Connected quantized Weyl algebras and quantum cluster algebras

For an algebraically closed field K, we investigate a class of noncommutative K-algebras called connected quantized Weyl algebras. Such an algebra has a PBW basis for a set of generators {x1,…,xn} such that each pair satisfies a relation of the form xixj=qijxjxi+rij, where ⁎ qij∈K⁎ and rij∈K, with, in some sense, sufficiently many pairs for which rij≠0. For such an algebra it turns out that there is a single parameter q such that each qij=q±1. Assuming that q≠±1, we classify connected quantized Weyl algebras, showing that there are two types linear and cyclic. When q is not a root of unity we determine the prime spectra for each type. The linear case is the easier, although the result depends on the parity of n, and all prime ideals are completely prime. In the cyclic case, which can only occur if n is odd, there are prime ideals for which the factors have arbitrarily large Goldie rank. We apply connected quantized Weyl algebras to obtain presentations of two classes of quantum cluster algebras. Let n≥3 be an odd integer. We present the quantum cluster algebra of a Dynkin quiver of type An−1 as a factor of a linear connected quantized Weyl algebra by an ideal generated by a central element. We also consider the quiver Pn+1(1) identified by Fordy and Marsh in their analysis of periodic quiver mutation. When n is odd, we show that the quantum cluster algebra of this quiver is generated by a cyclic connected quantized Weyl algebra in n variables and one further generator. We also present it as the factor of an iterated skew polynomial algebra in n+2 variables by an ideal generated by a central element. For both classes, the quantum cluster algebras are simple noetherian. We establish Poisson analogues of the results on prime ideals and quantum cluster algebras. We determine the Poisson prime spectra for the semiclassical limits of the linear and cyclic connected quantized Weyl algebras and show that, when n is odd, the cluster algebras of An−1 and Pn+1(1) are simple Poisson algebras that can each be presented as a Poisson factor of a polynomial algebra, with an appropriate Poisson bracket, by a principal ideal generated by a Poisson central element

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

UK Public Sector Information and Re-use Policy – A 2008 Analysis

INTRODUCTION: Earlier antiretroviral therapy (ART) initiation reduces HIV-1 incidence. This benefit may be offset by increased transmitted drug resistance (TDR), which could limit future HIV treatment options. We analyze the epidemiological impact and cost-effectiveness of strategies to reduce TDR. METHODS: We develop a deterministic mathematical model representing Kampala, Uganda, to predict the prevalence of TDR over a 10-year period. We then compare the impact on TDR and cost-effectiveness of: (1) introduction of pre-therapy genotyping; (2) doubling use of second-line treatment to 80% (50-90%) of patients with confirmed virological failure on first-line ART; and (3) increasing viral load monitoring from yearly to twice yearly. An intervention can be considered cost-effective if it costs less than three times the gross domestic product per capita per quality adjusted life year (QALY) gained, or less than $3420 in Uganda. RESULTS: The prevalence of TDR is predicted to rise from 6.7$1612 to $2234 (IQR$450-dominated) per QALY gained. CONCLUSIONS: While earlier treatment initiation will result in a predicted increase in the proportion of patients infected with drug-resistant HIV, the absolute numbers of patients infected with drug-resistant HIV is predicted to decrease. Increasing use of second-line treatment to all patients with confirmed failure on first-line therapy is a cost-effective approach to reduce TDR. Improving access to second-line ART is therefore a major priority

Influence of a Random Telegraph Process on the Transport through a Point Contact

We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitioning noise and the (classical) noise due to the two-level fluctuator. As a side result, we obtain the full counting statistics of a quantum point contact with time-dependent transmission probabilities.Comment: 8 pages, 2 figure; a new section about experiments and a figure showing the crossover from sub- to superpoissonian noise have been adde

Comparison of trunk muscle exercises in supine position during short arm centrifugation with 1 g at centre of mass and upright in 1 g

