Invitation to intersection problems for finite sets

Extremal set theory is dealing with families, . F of subsets of an . n-element set. The usual problem is to determine or estimate the maximum possible size of . F, supposing that . F satisfies certain constraints. To limit the scope of this survey most of the constraints considered are of the following type: any . r subsets in . F have at least . t elements in common, all the sizes of pairwise intersections belong to a fixed set, . L of natural numbers, there are no . s pairwise disjoint subsets. Although many of these problems have a long history, their complete solutions remain elusive and pose a challenge to the interested reader.Most of the paper is devoted to sets, however certain extensions to other structures, in particular to vector spaces, integer sequences and permutations are mentioned as well. The last part of the paper gives a short glimpse of one of the very recent developments, the use of semidefinite programming to provide good upper bound

A Survey of Binary Covering Arrays

Binary covering arrays of strength t are 0–1 matrices having the property that for each t columns and each of the possible 2[superscript t] sequences of t 0's and 1's, there exists a row having that sequence in that set of t columns. Covering arrays are an important tool in certain applications, for example, in software testing. In these applications, the number of columns of the matrix is dictated by the application, and it is desirable to have a covering array with a small number of rows. Here we survey some of what is known about the existence of binary covering arrays and methods of producing them, including both explicit constructions and search techniques

British nuclear test veterans: the complexities of identity, health and wellbeing, and the ageing process

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonFor 30 years ~22,000 men were silenced by the Official Secrets Act. They participated in 21 nuclear tests conducted by the UK in Australia and the South Pacific from 1952-1958. Since 1983 these men have been campaigning for recognition following premature deaths, illness, miscarriages, and offspring deformities, to no avail. They are the British Nuclear Test Veteran (BNTV) community and in 2021, almost 70 years since the first nuclear test, less than 3,000 of them remain. This unique ageing population face a double jeopardy of invisibility: hidden by government red tape, and now marginalised as the oldest old. The discourse is dominated by the health effects of radiation and the servicemen’s lived experiences, the nuances of ageing, and any health and wellbeing issues have not been investigated. This thesis therefore had three key objectives: to understand the complexities of BNTV identity; critically explore health and wellbeing issues among the BNTV community; and analyse types of leisure activities that enhance wellbeing and reasons for engagement. Using a life history approach, this interpretivist qualitative study conducted two rounds of in-depth interviews with 29 members of the BNTV community. A systematic framework for narrative analysis led to the construction of three creative nonfiction stories representing the ‘big’, ‘small’, shared, and exceptional experiences of the BNTVs. Key findings include loneliness and loss; collective nuclear experience and identity; illness following potential exposure; and staying active to reduce the perceived side effects of ageing. By challenging the politics of ageing, health, and wellbeing, from the perspective of this diverse ageing population, this work not only impacts the community which it interviewed but also provides the foundations for future programmes of support to address the salient issues that have been identified. Furthermore, these CNF stories provide the BNTV community with the recognition they have been seeking

Affective materials: a processual, relational, and material ethnography of creative making in community and primary care groups

This research concerns neglected affective, relational, material, and processual dimensions of amateur crafts practice in an arts-for-health context. Existing studies on the social impacts of the participatory arts are prone to blur the borders between advocacy and research, and are vulnerable to accusations of ‘policy-based evidence making’ (Belfiore and Bennett, 2007, p.138). Researchers have relied predominantly on interview material and surveys, and there is a lack of finegrained, long-term, ethnographic work based on participant observation. The distinctive potentials of making in this context, furthermore, have barely been investigated. This thesis addresses these deficits through a sustained ethnographic study of two wellbeing-oriented crafts groups supported by Arts for Health Cornwall (AFHC). One group was based in the community, the other in primary care. Observation produces novel understandings of the potential benefits of crafting for health as emergent properties of particular locations, relationships, and practices organized in distinctive ways around creative making. Firstly, as a counterweight to normative views of amateur crafts creativity as soothing and distracting, this study highlights a range of transformative affects including frustration, creative ambition, and enchantment. Secondly, countering an atomistic, stable depiction of such affects, this study describes them as fluid aspects of making processes. Thirdly, these unfolding processes are seen to be inseparable from the intersubjective (peer-to-peer and participant-facilitator) dimensions of creative groups. Lastly, this in vivo perspective problematizes a view of materials as an inert substratum upon which makers exercise their creative powers, and highlights the relevance of a ‘vital materialism’ (Bennett, 2010) for understanding the potential benefits of manual creativity. Sustained observation also produces a situated, spatial account of the extended networks of community belonging produced by the activities of such groups. Fieldwork is contextualized within a wider field using interviews with nine UK arts for health organizations. Consideration is also given to the influence of contemporary discourses of wellbeing, agency, and creativity on policy making in the area of arts for health. Findings have implications for good practice in the field, and for further research to inform political leadership concerning the role of the arts in health. These implications are drawn out in relation to the potential future contribution of the arts within a UK health economy undergoing rapid, crisis-driven transformation

