Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Plant derived and dietary phenolic antioxidants: Anticancer properties

n this paper, a review of the literature on the phenolic compounds with anticancer activity published between 2008 and 2012 is presented. In this overview only phenolic antioxidant compounds that display significant anticancer activity have been described. In the first part of this review, the oxidative and nitrosative stress relation with cancer are described. In the second part, the plant-derived food extracts, containing identified phenolic antioxidants, the phenolic antioxidants isolated from plants and plant-derived food or commercially available and the synthetic ones, along with the type of cancer and cells where they exert anticancer activity, are described and summarized in tables. The principal mechanisms for their anti-proliferative effects were also described. Finally, a critical analysis of the studies and directions for future research are included in the conclusion.