Discretization of highly persistent correlated AR(1) shocks

The finite state Markov-chain approximation methods developed by Tauchen (1986) and Tauchen and Hussey (1991) are widely used in economics, finance and econometrics to solve functional equations in which state variables follow autoregressive processes. For highly persistent processes, the methods require a large number of discrete values for the state variables to produce close approximations which leads to an undesirable reduction in computational speed, especially in a multivariate case. This paper proposes an alternative method of discretizing multivariate autoregressive processes. This method can be treated as an extension of Rouwenhorst's (1995) method which, according to our finding, outperforms the existing methods in the scalar case for highly persistent processes. The new method works well as an approximation that is much more robust to the number of discrete values for a wide range of the parameter space.

Discretization and solution of the inhomogeneous Bogoliubov-de Gennes equations

In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

A dielectric continuum molecular dynamics method

We introduce a novel method to simulate hydrated macromolecules with a dielectric continuum representation of the surrounding solvent. In our approach, the interaction between the solvent and the molecular degrees of freedom is described by means of a polarization density free energy functional which is minimum at electrostatic equilibrium. After a pseudospectral expansion of the polarization and a discretization of the functional, we construct the equations of motion for the system based on a Car-Parrinello technique. In the limit of the adiabatic evolution of the polarization field variables, our method provides the solution of the dielectric continuum problem "on the fly," while the molecular coordinates are propagated. In this first study, we show how our dielectric continuum molecular dynamics method can be successfully applied to hydrated biomolecules, with low cost compared to free energy simulations with explicit solvent. To our knowledge, this is the first time that stable and conservative molecular dynamic simulations of solutes can be performed for a dielectric continuum model of the solvent. (C) 2001 American Institute of Physics.

Coupled heat and moisture transfer in multi-layer building materials

A dynamic mathematical model for simulating the coupled heat and moisture migration through multilayer porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The discretization of the governing equations was done by the finite difference approach. A new experimental set-up was also developed in this study. The evolution of transient temperature and moisture distributions inside specimens were measured. The method for determining the temperature gradient coefficient was also presented. The moisture diffusion coefficient, temperature gradient coefficient, sorption–desorption isotherms were experimentally evaluated for some building materials (sandstone and lime-cement mortar). The model was validated by comparing with the experimental data with good agreement. Another advantage of the method lies in the fact that the required transport properties for predicting the non-isothermal moisture flow only contain the vapor diffusion coefficient and temperature gradient coefficient. They are relatively simple, and can be easily determined.

The Y-procedure: How to extract the chemical transformation rate from reaction-diffusion data with no assumption on the kinetic model

The paper presents a new method to extract the chemical transformation rate from reaction–diffusion data with no assumption on the kinetic model (“kinetic model-free procedure”). It is a new non-steady-state kinetic characterization procedure for heterogeneous catalysts. The mathematical foundation of the Y-procedure is a Laplace-domain analysis of the two inert zones in a TZTR followed by transposition to the Fourier domain. When combined with time discretization and filtering the Y-procedure leads to an efficient practical method for reconstructing the concentration and reaction rate in the active zone. Using the Y-procedure the concentration and reaction rate of a non-steady state catalytic process can be determined without any pre-assumption regarding the type of kinetic dependence. The Y-procedure is the basis for advanced software for non-steady state kinetic data interpretation. The Y-procedure can be used to relate changes in the catalytic reaction rate and kinetic parameters to changes in the surface composition (storage) of a catalyst.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Detecting Anomalies in Graphs with Numeric Labels

This paper presents Yagada, an algorithm to search labelled graphs for anomalies using both structural data and numeric attributes. Yagada is explained using several security-related examples and validated with experiments on a physical Access Control database. Quantitative analysis shows that in the upper range of anomaly thresholds, Yagada detects twice as many anomalies as the best-performing numeric discretization algorithm. Qualitative evaluation shows that the detected anomalies are meaningful, representing a com- bination of structural irregularities and numerical outliers.

Exploiting spatio-temporal constraints for robust 2D pose tracking

We present a Spatio-temporal 2D Models Framework (STMF) for 2D-Pose tracking. Space and time are discretized and a mixture of probabilistic "local models" is learnt associating 2D Shapes and 2D Stick Figures. Those spatio-temporal models generalize well for a particular viewpoint and state of the tracked action but some spatio-temporal discontinuities can appear along a sequence, as a direct consequence of the discretization. To overcome the problem, we propose to apply a Rao-Blackwellized Particle Filter (RBPF) in the 2D-Pose eigenspace, thus interpolating unseen data between view-based clusters. The fitness to the images of the predicted 2D-Poses is evaluated combining our STMF with spatio-temporal constraints. A robust, fast and smooth human motion tracker is obtained by tracking only the few most important dimensions of the state space and by refining deterministically with our STMF.

A Hamiltonian approach to simulation of acoustic systems involving nonlinear interactions

Nonlinear interactions take place in most systems that arise in music acoustics, usually as a result of player-instrument coupling. Several time-stepping methods exist for the numerical simulation of such systems. These methods generally involve the discretization of the Newtonian description of the system. However, it is not always possible to prove the stability of the resulting algorithms, especially when dealing with systems where the underlying force is a non-analytic function of the phase space variables. On the other hand, if the discretization is carried out on the Hamiltonian description of the system, it is possible to prove the stability of the derived numerical schemes. This Hamiltonian approach is applied to a series of test models of single or multiple nonlinear collisions and the energetic properties of the derived schemes are discussed. After establishing that the schemes respect the principle of conservation of energy, a nonlinear single-reed model is formulated and coupled to a digital bore, in order to synthesize clarinet-like sounds.

A Continuous Time Markov Chain Based Sequential Analytical Approach for Composite Power System Reliability Assessment

This paper proposes a continuous time Markov chain (CTMC) based sequential analytical approach for composite generation and transmission systems reliability assessment. The basic idea is to construct a CTMC model for the composite system. Based on this model, sequential analyses are performed. Various kinds of reliability indices can be obtained, including expectation, variance, frequency, duration and probability distribution. In order to reduce the dimension of the state space, traditional CTMC modeling approach is modified by merging all high order contingencies into a single state, which can be calculated by Monte Carlo simulation (MCS). Then a state mergence technique is developed to integrate all normal states to further reduce the dimension of the CTMC model. Moreover, a time discretization method is presented for the CTMC model calculation. Case studies are performed on the RBTS and a modified IEEE 300-bus test system. The results indicate that sequential reliability assessment can be performed by the proposed approach. Comparing with the traditional sequential Monte Carlo simulation method, the proposed method is more efficient, especially in small scale or very reliable power systems.

Numerical analysis of complex failure mechanisms in composite panels

A three-dimensional continuum damage mechanics-based material model has been implemented in an implicit Finite Element code to simulate the progressive degradation of advanced composite materials. The damage model uses seven damage variables assigned to tensile, compressive and non-linear shear damage at a laminae level. The objectivity of the numerical discretization is assured using a smeared formulation. The material model was benchmarked against experimental uniaxial coupon tests and it is shown to reproduce key aspects observable during failure, such as the inclined fracture plane in matrix compression and the shear band in a ±45° tension specimen.