Heisenberg characters, unitriangular groups, and Fibonacci numbers

Let \UT_n(\FF_q) denote the group of unipotent $n\times n$ upper triangular matrices over a finite field with $q$ elements. We show that the Heisenberg characters of \UT_{n+1}(\FF_q) are indexed by lattice paths from the origin to the line $x+y=n$ using the steps $(1,0), (1,1), (0,1), (1,1)$, which are labeled in a certain way by nonzero elements of \FF_q. In particular, we prove for $n\geq 1$ that the number of Heisenberg characters of \UT_{n+1}(\FF_q) is a polynomial in $q-1$ with nonnegative integer coefficients and degree $n$, whose leading coefficient is the $n$th Fibonacci number. Similarly, we find that the number of Heisenberg supercharacters of \UT_n(\FF_q) is a polynomial in $q-1$ whose coefficients are Delannoy numbers and whose values give a $q$-analogue for the Pell numbers. By counting the fixed points of the action of a certain group of linear characters, we prove that the numbers of supercharacters, irreducible supercharacters, Heisenberg supercharacters, and Heisenberg characters of the subgroup of \UT_n(\FF_q) consisting of matrices whose superdiagonal entries sum to zero are likewise all polynomials in $q-1$ with nonnegative integer coefficients.Comment: 25 pages; v2: material significantly revised and condensed; v3: minor corrections, final versio

Skill mismatches and worker shortages in the New Zealand arboriculture industry : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies at Massey University, Albany, New Zealand

There seems to be endemic shortages of skilled arborists in New Zealand. Economics largely treats labour shortages as a matter of wage with price determining the allocation of goods including labour. However, sociological and work psychology literature suggests working conditions and how people are treated by managers and the public may be important factors, especially in keeping employees. This study aims to explore factors that contribute to recruitment and retention difficulties with respect to skilled arborists. An online survey was distributed via the industry association followed by 11 qualitative interviews directed toward a mix of both workers and employers. Participants were questioned about their experiences with the field arborist role, both positive and negative, as well as how they thought the occupation could be improved. Upon completion of the initial analysis a second round of 4 confirmatory interviews were carried out. The findings suggest that the wage rates for skilled workers may be artificially low due to structural features such as intense product market competition, the dominance of small firms, and a lack of sector organisation by workers or firms. Supply is also limited due to the demanding nature of the work and insufficient training, as well as recent restrictions on overseas labour. However, this study also suggests that a focus on low wages as the cause of recruitment and retention problems provides an incomplete account of the problem. This is because low pay also contributes to skills mismatch in terms of labour deployment, reducing the intrinsic satisfiers associated with the role and subsequently pushing many workers into self-employment. This increases quantities of small and often unprofessional firms, while increasing competition for work and staff. Increased coordination of the industry to improve the wages and conditions of the field arborist role would provide benefits for both workers and employers. Fair Pay Agreements could be a mechanism for achieving this. I suggest, in that this process should be initiated by the firms themselves in the interest over overcoming the skill shortage and need not be driven by a union. Future study should take the form of action research documenting the implementation of this process

C-Band Airport Surface Communications System Standards Development, Phase I

This document is being provided as part of ITT's NASA Glenn Research Center Aerospace Communication Systems Technical Support (ACSTS) contract NNC05CA85C, Task 7: "New ATM Requirements--Future Communications, C-Band and L-Band Communications Standard Development." The proposed future C-band (5091- to 5150-MHz) airport surface communication system, referred to as the Aeronautical Mobile Airport Communications System (AeroMACS), is anticipated to increase overall air-to-ground data communications systems capacity by using a new spectrum (i.e., not very high frequency (VHF)). Although some critical services could be supported, AeroMACS will also target noncritical services, such as weather advisory and aeronautical information services as part of an airborne System Wide Information Management (SWIM) program. AeroMACS is to be designed and implemented in a manner that will not disrupt other services operating in the C-band. This report defines the AeroMACS concepts of use, high-level system requirements, and architecture; the performance of supporting system analyses; the development of AeroMACS test and demonstration plans; and the establishment of an operational AeroMACS capability in support of C-band aeronautical data communications standards to be advanced in both international (International Civil Aviation Organization, ICAO) and national (RTCA) forums. This includes the development of system parameter profile recommendations for AeroMACS based on existing Institute of Electrical and Electronics Engineering (IEEE) 802.16e- 2009 standard

