Computing pseudotriangulations via branched coverings

We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility complexes and on the extension of that theory to the setting of branched coverings. The problem of computing a pseudotriangulation that contains a given set of bitangent line segments is also examined.Comment: 66 pages, 39 figure

Redistribution and loss of soil organic carbon by overland flow under various soil management practices on the Chinese Loess Plateau

Field rainfall simulations with intensities of 85 and 170 mm/h were conducted in 2002 and 2005 on a 15-m long slope on a loess soil in Luoyang, Henan Province, P. R. China to study the effects of different soil management practices on the redistribution and loss of soil organic carbon (SOC) by runoff and soil erosion. Field plots under winter wheat ( Triticum aestivum L.) were set up in 2001 and included the following soil management practices: subsoiling with mulch (SSM), no-till with mulch (NTM), reduced tillage (RT) and conventional tillage control (CT). The results showed that SOC for topsoil (0 - 20 cm) increased in the NTM and SSM plots when compared with results from 2002 and 2005. For all treatments, SOC in the lower part of the plots was higher in 2005 than in 2002. The values from the upper parts of the plots were only lower in 2005 compared with the overall values for 2002 for RT and CT. The enrichment ratio of organic carbon (ERoc) in runoff sediment varied from 1.01 to 2.24 with a mean of 1.25. During the simulated rainfall events, ERoc was initially high and then reduced after a short period to reach a steady value at the end of the event, always remaining >= 1. The change in SOC loss rate was more dependent on the sediment loss rate than on the changes in SOC concentration in the sediment. The best results in terms of a reduction in soil and SOC loss were obtained with NTM: no runoff and hence no soil and SOC loss were observed. SOC losses observed for SSM were on average only 4% of those observed for CT. RT resulted in 71% SOC loss compared with CT although the runoff reduction was not pronounced. For farmers, SSM and NTM are the best alternatives in terms of SOC conservation. NTM has the additional advantage that it requires less labour and is more beneficial from economic and environmental perspectives

Assessment, disability, student engagement and responses to intervention

Assessment is central to the provision of meaningful and productive learning experiences for all students. The majority of students in today’s classroom benefit from core instruction; however, for a small percentage of students with a disability, learning requires more intensive instruction. It is this cohort of learners that we consider in this chapter. While the needs of these learners are diverse, they have in common some teaching and learning challenges that have direct implications for assessment practices. We consider three major challenges: (1) the various learning priorities for students in need of intensive instruction, and how to maximise the connection between current and targeted skills and knowledge; (2) how to measure change through skill or knowledge acquisition when the rate and magnitude of change may be achieved in small increments; and (3) how to determine whether change that does occur is attributable to our teaching, and what to do when teaching is not effective in achieving change. In the absence of this information, there is a serious risk that instruction will be less than effective, will lack social validity and that learners will fail to make progress and achieve positive learning outcomes. Within the context of a cycle typical of intensive instruction, we examine how assessment can play a key role in enhancing and facilitating teaching and learning in the classroom by addressing these three major challenges. We also review the practical challenges that teachers in regular classrooms face in utilising systematic assessment and programming strategies to meet the needs of all the students in their classrooms