Rhombic Tilings of Polygons and Classes of Reduced Words in Coxeter Groups

AbstractIn the standard Coxeter presentation, the symmetric groupSnis generated by the adjacent transpositions (1, 2), (2, 3), …, (n−1, n). For any given permutation, we consider all minimal-length factorizations thereof as a product of the generators. Any two transpositions (i, i+1) and (j, j+1) commute if the numbersiandjare not consecutive; thus, in any factorization, their order can be switched to obtain another factorization of the same permutation. Extending this to an equivalence relation, we establish a bijection between the resulting equivalence classes and rhombic tilings of a certain 2n-gon determined by the permutation. We also study the graph structure induced on the set of tilings by the other Coxeter relations. For a special case, we use lattice-path diagrams to prove an enumerative conjecture by Kuperberg and Propp, as well as aq-analogue thereof. Finally, we give similar constructions for two other families of finite Coxeter groups, namely those of typesBandD

A Health System Analysis Approach to Health Outcomes in Medicare Clients With Chronic Illnesses

Since 1863, outcomes measurement efforts have provided information to health care consumers, administrators, and policymakers in assessing concerns about access, quality and costs. With a growing population of older adults with chronic illnesses, cost-cutting strategies in health delivery systems, and federal endorsement of managed care systems, researchers have begun to evaluate the impact of different delivery system organizations on health. The current study combines two areas of health services research to provide the first published hierarchical analysis of the influence of delivery system factors, and a profile of population and community characteristics and utilization factors, on perceived health outcomes of a nationally representative sample of older adult Medicare beneficiaries with various chronic illnesses. This study was designed to analyze the difference in health status outcomes across Medicare fee-for-service and health maintenance organization systems nationwide, and to explain health delivery system factors\u27 effects on outcomes. Using a recently developed health outcomes classification scheme, a newly expanded Andersen and Aday Health System Model, and hierarchical multiple regression analysis methodology, health delivery system factors were found to have a significant impact on three of four client-centered outcome measures. The results of this study suggest there are health delivery system factors affecting health outcomes of older adults with chronic illnesses. In addition, the findings imply that hierarchical regression analysis is a useful tool for explaining the unique contribution of several individual variables as well as several blocks of variables on perceived health outcomes. Information from this study can be used to monitor outcomes of health care in this vulnerable population, inform development of chronic illness-related health policy, and encourage use of high quality public data resources available for health services research

Application of a disease-specific mapping function to estimate utility gains with effective treatment of schizophrenia

BACKGROUND: Most tools for estimating utilities use clinical trial data from general health status models, such as the 36-Item Short-Form Health Survey (SF-36). A disease-specific model may be more appropriate. The objective of this study was to apply a disease-specific utility mapping function for schizophrenia to data from a large, 1-year, open-label study of long-acting risperidone and to compare its performance with an SF-36-based utility mapping function. METHODS: Patients with schizophrenia or schizoaffective disorder by DSM-IV criteria received 25, 50, or 75 mg long-acting risperidone every 2 weeks for 12 months. The Positive and Negative Syndrome Scale (PANSS) and SF-36 were used to assess efficacy and health-related quality of life. Movement disorder severity was measured using the Extrapyramidal Symptom Rating Scale (ESRS); data concerning other common adverse effects (orthostatic hypotension, weight gain) were collected. Transforms were applied to estimate utilities. RESULTS: A total of 474 patients completed the study. Long-acting risperidone treatment was associated with a utility gain of 0.051 using the disease-specific function. The estimated gain using an SF-36-based mapping function was smaller: 0.0285. Estimates of gains were only weakly correlated (r = 0.2). Because of differences in scaling and variance, the requisite sample size for a randomized trial to confirm observed effects is much smaller for the disease-specific mapping function (156 versus 672 total subjects). CONCLUSION: Application of a disease-specific mapping function was feasible. Differences in scaling and precision suggest the clinically based mapping function has greater power than the SF-36-based measure to detect differences in utility

Interaction of a vortex pair with a free surface.

