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

Generalised Elliptic Functions

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed sees the functions defined as logarithmic derivatives of the sigma-function, a modified Riemann theta-function. We can make use of known properties of the sigma function to derive power series expansions and in turn the properties mentioned above. This approach has been extended to a wide range of non hyperelliptic and higher genus curves and an overview of recent results is given. The second approach defines the functions algebraically, after first modifying the curve into its equivariant form. This approach allows the use of representation theory to derive a range of results at lower computational cost. We discuss the development of this theory for hyperelliptic curves and how it may be extended in the future.Comment: 16 page

Deriving bases for Abelian functions

We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstrass identities for the case of the trigonal curve of genus four.Comment: 35page

Atlantic Ocean Heat Transport Enabled by Indo-Pacific Heat Uptake and Mixing

The ocean transports vast amounts of heat around the planet, helping to regulate regional climate. One important component of this heat transport is the movement of warm water from equatorial regions toward the poles, with colder water flowing in return. Here, we introduce a framework relating meridional heat transport to the diabatic processes of surface forcing and turbulent mixing that move heat across temperature classes. Applied to a (1/4)° global ocean model the framework highlights the role of the tropical Indo‐Pacific in the global ocean heat transport. A large fraction of the northward heat transport in the Atlantic is ultimately sourced from heat uptake in the eastern tropical Pacific. Turbulent mixing moves heat from the warm, shallow Indo‐Pacific circulation to the cold deeper‐reaching Atlantic circulation. Our results underscore a renewed focus on the tropical oceans and their role in global circulation pathways

Are HIV smartphone apps and online interventions fit for purpose?

Sexual health is an under-explored area of Human-Computer Interaction (HCI), particularly sexually transmitted infections such as HIV. Due to the stigma associated with these infections, people are often motivated to seek information online. With the rise of smartphone and web apps, there is enormous potential for technology to provide easily accessible information and resources. However, using online information raises important concerns about the trustworthiness of these resources and whether they are fit for purpose. We conducted a review of smartphone and web apps to investigate the landscape of currently available online apps and whether they meet the diverse needs of people seeking information on HIV online. Our functionality review revealed that existing technology interventions have a one-size-fits-all approach and do not support the breadth and complexity of HIV-related support needs. We argue that technology-based interventions need to signpost their offering and provide tailored support for different stages of HIV, including prevention, testing, diagnosis and management

Reviewing research evidence and the case of participation in sport and physical recreation by black and minority ethnic communities

The paper addresses the implications of using the process of systematic review in the many areas of leisure where there is a dearth of material that would be admitted into conventional Cochrane Reviews. This raises important questions about what constitutes legitimate knowledge, questions that are of critical import not just to leisure scholars, but to the formulation of policy. The search for certainty in an area that lacks conceptual consensus results in an epistemological imperialism that takes a geocentric form. While clearly, there is a need for good research design whatever the style of research, we contend that the wholesale rejection of insightful research is profligate and foolhardy. A mechanism has to be found to capitalise on good quality research of whatever form. In that search, we draw upon our experience of conducting a review of the material available on participation in sport and physical recreation by people from Black and minority ethnic groups. The paper concludes with a proposal for a more productive review process that makes better use of the full panoply of good quality research available. © 2012 © 2012 Taylor & Francis

Who uses NHS health checks? Investigating the impact of ethnicity and gender and method of invitation on uptake of NHS health checks

Background NHS Health Checks is a national risk assessment prevention programme for all individuals aged 40-74 that reside in England. Through the systematic assessment of an individual’s ten year disease risk, this programme aims to provide early identification and subsequent management of this risk. However, there is limited evidence on how socio-demographic factors impact on uptake and what influence the invitation method has on uptake to this programme. Methods NHS Health Check data from April 2013 to March 2014 was analysed (N = 50,485) for all 30 GP Practices in Luton, a culturally diverse town in England, UK. Data was collected for age, ethnicity, uptake (attendance and non attendance) and invitation method (letter written, verbal face-to-face, telephone). Actual usage of NHS Health Checks was determined for each ethnic group of the population and compared using Chi-square analysis. Results The overall uptake rate for Luton was 44 %, markedly lower that the set target of 50–75 %. The findings revealed a variation of uptake in relation to age, gender, level of deprivation. Ethnicity and gender variations were also found, with ‘White British’ ‘Black Caribbean’ and ‘Indian’ patients most likely to take up a NHS Health Check. However, patients from ‘Any Other White Background’ and ‘Black African’ were significantly less likely to uptake an NHS Health Check compared to all other ethnic groups. Ethnicity and gender differences were also noted in relation to invitation method. Conclusions The findings revealed that different invitation methods were effective for different ethnic and gender groups. Therefore, it is suggested that established protocols of invitation are specifically designed for maximizing the response rate for each population group. Future research should now focus on uncovering the barriers to uptake in particular culturally diverse population groups to determine how public health teams can better engage with these communities

Scholarly Communication Practices in Humanities and Social Sciences: A Study of Researchers’ Attitudes and Awareness of Open Access

This paper examines issues relating to the perceptions and adoption of open access (OA) and institutional repositories. Using a survey research design, we collected data from academics and other researchers in the humanities, arts and social sciences (HASS) at a university in Australia. We looked at factors influencing choice of publishers and journal outlets, as well as the use of social media and nontraditional channels for scholarly communication. We used an online questionnaire to collect data and used descriptive statistics to analyse the data. Our findings suggest that researchers are highly influenced by traditional measures of quality, such as journal impact factor, and are less concerned with making their work more findable and promoting it through social media. This highlights a disconnect between researchers’ desired outcomes and the efforts that they put in toward the same. Our findings also suggest that institutional policies have the potential to increase OA awareness and adoption. This study contributes to the growing literature on scholarly communication by offering evidence from the HASS field, where limited studies have been conducted. Based on the findings, we recommend that academic librarians engage with faculty through outreach and workshops to change perceptions of OA and the institutional repository

Abelian functions associated with a cyclic tetragonal curve of genus six

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y^4 = x^5 + λ[4]x^4 + λ[3]x^3 + λ[2]x^2 + λ[1]x + λ[0]. We construct Abelian functions using the multivariate sigma-function associated with the curve, generalizing the theory of theWeierstrass℘-function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi inversion problem, a power series expansion for σ(u) and a new addition formula