On the minimal free resolution of the universal ring for resolutions of length two

AbstractHochster established the existence of a commutative noetherian ring C˜ and a universal resolution U of the form 0→C˜e→C˜f→C˜g→0 such that for any commutative noetherian ring S and any resolution V equal to 0→Se→Sf→Sg→0, there exists a unique ring homomorphism C˜→S with V=U⊗C˜S. In the present paper we assume that f=e+g and we find the minimal resolution of C˜⊗ZQ by free B-modules, where B is a polynomial ring over the field of rational numbers. The modules of the resolution are described in terms of Schur functors. The graded strands of the differential are described in terms of Pieri maps

Formative evaluation of electricity distribution utilities using data envelopment analysis

The use of Data Envelopment Analysis (DEA) in the electricity distribution sector has been prolific in the number of papers published in research journals. However, while numerous studies have been documented, they have mostly been summative. Their aim has been predominantly descriptive and classificatory. This paper argues that evaluations of a formative nature are more effective than summative studies in promoting a better understanding of the structures and processes of electricity distribution utilities and, consequently, are more appropriate to contribute to performance improvement. To illustrate the use of DEA for formative evaluation, and highlight some of the difficulties of using DEA in practice, this paper compares the cost-efficiency of the Portuguese electricity distribution companies from 2002 to 2006. A dynamic analysis using Malmquist Indices is also conducted in order to evaluate the changes in productivity over this period. Our analysis shows that the application of DEA for formative purposes meets some difficulties. In particular it shows that while the modelling of productivity/efficiency scores using DEA is relatively straightforward, it is comparatively more difficult to develop models that are economically valid and that produce results with face validity. On the basis of the insights derived from this analysis, the paper provides some recommendations regarding the successful application of DEA for performance improvement

Hyperdeterminants as integrable discrete systems

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2x2x2x2-hyperdeterminant.Comment: Standard LaTeX, 11 pages. v2: corrected a small misprint in the abstrac

Non-commutative desingularization of determinantal varieties, I

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.Comment: 52 pages, 3 figures, all comments welcom

747-1 Progression of Aortic Regurgitation Assessed by Doppler Echocardiography in 127 Patients: Degree of Regurgitation

To assess the progression of chronic aortic regurgitation (AR), 127 patients 169 men; 59±21 yr) with AR (59 mild, 8 mild-to-moderate, 41 moderate, 4 moderate-to-severe, 15 severe) who had ≥6 months of follow-up (6–47 months) by color Doppler and 2-D echo were studied. The degree of AR was established at entry and follow-up studies using an algorithm (semi-quantitative) that takes into account several Doppler criteria (jet area and jet height ratios, jet length, pressure half-time, reversal of flow in descending aorta) and the jet height/LV outflow tract (LVOT) height ratio (quantitative). LV volume (Simpson) and LV mass (Devereux) were calculated. A significant increase in jet/LVOT height ratio was observed in the whole population (30±17 vs. 35±20%; p<0.00001) and in the subsets of patients with mild (18±7 vs. 22.3±9%; p<0.01), moderate (40±14 vs. 44±16%; p<0.01) and severe (54±19 vs. 65±15%; p<0.05) AR. An increase in the degree of AR (semi-quantitative) during the follow-up was observed in 38 (30%) of patients: 25% with mild, 37% with mild-to-moderate, 44% with moderate and 50% with moderate-to-severe AR (p<0.006). Patients were further divided according to the rank order in the rate of progression of jet/LVOT height ratio into “progressives” (n=18; rate>5.64%/yr) and “non-progressives” (n=109). Patients with “progressive” AR had a faster rate of progression of LV end-diastolic volume, LV end-systolic volume and LV mass than “non-progressives” (p<0.025).ConclusionsAR is a progressive disease even in patients with mild insufficiency. The progression in the degree of AR is more frequent in patients with more severe disease. The rate of progression of regurgitation appears to playa role in LV overload in patients with AR

Multiple triangulation and collaborative research using qualitative methods to explore decision making in pre-hospital emergency care.

BACKGROUND: Paramedics make important and increasingly complex decisions at scene about patient care. Patient safety implications of influences on decision making in the pre-hospital setting were previously under-researched. Cutting edge perspectives advocate exploring the whole system rather than individual influences on patient safety. Ethnography (the study of people and cultures) has been acknowledged as a suitable method for identifying health care issues as they occur within the natural context. In this paper we compare multiple methods used in a multi-site, qualitative study that aimed to identify system influences on decision making. METHODS: The study was conducted in three NHS Ambulance Trusts in England and involved researchers from each Trust working alongside academic researchers. Exploratory interviews with key informants e.g. managers (n = 16) and document review provided contextual information. Between October 2012 and July 2013 researchers observed 34 paramedic shifts and ten paramedics provided additional accounts via audio-recorded 'digital diaries' (155 events). Three staff focus groups (total n = 21) and three service user focus groups (total n = 23) explored a range of experiences and perceptions. Data collection and analysis was carried out by academic and ambulance service researchers as well as service users. Workshops were held at each site to elicit feedback on the findings and facilitate prioritisation of issues identified. RESULTS: The use of a multi-method qualitative approach allowed cross-validation of important issues for ambulance service staff and service users. A key factor in successful implementation of the study was establishing good working relationships with academic and ambulance service teams. Enrolling at least one research lead at each site facilitated the recruitment process as well as study progress. Active involvement with the study allowed ambulance service researchers and service users to gain a better understanding of the research process. Feedback workshops allowed stakeholders to discuss and prioritise findings as well as identify new research areas. CONCLUSION: Combining multiple qualitative methods with a collaborative research approach can facilitate exploration of system influences on patient safety in under-researched settings. The paper highlights empirical issues, strengths and limitations for this approach. Feedback workshops were effective for verifying findings and prioritising areas for future intervention and research