A differential model for growing sandpiles on networks

We consider a system of differential equations of Monge-Kantorovich type which describes the equilibrium configurations of granular material poured by a constant source on a network. Relying on the definition of viscosity solution for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions and P. E. Souganidis, we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out

A numerical method for Mean Field Games on networks

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares method for the solution of the discrete system. Numerical experiments are carried out

Ergodic Theorems for Lower Probabilities

We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers

VerbAtlas: a novel large-scale verbal semantic resource and its application to semantic role labeling

We present VerbAtlas, a new, hand-crafted lexical-semantic resource whose goal is to bring together all verbal synsets from WordNet into semantically-coherent frames. The frames define a common, prototypical argument structure while at the same time providing new concept-specific information. In contrast to PropBank, which defines enumerative semantic roles, VerbAtlas comes with an explicit, cross-frame set of semantic roles linked to selectional preferences expressed in terms of WordNet synsets, and is the first resource enriched with semantic information about implicit, shadow, and default arguments. We demonstrate the effectiveness of VerbAtlas in the task of dependency-based Semantic Role Labeling and show how its integration into a high-performance system leads to improvements on both the in-domain and out-of-domain test sets of CoNLL-2009. VerbAtlas is available at http://verbatlas.org

Probing the local temperature of a 2DEG microdomain with a quantum dot: measurement of electron-phonon interaction

We demonstrate local detection of the electron temperature in a two-dimensionalmicrodomain using a quantum dot. Our method relies on the observation that a temperature bias across the dot changes the functional form of Coulomb-blockade peaks. We apply our results to the investigation of electron-energy relaxation at subkelvin temperatures, find that the energy flux from electrons into phonons is proportional to the fifth power of temperature, and give a measurement of the coupling constant.Comment: 5 pages, 4 figure

Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques to approximate the solution to the PDE. In this paper, we provide the first rigorous recovery error bounds and effective recipes for the implementation of the CORSING technique in the multi-dimensional setting. Our theoretical analysis relies on new estimates for the local a-coherence, which measures interferences between wavelet and Fourier basis functions with respect to the metric induced by the PDE operator. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case

Parity dependent Josephson current through a helical Luttinger liquid

We consider a superconductor-two dimensional topological insulator- superconductor junction (S-2DTI-S) and study how the 2{\pi}- and 4{\pi}-periodic Josephson currents are affected by the electron-electron interaction. In the long-junction limit the supercurrent can by evaluated by modeling the system as a helical Luttinger liquid coupled to superconducting reservoirs. After having introduced bosonization in the presence of the parity constraint we turn to consider the limit of perfect and poor interfaces. For transparent interfaces, where perfect Andreev reflections occur at the boundaries, the Josephson current is marginally affected by the interaction. On the contrary, if strong magnetic scatterers are present in the weak link, the situation changes dramatically. Here Coulomb interaction plays a crucial role both in low and high temperature regimes. Furthermore, a phase-shift of Josephson current can be induced by changing the direction of the magnetization of the impurity

Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model

We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.fractals, iterated function system, self-similarity, Sierpinski gasket, stochastic growth