transversal aberrations {X,Y} calculated at a theoretical plane z=f, where f is the radius of a reference semisphere. However, when the ray identification is difficult to achieve at z=f, the use of {U,V} can be of great help. In the context of a least-squares fitting of the Hartmann data, the use of {U,V} is proposed by analyzing some simple examples for the case of a W with aberration terms up to the third order. These examples also consider the hypothesis f≫W, as presented in the majority of the optical applications.

Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances.

In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.