On distinguishing trees by their chromatic symmetric functions

Let $T$ be an unrooted tree. The \emph{chromatic symmetric function} $X_T$, introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of $T$. The \emph{subtree polynomial} $S_T$, first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of $T$ by their numbers of edges and leaves. We prove that $S_T =$, where $$ is the Hall inner product on symmetric functions and $\Phi$ is a certain symmetric function that does not depend on $T$. Thus the chromatic symmetric function is a stronger isomorphism invariant than the subtree polynomial. As a corollary, the path and degree sequences of a tree can be obtained from its chromatic symmetric function. As another application, we exhibit two infinite families of trees (\emph{spiders} and some \emph{caterpillars}), and one family of unicyclic graphs (\emph{squids}) whose members are determined completely by their chromatic symmetric functions.Comment: 16 pages, 3 figures. Added references [2], [13], and [15

Organizational Strategies for Addressing Disparities Among Marginalized Older Adults

As the United States older adult population expands, it is also becoming more diverse in terms of race, ethnicity, and sexual orientation (U.S. Census Bureau, 2010). This increased diversity necessitates that social workers research issues of cultural competency at the organizational level to ensure that community based organizations are able to meet the unique needs of a heterogeneous population of American elders. This qualitative study utilized a modified grounded theory approach to conduct individual interviews and focus groups with over 25 community based organizations serving diverse elders. This study also included analysis of over 100 agency documents, such as mission statements and annual reports. The primary research question was “what are the strategies that key informants within community based organizations attempting to alleviate disparities use to meet the needs of marginalized older adults?” In alignment with the Life Course Theory (Elder, 1975) and the Social Determinants of Health Framework (Marmot, 2006), this research demonstrates that the accumulated disadvantages often experienced by marginalized elders may also be present at the organizational level. Agencies that serve marginalized elders face more barriers in meeting the reporting requirements of funders, demonstrating the use of evidence based practice, and having enough resources and organizational capacity to successfully provide for the diverse needs of elders. Study participants also identified over thirty concrete organizational strategies that they perceived could lead to better services for diverse elderly clients. In terms of practice implications, this study demonstrates that non-profit, community based agencies serving diverse older adults need to be further supported in their efforts to collaborate, share resources and otherwise increase their organizational capacity. At the policy level, federal programs may need to expand to further promote the networking and collaborative efforts of smaller, community based agencies that may already be culturally aware of the needs of their own communities but lack adequate resources and capacity. Future studies could determine the best methods to implement the organizational strategies identified in this study, identify implementation barriers and supports, and research the specific needs of each unique elder group

Turning to see otherwise

This thesis dossier, in combination with an exhibition at the McIntosh Gallery, considers whether an archival collection can generate an alternative narrative other than that which may already exist in the original film and photographic documents. Rather than represent a singular truth, I seek to articulate the transformative realities of collective memory by re-orienting the material for broader viewer identification. I have mined photographic and filmic materials from a personal family archive to focus fragments that specifically record the gesture of the turning face—the turning towards the observer. This “turn” then includes both the turn towards the initial film-maker embedded in the documents, and, a later, fragmented turn which is re-oriented and looped to construct a new narrative which turns its gaze towards the art observer. Thus, the “turn” is both formally and metaphorically suggested and variously defined in this dossier. I used the action of the turn as a way to consider re-orientation, and, even disorientation, as a means to discover new ways of seeing. The thesis discusses my use of this specific gesture and the relevant archival materials in the context of contemporary art production and reception, calling on the three key theoretical themes: knowledge production, feminism and film theory. Through a close examination of the archival materials and these theoretical considerations, I found that, by articulating the archival image through seemingly disparate spatial and temporal relationships, an alternative narrative could be produced

Turning White: Co-Opting a Profession through the Myth of Progress, An Intersectional Historical Perspective of Brown v. Board of Education

The U.S. is currently experiencing a teacher shortage. Many school districts have been impacted by this issue and want to know: how do we recruit more qualified candidates into the profession, and, more importantly, how do we recruit more Teachers of Color? We may be experiencing a shortage of teachers in general, but there has been a paucity of Teachers of Color, particularly Black teachers, for decades. Looking back to the Brown v. Board decision (1954) to integrate public schools, thousands of Black teachers were pushed out of their jobs in various ways. In this article, we examine how this historical and groundbreaking decision had unintended negative consequences for Black teachers at the time of the decision and in the decades to follow. We speculate about the consequences for past, present, and future Students of Color with little to no exposure to and experience with Black teachers. Finally, we theorize intersectional solutions to the teacher shortage in general. Bringing issues of race to the forefront of our conversations about teaching is critical, but rare. According to Douglass Horsford (2019), “race remains not only a difficult and unwelcome topic among educators but also among education researchers, which perhaps leads to its undertheorizing in the field” (p. 262)

