Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation

Building on our previous works on perturbative solutions to a Schwinger-Dyson for the massless Wess-Zumino model, we show how to compute 1/n corrections to its asymptotic behavior. The coefficients are analytically determined through a sum on all the poles of the Mellin transform of the one loop diagram. We present results up to the fourth order in 1/n as well as a comparison with numerical results. Unexpected cancellations of zetas are observed in the solution, so that no even zetas appear and the weight of the coefficients is lower than expected, which suggests the existence of more structure in the theory.Comment: 16 pages, 2 figures. Some points clarified, typos corrected, matches the version to be published in Lett. Math. Phy

Integrable mappings and polynomial growth

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds of transformations on $q \times q$ matrices: the inversion of the $q \times q$ matrix and an (involutive) permutation of the entries of the matrix. We concentrate on the case where these permutations are elementary transpositions of two entries. In this case the birational transformations fall into six different classes. For each class we analyze the factorization properties of the iteration of these transformations. These factorization properties enable to define some canonical homogeneous polynomials associated with these factorization properties. Some mappings yield a polynomial growth of the complexity of the iterations. For three classes the successive iterates, for $q=4$, actually lie on elliptic curves. This analysis also provides examples of integrable mappings in arbitrary dimension, even infinite. Moreover, for two classes, the homogeneous polynomials are shown to satisfy non trivial non-linear recurrences. The relations between factorizations of the iterations, the existence of recurrences on one or several variables, as well as the integrability of the mappings are analyzed.Comment: 45 page

On-farm influence of production patterns on total polyphenol content in peach

Peach production in France is constantly confronted with marketing problems due to a decrease in fruit consumption and increasing competition with neighbouring Mediterranean countries. The production of higher quality products using production methods such as organic farming (OF) appears to be a tangible way of differentiating and enhancing peach production. To test this hypothesis, an on-farm study was conducted in one of the major production areas in South-eastern France. Focussing on the peach cultivar, cv. Spring Lady®, paired comparisons were conducted between plots in OF and conventional farming (CF). Farmers' practices were identified and checked against crop measurements and performances (yield, sugar content, size classes) in 2004 (12 plots) and in 2005 (10 plots). Polyphenol contents were assessed as an additional component of fruit quality, using the Folin-Ciocalteu colorimetric method. Organic peaches have a higher polyphenol content at harvest. Contents were 4.8 times higher in 2004, whereas the same phenomenon was not observed in 2005. Levels of nitrogen, yield and tree vigour management appeared to be the key elements responsible for the synthesis of total polyphenols and sugar content This implies new opportunities for improving the nutritional quality of peaches, based on production methods

A comment on free-fermion conditions for lattice models in two and more dimensions

We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions.Comment: 12 pages, plain Late

Relationships between social forms of organic horticultural production and indicators of environmental quality: a multidimensional approach in Brazil

Organic farming (OF) is increasingly considered as a possible alternative for designing a "new rural" in Brazil, where OF covers a wide range of production and certification systems. However, the ways small farmers adopt OF in green belts to meet an urban demand in organic vegetables have not been extensively investigated. Likewise, the impact of such practices on environmental quality components has not been sufficiently documented. Our objective was to relate forms of organisation to environmental assessment in a watershed where organic horticulture significantly contributes to landscape and water quality. We showed how small farmers were organised or how they organised themselves to meet urban demands and develop OF. We assumed that associated practices were consistent with environmental impacts, as evaluated by indicators. Based on interviews with stakeholders, we identified four forms of organisation and associated farmers' practices. We related them to environmental assessment in three compartments: landscape ecology, water quality and soil quality. Although organisations share some objectives, namely with regard to visual quality and the "right price" of products, differences appear in their scope and internal operation, their values and relationships with consumers, and their technical and environmental contents. As for technical content, input supply, planning processes and crop diversity vary among organisations, ranging from liberal to hierarchical. Our results also showed similarities and differences among various organisations in terms of environmental impact. Such results are interpreted and discussed in the light of technical and social dimensions that account for the progressive design of new systems in Brazil

Quantitative Analysis of Data from Participatory Methods in Plant Breeding

Although participatory plant breeding is gaining greater acceptance worldwide, the techniques needed to assess it are not well known. The papers in this volume address the three themes of the workshop: designing and analyzing joint experiments involving variety evaluation by farmers; identifying and analyzing farmers' evaluations of crop characteristics and varieties; and dealing with social heterogeneity and other research issues

Steady state fluctuation relations for systems driven by an external random force

We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever. We determine the corresponding probability density functions for different random forcing amplitudes ranging from a small fraction to several times the amplitude of the thermal noise. In both systems for sufficiently weak forcing amplitudes the work fluctuations satisfy the usual steady state fluctuation theorem. As the forcing amplitude drives the system far from equilibrium, deviations of the fluctuation theorem increase monotonically. The deviations can be recasted to a single master curve which only depends on the kind of stochastic external force.Comment: 6 pages, submitted to EP

On the Symmetries of Integrability

We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition $q^n=1$ so often mentioned in the theory of quantum groups, when no $q$ parameter is available.Comment: 23 page

A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution

We map the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model in the Borel plane, where the product of functions get mapped to a convolution product. The two-point function can be expressed as a superposition of general powers of the external momentum. The singularities of the anomalous dimension are shown to lie on the real line in the Borel plane and to be linked to the singularities of the Mellin transform of the one-loop graph. This new approach allows us to enlarge the reach of previous studies on the expansions around those singularities. The asymptotic behavior at infinity of the Borel transform of the solution is beyond the reach of analytical methods and we do a preliminary numerical study, aiming to show that it should remain bounded.Comment: 21 pages, 2 figures, use Tikz New version includes corrections asked by refere