Spaceflight is associated with reduced antigravitational muscle activity, which results in trunk muscle atrophy and may contribute to post-flight postural and spinal instability. Exercise in artificial gravity (AG) performed via short-arm human centrifugation (SAHC) is a promising multi-organ countermeasure, especially to mitigate microgravity-induced postural muscle atrophy. Here, we compared trunk muscular activity (mm. rectus abdominis, ext. obliques and multifidi), cardiovascular response and tolerability of trunk muscle exercises performed during centrifugation with 1 g at individual center of mass on a SAHC against standard upright exercising. We recorded heart rate, blood pressure, surface trunk muscle activity, motion sickness and rating of perceived exertion (BORG) of 12 participants (8 male/4 female, 34 ± 7 years, 178.4 ± 8.2 cm, 72.1 ± 9.6 kg). Heart rate was significantly increased (p < 0.001) during exercises without differences in conditions. Systolic blood pressure was higher (p < 0.001) during centrifugation with a delayed rise during exercises in upright condition. Diastolic blood pressure was lower in upright (p = 0.018) compared to counter-clockwise but not to clockwise centrifugation. Target muscle activation were comparable between conditions, although activity of multifidi was lower (clockwise: p = 0.003, counter-clockwise: p < 0.001) and rectus abdominis were higher (clockwise: p = 0.0023, counter-clockwise: < 0.001) during centrifugation in one exercise type. No sessions were terminated, BORG scoring reflected a relevant training intensity and no significant increase in motion sickness was reported during centrifugation. Thus, exercising trunk muscles during centrifugation generates comparable targeted muscular and heart rate response and appears to be well tolerated. Differences in blood pressure were relatively minor and not indicative of haemodynamic challenge. SAHC-based muscle training is a candidate to reduce microgravity-induced inter-vertebral disc pathology and trunk muscle atrophy. However, further optimization is required prior to performance of a training study for individuals with trunk muscle atrophy/dysfunction

Certified Athletic Trainers' knowledge and perceptions of posttraumatic osteoarthritis after knee injury

Context: Posttraumatic osteoarthritis (PTOA) is a specific phenotype of osteoarthritis (OA) that commonly develops after acute knee injury, such as anterior cruciate ligament (ACL) or meniscal injury (or both). Athletic trainers (ATs) are well positioned to educate patients and begin PTOA management during rehabilitation of the acute injury, yet it remains unknown if ATs currently prioritize long-term outcomes in patients with knee injury. Objective: To investigate ATs' knowledge and perceptions of OA and its treatment after ACL injury, ACL reconstruction, or meniscal injury or surgery. Design: Cross-sectional study. Patients or Other Participants: An online survey was administered to 2000 randomly sampled certified ATs. We assessed participants' perceptions of knee OA, the risk of PTOA after ACL or meniscal injury or surgery, and therapeutic management of knee OA. Results: Of the 437 ATs who responded (21.9%), the majority (84.7%) correctly identified the definition of OA, and 60.3% indicated that they were aware of PTOA. A high percentage of ATs selected full meniscectomy (98.9%), meniscal tear (95.4%), ACL injury (90.2%), and partial meniscectomy (90.1%) as injuries that would increase the risk of developing OA. Athletic trainers rated undertaking strategies to prevent OA development in patients after ACL injury or reconstruction (73.8%) or meniscal injury or surgery (74.7%) as extremely or somewhat important. Explaining the risk of OA to patients with an ACL or meniscal injury was considered appropriate by 98.8% and 96.8% of respondents, respectively; yet a lower percentage reported that they actually explained these risks to patients after an ACL (70.8%) or meniscal injury (80.6%). Conclusions: Although 84.7% of ATs correctly identified the definition of OA, a lower percentage (60.3%) indicated awareness of PTOA. These results may reflect the need to guide ATs on how to educate patients regarding the long-term risks of ACL and meniscal injuries and how to implement strategies that may prevent PTOA

