Application of the four-colour theorem to the surfaces of polyhedra

The four-colour map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colours are required to colour the regions of the map so that no two adjacent regions have the same colour. Two regions are considered to be adjacent if they share a common boundary that is not a corner (a point shared by three or more regions). The theorem was proposed in the 1850s and became the first theorem to be proved by computational methods in the 1970s. Despite the theorem being true, some geopolitical maps require more than four colours (if, for example, some regions are not contiguous) and the theorem has never been of great interest to mapmakers. This paper describes the theorem and explores how it could be extended to three dimensions. We restrict our study to the colouring of the surfaces of three-dimensional polytopes or polyhedra, specifically those that are convex. An analysis of the relationship between two-dimensional maps and three-dimensional surfaces is presented with regard to the minimum number of colours required. Visual examples are provided for regular polyhedral of increasing number of polygonal faces

Colour terms in the interior design process

Colour is a very important topic that interior designers need to consider. Considerable research has been conducted in the area of colour application in interior design; in this study we are concerned with colour terms in interior design, mainly the terms designers use and know about. Fifteen interior designers with varied professional backgrounds, but based in the Middle East (Saudi Arabia, Dubai, Bahrain, Lebanon, Egypt, and Turkey), were interviewed. Previously we reported that fourteen out of fifteen designers stated that colour thinking and decision making take place at the early stages of their design processes; eight of them reported that colour takes place in the first step when meeting clients and starting the project (Attiah et al., 2014). This study documented 137 terms which the fifteen designers use whilst brainstorming and working on a design project; subsequent analysis of these terms could form a basis for understanding how interior designers communicate the abstract properties of colour as part of their design processes. In this paper we show how the 137 terms were categorised according to a framework of four categories of colour terms: emotional, descriptive, cultural and functional. In addition, seventeen words (scientists names and technical terms), which are widely used in colour science (such as: CIELAB, Saturation, Itten) were shown to the designers; their knowledge was shown to be incomplete

Colour preferences for traditional Korean colours

Colour perception and preference have often been considered to be culturally linked. In this study, samples of young Korean and UK consumers have been tested to examine their colour preferences and also what they considered to be successful fashion colours. The traditional Korean colours (in various degrees of saturation) have been used for the test and, in the case of the Korean participants, they were also asked which colours they considered to the more traditional. Though there were some differences between the young Korean and young UK participants, the degree of similarly in choice and preference was quite marked. It is suggested that this may be due to exposure to global media and internet products in the modern environment. Also it was found that the reliability of both test groups was high

Market access agreements for pharmaceuticals in Europe: diversity of approaches and underlying concepts

<p>Abstract</p> <p>Background</p> <p>Market Access Agreements (MAA) between pharmaceutical industry and health care payers have been proliferating in Europe in the last years. MAA can be simple discounts from the list price or very sophisticated schemes with inarguably high administrative burden.</p> <p>Discussion</p> <p>We distinguished and defined from the health care payer perspective three kinds of MAA: Commercial Agreements (CA), Payment for Performance Agreements (P4P) and Coverage with Evidence Development (CED). Apart from CA, the agreements assumed collection and analysis of real-life health outcomes data, either from a cohort of patients (CED) or on per patient basis (P4P). We argue that while P4P aim at reducing drug cost to payers without a systematic approach to addressing uncertainty about drugs' value, CED were implemented provisionally to reduce payer's uncertainty about value of a medicine within a defined time period.</p> <p>Summary</p> <p>We are of opinion that while CA and P4P have a potential to reduce payers' expenditure on costly drugs while maintaining a high list price, CED address initial uncertainty related to assessing the real-life value of new drugs and enable a final HTA recommendation or reimbursement and pricing decisions. Further, we suggest that real cost to health care payers of drugs in CA and P4P should be made publicly available in a systematic manner, to avoid a perverse impact of these MAA types on the international reference pricing system.</p

Colour selection strategies in colour design

Our evolving hypothesis is that a colour-picker interface designed to challenge the novice user will better connect with their creative abilities and help develop their understanding of the interrelated digital colour challenges. An interface approach underpinned by a philosophy of engaging-in-use rather than ease-of-use may help to better rationalize a new user’s colour-selection process, thus improving their initial productivity and creativity within the digital design environment. This study challenges the established HCI (Human Computer Interaction) convention that consistently prescribes to a user-interface-strategy embracing ease-of-use. It considers if this ideal is necessarily the right approach for creative software application, assessing colour-pickers as the primary example. Interesting results are emerging from experimental work with an early prototype colour-picker tool that exploits our ongoing research into intuitive understanding of colour. The focus of this work is the creative colour selection process and not colour management per se, however it is recognised that the relationship between these two design and technical processes is not always mutually exclusive