Realizations of the associahedron and cyclohedron

We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them to the permutahedron of type A_n and B_n respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type A_n or B_n respectively as only input and which specialises to a procedure presented by J.-L. Loday for a certain orientation of A_n. The described realizations have cambrian fans of type A and B as normal fans. This settles a conjecture of N. Reading for cambrian fans of these types.Comment: v2: 18 pages, 7 figures; updated version has revised introduction and updated Section 4; v3: 21 pages, 2 new figures, added statement (b) in Proposition 1.4. and 1.7 plus extended proof; added references [1], [29], [30]; minor changes with respect to presentatio

Faster computation of the Tate pairing

This paper proposes new explicit formulas for the doubling and addition step in Miller's algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in the addition and doubling. Computing the coefficients of the functions and the sum or double of the points is faster than with all previously proposed formulas for pairings on Edwards curves. They are even competitive with all published formulas for pairing computation on Weierstrass curves. We also speed up pairing computation on Weierstrass curves in Jacobian coordinates. Finally, we present several examples of pairing-friendly Edwards curves.Comment: 15 pages, 2 figures. Final version accepted for publication in Journal of Number Theor

Permutahedra and generalized associahedra

AbstractGiven a finite Coxeter system (W,S) and a Coxeter element c, or equivalently an orientation of the Coxeter graph of W, we construct a simple polytope whose outer normal fan is N. Reading's Cambrian fan Fc, settling a conjecture of Reading that this is possible. We call this polytope the c-generalized associahedron. Our approach generalizes Loday's realization of the associahedron (a type A c-generalized associahedron whose outer normal fan is not the cluster fan but a coarsening of the Coxeter fan arising from the Tamari lattice) to any finite Coxeter group. A crucial role in the construction is played by the c-singleton cones, the cones in the c-Cambrian fan which consist of a single maximal cone from the Coxeter fan.Moreover, if W is a Weyl group and the vertices of the permutahedron are chosen in a lattice associated to W, then we show that our realizations have integer coordinates in this lattice

Verification of the code DYN3D for calculations of neutron flux fluctuations

Insufficiently explained magnitudes and patterns of flux fluctuation observed mainly in KWU PWRs are recently investigated by various European institutions. Among the numerical tools used to investigate the\ua0neutron flux\ua0fluctuations is the time-domain reactor dynamics code\ua0DYN3D. As\ua0DYN3D\ua0and comparable codes have not been developed with the primary intention to simulate low-amplitude neutron flux fluctuations, their applicability in this field has to be verified.In order to contribute to the verification of\ua0DYN3D\ua0for the simulation of neutron flux fluctuations, two special cases of perturbations of the neutron flux (a localized absorber of variable/oscillatory strength and a travelling oscillatory perturbation) are considered with\ua0DYN3D\ua0on the one hand and with the frequency-domain neutron noise tool\ua0CORE SIM\ua0as well as analytical frequency-domain approaches, respectively, on the other hand. The obtained results are compared with respect to the distributions of the amplitude and the phase of the induced neutron flux fluctuations. The comparisons are repeated with varied amplitudes and frequencies of the perturbation.The results agree well both qualitatively and quantitatively for each of the conducted calculations. The remaining deviations between the\ua0DYN3D\ua0results and the reference results exhibit a dependence on the perturbation magnitude, which is attributed to the neglect of higher-order terms (linear theory) of the perturbed quantities in the calculation of the reference solutions

A specific Gibberellin 20-oxidase dictates the flowering-runnering decision in diploid strawberry

Asexual and sexual reproduction occur jointly in many angiosperms. Stolons (elongated stems) are used for asexual reproduction in the crop species potato (Solanum tuberosum) and strawberry (Fragaria spp), where they produce tubers and clonal plants, respectively. In strawberry, stolon production is essential for vegetative propagation at the expense of fruit yield, but the underlying molecular mechanisms are unknown. Here, we show that the stolon deficiency trait of the runnerless (r) natural mutant in woodland diploid strawberry (Fragaria vesca) is due to a deletion in the active site of a gibberellin 20-oxidase (GA20ox) gene, which is expressed primarily in the axillary meristem dome and primordia and in developing stolons. This mutation, which is found in all r mutants, goes back more than three centuries. When FveGA20ox4 is mutated, axillary meristems remain dormant or produce secondary shoots terminated by inflorescences, thus increasing the number of inflorescences in the plant. The application of bioactive gibberellin (GA) restored the runnering phenotype in the r mutant, indicating that GA biosynthesis in the axillary meristem is essential for inducing stolon differentiation. The possibility of regulating the runnering-flowering decision in strawberry via FveGA20ox4 provides a path for improving productivity in strawberry by controlling the trade-off between sexual reproduction and vegetative propagation

Politeness for the Theory of Algebraic Datatypes (Extended Abstract)

peer reviewe

Towards in-line determination of EVA Gel Content during PV modules Lamination Processes

Poly (ethylene-co-vinyl acetate) (EVA) is the major polymer used for photovoltaic (PV) modules encapsulation. Its degree of cross-linking (related to its gel content) is taken as a major quality reference. Differential Scanning Calorimetry (DSC) has been proven to be fast and effective but is to determine the gel content, however, destructive for the PV module. With the aim to develop a non-destructive quality assessment tool, a detailed discussion on the DSC thermogram of EVA PV encapsulant is presented here. A possible path towards a fast and non-destructive method for determing EVA gel content is proposed based on the DSC analysis