Abstract
This paper proposes a calculational approach to prove properties of two well-known binary trees used to enumerate the rational numbers: the Stern-Brocot tree and the Eisenstein-Stern tree (also known as Calkin-Wilf tree). The calculational style of reasoning is enabled by a matrix formulation that is well-suited to naturally formulate path-based properties, since it provides a natural way to refer to paths in the trees. Three new properties are presented. First, we show that nodes with palindromic paths contain the same rational in both the Stern-Brocot and Eisenstein-Stern trees. Second, we show how certain numerators and denominators in these trees can be written as the sum of two squares x(2) and y(2), with the rational x/y appearing in specific paths. Finally, we show how we can construct Sierpifiski's triangle from these trees of rationals. (C) 2015 Published by Elsevier Inc.

Abstract
Background and objective: Cosmetic outcome of breast cancer conservative treatment (BCCT) remains without a standard evaluation method. Subjective methods, in spite of their low reproducibility, continue to be the most frequently used. Objective methods, although more reproducible, seem unable to translate all the subtleties involved in cosmetic outcome. The breast cancer conservative treatment cosmetic results (BCCT. core) software was developed in 2007 to try to overcome these pitfalls. The software is a semi-automatic objective tool that evaluates asymmetry, color differences and scar visibility using patient's digital pictures. The purpose of this work is to review the use of the BCCT. core software since its availability in 2007 and to put forward future developments. Methods: All the online requests for BCCT. core use were registered from June 2007 to December 2014. For each request the department, city and country as well as user intention (clinical use/research or both) were questioned. A literature search was performed in Medline, Google Scholar and ISI Web of Knowledge for all publications using and citing "BCCT.core". Results: During this period 102 centers have requested the software essentially for clinical use. The BCCT. core software was used in 19 full published papers and in 29 conference abstracts. Conclusions: The BCCT. core is a user friendly semi-automatic method for the objective evaluation of BCCT. The number of online requests and publications have been steadily increasing turning this computer program into the most frequently used tool for the objective cosmetic evaluation of BCCT.

Abstract
Mammoclass is a web tool that allows users to enter a small set of variable values that describe a finding in a mammography, and produces a probability of this finding being malignant or benign. The tool requires that the user types in every variable a value in order to perform a prediction. In this work, we present a speech-to-text interface integrated to MammoClass that allows radiologists to speak up a mammography report instead of typing it in. This new MammoClass module can take audio content, transcribe it into written words, and automatically extract the variable values by applying a parser to the recognized text. Results of spoken mammography reports show that the same variables are extracted for both types of input: typed in or dictated text.

Abstract
Prior to having available the High Dynamic Range (HDR) techniques, certain levels of luminance could only by captured by the human eye. Currently, HDR technology overcomes the limitations of conventional imaging technology (also referred as Low Dynamic Range or LDR) and allows the capture and delivery of contents that can match the dynamic range of the real world. However, the state of the art of HDR video focus mainly on conventional sized displays typical of TVs or PCs. As the usage of mobile devices for multimedia consumption is increasing considerably, there is a need for studying the impact of the viewing of HDR video on such devices. This will allow to take full advantage of HDR technology, creating a set of opportunities for the digital business as it allows, among others, the presentation of products in a much more efficient and captivating way. On this paper it is presented a study that evaluates the impact of the HDR video delivery on mobile devices and compares it with the impact of Low Dynamic Range (LDR) content. Results show that the delivery of HDR video on mobiles is possible without requiring much more resources when comparing the delivery of LDR video.

Abstract
One of the major concerns in Power Systems is surely related with their reliability. Long-term expansion planning studies traditionally use the well-known deterministic "N-1" contingency criterion. However, this criterion is applied based on worst-case analyses and the obtained plan may originate over-investments. Differently, probabilistic reliability approaches can incorporate different type of uncertainties that affect power systems. In this work, a long term multi-criteria AC Transmission Expansion Planning model was developed considering two objectives - the probabilistic reliability index Expected Energy Not Supplied (EENS) and the investment cost. The Pareto-Front associated with these two objectives was obtained using Genetic Algorithms and the final solution was selected using a fuzzy decision making function. This approach was applied to the IEEE 24 Bus Test System and the results ensure its robustness and efficiency.

Abstract
Each year thousands of people lose their lower limbs, mainly due to three causes: wars, accidents and vascular diseases. The development of prostheses is crucial to improve the quality of millions of people's lives by restoring their mobility. Lower limb prostheses can be divided into three major groups: passive, semi-active or variable damping and powered or intelligent. This contribution provides a literature review of the principal control strategies used in lower limb prostheses, i.e., the controllers used in energetically powered transfemoral and transtibial prostheses. We present a comparison of the presented literature review and the future trends of this important field. It is concluded that the use of bio-inspired concepts and continuous control combined with the other control approaches can be crucial in the improvement of prosthesis controllers, enhancing the quality of amputee's lives.