Validating multiple structural change models : A case study

In a recent article, Bai and Perron (2003, Journal of Applied Econometrics) present a comprehensive discussion of computational aspects of multiple structural change models along with several empirical examples. Here, we report on the results of a replication study using the R statistical software package. We are able to verify most of their findings; however, some confidence intervals associated with breakpoints cannot be reproduced. These confidence intervals require computation of the quantiles of a nonstandard distribution, the distribution of the argmax functional of a certain stochastic process. Interestingly, the difficulties appear to be due to numerical problems in GAUSS, the software package used by Bai and Perron. --structural change,breakpoints,econometric software,numerical accuracy,reproducibility,R,GAUSS

Toward sustainable management: 2D modelling of a self-cleaning system to improve geometry in front of the flushing gate

This paper aims to show how numerical modelling based on 2D SWE can be used to analyze the cleaning effectiveness of flushing waves in storm tanks. The case study under consideration is an existing storm tank located in Badalona, a municipality of Barcelona, Spain. Storm tank cleaning systems are critical features that must be carefully addressed. If not appropriately addressed, operation and maintenance work costs can drastically increase. There are numerous currently available technologies for cleaning storage tanks. However, no specific guide on this field has been identified. References are provided by the manufacturers through their commercial catalogues. Generally, this information is not based on experimental or numerical experiences or results have not been published in the literature of scientific papers. In this study, a public domain software (IBER) was used to develop 2D hydraulic analysis of the selected tank. The results obtained show how the phenomenon of recirculation is acting in some areas of the lane. This implies a dissipation of energy, thus causing difficulties in terms of cleaning procedures. Furthermore, two new scenarios have been tested to determine how a different lane width might affect hydrodynamic behavior. A newly suggested geometry for the existing lane of the tank is proposed by using the numerical modeling software. The proposed geometry in the current pilot tank achieves higher velocities and avoids recirculation areas. The results demonstrate that numerical modelling of these types of processes is possible with the computer models available (commercial codes) and can be used to optimize cleaning system designPeer ReviewedPostprint (published version

Lurupa - Rigorous Error Bounds in Linear Programming

Linear Programming has numerous applications, e.g., operations research, relaxations in global optimization, computational geometry. Recently it has been shown that many real world problems exhibit numerical difficulties due to ill-conditioning. Lurupa is a software package for computing rigorous optimal value bounds. The package can handle point and interval problems. Numerical experience with the Netlib lp library is given

Obtaining adjusted prevalence ratios from logistic regression model in cross-sectional studies

In the last decades, it has been discussed the use of epidemiological prevalence ratio (PR) rather than odds ratio as a measure of association to be estimated in cross-sectional studies. The main difficulties in use of statistical models for the calculation of PR are convergence problems, availability of adequate tools and strong assumptions. The goal of this study is to illustrate how to estimate PR and its confidence interval directly from logistic regression estimates. We present three examples and compare the adjusted estimates of PR with the estimates obtained by use of log-binomial, robust Poisson regression and adjusted prevalence odds ratio (POR). The marginal and conditional prevalence ratios estimated from logistic regression showed the following advantages: no numerical instability; simple to implement in a statistical software; and assumes the adequate probability distribution for the outcome

A dynamic convergence control scheme for the solution of the radial equilibrium equation in through-flow analyses

One of the most frequently encountered numerical problems in scientific analyses is the solution of non-linear equations. Often the analysis of complex phenomena falls beyond the range of applicability of the numerical methods available in the public domain, and demands the design of dedicated algorithms that will approximate, to a specified precision, the mathematical solution of specific problems. These algorithms can be developed from scratch or through the amalgamation of existing techniques. The accurate solution of the full radial equilibrium equation (REE) in streamline curvature (SLC) through-flow analyses presents such a case. This article discusses the development, validation, and application of an 'intelligent' dynamic convergence control (DCC) algorithm for the fast, accurate, and robust numerical solution of the non-linear equations of motion for two-dimensional flow fields. The algorithm was developed to eliminate the large extent of user intervention, usually required by standard numerical methods. The DCC algorithm was integrated into a turbomachinery design and performance simulation software tool and was tested rigorously, particularly at compressor operating regimes traditionally exhibiting convergence difficulties (i.e. far off-design conditions). Typical error histories and comparisons of simulated results against experimental are presented in this article for a particular case study. For all case studies examined, it was found that the algorithm could successfully 'guide' the solution down to the specified error tolerance, at the expense of a slightly slower iteration process (compared to a conventional Newton-Raphson scheme). This hybrid DCC algorithm can also find use in many other engineering and scientific applications that require the robust solution of mathematical problems by numerical instead of analytical means

Conservative bounds for the pfd of a 1-out-of-2 software-based system based on an assessor’s subjective probability of “not worse than independence”

We consider the problem of assessing the reliability of a 1-out-of-2 software-based system, in which failures of the two channels cannot be assumed to be independent with certainty. An informal approach to this problem assesses the channel pfds (probabilities of failure on demand) conservatively and then multiplies these together in the hope that the conservatism will be sufficient to overcome any possible dependence between the channel failures. Our intention here is to place this kind of reasoning on a formal footing. We introduce a notion of “not worse than independence” and assume that an assessor has a prior belief about this, expressed as a probability. We obtain a conservative prior system pfd, and show how a conservative posterior system pfd can be obtained following the observation of a number of demands without system failure. We present some illustrative numerical examples, discuss some of the difficulties involved in this way of reasoning, and suggest some avenues of future research

Graphical simulator of mathematical algorithms (GraSMA)

Our goal is to develop an interactive software GraSMA that illustrates the execution of mathematical algorithms in the context of numerical methods. We want to create a working tool for teachers and learning tool for students. To achieve it we only use free software (as it is the Open Source software). The strategy followed was to extend the original algorithm code, implemented in Octave, with inspector instructions, recording in a XML (eXtensible Markup Language) file everything that happened during the execution. Subsequently, the XML file is parsed by a Java application that graphically represents the mathematic objects and their behaviour during execution. In this paper, we report the procedures followed, the difficulties encountered and the first results we achieved

Effective numerical methods to model dynamic behavior of springs with torsion

Prof. Stephen Montgomery-Smith, Dissertation Supervisor.Includes vita.Field of Study: Mathematics ."July 2018."The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well studied. In this thesis we concentrate on the Kirchhoff problem. The goal is to create an effective and robust numerical method to model the dynamic behavior of springs that have a prescribed natural curvature. In addition to the mathematics, we also provide the implementation details of the numerical method using the computer language Python 3. We also discuss in detail the various difficulties of such a software implementation and how certain auxiliary computations can make the software more effective and robust.Includes bibliographical references (pages 105-114)