The extremal algebra on two hermitians with square 1

Let Ea(u,v) be the extremal algebra determined by two hermitians u and v with u2 = v2 = 1. We show that: Ea(u,v) = {f=gu:f,g ε C(T)}, where T is the unit circle; Ea(u,v) is C*-equivelant to C*(G), where G is the infinite dihedral group; most of the hermitian elements k od Ea(u,v) have the property that kn is hermitian for all odd n but for no even n; any two hermitian words in G generate an isometric copy of Ea(u,v) in Ea(u,v)

Some extremal algebras for hermitians

We study three extremal Banach algebras: (a) generated by two hermitian unitaries; (b) generated by an element of norm 1 all of whose odd positive powers are hermitian; (c) generated by an element of norm 1 all of whose even positive powers are hermitian. In all three cases the numerical range is found for various elements. The second algebra is shown to be isometrically isomorphic to a subalgebra of the first. The third algebra is identified with a space of functions

An Evaluation of Techniques for Sampling Skin Flora

Three methods of sampling skin bacteria were evaluated to determine whether the large differences observed from adjacent areas of the back were real or due to variability in sampling methods. It was found that in addition to actual differences in the skin flora populations of adjacent areas, there were significant differences in populations obtained by different sampling techniques and significant differences between individuals. Equally high bacterial populations were recovered from skin by the Teflon spatula method and the rayon swab method; however, scrubbing with rayon swabs gave the most consistent results

Automatic structures for semigroup constructions

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.Comment: 22 page

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.

Development and external validation of preoperative clinical prediction models for postoperative outcomes including preoperative aerobic fitness in patients approaching elective colorectal cancer surgery

Introduction: Preoperative aerobic fitness is associated with postoperative outcomes after elective colorectal cancer (CRC) surgery. This study aimed to develop and externally validate two clinical prediction models incorporating a practical test to assess preoperative aerobic fitness to distinguish between patients with and without an increased risk for 1) postoperative complications and 2) a prolonged time to in-hospital recovery of physical functioning after elective colorectal cancer (CRC) surgery. Materials and methods: Models were developed using prospective data from 256 patients and externally validated using prospective data of 291 patients. Postoperative complications were classified according to Clavien-Dindo. The modified Iowa level of assistance scale (mILAS) was used to determine time to postoperative in-hospital physical recovery. Aerobic fitness, age, sex, body mass index, American Society of Anesthesiologists (ASA) classification, neoadjuvant treatment, surgical approach, tumour location, and preoperative haemoglobin level were potential predictors. Areas under the curve (AUC), calibration plots, and Hosmer-Lemeshow tests evaluated predictive performance. Results: Aerobic fitness, sex, age, ASA, tumour location, and surgical approach were included in the final models. External validation of the model for complications and postoperative recovery presented moderate to fair discrimination (AUC 0.666 (0.598–0.733) and 0.722 (0.651–0.794), respectively) and good calibration. High sensitivity and high negative predictive values were observed in the lower predicted risk categories (&lt;40 %). Conclusion: Both models identify patients with and without an increased risk of complications or a prolonged time to in-hospital physical recovery. They might be used for improving patient-tailored preoperative risk assessment and targeted and cost-effective application of prehabilitation interventions.</p

Development and external validation of preoperative clinical prediction models for postoperative outcomes including preoperative aerobic fitness in patients approaching elective colorectal cancer surgery

Introduction: Preoperative aerobic fitness is associated with postoperative outcomes after elective colorectal cancer (CRC) surgery. This study aimed to develop and externally validate two clinical prediction models incorporating a practical test to assess preoperative aerobic fitness to distinguish between patients with and without an increased risk for 1) postoperative complications and 2) a prolonged time to in-hospital recovery of physical functioning after elective colorectal cancer (CRC) surgery. Materials and methods: Models were developed using prospective data from 256 patients and externally validated using prospective data of 291 patients. Postoperative complications were classified according to Clavien-Dindo. The modified Iowa level of assistance scale (mILAS) was used to determine time to postoperative in-hospital physical recovery. Aerobic fitness, age, sex, body mass index, American Society of Anesthesiologists (ASA) classification, neoadjuvant treatment, surgical approach, tumour location, and preoperative haemoglobin level were potential predictors. Areas under the curve (AUC), calibration plots, and Hosmer-Lemeshow tests evaluated predictive performance. Results: Aerobic fitness, sex, age, ASA, tumour location, and surgical approach were included in the final models. External validation of the model for complications and postoperative recovery presented moderate to fair discrimination (AUC 0.666 (0.598–0.733) and 0.722 (0.651–0.794), respectively) and good calibration. High sensitivity and high negative predictive values were observed in the lower predicted risk categories (&lt;40 %). Conclusion: Both models identify patients with and without an increased risk of complications or a prolonged time to in-hospital physical recovery. They might be used for improving patient-tailored preoperative risk assessment and targeted and cost-effective application of prehabilitation interventions.</p

Interactions Between Marine Megafauna and Plastic Pollution in Southeast Asia

Southeast (SE) Asia is a highly biodiverse region, yet it is also estimated to cumulatively contribute a third of the total global marine plastic pollution. This threat is known to have adverse impacts on marine megafauna, however, understanding of its impacts has recently been highlighted as a priority for research in the region. To address this knowledge gap, a structured literature review was conducted for species of cartilaginous fishes, marine mammals, marine reptiles, and seabirds present in SE Asia, collating cases on a global scale to allow for comparison, coupled with a regional expert elicitation to gather additional published and grey literature cases which would have been omitted during the structured literature review. Of the 380 marine megafauna species present in SE Asia, but also studied elsewhere, we found that 9.1 % and 4.5 % of all publications documenting plastic entanglement (n = 55) and ingestion (n = 291) were conducted in SE Asian countries. At the species level, published cases of entanglement from SE Asian countries were available for 10 % or less of species within each taxonomic group. Additionally, published ingestion cases were available primarily for marine mammals and were lacking entirely for seabirds in the region. The regional expert elicitation led to entanglement and ingestion cases from SE Asian countries being documented in 10 and 15 additional species respectively, highlighting the utility of a broader approach to data synthesis. While the scale of the plastic pollution in SE Asia is of particular concern for marine ecosystems, knowledge of its interactions and impacts on marine megafauna lags behind other areas of the world, even after the inclusion of a regional expert elicitation. Additional funding to help collate baseline data are critically needed to inform policy and solutions towards limiting the interactions of marine megafauna and plastic pollution in SE Asia