Quantum groups, non-commutative Lorentzian spacetimes and curved momentum spaces

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Quantum groups and noncommutative spacetimes with cosmological constant

Abstract Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum groups is reviewed. In this approach the quantum deformation parameter z is related to a Planck scale, and the cosmological constant plays the role of a second deformation parameter of geometric nature, whose limit Λ → 0 provides the corresponding noncommutative Minkowski spacetimes

Quantum groups and noncommutative spacetimes with cosmological constant

8th International Workshop DICE2016: Spacetime - Matter - Quantum Mechanics 12–16 September 2016, Castiglioncello, ItalyNoncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum groups is reviewed. In this approach the quantum deformation parameter z is related to a Planck scale, and the cosmological constant Λ plays the role of a second deformation parameter of geometric nature, whose limit Λ → 0 provides the corresponding noncommutative Minkowski spacetimes.Ministerio de Econom´ıa y Competitividad (MINECO, Spain) under grants MTM2013-43820-P and MTM2016-79639-P, by Junta de Castilla y Le´on (Spain) under grants BU278U14 and VA057U16 and by the Action MP1405 QSPACE from the European Cooperation in Science and Technology (COST

Curved momentum spaces from quantum groups with cosmological constant

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanish-ing cosmological constant . In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1 +1)and (2 +1)dimensions is explicitly constructed as a dual Poisson–Lie group manifold parametrized by . Such momentum space includes both the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit →0, where hyperbolic momenta decouple from translational mo-menta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3 +1)-dimensional ones.A.B., I.G-S and F.J.H. have been partially supported by Ministerio de Economía y Competitividad (MINECO, Spain) under grants MTM2013-43820-P and MTM2016-79639-P (AEI/FEDER, UE), by Junta de Castilla y León (Spain) under grants BU278U14 and VA057U16 and by the Action MP1405 QSPACE from the European Cooperation in Science and Technology (COST). G.G. acknowledges support from the John Templeton Foundation through grant Nr. 4763

Dietary α‐Linolenic Acid, Marine ω‐3 Fatty Acids, and Mortality in a Population With High Fish Consumption: Findings From the PREvención con DIeta MEDiterránea (PREDIMED) Study

Background: Epidemiological evidence suggests a cardioprotective role of α‐linolenic acid (ALA), a plant‐derived ω‐3 fatty acid. It is unclear whether ALA is beneficial in a background of high marine ω‐3 fatty acids (long‐chain n‐3 polyunsaturated fatty acids) intake. In persons at high cardiovascular risk from Spain, a country in which fish consumption is customarily high, we investigated whether meeting the International Society for the Study of Fatty Acids and Lipids recommendation for dietary ALA (0.7% of total energy) at baseline was related to all‐cause and cardiovascular disease mortality. We also examined the effect of meeting the society's recommendation for long‐chain n‐3 polyunsaturated fatty acids (≥500 mg/day). Methods and Results: We longitudinally evaluated 7202 participants in the PREvención con DIeta MEDiterránea (PREDIMED) trial. Multivariable‐adjusted Cox regression models were fitted to estimate hazard ratios. ALA intake correlated to walnut consumption (r=0.94). During a 5.9‐y follow‐up, 431 deaths occurred (104 cardiovascular disease, 55 coronary heart disease, 32 sudden cardiac death, 25 stroke). The hazard ratios for meeting ALA recommendation (n=1615, 22.4%) were 0.72 (95% CI 0.56–0.92) for all‐cause mortality and 0.95 (95% CI 0.58–1.57) for fatal cardiovascular disease. The hazard ratios for meeting the recommendation for long‐chain n‐3 polyunsaturated fatty acids (n=5452, 75.7%) were 0.84 (95% CI 0.67–1.05) for all‐cause mortality, 0.61 (95% CI 0.39–0.96) for fatal cardiovascular disease, 0.54 (95% CI 0.29–0.99) for fatal coronary heart disease, and 0.49 (95% CI 0.22–1.01) for sudden cardiac death. The highest reduction in all‐cause mortality occurred in participants meeting both recommendations (hazard ratio 0.63 [95% CI 0.45–0.87]). Conclusions: In participants without prior cardiovascular disease and high fish consumption, dietary ALA, supplied mainly by walnuts and olive oil, relates inversely to all‐cause mortality, whereas protection from cardiac mortality is limited to fish‐derived long‐chain n‐3 polyunsaturated fatty acids. Clinical Trial Registration URL: http://www.Controlled-trials.com/. Unique identifier: ISRCTN35739639

