Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

Subspace wavepacket evolution with Newton polynomials

Time-dependent wavepacket evolution techniques demand the action of the propagator, exp(-iHt/(h)over-bar), on a suitable initial wavepacket. When a complex absorbing potential is added to the Hamiltonian for combating unwanted reflection effects, polynomial expansions of the propagator are selected on their ability to cope with non-Hermiticity. An efficient subspace implementation of the Newton polynomial expansion scheme that requires fewer dense matrix-vector multiplications than its grid-based counterpart has been devised. Performance improvements are illustrated with some benchmark one and two-dimensional examples. (C) 2001 Elsevier Science B.V. All rights reserved.

On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified. (C) 2002 Elsevier Science (USA).

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Robust multivariable control of complex biological processes

This paper addresses advanced control of a biological nutrient removal (BNR) activated sludge process. Based on a previously validated distributed parameter model of the BNR activated sludge process, we present robust multivariable controller designs for the process, involving loop shaping of plant model, robust stability and performance analyses. Results from three design case studies showed that a multivariable controller with stability margins of 0.163, 0.492 and 1.062 measured by the normalised coprime factor, multiplicative and additive uncertainties respectively give the best results for meeting performance robustness specifications. The controller robustly stabilises effluent nutrients in the presence of uncertainties with the behaviour of phosphorus accumulating organisms as well as to effectively attenuate major disturbances introduced as step changes. This study also shows that, performance of the multivariable robust controller is superior to multi-loops SISO PI controllers for regulating the BNR activated sludge process in terms of robust stability and performance and controlling the process using inlet feed flowrate is infeasible. (C) 2003 Elsevier Ltd. All rights reserved.

On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

A review of two journals found that articles using multivariable logistic regression frequently did not report commonly recommended assumptions

Background and Objective: To examine if commonly recommended assumptions for multivariable logistic regression are addressed in two major epidemiological journals. Methods: Ninety-nine articles from the Journal of Clinical Epidemiology and the American Journal of Epidemiology were surveyed for 10 criteria: six dealing with computation and four with reporting multivariable logistic regression results. Results: Three of the 10 criteria were addressed in 50% or more of the articles. Statistical significance testing or confidence intervals were reported in all articles. Methods for selecting independent variables were described in 82%, and specific procedures used to generate the models were discussed in 65%. Fewer than 50% of the articles indicated if interactions were tested or met the recommended events per independent variable ratio of 10: 1. Fewer than 20% of the articles described conformity to a linear gradient, examined collinearity, reported information on validation procedures, goodness-of-fit, discrimination statistics, or provided complete information on variable coding. There was no significant difference (P >.05) in the proportion of articles meeting the criteria across the two journals. Conclusion: Articles reviewed frequently did not report commonly recommended assumptions for using multivariable logistic regression. (C) 2004 Elsevier Inc. All rights reserved.

Identification of MIMO Hammerstein systems using cardinal spline functions

A new approach to identify multivariable Hammerstein systems is proposed in this paper. By using cardinal cubic spline functions to model the static nonlinearities, the proposed method is effective in modelling processes with hard and/or coupled nonlinearities. With an appropriate transformation, the nonlinear models are parameterized such that the nonlinear identification problem is converted into a linear one. The persistently exciting condition for the transformed input is derived to ensure the estimates are consistent with the true system. A simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches based on polynomials. (C) 2006 Elsevier Ltd. All rights reserved.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

How well does B-type natriuretic peptide predict death and cardiac events in patients with heart failure: systematic review

Objective To assess how well B-type natriuretic peptide (BNP) predicts prognosis in patients with heart failure. Design Systematic review of studies assessing BNP for prognosis m patients with heart failure or asymptomatic patients. Data sources Electronic searches of Medline and Embase from January 1994 to March 2004 and reference lists of included studies. Study selection and data extraction We included all studies that estimated the relation between BNP measurement and the risk of death, cardiac death, sudden death, or cardiovascular event in patients with heart failure or asymptomatic patients, including initial values and changes in values in response to treatment. Multivariable models that included both BNP and left ventricular ejection fraction as predictors were used to compare the prognostic value of each variable. Two reviewers independently selected studies and extracted data. Data synthesis 19 studies used BNP to estimate the relative risk of death or cardiovascular events in heart failure patients and five studies in asymptomatic patients. In heart failure patients, each 100 pg/ml increase was associated with a 35% increase in the relative risk of death. BNP was used in 35 multivariable models of prognosis. In nine of the models, it was the only variable to reach significance-that is, other variables contained no prognostic information beyond that of BNP. Even allowing for the scale of the variables, it seems to be a strong indicator of risk. Conclusion Although systematic reviews of prognostic studies have inherent difficulties, including die possibility of publication bias, the results of the studies in this review show that BNP is a strong prognostic indicator for both asymptomatic patients mid for patients with heart failure at all stages of disease.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

An analysis of valve re-replacement after aortic valve replacement with biologic devices

Biologic valve re-replacement was examined in a series of 1343 patients who underwent aortic valve replacement at The Prince Charles Hospital, Brisbane, with a cryopreserved or 4 degrees C stored allograft valve or a xenograft valve, A parametric model approach was used to simultaneously model the competing risks of death without re-replacement and re-replacement before death, One hundred eleven patients underwent a first re-replacement for a variety of reasons (69 patients with xenograft valves, 28 patients with 4 degrees C stored allograft valves, and 14 patients with cryopreserved allograft valves), By multivariable analysis younger age at operation was associated with xenograft, 4 degrees C stored allograft, and cryopreserved allograft valve re-replacement, However, this effect was examined in the context of longer survival of younger patients, which increases their exposure to the risk of re-replacement as compared with that in older patients whose decreased survival reduced their probability of requiring valve re-replacement, In patients older than 60 years at the time of aortic valve replacement, the probability of re-replacement (for any reason) before death was similar for xenografts and cryopreserved allograft valves but higher for 4 degrees C stored valves, However, in patients younger than 60 years, the probability of re-replacement at any time during the remainder of the life of the patient was lower with the cryopreserved allograft valve compared with the xenograft valve and 4 degrees C stored allografts.