Loc’d and Faded, Yoga Pants and Spaghetti Straps: Discrimination in Dress Codes and School Pushout

In this paper, we review the current dress code violations that have made national news. These issues have spotlighted racist and sexist issues embedded within common K-12 dress codes. We also analyze all school dress codes within one county in a mid-western state to examine various racist and sexist issues. We end the paper with an assessment for readers to determine the levels of racism and sexism in their own K-12 district dress codes

Bragging about bragg

Jennifer L. Martin, an ARC Australian Laureate Fellow at the University of Queensland, considers Lawrence Bragg as one of the best scientists in the world. She is ashamed of those people, generally Australians, who do not recognize Bragg. He was born in Adelaide on 31st March 1890 and was the first Australian to win a Nobel Prize. Lawrence and his father William H. Bragg were jointly awarded the Nobel Prize for their services in the analysis of crystal structure by means of X-rays. Bragg's law unlocked the secrets of atomic structure and chemical bonding and established an entirely new field of science. Lawrence Bragg became the director of the Cavendish Laboratory in Cambridge where he fostered the careers of many other researchers. Later, as Director of the Royal Institution in London, he mentored other protein crystallography greats including David Phillips and Louise Johnson

Exercise and progressive supranuclear palsy : the need for explicit exercise reporting

Background Progressive Supranuclear Palsy (PSP) is the most frequent form of atypical Parkinsonism. Although there is preliminary evidence for the benefits of gait rehabilitation, balance training and oculomotor exercises in PSP, the quality of reporting of exercise therapies appears mixed. The current investigation aims to evaluate the comprehensiveness of reporting of exercise and physical activity interventions in the PSP literature. Methods Two independent reviewers used the Consensus on Exercise Reporting Template (CERT) to extract all exercise intervention data from 11 studies included in a systematic review. CERT items covered: ‘what’ (materials), ‘who’ (instructor qualifications), ‘how’ (delivery), ‘where’ (location), ‘when’, ‘how much’ (dosage), ‘tailoring’ (what, how), and ‘how well’ (fidelity) exercise delivery complied with the protocol. Each exercise item was scored ‘1’ (adequately reported) or ‘0’ (not adequately reported or unclear). The CERT score was calculated, as well as the percentage of studies that reported each CERT item. Results The CERT scores ranged from 3 to 12 out of 19. No PSP studies adequately described exercise elements that would allow exact replication of the interventions. Well-described items included exercise equipment, exercise settings, exercise therapy scheduling, frequency and duration. Poorly described items included decision rules for exercise progression, instructor qualifications, exercise adherence, motivation strategies, safety and adverse events associated with exercise therapies. Discussion The results revealed variability in the reporting of physical therapies for people living with PSP. Future exercise trials need to more comprehensively describe equipment, instructor qualifications, exercise and physical activity type, dosage, setting, individual tailoring of exercises, supervision, adherence, motivation strategies, progression decisions, safety and adverse events. Conclusion Although beneficial for people living with PSP, exercise and physical therapy interventions have been inadequately reported. It is recommended that evidence-based reporting templates be utilised to comprehensively document therapeutic exercise design, delivery and evaluation

Military load carriage: an innovative method of interface pressure measurement and evaluation of novel load carriage designs

This thesis is concerned with the measurement and effects of pressure on the body as a result of military load carriage. High skin pressures are associated with impaired blood flow, brachial plexus disorders and user pain and discomfort. Load carriage research has largely overlooked this issue, mainly due to the lack of an appropriate methodology. The thesis consists of two parts. The aim of part I was to develop and validate a novel method of measuring on-body interface pressures underneath military load carriage equipment. The Tekscan system was used, which provides 954 individual sensing elements over a total sensing area of 238.5cm2. A number of small experiments were undertaken to establish appropriate calibration and measurement error. A five-point rating scale was developed, and included within the experimental procedure; to measure user discomfort at the shoulder area where was 'no discomfort' and 5 was 'unbearably uncomfortable'. Following a pilot study the method was shown to produce reliable data that was sensitive to differences in design of load carriage systems within a comparative experimental design. [Continues.

Backbone and side chain H-1, N-15 and C-13 assignments for the oxidised and reduced forms of the oxidoreductase protein DsbA from Staphylococcus aureus

The function and dynamics of the thiol-disulfide oxidoreductase DsbA in the low-GC gram positive bacterium, Staphylococcus aureus, are yet to be elucidated. Here we report 13C, 15N and 1H assignments for the oxidised and reduced forms of SaDsbA as a prelude to further studies on the enzyme