On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

A novel antibody-like material for breast cancer antigen CA15-3, used to track breast cancer by potentiometric transduction

This work presents the development of a low cost sensor device for the diagnosis of breast cancer in point-of-care, made with new synthetic biomimetic materials inside plasticized poly(vinyl chloride), PVC, membranes, for subsequent potentiometric detection. This concept was applied to target a conventional biomarker in breast cancer: Breast Cancer Antigen (CA15-3). The new biomimetic material was obtained by molecularly-imprinted technology. In this, a plastic antibody was obtained by polymerizing around the biomarker that acted as an obstacle to the growth of the polymeric matrix. The imprinted polymer was specifically synthetized by electropolymerization on an FTO conductive glass, by using cyclic voltammetry, including 40 cycles within -0.2 and 1.0 V. The reaction used for the polymerization included monomer (pyrrol, 5.0×10-3 mol/L) and protein (CA15-3, 100U/mL), all prepared in phosphate buffer saline (PBS), with a pH of 7.2 and 1% of ethylene glycol. The biomarker was removed from the imprinted sites by proteolytic action of proteinase K. The biomimetic material was employed in the construction of potentiometric sensors and tested with regard to its affinity and selectivity for binding CA15-3, by checking the analytical performance of the obtained electrodes. For this purpose, the biomimetic material was dispersed in plasticized PVC membranes, including or not a lipophilic ionic additive, and applied on a solid conductive support of graphite. The analytical behaviour was evaluated in buffer and in synthetic serum, with regard to linear range, limit of detection, repeatability, and reproducibility. This antibody-like material was tested in synthetic serum, and good results were obtained. The best devices were able to detect 5 times less CA15-3 than that required in clinical use. Selectivity assays were also performed, showing that the various serum components did not interfere with this biomarker. Overall, the potentiometric-based methods showed several advantages compared to other methods reported in the literature. The analytical process was simple, providing fast responses for a reduced amount of analyte, with low cost and feasible miniaturization. It also allowed the detection of a wide range of concentrations, diminishing the required efforts in previous sample pre-treating stages.

Analysis of Systems with Backlash and Impacts through the Describing Function

This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. The dynamics is illustrated using the Nyquist and Bode plots and the results are compared with those of standard models.

Longitudinal analysis of tumor marker CEA of breast cancer patients from Braga's hospital

Allied to an epidemiological study of population of the Senology Unit of Braga’s Hospital that have been diagnosed with malignant breast cancer, we describe the progression in time of repeated measurements of tumor marker Carcinoembryonic antigen (CEA). Our main purpose is to describe the progression of this tumor marker as a function of possible risk factors and, hence, to understand how these risk factors influences that progression. The response variable, values of CEA, was analyzed making use of longitudinal models, testing for different correlation structures. The same covariates used in a previous survival analysis were considered in the longitudinal model. The reference time used was time from diagnose until death from breast cancer. For diagnostic of the models fitted we have used empirical and theoretical variograms. To evaluate the fixed term of the longitudinal model we have tested for a changing point on the effect of time on the tumor marker progression. A longitudinal model was also fitted only to the subset of patients that died from breast cancer, using the reference time as time from date of death until blood test.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.