Optimized White Reflectance in Photonic Network Structures

Three-dimensional disordered networks are receiving increasing attention as versatile architectures for highly scattering materials. However, due to their complex morphology, little is still known about the interplay between their structural and optical properties. Here, we describe a simple algorithm that allows to generate photonic network structures inspired by that of the Cyphochilus beetle, famous for the bright white reflectance of its thin cuticular scales. The model allows to vary the degree of structural anisotropy and filling fraction of the network independently, revealing the key contribution of these two parameters to the overall scattering efficiency. Rigorous numerical simulations show that the obtained structures can exceed the broadband reflectance of the beetle while using less material, providing new insights for the design of advanced scattering materials.Comment: 10 pages, 3 figures. peer reviewed version, published in final form at https://doi.org/10.1002/adom.20190004

From local to global deformation quantization of Poisson manifolds

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.Comment: 16 pages. Reference and dedication added. Sign corrected, remark on Poisson vector fields adde

Distributed Adaptive Learning of Graph Signals

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201

Fedosov connections on jet bundles and deformation quantization

We review our construction of star-products on Poisson manifolds and discuss some examples. In particular, we work out the relation with Fedosov's original construction in the symplectic case.Comment: Contribution to the proceedings of the conference "Deformation Quantization", Strasbourg, May 31-June 2, 200

Determination of hidden variable models reproducing the spin-singlet

The experimental violation of Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at the basis of Bell's theorem: free will, no-signaling, and outcome-Independence. Quantum mechanics satisfies the first two hypotheses but not the latter. Experiments not only violate Bell inequality, but show an excellent agreement with quantum mechanics. This fact restricts further the class of admissible theories. In this work, the author determines the form of the hidden-variable models that reproduce the quantum mechanical predictions for a spin singlet while satisfying both the hypotheses of free will and no-signaling. Two classes of hidden-variable models are given as an example, and a general recipe to build infinitely many possible models is provided.Comment: Slightly revised version, 7 pages, no figures, to appear in PRA. Final version, removed extra references no longer cite

The Probabilistic Representative Values

In this paper we define a new family of solutions for the class of cooperative games with transferable utility, in which the set of players exhibits a structure of a priori unions.This family is deeply connected with the Shapley value for games with transferable utility but, moreover, we assume a solidarity strong connection among all the components of each union.As a consequence of this, they are disposed to delegate one coalition of members of the union to negotiate with the other unions, and, therefore, each union will have a representative coalition.Furthermore, three interesting solutions that belong to this family of values are studied, as well as the non cooperative selection of the best representative coalition for each union.TU-games with unions;Shapley value;representative coalition