The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional perspective provides the most natural extension to exhibit the role of these discrete functions as matrix elements that appear at the very foundation of the modern theory of classical discrete orthogonal polynomials. Here we present 2D and 1D recursion relations that are useful for the direct computation of the orthonormal 6j, which we name U. We present a convention for the order of the arguments of the 6j that is based on their classical and Regge symmetries, and a detailed investigation of new geometrical aspects of the 6j symbols. Specifically we compare the geometric recursion analysis of Schulten and Gordon with the methods of this paper. The 1D recursion relation, written as a matrix diagonalization problem, permits an interpretation as a discrete Schr\"odinger-like equations and an asymptotic analysis illustrates semiclassical and classical limits in terms of Hamiltonian evolution.Comment: 14 pages,9 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior

The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.Comment: 14 pages, 8 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Application

Effects of various levels of organic acids and of virginiamycin on performance, blood parameters, immunoglobulins and microbial population of broiler chicks

This experiment was conducted to investigate the effects of various levels of organic acids and virginiamycin on performance, blood parameters, immunoglobulin and microbial population of broiler chickens. This trial was conducted in a completely randomized design using five treatments and four replicates. The dietary treatments included a control diet without additives, diets containing 0.05%, 0.10% and 0.15% mixtures of organic acids, and a diet containing virginiamycin as an antibiotic. Based on the results, there was no significant effect of the experimental diets on feed intake of the broilers during the starter period. However, at the end of the grower period and throughout the rearing period, feed intake was significantly improved by experimental dietary treatments. Moreover, diets including organic acids enhanced the microbial population of broiler gut. Thus, the current findings support the conclusion that organic acids improve productive traits and health status in broiler chickens.Keywords: Broiler, growth, haematology, gu

Exact and asymptotic computations of elementary spin networks: classification of the quantum-classical boundaries

Increasing interest is being dedicated in the last few years to the issues of exact computations and asymptotics of spin networks. The large-entries regimes (semiclassical limits) occur in many areas of physics and chemistry, and in particular in discretization algorithms of applied quantum mechanics. Here we extend recent work on the basic building block of spin networks, namely the Wigner 6j symbol or Racah coefficient, enlightening the insight gained by exploiting its self-dual properties and studying it as a function of two (discrete) variables. This arises from its original definition as an (orthogonal) angular momentum recoupling matrix. Progress also derives from recognizing its role in the foundation of the modern theory of classical orthogonal polynomials, as extended to include discrete variables. Features of the imaging of various regimes of these orthonormal matrices are made explicit by computational advances -based on traditional and new recurrence relations- which allow an interpretation of the observed behaviors in terms of an underlying Hamiltonian formulation as well. This paper provides a contribution to the understanding of the transition between two extreme modes of the 6j, corresponding to the nearly classical and the fully quantum regimes, by studying the boundary lines (caustics) in the plane of the two matrix labels. This analysis marks the evolution of the turning points of relevance for the semiclassical regimes and puts on stage an unexpected key role of the Regge symmetries of the 6j.Comment: 15 pages, 11 figures. Talk presented at ICCSA 2012 (12th International Conference on Computational Science and Applications, Salvador de Bahia (Brazil) June 18-21, 2012

The Screen representation of spin networks. Images of 6j symbols and semiclassical features

This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a function of two variables - a natural choice due to their origin as elements of a square orthogonal matrix - and illustrated by use of a projection on a square "screen" introduced recently. On these screens, shown are images which provide a systematic classification of features previously introduced to represent the caustic and ridge curves (which delimit the boundaries between oscillatory and evanescent behaviour according to the asymptotic analysis of semiclassical approaches). Particular relevance is given to the surprising role of the intriguing symmetries discovered long ago by Regge and recently revisited; from their use, together with other newly discovered properties and in conjunction with the traditional combinatorial ones, a picture emerges of the amplitudes and phases of these discrete wavefunctions, of interest in wide areas as building blocks of basic and applied quantum mechanics.Comment: 16 pages, 13 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

Effects of Dietary Extruded Linseed (Linum usitatissimum) and Oregano (Origanum vulgare) on Growth Traits, Carcass Composition and Meat Quality of Grigia di Potenza Suckling Kids

The aim of this trial was to compare the influence of supplementing diets with extruded linseed and oregano on growth parameters and meat qualitative traits in Grigia di Potenza breed suckling kids. Twenty-four male kids, exclusively fed milk from their dams, were assigned to the following diets: C) group control fed without any supplement; L) group fed control feed containing 3% extruded linseed (Linum usitatissimum L.); and LO) group fed control diet with 0.6% dried oregano (Origanum vulgare) and 3% extruded linseed. Growth performance as well as slaughtering traits and meat cuts of kids were not significantly influenced (P > 0.05) by dietary treatments. Conversely, kids in linseed group reported the lower (P < 0.05) percentage of dissectible fat in leg and loin. The meat from Longissimus lumborum and Semimembranosus muscles of kids in linseed diet had the lowest (P < 0.05) cooking loss percentage, whereas the proximate chemical composition of both meat muscles did not vary among treatments (P > 0.05). The experimental diets partially modulated the kid meat fatty acid composition in both muscles, where feeding linseed and oregano improved (P < 0.05) the content of DPA and reduced MUFA. Based on the current findings, it can be concluded that linseed and oregano supplementation can be used in goat diet as no significant detrimental effects on productive performance and meat quality of suckling kids were observed

Quantification of the starling population, estimation and mapping of the damage to olive crops in the apulia region

The presence of wildlife in areas with a high concentration of farming activities can create a conflict between conservation objectives and productive purposes. Near Brindisi (Apulia, S-E Italy), a substantial amount of cash compensation claims for damages reported by local farmers and attributed to starlings (Sturnus vulgaris) has been registered. The aim of this study was to quantify the starling population wintering in the Apulia region, in order to assess the potential damage to crop production caused by this species. Our analysis was conducted over three years and included three main activities: a study of starling abundance and movements, the identification of areas and crops affected by damages, and a determination of the damage to the agricultural system in terms of quantity and concentration (heatmap). The study showed a loss of expected production that was coherent with the eating capacity of starlings wintering in the region. This means a loss, in terms of gross profitable production, of around 550,000 euros concentrated in a few narrow areas close to the roosts. Results on species behavior, damage quantification, and mapping are useful elements aimed to activate trade-off measures to preserve production and protection objectives, and to allow policymakers to address enforcement interventions and to establish parameters for financial compensation

Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Application