Solving math problems: Where and why does the solution process go astray?

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The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set

Background Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables. Methods Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set. Results Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001). Conclusions The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy

A proposed integrated multi-signature model for peritidal cycles in carbonates

A new integrated multi-signature model for meter-scale peritidal carbonate cycles presented here is relevant to the interpretation of these cycles in the stratigraphic record. Meter-scale shallowing-upward (micro)facies cycles are the most common type of peritidal parasequence. Peritidal parasequences are a fundamental component of carbonate sequence stratigraphic models. However, the existence of meter-scale cycles in the geological record has been questioned owing to the failure to prove statistically the existence of these cycles using data on (micro)facies and stacking pattern taken from previous studies. Nevertheless, the shallowing-upwards (micro)facies interpretive template remains widely used to identify these cycles and parasequences. We propose that the sedimentary signatures of meter-scale peritidal cycles vary systematically during the various phases of an underlying 3rd-order relative sea-level cycle. Although during specific phases of a 3rd-order relative sea-level cycle meter-scale peritidal cycles may be characterized by shallowing-upward units (e.g., early transgressive systems tract), during other periods the stratigraphic signal of cyclicity may be more cryptic and complex, causing them to be overlooked (e.g., late transgressive systems tract and highstand systems tract). We also propose that there is a half-cycle phase shift in periods of deposition and the formation of drowning surfaces, relative to 4th- to 5th-order relative sea-level cycles, over the course of a 3rd-order relative sea-level cycle. These points have ramifications for defining parasequences and using stacking patterns to determine peritidal cycle periodicity. Specifically, parasequences defined using flooding surfaces identify sedimentary units that inconsistently partition 4th- to 5th-order relative sea-level cycles at different stages of a 3rd-order relative sea-level cycle. We propose testable, new physical stratigraphic signatures for identifying meter-scale cycles that have consistent genetic significance, each cycle recording a relative sea-level cycle characterized by a 4th- to 5th-order relative sea-level rise and fall. Meter-scale peritidal cycles are recorded by an ordered pattern of systematically varying (micro)facies signatures related to their position within a 3rd-order relative sea-level cycle. The integrated multi-signature model of meter-scale peritidal carbonate cycles we propose here may assist in explaining the apparently contradictory evidence both for and against their existence in the geological record. As a result of the detailed consideration in this paper of the nature of parasequences and their variations with 3rd-order relative sea-level changes, a redefinition of parasequence is required and one is presented here

Unravelling the microfacies signatures of parasequences using computer-optimized similarity matrices

The microfacies of a Lower Cretaceous carbonate drillcore from Oman are characterized using optimizing matrices of Jaccard's similarity coefficients of community. Other than systems tract boundaries, there is no obvious evidence of individual parasequences in the core. However, diagnostic patterns in microfossil distribution identify environmental gradients recording changes in water depth. These gradients are used to define individual parasequences, parasequence sets, stacking patterns and key surfaces. The patterns suggest that deposition was controlled by successive fourth- to fifth-order (high-frequency) relative sea-level cycles superimposed on an underlying third-order relative sea-level rise. Although the correlation of these depositional subunits to systematic changes in water depth and the rate of carbonate accumulation alone is not incontrovertible proof of such a sea-level control, concurrent multiorder relative sea-level cyclicity provides by far the most likely explanation. A microfacies deposited when the water depth was shallowing is characterized by a relay of microfossils with affinities that shallow upwards. Conversely, a microfacies that records a gradual increase in water depth has a relay of microfossils with affinities that deepen upwards. Microfacies characterized by an assemblage of microfossils with similar affinities record deposition when the benthic environmental conditions remained stable, either because of an equilibrium between shallow water carbonate deposition and rising sea level, or in deeper water where sediment composition was relatively insensitive to changes of water depth. Microfacies characterized by mixed affinity assemblages record syndepositional reworking. During periods of embedded multiorder sea-level changes, individual parasequences within systems tracts are shown to record more complex environmental gradients than simply the repetition of successive shallowing-up units as traditionally represented in carbonate sequence stratigraphic models. The microfacies of an individual parasequence may shallow up, or may record both deepening-up and shallowing-up depositional phases, as well as periods of sedimentation when benthic environments remained stable. Individual parasequence boundaries may be submarine or subaerial unconformities, or be conformable, as part of a predictable stratigraphic pattern related to the temporal position of an individual parasequence within the underlying third-order cycle of relative sea-level change. The hitherto ubiquitous use of assemblages to describe carbonate microfacies, coupled with the widespread use of the metre-scale shallowing-up template to identify parasequences, may have led to such complexities previously being overlooked