Black British and Black Caribbean Women’s Trajectories through the Wildernesses of Subordinated Spaces, (NHS workplace) and Unfamiliar Places (Higher Education): An Autoethnography

In 2014, the NHS Five Year Forward View (FYFV) set out new models of care and care strategies. Amongst them was the introduction of the role of Assistant Practitioner (AP). The AP role was positioned at Band 4 (of 9) on the NHS Careers Framework, gained through the successful completion of a foundation degree (fd). Those already in employment accessed the fd through day release to university and work-place clinical skills development. A qualified AP would work under the supervision of a registered nurse. This thesis examines and centralises the experiences of ten Black British and Black Caribbean women’s experiences of the fd programme and its impact on their personal and professional identities. It (re)tells, (re)captures and (re)presents their accounts of getting in, moving on and getting through Higher Education. This study disrupts the silence of Black women in the NHS. Black Feminist Methodological Stance is put to work to centre and privilege Black women who transitioned through the research process unearthing, examining and unapologetically speaking their ‘truths’. The analysis is intentionally theoretically provocative, it uses performative autoethnograpy to present the voices of the women through characters in fictional settings. The characters use the works of predominantly Black philosophers to critically reflect on their experiences of education. Their exposures to philosophies and their sharing of life leads them to Black feminist epistemologies. This study demands engagement, it challenges all who access it, to come and reside in our spaces… to feel the discomforts… to rethink the stereotypes… to speak of the biases… then to co-align with us… it questions… challenges… and seeks honest approaches to fairness in nursing education and professions; two areas, where for seven decades Black women have been professionally subordinated and exploited. This thesis demonstrates the courage of the author to engage in research which breaks the silence of Black women in NHS and makes the theorised assertion of our ‘right to write’ as Black women about Black women. The presentation of the data as performance autoethnography, renders this work accessible to the contributors, as well as significant and important for academic scholarship. This study strives for engagement, it resists recommendations which, historically are ineffective liberatory tools of the master’s house, in that they fail to make a difference to the Black women’s assigned subordinated space. Finally, this work challenges Black women in the NHS to become active agents of their professional emancipation. New Knowledge Contribution: This thesis contributes the following new knowledge: The production of a literature review which resists the normative approach to the production of a thesis, it utilises oral accounts which work to both contradict as well as illuminate accounts presented in written text. It retells the stories of ten Black female Health Care Assistants (HCAs). Because of their low professional status, HCAs are generally invisible and voiceless in research studies. This study centralises their experiences, making them visible, therefore providing a partial illumination of their educational experiences. The literature provides Black nurses of the 21st Century with an example of how Black nurses in the past coalesced to redress the inequitable nursing education provision they experienced during colonial times. Black nurses of the Caribbean broke the nursing profession’s class ceiling securing positions previously solely reserved for Caucasians. The unearthing and presentation of Black Caribbean women’s nursing education history provides Black nurses with a positive self-liberatory learning example from Caribbean nurses of the past. This study demonstrates the courage of the author to present the data analysis as performance autoethnography, in so doing, it renders this work accessible to the contributors, the academic as well as ordinary members of the Black community. This thesis strives for engagement and discussion asking questions of institutions rather than being prescriptive and autocratic (making recommendations). It also challenges Black women in the NHS to become active conduits of their own professional emancipation rather than awaiting ‘redemption from those using the tick box tools of the ‘master’s house’