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Discrete Variables (discrete + variable)

Distribution by Scientific Domains

Engineering	42%
Mathematics and Statistics	28%

Selected Abstracts

Fifth-order Hermitian schemes for computational linear aeroacoustics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2007
Article first published online: 17 APR 200, G. Capdeville
Abstract We develop a class of fifth-order methods to solve linear acoustics and/or aeroacoustics. Based on local Hermite polynomials, we investigate three competing strategies for solving hyperbolic linear problems with a fifth-order accuracy. A one-dimensional (1D) analysis in the Fourier series makes it possible to classify these possibilities. Then, numerical computations based on the 1D scalar advection equation support two possibilities in order to update the discrete variable and its first and second derivatives: the first one uses a procedure similar to that of Cauchy,Kovaleskaya (the ,,-P5 scheme'); the second one relies on a semi-discrete form and evolves in time the discrete unknowns by using a five-stage Runge,Kutta method (the ,RGK-P5 scheme'). Although the RGK-P5 scheme shares the same local spatial interpolator with the ,-P5 scheme, it is algebraically simpler. However, it is shown numerically that its loss of compactness reduces its domain of stability. Both schemes are then extended to bi-dimensional acoustics and aeroacoustics. Following the methodology validated in (J. Comput. Phys. 2005; 210:133,170; J. Comput. Phys. 2006; 217:530,562), we build an algorithm in three stages in order to optimize the procedure of discretization. In the ,reconstruction stage', we define a fifth-order local spatial interpolator based on an upwind stencil. In the ,decomposition stage', we decompose the time derivatives into simple wave contributions. In the ,evolution stage', we use these fluctuations to update either by a Cauchy,Kovaleskaya procedure or by a five-stage Runge,Kutta algorithm, the discrete variable and its derivatives. In this way, depending on the configuration of the ,evolution stage', two fifth-order upwind Hermitian schemes are constructed. The effectiveness and the exactitude of both schemes are checked by their applications to several 2D problems in acoustics and aeroacoustics. In this aim, we compare the computational cost and the computation memory requirement for each solution. The RGK-P5 appears as the best compromise between simplicity and accuracy, while the ,-P5 scheme is more accurate and less CPU time consuming, despite a greater algebraic complexity. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Analysis of multivariable controllers using degree of freedom data

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7-9 2003
T. J. Harris
Abstract Most approaches for monitoring, diagnosis and performance analysis of multivariable control loops employ time series methods and use non-parametric statistics to analyse the process inputs and outputs. In this paper, we explore the use of a discrete variable that summarizes the status of the constraint set of the controller to analyse the long run behaviour of control systems. We introduce a number of waiting and holding time statistics that describe the status of this data, which we call the degree of freedom data. We demonstrate how Markov Chains might be used to model the status of the degree of freedom data. This model-based approach has the potential to provide considerable insight into the behaviour of a model based control scheme with relative ease. We demonstrate the methodologies on simulated and industrial data. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A priori step size adaptation for the simulation of non-smooth systems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007
Ralf Uwe PfauArticle first published online: 19 JUN 200
Abstract The simulation of technical system include systems with discontinuities, jumps, discrete variables, slip,stick-changes and similar. The solution of those systems with standard ODE solvers normally leads to a break-down in the efficiency due to the changes in the systems which causes the step size selection rule to perform poorly. We present a strategy how to modify the standard step size selection with a priori information from the system to react on the upcoming change. This improves the efficiency and accuracy of the solution.Copyright © 2006 John Wiley & Sons, Ltd. [source]

Predictors of rehospitalization after total weight recovery in adolescents with anorexia nervosa

INTERNATIONAL JOURNAL OF EATING DISORDERS, Issue 1 2004
Josefina Castro
Abstract Objective The current study analyzed the variables related to rehospitalization after total weight recovery in adolescents with anorexia nervosa. Method One hundred and one patients first admitted for inpatient treatment, aged 11,19 years, were followed up for 12 months after discharge. Results Twenty-five subjects (24.8%) required readmission after complete weight recovery and 76 (75.2%) did not. Duration of disorder, weight loss, body mass index at first admission, and global body image distortion were similar in the two groups. Patients needing readmission had a lower rate of weight gain (p < .001), a lower mean age (p = .007), a higher mean score on the Eating Attitudes Test (EAT; p = .009), and a higher percentage of hips overestimation (p = .049). In a stepwise logistic regression analysis, these three variables predicted readmission and correctly classified 77.6% of patients. Taken as discrete variables, age younger than 15 years old, EAT score above 55, and a rate of weight gain lower than 150 grams per day were associated with a higher percentage of readmissions. Discussion The variables most clearly related to readmission were young age, abnormal eating attitudes, and a low rate of weight gain. © 2004 by Wiley Periodicals, Inc. Int J Eat Disord 36: 22,30, 2004. [source]

Maximum entropy inference for mixed continuous-discrete variables

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 4 2010
Hermann Singer
We represent knowledge by probability distributions of mixed continuous and discrete variables. From the joint distribution of all items, one can compute arbitrary conditional distributions, which may be used for prediction. However, in many cases only some marginal distributions, inverse probabilities, or moments are known. Under these conditions, a principle is needed to determine the full joint distribution of all variables. The principle of maximum entropy (Jaynes, Phys Rev 1957;106:620,630 and 1957;108:171,190; Jaynes, Probability Theory,The Logic of Science, Cambridge, UK: Cambridge University Press, 2003; Haken, Synergetics, Berlin: Springer-Verlag, 1977; Guiasu and Shenitzer, Math Intell 1985;117:83,106) ensures an unbiased estimation of the full multivariate relationships by using only known facts. For the case of discrete variables, the expert shell SPIRIT implements this approach (cf. Rödder, Artif Intell 2000;117:83,106; Rödder and Meyer, in Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, San Francisco, CA, 2006; Rödder et al., Logical J IGPL 2006;14(3):483,500). In this paper, the approach is generalized to continuous and mixed continuous-discrete distributions and applied to the problem of credit scoring. © 2010 Wiley Periodicals, Inc. [source]

Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2006
Francesco Bartolucci
Summary., For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976,1980. [source]

A Dependence Metric for Possibly Nonlinear Processes

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2004
C. W. Granger
Abstract., A transformed metric entropy measure of dependence is studied which satisfies many desirable properties, including being a proper measure of distance. It is capable of good performance in identifying dependence even in possibly nonlinear time series, and is applicable for both continuous and discrete variables. A nonparametric kernel density implementation is considered here for many stylized models including linear and nonlinear MA, AR, GARCH, integrated series and chaotic dynamics. A related permutation test of independence is proposed and compared with several alternatives. [source]