C-Band Airport Surface Communications System Standards Development. Phase II Final Report. Volume 1: Concepts of Use, Initial System Requirements, Architecture, and AeroMACS Design Considerations

This report is provided as part of ITT s NASA Glenn Research Center Aerospace Communication Systems Technical Support (ACSTS) contract NNC05CA85C, Task 7: New ATM Requirements-Future Communications, C-Band and L-Band Communications Standard Development and was based on direction provided by FAA project-level agreements for New ATM Requirements-Future Communications. Task 7 included two subtasks. Subtask 7-1 addressed C-band (5091- to 5150-MHz) airport surface data communications standards development, systems engineering, test bed and prototype development, and tests and demonstrations to establish operational capability for the Aeronautical Mobile Airport Communications System (AeroMACS). Subtask 7-2 focused on systems engineering and development support of the L-band digital aeronautical communications system (L-DACS). Subtask 7-1 consisted of two phases. Phase I included development of AeroMACS concepts of use, requirements, architecture, and initial high-level safety risk assessment. Phase II builds on Phase I results and is presented in two volumes. Volume I (this document) is devoted to concepts of use, system requirements, and architecture, including AeroMACS design considerations. Volume II describes an AeroMACS prototype evaluation and presents final AeroMACS recommendations. This report also describes airport categorization and channelization methodologies. The purposes of the airport categorization task were (1) to facilitate initial AeroMACS architecture designs and enable budgetary projections by creating a set of airport categories based on common airport characteristics and design objectives, and (2) to offer high-level guidance to potential AeroMACS technology and policy development sponsors and service providers. A channelization plan methodology was developed because a common global methodology is needed to assure seamless interoperability among diverse AeroMACS services potentially supplied by multiple service providers

Observing the Symmetry of Attractors

We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and have been considered untrustworthy. We find conditions under which an equivariant projection generically shows the correct symmetry of the attractor.Comment: 28 page LaTeX document with 9 ps figures included. Supplementary color figures available at http://odin.math.nau.edu/~jws

A phenomenological study on the experiences of parents of substance users from resource-constrained contexts in the Western Cape, South Africa

Adolescent substance use continues to remain a significant problem, especially in low-income communities in South Africa. This phenomenon not only affects individuals and society, but also the parents of the user. Parents within low-income contexts may feel disregarded or ‘unseen’ in planning and service delivery initiatives, which may lead to a lack of appropriate knowledge and resources when confronted with a child who uses substances. The situation may also be amplified by challenges within resource-constrained environments. The aim of this paper is to explore the subjective experiences of parents of substance users and their access to available treatment resources in low-income settings. The study, embedded in the Conservation of Resources (COR) theory, employed a phenomenological research design. Eight semi-structured interviews were conducted with parents/guardians of substance users from various resource-constrained communities in the Western Cape, South Africa. Using an interpretative phenomenological analysis technique, major themes emerging from the analysis included: 1) the experiences and perceptions of a parent with a child who uses substances, and 2) access to treatment: “just make it easy”. Study findings highlight the multifaceted nature of this journey and how the experience of gaining access to treatment resources may facilitate or hinder coping, particularly in low-income contexts, which may aid in addressing structural barriers that prevent access to resources and ultimately, increase support structures that are rich in quality and accessible across various socio-economic contexts

Predictors of poor function in RA based on two prospective UK inception cohorts. Do comorbidities matter?

