Generating functions for Wilf equivalence under generalized factor order

Kitaev, Liese, Remmel, and Sagan recently defined generalized factor order on words comprised of letters from a partially ordered set $(P, \leq_P)$ by setting $u \leq_P w$ if there is a subword $v$ of $w$ of the same length as $u$ such that the $i$-th character of $v$ is greater than or equal to the $i$-th character of $u$ for all $i$. This subword $v$ is called an embedding of $u$ into $w$. For the case where $P$ is the positive integers with the usual ordering, they defined the weight of a word $w = w_1\ldots w_n$ to be $\text{wt}(w) = x^{\sum_{i=1}^n w_i} t^{n}$, and the corresponding weight generating function $F(u;t,x) = \sum_{w \geq_P u} \text{wt}(w)$. They then defined two words $u$ and $v$ to be Wilf equivalent, denoted $u \backsim v$, if and only if $F(u;t,x) = F(v;t,x)$. They also defined the related generating function $S(u;t,x) = \sum_{w \in \mathcal{S}(u)} \text{wt}(w)$ where $\mathcal{S}(u)$ is the set of all words $w$ such that the only embedding of $u$ into $w$ is a suffix of $w$, and showed that $u \backsim v$ if and only if $S(u;t,x) = S(v;t,x)$. We continue this study by giving an explicit formula for $S(u;t,x)$ if $u$ factors into a weakly increasing word followed by a weakly decreasing word. We use this formula as an aid to classify Wilf equivalence for all words of length 3. We also show that coefficients of related generating functions are well-known sequences in several special cases. Finally, we discuss a conjecture that if $u \backsim v$ then $u$ and $v$ must be rearrangements, and the stronger conjecture that there also must be a weight-preserving bijection $f: \mathcal{S}(u) \rightarrow \mathcal{S}(v)$ such that $f(u)$ is a rearrangement of $u$ for all $u$.Comment: 23 page

LET’S GET MOVING TO REDUCE FALLS: NURSES INCREASE PATIENT MOBILIZATION AFTER BRIEF TRAINING

BACKGROUND: Patients in hospitals are at a high risk for falls. There are many reasons for this, but one common reason is that patients in hospitals spend a lot of time being inactive. The less time patients spend being mobile, the less capable they are of maintaining mobility and the more likely they are to fall. During the first two years of the COVID-19 pandemic, Wildcat Hospital experience their fall rates increase two- to three-fold on inpatient units. METHODS: This quality improvement project was guided by the Plan, Do, Study, Act (PDSA) framework to improve nurse knowledge of mobility and falls data, the importance of patient mobilization, and the implementation of this knowledge. A pre- and post-intervention survey (Appendix A) was used to determine the efficacy of the intervention. INTERVENTIONS: A brief educational presentation informed nurses and nursing aids of national and unit-specific hospital falls data. The presentation also covered primary reasons why patients fall in hospitals and how increasing patient mobilization can benefit patients and reduce the occurrence of falls. Methods of incorporating mobility into existing practice were also offered. RESULTS: Nursing staff scored dramatically better on most of the topics that were covered in the brief presentation. Scores on many of the topics that were not addressed remained generally unchanged or had limited improvement. CONCLUSION: Nurses were able to learn most of the information that was presented in the 5-minute presentation while minimizing the impacts on nurses and patients. The acquisition of knowledge also indicates that nurses were more likely to utilize the information to encourage and assist patients to mobilize more frequently. Increasing mobilization has been shown to improve patient health and reduce falls. Future studies should assess the effectiveness of brief presentations on the number of times patients are mobilized and the impact on fall rates

Victims of the same destiny : Italy in the postcolonial, the postcolonial in Italy

PhD ThesisThis thesis concentrates on a series of canonical Italian anti-Fascist writers, and argues that their work is informed and underpinned by an engagement with colonialism. Working between Italian and English, the thesis establishes an original framework for comparative reading, in which it traces neglected lines of literary influence and networks of intellectual and political dialogue between Italian and Indian writers in the inter-war and post-war periods. The first chapter explores the contours of the ‘anti-colonial imagination’ underpinning the work of Italian Marxist Antonio Gramsci. Focusing particularly on his lesser-known and often un-translated pre-prison writings, it suggests that the critical terminology for which he has become best known in postcolonial studies emerges as part of his gradual elaboration of an anti-colonial position. The second chapter looks at the ways in which Ignazio Silone’s novel Fontamara represents Fascism as a form of internal colonialism, before moving on to think about the significance of its influence on Raja Rao’s Kanthapura and what the implications of this line of influence might be for our understanding of what defines postcolonial writing. The third chapter turns to the work of Carlo Levi, and argues that his lifelong commitment to exposing the internal colonization of the Italian South forms part of a broader anti-colonial commitment that carries him to India and brings him into dialogue with writers like Mulk Raj Anand. Finally, the fourth chapter charts the remarkably pervasive yet critically neglected textual relationship between Italo Calvino and Salman Rushdie, and argues that Rushdie’s postcolonial aesthetics emerge partly through his readings and re-workings of Calvino. Taken together, these four cases tell us much about how a certain trajectory of Italian anti-Fascist writing laboured towards what we might think of as forms of anti-colonial and postcolonial thought. Simultaneously, they invite us to ask questions about the unseen role that these writers have played in shaping our sense of what it means for writing to be ‘postcolonial’.Arts and Humanities Research Counci