Curved momentum spaces from quantum groups with cosmological constant

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant Λ. In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is explicitly constructed as a dual Poisson–Lie group manifold parametrized by Λ. Such momentum space includes both the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit Λ→0, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3+1)-dimensional ones

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Dietary α-linolenic acid, marine ω-3 fatty acids, and mortality in a population with high fish consumption: Findings from the PREvención con DIeta MEDiterránea (PREDIMED) Study

12 Páginas.-- 6 Tablas.-- 1 FiguraBackground-Epidemiological evidence suggests a cardioprotective role of α-linolenic acid (ALA), a plant-derived ω-3 fatty acid. It is unclear whether ALA is beneficial in a background of high marine ω-3 fatty acids (long-chain n-3 polyunsaturated fatty acids) intake. In persons at high cardiovascular risk from Spain, a country in which fish consumption is customarily high, we investigated whether meeting the International Society for the Study of Fatty Acids and Lipids recommendation for dietary ALA (0.7% of total energy) at baseline was related to all-cause and cardiovascular disease mortality. We also examined the effect of meeting the society's recommendation for long-chain n-3 polyunsaturated fatty acids (≥500 mg/day). Methods and Results-We longitudinally evaluated 7202 participants in the PREvención con DIeta MEDiterránea (PREDIMED) trial. Multivariable-adjusted Cox regressionmodels were fitted to estimate hazard ratios. ALA intake correlated towalnut consumption (r=0.94). During a 5.9-y follow-up, 431 deaths occurred (104 cardiovascular disease, 55 coronary heart disease, 32 sudden cardiac death, 25 stroke). The hazard ratios formeeting ALArecommendation (n=1615, 22.4%) were 0.72 (95% CI 0.56-0.92) for all-causemortality and 0.95 (95% CI 0.58-1.57) for fatal cardiovascular disease. The hazard ratios formeeting the recommendation for long-chain n-3 polyunsaturated fatty acids (n=5452, 75.7%) were 0.84 (95% CI 0.67-1.05) for all-causemortality, 0.61 (95% CI 0.39-0.96) for fatal cardiovascular disease, 0.54 (95% CI 0.29-0.99) for fatal coronary heart disease, and 0.49 (95% CI 0.22-1.01) for sudden cardiac death. The highest reduction in all-cause mortality occurred in participants meeting both recommendations (hazard ratio 0.63 [95% CI 0.45-0.87]). Conclusions-In participants without prior cardiovascular disease and high fish consumption, dietary ALA, supplied mainly by walnuts and olive oil, relates inversely to all-cause mortality, whereas protection from cardiac mortality is limited to fish-derived long-chain n-3 polyunsaturated fatty acids.This study was funded in part by Instituto de Salud Carlos III (ISCIII) (Spanish Ministry of Economy) through grants RTIC G03/140, RTIC RD 06/0045, Centro Nacional de Investigaciones Cardiovasculares CNIC 06/2007, ISCIII FIS PS09/01292, the Spanish Ministry of Science and Innovation (MICINN) AGL2010‐22319‐C03‐02 and AGL2009‐13906‐C02‐02, and an unrestricted grant from the California Walnut Commission. Sala‐Vila holds a Miguel Servet I fellowship from the Ministry of Economy and Competitiveness through the ISCIII

Prediction of Cardiovascular Disease by the Framingham‐REGICOR Equation in the High‐Risk PREDIMED Cohort: Impact of the Mediterranean Diet Across Different Risk Strata

Background: The usefulness of cardiovascular disease (CVD) predictive equations in different populations is debatable. We assessed the efficacy of the Framingham‐REGICOR scale, validated for the Spanish population, to identify future CVD in participants, who were predefined as being at high‐risk in the PREvención con DIeta MEDiterránea (PREDIMED) study—a nutrition‐intervention primary prevention trial—and the impact of adherence to the Mediterranean diet on CVD across risk categories. Methods and Results: In a post hoc analysis, we assessed the CVD predictive value of baseline estimated risk in 5966 PREDIMED participants (aged 55–74 years, 57% women; 48% with type 2 diabetes mellitus). Major CVD events, the primary PREDIMED end point, were an aggregate of myocardial infarction, stroke, and cardiovascular death. Multivariate‐adjusted Cox regression was used to calculate hazard ratios for major CVD events and effect modification from the Mediterranean diet intervention across risk strata (low, moderate, high, very high). The Framingham‐REGICOR classification of PREDIMED participants was 25.1% low risk, 44.5% moderate risk, and 30.4% high or very high risk. During 6‐year follow‐up, 188 major CVD events occurred. Hazard ratios for major CVD events increased in parallel with estimated risk (2.68, 4.24, and 6.60 for moderate, high, and very high risk), particularly in men (7.60, 13.16, and 15.85, respectively, versus 2.16, 2.28, and 3.51, respectively, in women). Yet among those with low or moderate risk, 32.2% and 74.3% of major CVD events occurred in men and women, respectively. Mediterranean diet adherence was associated with CVD risk reduction regardless of risk strata (P>0.4 for interaction). Conclusions: Incident CVD increased in parallel with estimated risk in the PREDIMED cohort, but most events occurred in non–high‐risk categories, particularly in women. Until predictive tools are improved, promotion of the Mediterranean diet might be useful to reduce CVD independent of baseline risk

