From modular invariants to graphs: the modular splitting method

28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determined.International audienceWe start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9

Eating Pattern Response to a Low-Fat Diet Intervention and Cardiovascular Outcomes in Normotensive Women: The Women's Health Initiative.

BackgroundWomen without cardiovascular disease (CVD) or hypertension at baseline assigned to intervention in the Women's Health Initiative Dietary Modification (DM) trial experienced 30% lower risk of coronary heart disease (CHD), whereas results in women with hypertension or prior CVD could have been confounded by postrandomization use of statins.ObjectivesIntervention participants reported various self-selected changes to achieve the 20% total fat goals. Reviewed are intervention compared with comparison group HRs for CHD, stroke, and total CVD in relation to specific dietary changes in normotensive participants.MethodsDietary change was assessed by comparing baseline with year 1 FFQ data in women (n = 10,371) without hypertension or CVD at baseline with intake of total fat above the median to minimize biases due to use of the FFQ in trial eligibility screening.ResultsIntervention participants self-reported compensating reduced energy intake from total fat by increasing carbohydrate and protein. Specifically they increased plant protein, with those in the upper quartile (increased total protein by ≥3.3% of energy) having a CHD HR of 0.39 (95% CI: 0.22, 0.71), compared with 0.92 (95% CI: 0.57, 1.48) for those in the lower quartile of change (decreased total protein ≥0.6% of energy), with P-trend of 0.04. CHD HR did not vary significantly with change in percentage energy from carbohydrate, and stroke HR did not vary significantly with any macronutrient changes. Scores reflecting adherence to recommended dietary patterns including the Dietary Approaches to Stop Hypertension Trial and the Healthy Eating Index showed favorable changes in the intervention group.ConclusionsIntervention group total fat reduction replaced with increased carbohydrate and some protein, especially plant-based protein, was related to lower CHD risk in normotensive women without CVD who reported high baseline total fat intake. This trial was registered at clinicaltrials.gov as NCT00000611. Link to the WHI trial protocol: https://www.whi.org/about/SitePages/Dietary%20Trial.aspx

Phase behavior of reverse poloxamers and poloxamines in water

The phase behavior of two types of poly(ethylene oxide)/ poly(propylene oxide) (PEO/PPO) copolymers in aqueous solutions was studied by light scattering, viscometry and infrared spectroscopy. Both the reverse poloxamer (Pluronic 10R5) and the star type poloxamine (Tetronic 90R4) have practically the same PEO/PPO ratio with their hydrophobic blocks (PPO) located in the outer part. The temperature-composition phase diagrams show that both 10R5 and 90R4 tend to form aggregates in water. Up to four different phases can be detected in the case of Tetronic 90R4 for each temperature: unimers, random networks, micellar networks and macrophase separation. Viscometric and infrared measurements complemented the results obtained by light scattering and visual inspection

Non-covalent hydrogels of cyclodextrins and poloxamines for the controlled release of proteins

Different types of gels were prepared by combining poloxamines (Tetronic), i.e. poly(ethylene oxide)/poly(propylene oxide) (PEO/PPO) octablock star copolymers, and cyclodextrins (CD). Two different poloxamines with the same molecular weight (ca. 7000) but different molecular architectures were used. For each of their four diblock arms, direct Tetronic 904 presents PEO outer blocks while in reverse Tetronic 90R4 the hydrophilic PEO blocks are the inner ones. These gels were prepared by combining α-CD and poloxamine aqueous solutions. The physicochemical properties of these systems depend on several factors such as the structure of the block copolymers and the Tetronic/α-CD ratio. These gels were characterized using differential scanning calorimetry (DSC), viscometry and X-ray diffraction measurements. The 90R4 gels present a consistency that makes them suitable for sustained drug delivery. The resulting gels were easily eroded: these complexes were dismantled when placed in a large amount of water, so controlled release of entrapped large molecules such as proteins (Bovine Serum Albumin, BSA) is feasible and can be tuned by varying the copolymer/CD ratio

Self-assembled supramolecular gels of reverse poloxamers and cyclodextrins

A series of supramolecular aggregates were prepared using a poly(propylene oxide)-poly(ethylene oxide)-poly(propylene oxide) (PPO-PEO-PPO) block copolymer and β- or α-cyclodextrins (CD). The combination of β-CD and the copolymer yields inclusion complexes (IC) with polypseudorotaxane structures. These are formed by complexation of the PPO blocks with β-CD molecules producing a powder precipitate with a certain crystallinity degree that can be evaluated by X-ray diffraction (XRD). In contrast, when combining α-CD with the block copolymer, the observed effect is an increase in the viscosity of the mixtures yielding fluid gels. Two cooperative effects come into play: the complexation of PEO blocks with α-CD and the hydrophobic interactions between PPO blocks in aqueous media. These two combined interactions lead to the formation of a macromolecular network. The resulting fluid gels were characterized using different techniques such as differential scanning calorimetry (DSC), viscometry and XRD measurements