© The Author(s) 2021. Published by Oxford University Press on behalf of the British Society for Rheumatology. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/)Objectives. Evidence suggests that factors beyond disease activity associate with functional disability in RA. The primary study objective was to explore associations between comorbidities, sociodemographic factors and functional outcomes at five and 10 years.  Methods. RA patients from two UK prospective cohorts were grouped into low (<1.5) and high (1.5) five- and 10-year health assessment questionnaire (HAQ) score. Clinical variables (e.g. disease activity, rheumatoid nodules, erosions) and sociodemographic factors (e.g. ethnicity, deprivation) were recorded at baseline and yearly thereafter. Comorbidity was measured using the Rheumatic Diseases Comorbidity Index (RDCI). Binary logistic regression models were fitted using multiple imputation.  Results. In total, 2701 RA patients were recruited (mean age 56.1 years, 66.9% female). A total of 1718 (63.4%) had five-year and 820 (30.4%) 10-year follow-up data. In multivariable analysis, no association was found between RDCI and HAQ 1.5 at five or 10 years. Sociodemographic factors (increased age at disease onset, female gender, minority ethnicity) were associated with higher odds of HAQ 1.5 at five and 10 years, with worse deprivation additionally associated with HAQ 1.5 at 10 years (OR 0.79, 95% CI: 0.69, 0.90).  Conclusion. Comorbidities at baseline have not been found to be associated with worse RA functional outcome in the long-term. On the other hand, sociodemographic factors, independently of disease measures, are associated with worse functional outcome in RA at five and 10 years, in models adjusting for comorbidity burden. Tailoring management interventions according to not only clinical disease parameters but also patient sociodemographic factors may improve long-term outcomes including functional disability.Peer reviewe

A Qualitative Study of Traditional Bone Setters in South India: A Case Series

INTRODUCTION. There are approximately 70,000 Traditional Bone Setters (TBS) in India, who have no formal education or training in modern medicine but treat approximately 60% of bone related trauma. This study investigated the history of TBS, why they are so popular, and their methods. METHODS. From a list of TBS from four states in South India, a purposive and convenience sampling method identified participants. One lead TBS from each state was interviewed. With recommendations from these TBS, a total of six participants were interviewed on Zoom® in their native dialect and these interviews were transcribed into English. The data were analyzed using a constant comparative method which included several iterations to refine common themes and determine counterfactual and specific focal points from each interview. RESULTS. Six overarching themes emerged: (1) history of traditional bone setters, (2) occupations outside bone setting, (3) training, certification, education, accolades, (4) patient characteristics and success stories, (5) infrastructure and approach to diagnosis/treatment, and (6) limitations of practice, challenges, and social relevance. The history of traditional bone setting is thousands of years old and passed down within families generationally. CONCLUSIONS. In rural India, where a large part of the population lives in poverty and without access to modern medicine, traditional healers provide a much-needed service, often without charge, and consequently, the income is not sufficient without other occupations such as farming. They follow a similar approach to diagnosis and treatment of simple fractures and dislocations as modern medical practitioners. Most would like to share their knowledge and collaborate with ayurvedic and allopathic practitioners and simply want to be respected and supported

New social adaptability index predicts overall mortality

Introduction: Definitions of underprivileged status based on race, gender and geographic location are neither sensitive nor specific; instead we proposed and validated a composite index of social adaptability (SAI). Material and methods: Index of social adaptability was calculated based on employment, education, income, marital status, and substance abuse, each factor contributing from 0 to 3 points. Index of social adaptability was validated in NHANES-3 by association with all-cause and cause-specific mortality. Results: Weighted analysis of 19,593 subjects demonstrated mean SAI of 8.29 (95% CI 8.17-8.40). Index of social adaptability was higher in Whites, followed by Mexican-Americans and then the African-American population (ANOVA, p < 0.001). The SAI was higher in subjects living in metropolitan compared to rural areas (T-test, p < 0.001), and was greater in men than in women (T-test, p < 0.001). In Cox models adjusted for age, comorbidity index, BMI, race, sex, geographic location, hemoglobin, serum creatinine, albumin, cholesterol, and glycated hemoglobin levels, SAI was inversely associated with mortality (HR 0.87 per point, 95% CI 0.84-0.90, p < 0.001). This association was confirmed in subgroups. Conclusions: We proposed and validated an indicator of social adaptability with a strong association with mortality, which can be used to identify underprivileged populations at risk of death