Poisson-Lie duals of the eta deformed symmetric space sigma model

Poisson-Lie dualising the eta deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated lambda deformed model. In this paper we investigate when the eta deformed model can be dualised with respect to a subgroup G_0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G_0 is associated to a sub-Dynkin diagram. Additional U_1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the eta deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the eta deformed AdS_5 x S^5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the lambda deformed model are.Comment: 37 pages, v2: minor change

An ultra scale-down analysis of the recovery by dead-end centrifugation of human cells for therapy.

An ultra scale-down method is described to determine the response of cells to recovery by dead-end (batch) centrifugation under commercially defined manufacturing conditions. The key variables studied are the cell suspension hold time prior to centrifugation, the relative centrifugal force (RCF), time of centrifugation, cell pellet resuspension velocities, and number of resuspension passes. The cell critical quality attributes studied are the cell membrane integrity and the presence of selected surface markers. Greater hold times and higher RCF values for longer spin times all led to the increased loss of cell membrane integrity. However, this loss was found to occur during intense cell resuspension rather than the preceding centrifugation stage. Controlled resuspension at low stress conditions below a possible critical stress point led to essentially complete cell recovery even at conditions of extreme centrifugation (e.g., RCF of 10000 g for 30 mins) and long (~2 h) holding times before centrifugation. The susceptibility to cell loss during resuspension under conditions of high stress depended on cell type and the age of cells before centrifugation and the level of matrix crosslinking within the cell pellet as determined by the presence of detachment enzymes or possibly the nature of the resuspension medium. Changes in cell surface markers were significant in some cases but to a lower extent than loss of cell membrane integrity. Biotechnol. Bioeng. 2015;112: 997-1011. © 2014 Wiley Periodicals, Inc

Unifying Requirements and Code: an Example

Requirements and code, in conventional software engineering wisdom, belong to entirely different worlds. Is it possible to unify these two worlds? A unified framework could help make software easier to change and reuse. To explore the feasibility of such an approach, the case study reported here takes a classic example from the requirements engineering literature and describes it using a programming language framework to express both domain and machine properties. The paper describes the solution, discusses its benefits and limitations, and assesses its scalability.Comment: 13 pages; 7 figures; to appear in Ershov Informatics Conference, PSI, Kazan, Russia (LNCS), 201

On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency

Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal verification techniques. Among these, symbolic techniques have been shown to be particularly effective at finding concurrency-related bugs because they can leverage highly optimized decision procedures such as SAT/SMT solvers. This paper gives new fundamental results on partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency. In particular, we give the theoretical basis for a decision procedure that can handle a fragment of concurrent programs endowed with least fixed point operators. In addition, we show that a certain partial order semantics of relaxed sequential consistency is equivalent to the conjunction of three extensively studied weak memory axioms by Alglave et al. An important consequence of this equivalence is an asymptotically smaller symbolic encoding for bounded model checking which has only a quadratic number of partial order constraints compared to the state-of-the-art cubic-size encoding.Comment: 15 pages, 3 figure

Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids

We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.Comment: 16 pages, 2 figure

The Nutritional Content of Main Course Ready-meals Aimed at Children Aged 12 Months to 3 Years

Background: Rapid changes to dietary and lifestyle patterns have transformed the home and food environment with an increased trend towards convenience in home food preparation and ready-meal availability [1]. Despite the widespread use of convenience foods, there is a lack of research into the nutritional quality of convenience foods for young children. This study examined the nutritional content of ready-meals for children aged 12 months to 3 years. The objectives of this study were to (i) investigate the nutritional quality of ready-meals, on sale in the UK market for children aged 12 months to 3 years, comparing their nutrition labelling information to dietary standards, (ii) identify the nutrition claims on the packaging of ready-meals for this age group and (iii) determine whether the nutrition claims identified met European Union legislation. Methods: A sample of main course ready-meals (n=38) marketed to children aged 12 months to 3 years from five brands, available in the UK was assessed. One ready-meal represents only a proportion of energy and nutrients consumed per day, therefore dietary standards were obtained taking 30% of age-appropriate dietary reference values (DRVs). The energy, protein and sodium content of these ready-meals were compared to the calculated dietary standards using one sample t-tests. Descriptive analysis was performed on all nutritional information (energy, carbohydrate, sugars, protein, fat, saturated fat, fibre, sodium and iron) collected. Nutrition claims were validated against legislative requirements [2,3,4]. Results: All ready-meals examined were significantly lower in energy (p=0.000) and higher in protein (p=0.000) compared to the dietary standards. Sodium was significantly higher than the dietary standard in three brands; brand 1 (p=0.000), 3 (p=0.004) and 5 (p=0.03), with brand 5 containing only 65mg less than the DRV (500mg) for total daily allowance. Four of the nutrition claims made across the brands were assessed - “no added salt”, “no added sugar”, “low salt” and “source of iron”. Only brand 1 and 5 did not meet legislation for “no added salt” as the ready-meals contained more than the amount of sodium per 100g permitted. All other nutrition claims conformed to legislative requirements; however the majority of ready-meals from brand 1 did contain ingredients with added salt and/or sugar e.g. mustard or sun-dried tomato, despite claims of “no added salt/sugar” and this could misinform consumers. Discussion: The ready-meals investigated did not meet calculated dietary standards and although the majority of nutrition claims displayed on the packaging did meet legislation, some claims did not and there were claims that could mislead consumers. There is paucity in research into the nutritional quality of convenience foods for young children and therefore comparisons between this study and other work cannot be drawn. Furthermore, since comprehensive dietary standards are unavailable for this age group, it is difficult to fully assess the nutritional adequacy of these ready-meals. Conclusion: The development of nutritional standards and transparent nutrition claim legislation would enable practitioners to fully assess the adequacy of children’s diets and enable consumers to make healthier food choices. Keywords : Children’s ready-meals; convenience foods; nutrition labelling

Quicksort Revisited: Verifying Alternative Versions of Quicksort

© Springer International Publishing Switzerland 2016.We verify the correctness of a recursive version of Tony Hoare’s quicksort algorithm using the Hoare-logic based verification tool Dafny. We then develop a non-standard, iterative version which is based on a stack of pivot-locations rather than the standard stack of ranges. We outline an incomplete Dafny proof for the latter

Bi-η\eta and bi-λ\lambda deformations of Z4\mathbb{Z}_4 permutation supercosets

Integrable string sigma models on AdS$_3$ backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-$\eta$ and bi-$\lambda$ deformations of two classes of $\mathbb{Z}_4$ permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS$_3$ backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-$\lambda$ deformation.Comment: 35 pages, published versio