U(N) Coherent States for Loop Quantum Gravity

We investigate the geometry of the space of N-valent SU(2)-intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations. These states are labeled by elements of the Grassmannian Gr(N,2), they possess a direct geometrical interpretation in terms of framed polyhedra and are shown to be related to the well-known coherent intertwiners.Comment: 23 page

The Fine Structure of SU(2) Intertwiners from U(N) Representations

In this work we study the Hilbert space space of N-valent SU(2) intertwiners with fixed total spin, which can be identified, at the classical level, with a space of convex polyhedra with N face and fixed total boundary area. We show that this Hilbert space provides, quite remarkably, an irreducible representation of the U(N) group. This gives us therefore a precise identification of U(N) as a group of area preserving diffeomorphism of polyhedral spheres. We use this results to get new closed formulae for the black hole entropy in loop quantum gravity.Comment: 21 page

Farmer Associations, Decentralization and Development in Rwanda: Challenges Ahead

This paper summarizes the findings from FSRP/DSA surveys designed to identify some of the key institutional issues surrounding the role of farmer associations in the delivery of, and access to agricultural services. Specifically, the surveys focus on the capacity of four actors–MINAGRI Regional and District Agents, NGOs, District Governments (the Mayors) and farmer associations and intergroupements to provide farmers with agricultural services that might help in the transition from semi-subsistence to commercial agriculture. As this synthesis paper indicates, some of these services have been provided on an irregular basis for many years through a variety of government, NGO, donor agency and private business efforts. Moreover, this paper highlights the strengths and weaknesses of these four key actors; it also identifies areas for improvement, and recommends ways for enhancing the efficiency and equity of services available to farmers through farmer associations.food security, food policy, Rwanda, farmer associations, International Development, Q18,

Relative periodic orbits in point vortex systems

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.Comment: 27 pages, 17 figure

Contractual Tradeoffs and SMEs Choice of Organizational Form, A View from U.S. and French History, 1830-2000

Today the vast majority of multi-owner firms in the United States are corporations, but that was not the case in the past. Before the advent of the income tax, tort litigation, and significant federal regulation, entrepreneurs more often than not chose to organize as partnerships, a form that economists consider seriously flawed. Why would they make such a terrible mistake? We begin by noting that corporations created new types of contracting problems for businesses at the same time as they solved problems afflicting partnerships. We then model the tradeoffs involved in the choice of corporations versus partnerships and confirm that the model’s assumptions are consistent with U.S. legal rules up through the 1940s. The model implies that partnerships and corporations are complementary organizational forms, and we show that data from the U.S. Census of Manufactures strongly supports that implication. We also verify that the model’s assumptions hold for the broader set of organizational choices available under the French Code de Commerce and use data on multi-owner firms registered in Paris in the 1830s and 1840s to demonstrate the complementary character of the basic forms. Despite much literature emphasizing the fundamentally different environments for business associated with the French and U.S. legal regimes, the basic calculus underpinning the choice of organizational form was the same in both countries.

Detection of exomoons in simulated light curves with a regularized convolutional neural network

Many moons have been detected around planets in our Solar System, but none has been detected unambiguously around any of the confirmed extrasolar planets. We test the feasibility of a supervised convolutional neural network to classify photometric transit light curves of planet-host stars and identify exomoon transits, while avoiding false positives caused by stellar variability or instrumental noise. Convolutional neural networks are known to have contributed to improving the accuracy of classification tasks. The network optimization is typically performed without studying the effect of noise on the training process. Here we design and optimize a 1D convolutional neural network to classify photometric transit light curves. We regularize the network by the total variation loss in order to remove unwanted variations in the data features. Using numerical experiments, we demonstrate the benefits of our network, which produces results comparable to or better than the standard network solutions. Most importantly, our network clearly outperforms a classical method used in exoplanet science to identify moon-like signals. Thus the proposed network is a promising approach for analyzing real transit light curves in the future

On Generalized Self-Duality Equations Towards Supersymmetric Quantum Field Theories Of Forms

We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T invariant under a sub-group H of SO(D). Second, the representation for the SO(D) curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the `self-duality' equations can be candidates as gauge functions for SO(D)-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for dimensions greater than 9, for various p-form gauge fields.Comment: 20 pages, Late

3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory

We show that the effective dynamics of matter fields coupled to 3d quantum gravity is described after integration over the gravitational degrees of freedom by a braided non-commutative quantum field theory symmetric under a kappa-deformation of the Poincare group.Comment: 4 pages, to appear in Phys. Rev. Letters, Proceedings of the conference "Quantum Theory and Symmetries 4" 2005 (Varna, Bulgaria), v2: some clarifications on the Feynman propagator and slight change in titl