Correlated Binomial Models and Correlation Structures

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.Comment: 12 pages, 7 figure

Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum

Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting from this model, we use a Poisson-bracket formalism to derive the equations governing the dynamics of nematic liquid crystals. We treat the spin angular momentum density arising from the rotation of constituent molecules about their centers of mass as an independent field and derive equations for it, the mass density, the momentum density, and the nematic director. Our equations reduce to the original Leslie-Ericksen equations, including the inertial director term that is neglected in the hydrodynamic limit, only when the moment of inertia for angular momentum parallel to the director vanishes and when a dissipative coefficient favoring locking of the angular frequencies of director rotation and spin angular momentum diverges. Our equations reduce to the equations of nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients that depend on the coefficient that must diverge to produce the Leslie-Ericksen equations.Comment: 10 pages, to be published in Phys. Rev. E 72(5

Modified BMIA/CAG method for the electromagnetic analysis of large-scale problems of random rough surface scattering

An efficient technique based on two-dimensional Fast Fourier Transform (FFT) and linear interpolation is presented for the evaluation of the scattering by a rough terrain surface which is of interest in remote-sensing applications characterized by a very large correlation length. Such technique, where introduced in a BMIA/CAG method, can reduce the computation time appreciably

Dynamics of supercooled liquids: density fluctuations and Mode Coupling Theory

We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the exact Newtonian equations. Following established ideas, we choose to separate these trial functions into a set representing integrable motions of density waves, and a set containing all effects of non-integrability. It transpires that the static structure factor is fixed by this minimum condition to be the solution of the Yvon-Born-Green (YBG) equation. The residual interactions between density waves are explicitly isolated in their Newtonian representation and expanded by choosing the dominant objects in the phase space of the system, that can be represented by a dissipative term with memory and a random noise. This provides a mapping between deterministic and stochastic dynamics. Imposing the Fluctuation-Dissipation Theorem (FDT) allows us to calculate the memory kernel. We write exactly the expression for it, following two different routes, i.e. using explicitly Newtons equations, or instead, their implicit form, that must be projected onto density pairs, as in the development of the well-established Mode Coupling Theory (MCT). We compare these two ways of proceeding, showing the necessity to enforce a new equation of constraint for the two schemes to be consistent. Thus, while in the first `Newtonian' representation a simple gaussian approximation for the random process leads easily to the Mean Spherical Approximation (MSA) for the statics and to MCT for the dynamics of the system, in the second case higher levels of approximation are required to have a fully consistent theory

Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes

Statistical properties of the inhomogeneous version of the Olami-Feder-Christensen (OFC) model of earthquakes is investigated by numerical simulations. The spatial inhomogeneity is assumed to be dynamical. Critical features found in the original homogeneous OFC model, e.g., the Gutenberg-Richter law and the Omori law are often weakened or suppressed in the presence of inhomogeneity, whereas the characteristic features found in the original homogeneous OFC model, e.g., the near-periodic recurrence of large events and the asperity-like phenomena persist.Comment: Shortened from the first version. To appear in European Physical Journal

Study of metal recovery from printed circuit boards by physical-mechanical treatment processes

The acceleration of the global production and consumption of electronics device and the concerns related to waste electrical and electronic equipment (WEEE) motivated this research. Printed circuit board (PCB) can be found in almost all type of electronic devices, making it an important component of WEEE. It has a heterogenous composition made of polymers, ceramic material, and metals. It contains heavy metals that can cause environmental impacts due to improper disposal. But on the other hand, there are elements with added value, such as copper, gold, silver, iron, aluminum and critical raw materials, such tantalum that can be recovered, making PCB scrap an economically attractive for recycling. The metal recovery can conserve natural resources, since it prevents new minerals from being extracted and it is a great contribution to the circular economy, removing the waste from its disposal and reinserts in the production cycle. The mechanical recycling of PCBs was studied through different operations, with the following sequence, comminution, granulometric classification, magnetic separation, gravity separation and electrostatic separation. The goal is to concentrate metals, especially copper, identifying the main elements obtained through cheaper processes to recycle e-waste. The PCB composition was initially carried out through the scanning electron microscope analysis. Then, it was shredded in a cutting mill and classified according to their grain size by sieving. Afterwards, a magnetic separation has been performed together with gravity and electrostatic separation of the non-magnetic fraction. The products obtained were observed with the macroscope to qualitatively assess the metallic content. The results obtained allowed to conclude that physical-mechanical techniques have high potential to produce a concentrate product with high added value. The application of magnetic separation proved to be efficient, as it enabled the recovery of high percentage of iron. In gravity separation, the metal recovery was satisfactory for the particle size -0.6 + 0.3 mm and for the particle size -1.18 + 0.6mm. In the recovery of metals by electrostatic separation the efficiencies obtained was really high the lower particle size (-0.3mm)

Label-Dependencies Aware Recurrent Neural Networks

In the last few years, Recurrent Neural Networks (RNNs) have proved effective on several NLP tasks. Despite such great success, their ability to model \emph{sequence labeling} is still limited. This lead research toward solutions where RNNs are combined with models which already proved effective in this domain, such as CRFs. In this work we propose a solution far simpler but very effective: an evolution of the simple Jordan RNN, where labels are re-injected as input into the network, and converted into embeddings, in the same way as words. We compare this RNN variant to all the other RNN models, Elman and Jordan RNN, LSTM and GRU, on two well-known tasks of Spoken Language Understanding (SLU). Thanks to label embeddings and their combination at the hidden layer, the proposed variant, which uses more parameters than Elman and Jordan RNNs, but far fewer than LSTM and GRU, is more effective than other RNNs, but also outperforms sophisticated CRF models.Comment: 22 pages, 3 figures. Accepted at CICling 2017 conference. Best Verifiability, Reproducibility, and Working Description awar

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the 'perturbed Kalman filter' (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified

Hydrodynamics of polar liquid crystals

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local $C_{\infty v}$-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals ($D_{\infty h}$) in that it contains terms violating the ${\bf{n}}\to -{\bf{n}}$ symmetry. First we show that these $\mathcal{Z}_2$-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.Comment: 9 pages, corrected typos, added references, revised content, to appear in PR