The trailing vortices generated by the control planes of submarines give rise to surface signatures in the form of scars and striations. Two counter-rotating vortices were generated in a novel experimental system and their interaction with the free surface was investigated. In addition, the governing equations have been solved through the use of the boundary-element method for a representative Froude number. The results have been expressed in terms of the depth of submergence of the vortices, their mutual induction velocity, and the initial vortex separation. It has been shown that the free surface begins to deform when the vortices are at a distance of about one initial vortex separation from the free surface. The height of the maximum deformation is attained at a normalized time of about 0.1, when the vortices are at a distance of about 0.5 bₒ from the free surface. The elevated part of the surface is bounded by two scars, whose motion is slaved to that of the vortices.http://archive.org/details/interactionofvor00elniLieutenant, United States NavyApproved for public release; distribution is unlimited

Lessons Learned in Pilot Testing Specialty Consultations to Benefit Individuals with Lower Limb Loss

Telerehabilitation technologies enable the delivery of rehabilitation services from providers to people with disabilities as well as specialty care consultations. This article discusses the barriers experienced when planning and pilot testing a telerehabilitation multi-site specialty consultation for specialists in their medical centers, and the lessons learned. The barriers included integration and participation, coordination across organizational units, and privacy and information security. Lessons learned included the need for collaboration across multiple departments, telerehabilitation equipment back-ups, and anonymous and private communication protocols. Despite delays resulting from coordination at multiple levels of a national organization, we developed a program plan and successfully implemented a pilot test of the southeast region program.  Specialty consultation using telerehabilitation delivery methods requires identifying provider preferences for technological features. Lessons learned could inform development of outpatient telerehabilitation for patients with amputations and studies of patients and providers involved in telerehabilitation

Generalized Integer Partitions, Tilings of Zonotopes and Lattices

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory. We show that the sets of partitions ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of zonotopes, ordered with a simple and classical dynamics, is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical systems exist. These results give a better understanding of the behaviour of tilings of zonotopes with flips and dynamical systems involving partitions.Comment: See http://www.liafa.jussieu.fr/~latapy

Documentation of in-hospital falls on incident reports: Qualitative investigation of an imperfect process

<p>Abstract</p> <p>Background</p> <p>Incident reporting is the prevailing approach to gathering data on accidental falls in hospitals for both research and quality assurance purposes, though is of questionable quality as staff time pressures, perception of blame and other factors are thought to contribute to under-reporting.</p> <p>Methods</p> <p>This research aimed to identify contextual factors influencing recording of in-hospital falls on incident reports. A qualitative multi-centre investigation using an open written response questionnaire was undertaken. Participants were asked to describe any factors that made them feel more or less likely to record a fall on an incident report. 212 hospital staff from 30 wards in 7 hospitals in Queensland, Australia provided a response. A framework approach was employed to identify and understand inter-relationships between emergent categories.</p> <p>Results</p> <p>Three main categories were developed. The first, determinants of reporting, describes a hierarchical structure of primary (principle of reporting), secondary (patient injury), and tertiary determinants that influenced the likelihood that an in-hospital fall would be recorded on an incident report. The tertiary determinants frequently had an inconsistent effect. The second and third main categories described environmental/cultural facilitators and barriers respectively which form a background upon which the determinants of reporting exists.</p> <p>Conclusion</p> <p>A distinctive framework with clear differences to recording of other types of adverse events on incident reports was apparent. Providing information to hospital staff regarding the purpose of incident reporting and the usefulness of incident reporting for preventing future falls may improve incident reporting practices.</p

Aquatic insects dealing with dehydration: do desiccation resistance traits differ in species with contrasting habitat preferences?

Background Desiccation resistance shapes the distribution of terrestrial insects at multiple spatial scales. However, responses to drying stress have been poorly studied in aquatic groups, despite their potential role in constraining their distribution and diversification, particularly in arid and semi-arid regions. Methods We examined desiccation resistance in adults of four congeneric water beetle species (Enochrus, family Hydrophilidae) with contrasting habitat specificity (lentic vs. lotic systems and different salinity optima from fresh- to hypersaline waters). We measured survival, recovery capacity and key traits related to desiccation resistance (fresh mass, % water content, % cuticle content and water loss rate) under controlled exposure to desiccation, and explored their variability within and between species. Results Meso- and hypersaline species were more resistant to desiccation than freshwater and hyposaline ones, showing significantly lower water loss rates and higher water content. No clear patterns in desiccation resistance traits were observed between lotic and lentic species. Intraspecifically, water loss rate was positively related to specimens’ initial % water content, but not to fresh mass or % cuticle content, suggesting that the dynamic mechanism controlling water loss is mainly regulated by the amount of body water available. Discussion Our results support previous hypotheses suggesting that the evolution of desiccation resistance is associated with the colonization of saline habitats by aquatic beetles. The interespecific patterns observed in Enochrus also suggest that freshwater species may be more vulnerable than saline ones to drought intensification expected under climate change in semi-arid regions such as the Mediterranean Basin