Primal-Dual Estimation of a Linear Expenditure Demand System

Efficient estimates require the utilization of all the available theoretical and statistical information. This fact suggests that econometric models based on an explicit optimization theory might achieve more efficient estimates when all the primal and dual relations are used for a joint estimation of the model’s parameters. We present a discussion of this idea using a Linear Expenditure System (LES) of consumer demand. We assume that the risk-neutral household chooses its consumption plan on the basis of expected information. Some time after that decision, the econometrician attempts to measure quantities and prices and in so doing commits measurement errors. Hence, the econometric model is an errors-in-variables nonlinear system of equations for which there is no known consistent estimator. We propose an easy-to-implement estimator and analyze its empirical properties by a Monte Carlo simulation that shows a relatively small bias.Consumer demand functions, primal-dual, linear expenditure system, Demand and Price Analysis, Research Methods/ Statistical Methods, D0,

Probing the sign of on-site Hubbard interaction by two-particle quantum walks

We consider two identical bosons propagating on a one-dimensional lattice and address the prob- lem of discriminating whether their mutual on-site interaction is attractive or repulsive. We suggest a probing scheme based on the properties of the corresponding two-particle quantum walks, and show that the sign of the interaction introduces specific and detectable features in the dynamics of quantum correlations, thus permitting to discriminate between the two cases. We also discuss how these features are connected to the band-structure of the Hubbard Hamiltonian, and prove that discrimination may be obtained only when the two walkers are initially prepared in a superposition of localized states.Comment: 9 pages, 9 figure

On the prediction of settling velocity for plastic particles of different shapes.

Abstract Transport processes of plastic particles in freshwater and marine environments are one of the relevant advances of knowledge in predicting the fate of plastic in the environment. Here, we investigated the effect of different shapes on the settling velocity, finding a representative reference diameter which encompasses three-dimensional shapes like pellets or spherules, two-dimensional shapes like fragments or disks, and one-dimensional shapes like filaments or fibers. The new method is able to predict the settling velocity of plastic and natural particles given the representative size and the Corey shape factor coefficient, over the entire range of viscous to turbulent flow regime. The calibration of the method with experimental data, and the validation with an independent dataset, support its application in a wide range of hydraulic conditions

Continuous-time quantum walks on planar lattices and the role of the magnetic field

We address the dynamics of continuous-time quantum walk (CTQW) on planar two-dimensional (2D) lattice graphs, i.e., those forming a regular tessellation of the Euclidean plane (triangular, square, and honeycomb lattice graphs). We first consider the free particle: On square and triangular lattice graphs we observe the well-known ballistic behavior, whereas on the honeycomb lattice graph we obtain a sub-ballistic one, although still faster than the classical diffusive one. We impute this difference to the different amount of coherence generated by the evolution and, in turn, to the fact that, in 2D, the square and the triangular lattices are Bravais lattices, whereas the honeycomb one is non-Bravais. From the physical point of view, this means that CTQWs are not universally characterized by the ballistic spreading. We then address the dynamics in the presence of a perpendicular uniform magnetic field and study the effects of the field by two approaches: (i) introducing the Peierls phase factors, according to which the tunneling matrix element of the free particle becomes complex or (ii) spatially discretizing the Hamiltonian of a spinless charged particle in the presence of a magnetic field. Either way, the dynamics of an initially localized walker is characterized by a lower spread compared to the free particle case; larger fields correlate to more localized stays of the walker. Remarkably, upon analyzing the dynamics by spatial discretization of the Hamiltonian (vector potential in the symmetric gauge), we obtain that the variance of the space coordinate is characterized by pseudo-oscillations, a reminiscence of the harmonic oscillator behind theHamiltonian in the continuum, whose energy levels are the well-known Landau levels