Noncommutative Uncertainty Principles

The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We prove the Hausdorff-Young inequality, Young's inequality, the Hirschman-Beckner uncertainty principle, the Donoho-Stark uncertainty principle. We characterize the minimizers of the uncertainty principles. We also prove that the minimizer is uniquely determined by the supports of itself and its Fourier transform. The proofs take the advantage of the analytic and the categorial perspectives of subfactor planar algebras. Our method to prove the uncertainty principles also works for more general cases, such as Popa's $\lambda$-lattices, modular tensor categories etc.Comment: 41 pages, 71 figure

Removal of pharmaceutical residues by Ferrate(VI)

BACKGROUND: Pharmaceuticals and their metabolites are inevitably emitted into the waters. The adverse environmental and human health effects of pharmaceutical residues in water could take place under a very low concentration range; from several µg/L to ng/L. These are challenges to the global water industries as there is no unit process specifically designed to remove these pollutants. An efficient technology is thus sought to treat these pollutants in water and waste water. METHODOLOGY/MAJOR RESULTS: A novel chemical, ferrate, was assessed using a standard jar test procedure for the removal of pharmaceuticals. The analytical protocols of pharmaceuticals were standard solid phase extraction together with various instrumentation methods including LC-MS, HPLC-UV and UV/Vis spectroscopy. Ferrate can remove more than 80% of ciprofloxacin (CIP) at ferrate dose of 1 mg Fe/L and 30% of ibuprofen (IBU) at ferrate dose of 2 mg Fe/L. Removal of pharmaceuticals by ferrate was pH dependant and this was in coordinate to the chemical/physical properties of pharmaceuticals. Ferrate has shown higher capability in the degradation of CIP than IBU; this is because CIP has electron-rich organic moieties (EOM) which can be readily degraded by ferrate oxidation and IBU has electron-withdrawing groups which has slow reaction rate with ferrate. Promising performance of ferrate in the treatment of real waste water effluent at both pH 6 and 8 and dose range of 1-5 mg Fe/L was observed. Removal efficiency of ciprofloxacin was the highest among the target compounds (63%), followed by naproxen (43%). On the other hand, n-acetyl sulphamethoxazole was the hardest to be removed by ferrate (8% only). CONCLUSIONS: Ferrate is a promising chemical to be used to treat pharmaceuticals in waste water. Adjusting operating conditions in terms of the properties of target pharmaceuticals can maximise the pharmaceutical removal efficiency

Survival of AIDS Patients Treated with Traditional Chinese Medicine in Rural Central China: A Retrospective Cohort Study, 2004–2012

This study aimed to explore the survival of AIDS patients treated with traditional Chinese medicine (TCM) in addition to combined antiretroviral therapy (cART) and of AIDS patients treated with cART. Data of patients taking cART between 30 October 2003 and 30 October 2004 in the National TCM HIV Treatment Trial Program area were retrospectively analyzed, with follow-up from 30 October 2004 to 30 October 2012. The log-rank test was used to compare survival between the two groups. A Cox proportional hazards model was used to determine hazard ratios to identify prognostic factors. The study included 521 patients in the TCM + cART group followed up for 3548 person-years and 375 patients in the cART group followed up for 2523 person-years. Mortality rates were 3.2/100 person-years and 4.2/100 person-years in the TCM + cART and cART groups, respectively. The difference in survival was significant. After adjusting for explanatory variables, the mortality rate of AIDS patients in the cART group was 1.7 times higher than in the TCM + cART group. Male sex, older age, little education, and lower CD4 cell count were risk factors for mortality. TCM intervention in addition to cART could increase survival of AIDS patients

Denosumab, teriparatide and bisphosphonates for glucocorticoid-induced osteoporosis: a Bayesian network meta-analysis

Background: Several medications have been used for glucocorticoids-induced osteoporosis (GIO). However, the best therapeutic option for GIO is still controversial. A Bayesian network meta-analysis was conducted to compare the efficacy and safety of denosumab, teriparatide and bisphosphonates for patients with GIO.Methods: Relevant randomized controlled trials published in PubMed, Embase, Cochrane Library and ClinicalTrials.gov up to August 2023 were searched. The following efficiency and safety outcomes were extracted for comparison: bone mineral density (BMD) percentage changes in lumbar spine, femur neck and total hip, and incidences of adverse events (AEs), serious adverse events (SAEs), vertebrae and non-vertebrae fracture. Bayesian random effects models were used for multiple treatment comparisons.Results: 11 eligible RCTs involving 2,877 patients were identified. All the six medications including alendronate, risedronate, etidronate, zoledronate, teriparatide, and denosumab and were effective in increasing BMD. Teriparatide and denosumab were more effective in improving lumbar spine and femur neck BMD, and reducing vertebrae fracture. Alendronate and denosumab were more effective in improving total hip BMD. Alendronate and teriparatide had the lowest incidences of AEs and SAEs.Conclusion: Teriparatide denosumab and the bisphosphonates are all effective in improving BMD for GIO patients. Based on this network meta-analysis, teriparatide and denosumab have higher efficiency in improving lumbar spine and femur neck BMD, and reducing vertebrae fracture.Systematic Review Registration:10.17605/OSF.IO/2G8YA, identifier CRD42023456305