Until unequivocal genetic predictors of CPSP are understood, the authors encourage systematic use of clinical factors for predicting and managing CPSP risk.

Let F be a set of polynomials in the variables x = x 1 , . . . , xn with coefficients in R[a], where R is a UFD and a = a 1 , . . . , am a set of parameters. In this paper we present a new algorithm for discussing Gröbner bases with parameters. The algorithm obtains all the cases over the parameters leading to different reduced Gröbner basis, when the parameters in F are substituted in an extension field K of R. This new algorithm improves Weispfenning's comprehensive Gröbner basis CGB algorithm, obtaining a reduced complete set of compatible and disjoint cases. A final improvement determines the minimal singular variety outside of which the Gröbner basis of the generic case specializes properly. These constructive methods provide a very satisfactory discussion and rich geometrical interpretation in the applications.

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No externally validated presurgical risk score for chronic postsurgical pain (CPSP) is currently available. We tested the generalizability of a six-factor risk model for CPSP developed from a prospective cohort of 2929 patients in 4 surgical settings. Seventeen centers enrolled 1225 patients scheduled for inguinal hernia repair, hysterectomy (vaginal or abdominal), or thoracotomy. The 6 clinical predictors were surgical procedure, younger age, physical health (Short Form Health Survey-12), mental health (Short Form Health Survey-12), preoperative pain in the surgical field, and preoperative pain in another area. Chronic postsurgical pain was confirmed by physical examination at 4 months. The model's discrimination (c-statistic), calibration, and diagnostic accuracy (sensitivity, specificity, and positive and negative likelihood ratios) were calculated to assess geographic and temporal transportability in the full cohort and 2 subsamples (historical and new centers). The full data set after exclusions and losses included 1088 patients; 20.6% had developed CPSP at 4 months. The c-statistics (95% confidence interval) were similar in the full validation sample and the 2 subsamples: 0.69 (0.65-0.73), 0.69 (0.63-0.74), and 0.68 (0.63-0.74), respectively. Calibration was good (slope b and intercept close to 1 and 0, respectively, and nonsignificance in the Hosmer–Lemeshow goodness-of-fit test). The validated model based on 6 clinical factors reliably identifies risk for CPSP risk in about 70% of patients undergoing the surgeries studied, allowing surgeons and anesthesiologists to plan and initiate risk-reduction strategies in routine practice and researchers to screen for risk when randomizing patients in trials.

The survey shows that the management of postoperative pain in hospitals with >200 beds in Spain is suboptimal and this is associated with dissatisfaction among many anaesthesiologists.

The main proposal in this paper is the merging of two techniques that have been recently developed. On the one hand, we consider a new approach for computing some specializable Gröbner basis, the so called Minimal Canonical Comprehensive Gröbner Systems (MCCGS) that is -roughly speaking-a computational procedure yielding "good" bases for ideals of polynomials over a field, depending on several parameters, that specialize "well", for instance, regarding the number of solutions for the given ideal, for different values of the parameters. The second ingredient is related to automatic theorem discovery in elementary geometry. Automatic discovery aims to obtain complementary (equality and inequality type) hypotheses for a (generally false) geometric statement to become true. The paper shows how to use MCCGS for automatic discovering of theorems and gives relevant examples.

In 1992, V. Weispfenning proved the existence of Comprehensive Gröbner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more efficient algorithm (DISPGB) for Discussing Parametric Gröbner Bases. Inspired in its philosophy, V. Weispfenning defined, in 2002, how to obtain a Canonical Comprehensive Gröbner Basis (CCGB) for parametric polynomial ideals, and provided a constructive method.In this paper we use Weispfenning's CCGB ideas to make substantial improvements on Montes DISPGB algorithm. It now includes rewriting of the discussion tree using the Discriminant Ideal and provides a compact and effective discussion. We also describe the new algorithms in the DPGB library containing the improved DISPGB as well as new routines to check whether a given basis is a CGB or not, and to obtain a CGB. Examples and tests are also provided.

The presence of an APS or APMP is associated with better results on indicators of quality of acute postoperative pain management.