Legume consumption is inversely associated with type 2 diabetes incidence in adults: A prospective assessment from the PREDIMED study

Background & aims: Legumes, a low-energy, nutrient-dense and low glycemic index food, have shown beneficial effects on glycemic control and adiposity. As such, legumes are widely recommended in diabetic diets, even though there is little evidence that their consumption protects against type 2 diabetes. Therefore the aim of the present study was to examine the associations between consumption of total legumes and specific subtypes, and type 2 diabetes risk. We also investigated the effect of theoretically substituting legumes for other protein- or carbohydrate-rich foods. Methods: Prospective assessment of 3349 participants in the PREvención con DIeta MEDiterránea (PREDIMED) study without type 2 diabetes at baseline. Dietary information was assessed at baseline and yearly during follow-up. We used Cox regression models to estimate hazard ratios (HRs) and 95% confidence intervals (95% CIs) for type-2 diabetes incidence according to quartiles of cumulative average consumption of total legumes, lentils, chickpeas, dry beans and fresh peas. Results: During a median follow-up of 4.3 years, 266 new cases of type 2 diabetes occurred. Individuals in the highest quartile of total legume and lentil consumption had a lower risk of diabetes than those in the lowest quartile (HR: 0.65; 95% CI: 0.43, 0.96; P-trend = 0.04; and HR: 0.67; 95% CI: 0.46–0.98; P-trend = 0.05, respectively). A borderline significant association was also observed for chickpeas consumption (HR 0.68; 95% CI: 0.46, 1.00; P-trend = 0.06). Substitutions of half a serving/day of legumes for similar servings of eggs, bread, rice or baked potato was associated with lower risk of diabetes incidence. Conclusions: A frequent consumption of legumes, particularly lentils, in the context of a Mediterranean diet, may provide benefits on type 2 diabetes prevention in older adults at high cardiovascular risk. Trial registration: The trial is registered at http://www.controlled-trials.com (ISRCTN35739639). Registration date: 5th October 2005.The authors disclose no conflict of interest related with the article. Centro de Investigación Biomédica en Red Fisiopatología de la Obesidad y Nutrición (CIBEROBN) is an initiative of the Instituto de Salud Carlos III (ISCIII) of Spain which is supported by FEDER funds (CB06/03). Supported by the official funding agency for biomedical research of the Spanish government, ISCIII, through grants provided to research networks specifically developed for the trial (RTIC G03/140 and RD 06/0045) through CIBEROBN, and by grants from Centro Nacional de Investigaciones Cardiovasculares (CNIC 06/2007), Fondo de Investigación Sanitaria–FondoEuropeo de Desarrollo Regional (PI04–2239, PI05/2584, CP06/00100, PI07/0240, PI07/1138, PI07/0954, PI 07/0473, PI10/01407, PI10/02658, PI11/01647, and PI11/02505; PI13/00462), Ministerio de Ciencia e Innovación (AGL-2009–13906-C02 and AGL2010–22319-C03), Fundación Mapfre 2010, Consejería de Salud de la Junta de Andalucía (PI0105/2007), Public Health Division of the Department of Health of the Autonomous Government of Catalonia, Generalitat Valenciana (ACOMP06109, GVA-COMP2010–181, GVACOMP2011–151, CS2010-AP-111, and CS2011-AP-042), and the Navarra Regional Government (27/2011). The Fundación Patrimonio Comunal Olivarero and Hojiblanca SA (Málaga, Spain), California Walnut Commission (Sacramento, CA), Borges SA (Reus, Spain), and Morella Nuts SA (Reus, Spain) donated the olive oil, walnuts, almonds, and hazelnuts, respectively, used in the study. None of the funding sources played a role in the design, collection, analysis or interpretation of the data or in the decision to submit the manuscript for publication. Acknowledgements: The authors thank all the participants for their collaboration, all the PREDIMED personnel for their assistance and all the personnel of affiliated primary care centers for making the study possible. CIBEROBN is an initiative of ISCIII, Spain.Peer Reviewe