Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting

Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem within Euclidean spaces of changing dimension. Recently, an alternative approach which first decomposes complex space using triangular decomposition before refining to real space has been introduced and implemented within the RegularChains Library of Maple. We here describe a freely available package ProjectionCAD which utilises the routines within the RegularChains Library to build CADs by projection and lifting. We detail how the projection and lifting algorithms were modified to allow this, discuss the motivation and survey the functionality of the package

Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art

Some New Addition Formulae for Weierstrass Elliptic Functions

We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialisation of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalisation of Weierstrass' functions to curves of higher genus.Comment: 20 page

Do people with intellectual disabilities understand their prescription medication? A scoping review

© 2019 The Authors. Journal of Applied Research in Intellectual Disabilities Published by John Wiley & Sons Ltd.Background: People with intellectual disabilities are more likely to experience poor health than the general population and are frequently prescribed multiple medications. Therefore, it is important that people with intellectual disabilities understand their medication and potential adverse effects. Method: A scoping review explored people with intellectual disabilities' knowledge of prescription medications, their risks and how medication understanding can be improved. Results: Ten journal articles were included. People with intellectual disabilities often lacked understanding of their medication, including its name, purpose and when and how to take it. Participants were often confused or unaware of adverse effects associated with their medication. Information was sometimes explained to carers rather than people with intellectual disabilities. Some interventions and accessible information helped to improve knowledge in people with intellectual disabilities. Conclusion: There is a need for accessible and tailored information about medication to be discussed with people with intellectual disabilities in order to meet legal and best practice standards.Peer reviewe

Vascular Flora of the Upper Rock Creek Watershed, Eastern Sierra Nevada, California

The upper Rock Creek watershed is located on the east slope of the Sierra Nevada in Inyo and Mono counties. It is ca. 36.5 square miles (94.5 square km) in area and varies in elevation from 7360 to 13,750 ft (2243 to 4191 m). Quaternary glacial erosion and deposition produced striking landscape features, including alpine fell fields and numerous small lakes. Previous floristic inventories in Rock Creek recorded a combined 396 minimum-rank taxa (species, subspecies, varieties, named hybrids) but were restricted to Little Lakes Valley and the surrounding high areas. An updated, annotated checklist of vascular plants is presented, based on preexisting specimens and new collections. I conducted intensive fieldwork from 2012 through 2016, resulting in 1506 collections (including two collections from a brief 2018 visit). More than 1000 historical collections were examined. The resulting checklist contains 591 taxa, of which 25 (4.2%) are non-native to California and 32 (5.4%) are special-status plants. My fieldwork resulted in 128 taxa previously undocumented for the watershed. Eighty-one species historically collected were not rediscovered and are noted as such in the checklist. Nine taxa are new county records. The flora is represented by 77 families, 248 genera and 572 species. For each taxon, the checklist cites at least one collection and indicates the vegetation type(s) where it has been documented and its abundance in the watershed. A brief review of botanical exploration in the watershed during the past century is presented, along with geology, climate, vegetation and history of human activity

Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Whole body interaction

In this workshop we explore the notation of whole body interaction. We bring together different disciplines to create a new research direction for study of this emerging form of interaction