Experiences on using Arduino for laboratory experiments of Automatic Control and Robotics

The free hardware platforms have become very important in engineering education in recent years. Among these platforms, Arduino highlights, characterized by its versatility, popularity and low price. This paper describes the implementation of four laboratory experiments for Automatic Control and Robotics courses at the University of Alicante, which have been developed based on Arduino and other existing equipment. Results were evaluated taking into account the views of students, concluding that the proposed experiments have been attractive to them, and they have acquired the knowledge about hardware configuration and programming that was intended.

Automatic Abdominal Aortic Aneurysm segmentation in MR images

Abdominal Aortic Aneurism is a disease related to a weakening in the aortic wall that can cause a break in the aorta and the death. The detection of an unusual dilatation of a section of the aorta is an indicative of this disease. However, it is difficult to diagnose because it is necessary image diagnosis using computed tomography or magnetic resonance. An automatic diagnosis system would allow to analyze abdominal magnetic resonance images and to warn doctors if any anomaly is detected. We focus our research in magnetic resonance images because of the absence of ionizing radiation. Although there are proposals to identify this disease in magnetic resonance images, they need an intervention from clinicians to be precise and some of them are computationally hard. In this paper we develop a novel approach to analyze magnetic resonance abdominal images and detect the lumen and the aortic wall. The method combines different algorithms in two stages to improve the detection and the segmentation so it can be applied to similar problems with other type of images or structures. In a first stage, we use a spatial fuzzy C-means algorithm with morphological image analysis to detect and segment the lumen; and subsequently, in a second stage, we apply a graph cut algorithm to segment the aortic wall. The obtained results in the analyzed images are pretty successful obtaining an average of 79% of overlapping between the automatic segmentation provided by our method and the aortic wall identified by a medical specialist. The main impact of the proposed method is that it works in a completely automatic way with a low computational cost, which is of great significance for any expert and intelligent system.

An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.

A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.