The implicit construction of multiplicity lists for classes of trees and verification of some conjectures

For the problem of understanding what multiplicities are possible for eigenvalues among real symmetric matrices with a given graph, constructing matrices with conjectured multiplicities is generally more difficult than finding constraining conditions. Here, the implicit function theorem method for constructing matrices with a given graph and given multiplicity list is refined and extended. In particular, the breadth of known circumstances in which the Jacobian is nonsingular is increased. This allows characterization of all multiplicity lists for binary, diametric, depth one trees. In addition the degree conjecture and a conjecture about the minimum number of multiplicities equal to 1 is proven for diametric trees. Finally, an intriguing conjecture about the eigenvalues of a matrix whose graph is a path and its submatrices is given, along with a discussion of some ides that would support a proof of the degree conjecture and the minimum number of 1\u27s conjecture, in general. (c) 2012 Elsevier Inc. All rights reserved

Acute pain pathways:protocol for a prospective cohort study

INTRODUCTION: Opioid analgesics are often used to treat moderate-to-severe acute non-cancer pain; however, there is little high-quality evidence to guide clinician prescribing. An essential element to developing evidence-based guidelines is a better understanding of pain management and pain control among individuals experiencing acute pain for various common diagnoses. METHODS AND ANALYSIS: This multicentre prospective observational study will recruit 1550 opioid-naïve participants with acute pain seen in diverse clinical settings including primary/urgent care, emergency departments and dental clinics. Participants will be followed for 6 months with the aid of a patient-centred health data aggregating platform that consolidates data from study questionnaires, electronic health record data on healthcare services received, prescription fill data from pharmacies, and activity and sleep data from a Fitbit activity tracker. Participants will be enrolled to represent diverse races and ethnicities and pain conditions, as well as geographical diversity. Data analysis will focus on assessing patients’ patterns of pain and opioid analgesic use, along with other pain treatments; associations between patient and condition characteristics and patient-centred outcomes including resolution of pain, satisfaction with care and long-term use of opioid analgesics; and descriptive analyses of patient management of leftover opioids. ETHICS AND DISSEMINATION: This study has received approval from IRBs at each site. Results will be made available to participants, funders, the research community and the public. TRIAL REGISTRATION NUMBER: NCT04509115

Trees and the Implicit Construction of Eigenvalue Multiplicities

Our ultimate goal is to find the possible eigenvalue multiplicity lists which can occur among Hermitian matrices whose graph is a given tree (no restriction is placed on diagonal entries). We expand the implicit construction method pioneered by Johnson et al. to find all multiplicity lists for binary, diametric, depth-one trees, as well as provide an upper bound for the minimum number of 1's among multiplicity lists for a given tree

Economic evaluation of quality improvement interventions to prevent catheter-associated urinary tract infections in the hospital setting: a systematic review.

BACKGROUND: Hospitals have implemented diverse quality improvement (QI) interventions to reduce rates of catheter-associated urinary tract infections (CAUTIs). The economic value of these QI interventions is uncertain. OBJECTIVE: To systematically review economic evaluations of QI interventions designed to prevent CAUTI in acute care hospitals. METHODS: A search of Ovid MEDLINE, Econlit, Centre for Reviews & Dissemination, New York Academy of Medicines Grey Literature Report, WorldCat, IDWeek conference abstracts and prior systematic reviews was conducted from January 2000 to October 2020.We included English-language studies of any design that evaluated organisational or structural changes to prevent CAUTI in acute care hospitals, and reported programme and infection-related costs.Dual reviewers assessed study design, effectiveness, costs and study quality. For each eligible study, we performed a cost-consequences analysis from the hospital perspective, estimating the incidence rate ratio (IRR) and incremental net cost/savings per hospital over 3 years. Unadjusted weighted regression analyses tested predictors of these measures, weighted by catheter days per study. RESULTS: Fifteen unique economic evaluations were eligible, encompassing 74 hospitals. Across 12 studies amenable to standardisation, QI interventions were associated with a 43% decline in infections (mean IRR 0.57, 95% CI 0.44 to 0.70) and wide ranges of net costs (mean US$52 000, 95$288 000 to $392 000), relative to usual care. CONCLUSIONS: QI interventions were associated with large declines in infection rates and net costs to hospitals that varied greatly but that, on average, were not significantly different from zero over 3 years. Future research should examine specific practices associated with cost-savings and clinical effectiveness, and examine whether or not more comprehensive interventions offer hospitals and patients the best value