Integral homology of real isotropic and odd orthogonal Grassmannians

We obtain a combinatorial expression for the coefficients of the boundary map of real isotropic and odd orthogonal Grassmannians providing a natural generalization of the formulas already obtained for Lagrangian and maximal isotropic Grassmannians. The results are given in terms of the classification into four types of covering pairs among the Schubert cells when identified with signed $k$-Grassmannian permutations. It turns out that these coefficients only depend on the positions changed over each pair of permutations. As an application, we give an orientability criterion, exhibit a symmetry of these coefficients and, compute low-dimensional homology groups.Comment: 24 pages, 8 figures. We have improved the main result

Local Isometric immersions of pseudo-spherical surfaces and evolution equations

The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to $-1$. The class of differential equations describing pseudo-spherical surfaces carries close ties to the property of complete integrability, as manifested by the existence of infinite hierarchies of conservation laws and associated linear problems. As such, it contains many important known examples of integrable equations, like the sine-Gordon, Liouville and KdV equations. It also gives rise to many new families of integrable equations. The question we address in this paper concerns the local isometric immersion of pseudo-spherical surfaces in ${\bf E}^{3}$ from the perspective of the differential equations that give rise to the metrics. Indeed, a classical theorem in the differential geometry of surfaces states that any pseudo-spherical surface can be locally isometrically immersed in ${\bf E}^{3}$. In the case of the sine-Gordon equation, one can derive an expression for the second fundamental form of the immersion that depends only on a jet of finite order of the solution of the pde. A natural question is to know if this remarkable property extends to equations other than the sine-Gordon equation within the class of differential equations describing pseudo-spherical surfaces. In an earlier paper [11], we have shown that this property fails to hold for all other second order equations, except for those belonging to a very special class of evolution equations. In the present paper, we consider a class of evolution equations for $u(x,t)$ of order $k\geq 3$ describing pseudo-spherical surfaces. We show that whenever an isometric immersion in ${\bf E}^3$ exists, depending on a jet of finite order of $u$, then the coefficients of the second fundamental forms are functions of the independent variables $x$ and $t$ only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and Applications, pp.N

General method for constructing local-hidden-variable models for entangled quantum states

Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and that can be implemented by semidefinite programming. This method can be applied to any given state and for the construction of new examples of states with local hidden-variable models for both projective and general measurements. As applications we provide a lower bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those which arise from physical noise models, Bell-diagonal states, and noisy GHZ and W states.Comment: Published version with new title and abstract, improved presentation and new examples of LHV states. Codes are available at https://github.com/paulskrzypczyk/localhiddenstatemodels (please cite this paper if you use them). See also the related work by F. Hirsch et al arXiv:1512.0026

Public Systems for Public Employees in Brazil: Options for Reform

This paper discusses the reform of the Federal employee retirement system in the U.S. The paper argues that this reform experience may provide interesting insights for the reform of public-sector pensions in Brazil and other developing countries

Porous glass-ceramics from alkali activation and sinter-crystallization of mixtures of waste glass and residues from plasma processing of municipal solid waste

Alkali-activated aqueous slurries of fine glass powders, mostly deriving from the plasma processing of municipal solid waste ('Plasmastone'), were found to undergo progressive hardening at low temperature (75 degrees C) owing to the formation of C-S-H (calcium silicate hydrate) gels. Before complete setting, slurries could be easily foamed by vigorous mechanical stirring, with the help of a surfactant; finally, the resulting open-celled structure could be 'frozen' by a subsequent sintering treatment, with crystallization of Ca-Fe silicates. The densification of the struts upon firing was enhanced by mixing Plasmastone with up to 30 wt% recycled glasses and increasing the firing temperature from 800 to 1000 degrees C. A total porosity exceeding 75 vol%, comprising both well-interconnected macro- and micro-sized pores on cell walls, was accompanied by good compressive strength, well above 1 MPa. The stabilization of pollutants generally increased with increasing firing temperature and glass content, with some exceptions; no practical leaching was observed from samples deriving from Plasmastone combined with 30 wt% boro-aluminosilicate glass from the recycling of pharmaceutical vials