An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Longitudinal evaluation, acceptability and long-term retention of knowledge on a horizontally integrated organic and functional systems course

Undergraduate medical education is moving from traditional disciplinary basic science courses into more integrated curricula. Integration models based on organ systems originated in the 1950s, but few longitudinal studies have evaluated their effectiveness. This article outlines the development and implementation of the Organic and Functional Systems (OFS) courses at the University of Minho in Portugal, using evidence collected over 10 years. It describes the organization of content, student academic performance and acceptability of the courses, the evaluation of preparedness for future courses and the retention of knowledge on basic sciences. Students consistently rated the OFS courses highly. Physician tutors in subsequent clinical attachments considered that students were appropriately prepared. Performance in the International Foundations of Medicine examination of a self-selected sample of students revealed similar performances in basic science items after the last OFS course and 4 years later, at the moment of graduation. In conclusion, the organizational and pedagogical approaches of the OFS courses achieve high acceptability by students and result in positive outcomes in terms of preparedness for subsequent training and long-term retention of basic science knowledge.

Detection of road accident accumulation zones with a visual analytics approach

Nowadays, road accidents are a major public health problem, which increase is forecasted if road safety is not treated properly, dying about 1.2 million people every year around the globe. In 2012, Portugal recorded 573 fatalities in road accidents, on site, revealing the largest decreasing of the European Union for 2011, along with Denmark. Beyond the impact caused by fatalities, it was calculated that the economic and social costs of road accidents weighted about 1.17% of the Portuguese gross domestic product in 2010. Visual Analytics allows the combination of data analysis techniques with interactive visualizations, which facilitates the process of knowledge discovery in sets of large and complex data, while the Geovisual Analytics facilitates the exploration of space-time data through maps with different variables and parameters that are under analysis. In Portugal, the identification of road accident accumulation zones, in this work named black spots, has been restricted to annual fixed windows. In this work, it is presented a dynamic approach based on Visual Analytics techniques that is able to identify the displacement of black spots on sliding windows of 12 months. Moreover, with the use of different parameterizations in the formula usually used to detect black spots, it is possible to identify zones that are almost becoming black spots. Through the proposed visualizations, the study and identification of countermeasures to this social and economic problem can gain new grounds and thus the decision- making process is supported and improved.