A Decomposition of the Pure Parsimony Problem

We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NP-Hard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models

A Cross-Sectional Study of the Impact of Standardized Tobacco Packaging Legislation on University Students

Background: European Union and national legislation implemented from May 2016 mean that from May 2017 all tobacco products in the United Kingdom must be sold in standardized packs without external branding and with prominent graphic health warnings. This study investigates the level of awareness and acceptability of the legislation in students during the implementation period, and how the legislation may impact on student perceptions of pack attributes, health warning effectiveness, student smokers' willingness to pay for cigarette packs, and intentions to quit.Methods: An online survey link was e-mailed to randomly selected University of Nottingham students in autumn 2016. Descriptive statistics and multivariate logistic regression models were used to investigate awareness, acceptability, and potential quitting behavior.Results: 546 students (175 smokers, 371 nonsmokers) responded. Very few of students had seen a standardized pack. Smokers were more likely to be aware of the new legislation than non-smokers. More smokers noticed the warnings on standardized packs than on branded ones. Fewer smokers were willing to pay current prices for standardized packs than for 20 branded packs. Just under half of smokers anticipated quitting in response to the new legislation, with those who smoke infrequently being more likely to anticipate quitting than daily smokers.Conclusions: Few students had seen a standardized pack, suggesting that the level of implementation of the legislation was low five to six months into the implementation period. However, the findings suggest that the legislation has the potential to increase quitting behavior in smoking students

Big Cwatsets and Hamming Code

In contrast to Lagrange\u27s Theorem in Finite Group Theory, we show that the ratio of the largest proper cwatset of degree d to the size of binary d-space approaches 1 as d approaches infinity. We show how to explicitly construct large cwatsets as cosets of Hamming Codes, and discuss many open questions that arise

Relative age in the school year and risk of mental health problems in childhood, adolescence, and young adulthood

Purpose Relative age within the school year (‘relative age’) is associated with increased rates of symptoms and diagnoses of mental health disorders, including ADHD. We aimed to investigate how relative age influences mental health and behaviour before, during and after school (age range: 4–25 years). Method We used a regression discontinuity design to examine the effect of relative age on risk of mental health problems using data from a large UK population-based cohort (Avon Longitudinal Study of Parents and Children (ALSPAC); N = 14,643). We compared risk of mental health problems between ages 4 and 25 years using the parent-rated Strengths and Difficulties Questionnaire (SDQ), and depression using self-rated and parent-rated Short Mood and Feelings Questionnaire (SMFQ) by relative age. Results The youngest children in the school year have greater parent-rated risk of mental health problems, measured using parent-rated SDQ total difficulties scores. We found no evidence of differences before school entry [estimated standardised mean difference (SMD) between those born on 31 August and 1 September: .02 (−.05, .08)]. We found that estimates of effect size for a 1-year difference in relative age were greatest at 11 years [SMD: .22 (.15, .29)], but attenuated to the null at 25 years [SMD: −.02 (−.11, .07)]. We did not find consistent evidence of differences in self-rated and parent-rated depression by relative age. Conclusions Younger relative age is associated with poorer parent-rated general mental health, but not symptoms of depression

NCAM: a surface marker for human small cell lung cancer cells

Immunocytochemical and immunochemical techniques were used to study the expression of the neural cell adhesion molecule (NCAM) by human lung cancer cell lines. Intense surface staining for NCAM was found at light and electron microscopic levels on small cell lung cancer cells. The NCAM polypeptide of Mr 140000 (NCAM 140) was detected by immunoblotting in all of 7 small cell lung cancer cell lines examined and in one out of two of the closely related large cell cancer cell lines: it was not detected in cell lines obtained from one patient with a mesothelioma, in two cases of adenocarcinoma, nor in two cases of squamous cell cancer. In contrast, neuron-specific enolase was found by immunoblotting in all the lung cancer cell lines tested and synaptophysin in all but the adenocarcinoma cell lines. These antigens were localized intracellularly. The specific expression of NCAM 140 by human small and large cell lung carcinomas suggests its potential as a diagnostic marker

The impact of cafeteria feeding during lactation in the rat on novel object discrimination in the offspring

There is increasing evidence that hyperenergetic diets impact on memory in rodents. However, it is largely unknown how diets, such as a cafeteria diet (CD), that mimic a Western diet act on learning and memory, in particular when fed during early stages of development. Here, we fed lactating dams a cafeteria diet and exposed both male and female offspring to a novel object discrimination (NOD) task, a two-trial test of recognition memory in which rats exposed to two identical objects during a training/familiarisation trial can discriminate a novel from a familiar object during the subsequent choice trial. The choice trial was performed following inter-trial interval (ITI) delays of up to 4 h. Maternal diet did not impact on exploration of the objects by either sex during the familiarisation trial. Control males discriminated the novel from the familiar object indicating intact memory with an ITI of 1h, but not 2 or 4h. CD delayed this natural forgetting in male rats such that discrimination was also evident after a 2h ITI. In contrast, control females exhibited discrimination following both 1 and 2h ITIs, but CD impaired performance. In summary, the present study shows that maternal exposure to CD programmes NOD in the adult. In better performing females dietary programming interferes with NOD whereas NOD was improved in males after lactational CD feeding