Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments. (C) 2003 Elsevier B.V. All rights reserved.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Modeling the optical constants of AlxGa1-xAs alloys

The extension of Adachi's model with a Gaussian-like broadening function, in place of Lorentzian, is used to model the optical dielectric function of the alloy AlxGa1-xAs. Gaussian-like broadening is accomplished by replacing the damping constant in the Lorentzian line shape with a frequency dependent expression. In this way, the comparative simplicity of the analytic formulas of the model is preserved, while the accuracy becomes comparable to that of more intricate models, and/or models with significantly more parameters. The employed model accurately describes the optical dielectric function in the spectral range from 1.5 to 6.0 eV within the entire alloy composition range. The relative rms error obtained for the refractive index is below 2.2% for all compositions. (C) 1999 American Institute of Physics. [S0021-8979(99)00512-5].

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Two-dimensional approximation for tidal dynamics in coastal aquifers: Capillarity correction

Most previous investigations on tide-induced watertable fluctuations in coastal aquifers have been based on one-dimensional models that describe the processes in the cross-shore direction alone, assuming negligible along-shore variability. A recent study proposed a two-dimensional approximation for tide-induced watertable fluctuations that took into account coastline variations. Here, we further develop this approximation in two ways, by extending the approximation to second order and by taking into account capillary effects. Our results demonstrate that both effects can markedly influence watertable fluctuations. In particular, with the first-order approximation, the local damping rate of the tidal signal could be subject to sizable errors.

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighboring P-donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position, and interdonor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, while the magnitude of the double occupancy probability can affect the error rate.

Estimating correlations from epidemiological data in the presence of measurement error

Analysis of a major multi-site epidemiologic study of heart disease has required estimation of the pairwise correlation of several measurements across sub-populations. Because the measurements from each sub-population were subject to sampling variability, the Pearson product moment estimator of these correlations produces biased estimates. This paper proposes a model that takes into account within and between sub-population variation, provides algorithms for obtaining maximum likelihood estimates of these correlations and discusses several approaches for obtaining interval estimates. (C) 1997 by John Wiley & Sons, Ltd.

A systematic approach to error isolation in computerized wastewater simulation models

Activated sludge models are used extensively in the study of wastewater treatment processes. While various commercial implementations of these models are available, there are many people who need to code models themselves using the simulation packages available to them, Quality assurance of such models is difficult. While benchmarking problems have been developed and are available, the comparison of simulation data with that of commercial models leads only to the detection, not the isolation of errors. To identify the errors in the code is time-consuming. In this paper, we address the problem by developing a systematic and largely automated approach to the isolation of coding errors. There are three steps: firstly, possible errors are classified according to their place in the model structure and a feature matrix is established for each class of errors. Secondly, an observer is designed to generate residuals, such that each class of errors imposes a subspace, spanned by its feature matrix, on the residuals. Finally. localising the residuals in a subspace isolates coding errors. The algorithm proved capable of rapidly and reliably isolating a variety of single and simultaneous errors in a case study using the ASM 1 activated sludge model. In this paper a newly coded model was verified against a known implementation. The method is also applicable to simultaneous verification of any two independent implementations, hence is useful in commercial model development.

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.