New Magnetic Anomaly Map of the Antarctic

The second generation Antarctic magnetic anomaly compilation for the region south of 60 degrees S includes some 3.5 million line-km of aeromagnetic and marine magnetic data that more than doubles the initial map's near-surface database. For the new compilation, the magnetic data sets were corrected for the International Geomagnetic Reference Field, diurnal effects, and high-frequency errors and leveled, gridded, and stitched together. The new magnetic data further constrain the crustal architecture and geological evolution of the Antarctic Peninsula and the West Antarctic Rift System in West Antarctica, as well as Dronning Maud Land, the Gamburtsev Subglacial Mountains, the Prince Charles Mountains, Princess Elizabeth Land, and Wilkes Land in East Antarctica and the circumjacent oceanic margins. Overall, the magnetic anomaly compilation helps unify disparate regional geologic and geophysical studies by providing new constraints on major tectonic and magmatic processes that affected the Antarctic from Precambrian to Cenozoic times.Korea Polar Research Institute (KOPRI) programs, PM15040 and PE17050Germany's AWI/Helmholtz Center for Polar and Marine ResearchFederal Institute for Geosciences and Natural ResourcesBritish Antarctic Survey/Natural Environmental Research CouncilItalian Antarctic Research ProgrammeRussian Ministry of Natural ResourcesU.S. National Science Foundation and National Space and Aeronautics AdministrationAustralian Antarctic Division and Antarctic Climate & Ecosystem Cooperative Research CentreFrench Polar InstituteGlobal geomagnetic observatories network (INTERMAGNET

Effects of short-term hypercaloric nutrition on orthostatic tolerance in healthy individuals: a randomized controlled crossover study

Reduced-caloric intake lowers blood pressure through sympathetic inhibition, and worsens orthostatic tolerance within days. Conversely, hypercaloric nutrition augments sympathetic activity and blood pressure. Because dietary interventions could be applied in patients with syncope, we tested the hypothesis that short-term hypercaloric dieting improves orthostatic tolerance. In a randomized crossover trial, 20 healthy individuals (7 women, 26.7 ± 8 years, 22.6 ± 2 kg/m²) followed a 4-day hypercaloric (25% increase of energy intake by fat) or normocaloric nutritional plan, with a washout period of at least 23 days between interventions. We then performed head-up tilt table testing with incremental lower body negative pressure while recording beat-by-beat blood pressure and heart rate. The primary endpoint was orthostatic tolerance defined as time to presyncope. Time to presyncope during combined head-up tilt and lower body negative pressure did not differ between hypercaloric and normocaloric dieting (median 23.19 versus 23.04 min, ratio of median 1.01, 95% CI of ratio 0.5-1.9). Heart rate, blood pressure, heart rate variability, and blood pressure variability in the supine position and during orthostatic testing did not differ between interventions. We conclude that 4 days of moderate hypercaloric nutrition does not significantly improve orthostatic tolerance in healthy individuals. Nevertheless, given the important interaction between energy balance and cardiovascular autonomic control in the brain, caloric intake deserves more attention as a potential contributor and treatment target for orthostatic intolerance

Search for venous endothelial biomarkers heralding venous thromboembolism in space: a qualitative systematic review of terrestrial studies

Background: The recent discovery of a venous thrombosis in the internal jugular vein of an astronaut has highlighted the need to predict the risk of venous thromboembolism in otherwise healthy individuals (VTE) in space. Virchow's triad defines the three classic risk factors for VTE: blood stasis, hypercoagulability, and endothelial disruption/dysfunction. Among these risk factors, venous endothelial disruption/dysfunction remains incompletely understood, making it difficult to accurately predict risk, set up relevant prophylactic measures and initiate timely treatment of VTE, especially in an extreme environment. Methods: A qualitative systematic review focused on endothelial disruption/dysfunction was conducted following the guidelines produced by the Space Biomedicine Systematic Review Group, which are based on Cochrane review guidelines. We aimed to assess the venous endothelial biochemical and imaging markers that may predict increased risk of VTE during spaceflight by surveying the existing knowledge base surrounding these markers in analogous populations to astronauts on the ground. Results: Limited imaging markers related to endothelial dysfunction that were outside the bounds of routine clinical practice were identified. While multiple potential biomarkers were identified that may provide insight into the etiology of endothelial dysfunction and its link to future VTE, insufficient prospective evidence is available to formally recommend screening potential astronauts or healthy patients with any currently available novel biomarker. Conclusion: Our review highlights a critical knowledge gap regarding the role biomarkers of venous endothelial disruption have in predicting and identifying VTE. Future population-based prospective studies are required to link potential risk factors and biomarkers for venous endothelial dysfunction to occurrence of VTE