Finding simultaneous Diophantine approximations with prescribed quality

We give an algorithm that finds a sequence of approximations with Dirichlet coefficients bounded by a constant only depending on the dimension. The algorithm uses the LLL-algorithm for lattice basis reduction. We present a version of the algorithm that runs in polynomial time of the input.Comment: 16 pages, 7 figure

Tong's spectrum for Rosen continued fractions

The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best possible upper bound for the minimum in appropriate consecutive blocks of approximation coefficients (in the sense of Diophantine approximation by continued fraction convergents). We also obtain metrical results for large blocks of ``bad'' approximations.Comment: 22 pages, 5 figure

Variability in the interpretation of probability phrases used in Dutch news articles — a risk for miscommunication

Analysis and Stochastic

Radioactive Needlework, Reconstruction of needle-positions in radiation treatment

Nucletron presented a medical problem to the SWI 2006: how to find needles used for cancer treatment in a prostate? More concretely: how to find the positions of these needles from distorted images from an ultrasound probe? Section 1 explains the background of this problem. In Section 2 we deal with physical explanations for the distortions. In Section 3 we give a brief overview of medical imaging and explain which techniques we used to clean up the images

Species identification skills predict in-depth knowledge about species

To raise biodiversity awareness effectively, communicators should be aware of knowledge levels in their audiences. Species identification skills have been used in the past as a measure of what people know about species, yet it is not known whether they serve as good indicators. To study the link between species identification and in-depth species knowledge, we presented an animal knowledge test to an online audience of over 7,000 Dutch adults, and used correlation and regression analyses to determine the extent to which species identification predicts in-depth knowledge about species’ origin, habitat, diet, and behavior. We found that in-depth knowledge was higher in those who correctly identified species as compared with those who did not correctly identify species, for all four types of in-depth knowledge. Moreover, as compared to alternative variables (work, age, gender, and educational level), species identification was by far the best predictor for in-depth knowledge about species. However, species identification levels were generally higher than levels of in-depth knowledge, and knowledge gaps and misconceptions were uncovered. The results confirm the value of species identification tests, but also highlight limitations and challenges that should be taken into account when establishing knowledge levels and communicating biodiversity

Misleading graphs in context:Less misleading than expected

Misleading graphs are a source of misinformation that worry many experts. Especially people with a low graph literacy are thought to be persuaded by graphs that misrepresent the underlying data. But we know little about how people interpret misleading graphs and how these graphs influence their opinions. In this study we focus on the effect of truncating the y-axis for a line chart which exaggerates an upgoing trend. In a randomized controlled trial, we showed participants either a normal or a misleading chart, and we did so in two different contexts. After they had seen the graphs, we asked participants their opinion on the trend and to give an estimation of the increase. Finally we measured their graph literacy. Our results show that context is the only significant factor in opinion-forming; the misleading graph and graph literacy had no effect. None of these factors had a significant impact on estimations for the increase. These results show that people might be less susceptible to misleading graphs than we thought and that context has more impact than a misleading y-axis.Science Communication and Societ