h-deformation of Gr(2)

The $h$-deformation of functions on the Grassmann matrix group $Gr(2)$ is presented via a contraction of $Gr_q(2)$. As an interesting point, we have seen that, in the case of the $h$-deformation, both R-matrices of $GL_h(2)$ and $Gr_h(2)$ are the same

Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur

Tensor Operators for Uh(sl(2))

Tensor operators for the Jordanian quantum algebra Uh(sl(2)) are considered. Some explicit examples of them, which are obtained in the boson or fermion realization, are given and their properties are studied. It is also shown that the Wigner-Eckart's theorem can be extended to Uh(sl(2)).Comment: 11pages, LaTeX, to be published in J. Phys.

Glassy Dynamics of Protein Folding

A coarse grained model of a random polypeptide chain, with only discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues is shown to display stretched exponential relaxation under Metropolis dynamics at low temperatures with the exponent $\beta\simeq 1/4$, in agreement with the best experimental results. The time dependent correlation functions for fluctuations about the native state, computed in the Gaussian approximation for real proteins, have also been found to have the same functional form. Our results indicate that the energy landscape exhibits universal features over a very large range of energies and is relatively independent of the specific dynamics.Comment: RevTeX, 4 pages, multicolumn, including 5 figures; larger computations performed, error bars improve

h-deformation of GL(1|1)

h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL_q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.Comment: latex file, 8 pages, minor change

Duality for Exotic Bialgebras

In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq

Changes in hospital mortality in patients with cancer during the COVID-19 pandemic (ISARIC-CCP-UK):a prospective, multicentre cohort study

BACKGROUND: Patients with cancer are at greater risk of dying from COVID-19 than many other patient groups. However, how this risk evolved during the pandemic remains unclear. We aimed to determine, on the basis of the UK national pandemic protocol, how factors influencing hospital mortality from COVID-19 could differentially affect patients undergoing cancer treatment. We also examined changes in hospital mortality and escalation of care in patients on cancer treatment during the first 2 years of the COVID-19 pandemic in the UK.METHODS: We conducted a prospective cohort study of patients aged older than 19 years and admitted to 306 health-care facilities in the UK with confirmed SARS-CoV-2 infection, who were enrolled in the International Severe Acute Respiratory and emerging Infections Consortium (ISARIC) WHO Clinical Characterisation Protocol (CCP) across the UK from April 23, 2020, to Feb 28, 2022; this analysis included all patients in the complete dataset when the study closed. The primary outcome was 30-day in-hospital mortality, comparing patients on cancer treatment and those without cancer. The study was approved by the South Central-Oxford C Research Ethics Committee in England (Ref: 13/SC/0149) and the Scotland A Research Ethics Committee (Ref 20/SS/0028), and is registered on the ISRCTN Registry (ISRCTN66726260).FINDINGS: 177 871 eligible adult patients either with no history of cancer (n=171 303) or on cancer treatment (n=6568) were enrolled; 93 205 (52·4%) were male, 84 418 (47·5%) were female, and in 248 (13·9%) sex or gender details were not specified or data were missing. Patients were followed up for a median of 13 (IQR 6-21) days. Of the 6568 patients receiving cancer treatment, 2080 (31·7%) died at 30 days, compared with 30 901 (18·0%) of 171 303 patients without cancer. Patients aged younger than 50 years on cancer treatment had the highest age-adjusted relative risk (hazard ratio [HR] 5·2 [95% CI 4·0-6·6], p&lt;0·0001; vs 50-69 years 2·4 [2·2-2·6], p&lt;0·0001; 70-79 years 1·8 [1·6-2·0], p&lt;0·0001; and &gt;80 years 1·5 [1·3-1·6], p&lt;0·0001) but a lower absolute risk (51 [6·7%] of 763 patients &lt;50 years died compared with 459 [30·2%] of 1522 patients aged &gt;80 years). In-hospital mortality decreased for all patients during the pandemic but was higher for patients on cancer treatment than for those without cancer throughout the study period.INTERPRETATION: People with cancer have a higher risk of mortality from COVID-19 than those without cancer. Patients younger than 50 years with cancer treatment have the highest relative risk of death. Continued action is needed to mitigate the poor outcomes in patients with cancer, such as through optimising vaccination, long-acting passive immunisation, and early access to therapeutics. These findings underscore the importance of the ISARIC-WHO pandemic preparedness initiative.FUNDING: National Institute for Health Research and the Medical Research Council.</p

Baseline assessment of WHO's target for both availability and affordability of essential medicines to treat non-communicable diseases

Background: WHO has set a voluntary target of 80% availability of affordable essential medicines, including generics, to treat major non-communicable diseases (NCDs), in the public and private sectors of countries by 2025. We undertook a secondary analysis of data from 30 surveys in low- and middle-income countries, conducted from 2008-2015 using the World Health Organization (WHO)/Health Action International (HAI) medicine availability and price survey methodology, to establish a baseline for this target. Methods Data for 49 medicines (lowest priced generics and originator brands) to treat cardiovascular diseases (CVD), diabetes, chronic obstructive pulmonary diseases (COPD) and central nervous system (CNS) conditions were analysed to determine their availability in healthcare facilities and pharmacies, their affordability for those on low incomes (based on median patient prices of each medicine), and the percentage of medicines that were both available and affordable. Affordability was expressed as the number of days' wages of the lowestpaid unskilled government worker needed to purchase 30 days' supply using standard treatment regimens. Paying more than 1 days' wages was considered unaffordable. Findings In low-income countries, 15.2% and 18.9% of lowest-priced generics met WHO's target in the public and private sectors, respectively, and 2.6% and 5.2% of originator brands. In lower-middle income countries, 23.8% and 23.2% of lowest priced generics, and 0.8% and 1.4% of originator brands, met the target in the public and private sectors, respectively. In upper-middle income countries, the situation was better for generics but still suboptimal as 36.0% and 39.4% met the target in public and private sectors, respectively. For originator brands in upper-middle income countries, none reached the target in the public sector and 13.7% in the private sector. Across the therapeutic groups for lowest priced generics, CVD medicines in low-income countries (11.9%), and CNS medicines in lower-middle (10.2%) and upper-middle income countries (33.3%), were least available and affordable in the public sector. In the private sector for lowest priced generics, CNS medicines were least available and affordable in all three country income groups (11.4%, 5.8% and 29.3% in low-, lower-middle and upper-middle income countries respectively). Interpretation This data, which can act as a baseline for the WHO target, shows low availability and/or poor affordability is resulting in few essential NCD medicines meeting the target in low- and middle-income countries. In the era of Sustainable Development Goals, and as countries work to achieve Universal Health Coverage, increased commitments are needed by governments to improve the situation through the development of evidence-informed, nationallycontextualised interventions, with regular monitoring of NCD medicine availability, patient prices and affordability.IS