Search

The influence of finite sample size on the behavior of Johansen's maximum likelihood method for projecting long-term equilibrium relationships or cointegrating vectors was determined using the Monte Carlo method. It was found that, with finite size samples, the Johansen test tends to find cointegration more often than asymptotic theory suggests. This bias is further amplified as the dimensions and lag length of the system under study increase.

A log logistic function is presented as an alternative to the probit and logistic functions normally used in mathematical economics to model saturation effects including ownership. The log logistic function is best suited to systems with strict positivity. The log logistic model demonstrates excellent goodness of fit at unconstrained and constrained ownership levels where the logistic model fails.

Two methods of measuring inflation uncertainty are evaluated. The projections of the autoregressive conditional heteroscedasticity model which calculates inflation uncertainty on the basis of past forecast errors are compared with those projected by economic forecasters participating in the quarterly ASA-NBER survey. The two methods yielded very different statistical characteristics. This variance is due to the subjective nature of the survey method and the historical limitations of the model-based approach.

Algebraic modeling languages for mathematical programming applications are evaluated. An algebraic language is a formal description of objective functions and constraints of an optimization model in an algebraic format. Prominent features of the languages are analyzed to determine their level of applicability to human techniques of model derivation. Features include model and data separation and language interpreter integration to other mathematical programming components.

A numerical simulator of an heterojunction bipolar transistor (HBT), which solves the moments of the Boltzmann transport equation, is employed to examine the behavior of several large-signal analytical models at millimeter-wave frequencies. Transit-time delays are shown to cause poor millimeter-wave performance for both the Gummel-Poon and Ebers-Moll models. An enhanced Ebers-Moll model is developed for which large-signal measurements of an HBT at 10-27 GHz are conducted to verify its validity.

A performance measure technique for evaluating the predictive validity of software reliability models is presented. The method is based on the use of Kolmogorov-Smirnov tables for testing goodness-of-fit between modeled and measured data. A new statistical tool for performance evaluation is introduced to surmount a major shortcoming of the Littlewood approach.

The prediction of single event rates depends upon the proper interpretation of ground test data and upon the way the data is used in the rate calculations. This work performs a critical review of various methods used for heavy ion predictions and recommends a standard approach.

Analysis of vibration signals emitted by the knee joint has the potential for the development of a noninvasive procedure for the diagnosis and monitoring of knee pathology. In order to obtain as much information as possible from the power density spectrum of the knee vibration signal, it is necessary to identify the physiological factors (or physiologically relevant parameters) that shape the spectrum. This paper presents a mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement. It demonstrates through the mathematical model that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm was developed, which generates PFP signals with adjustable repetition rate and IPI variance. Signals generated by simulation were seen to possess representative spectral characteristics typically observed in physiological PFP signals. This simulation procedure allows an interactive examination of several factors which affect the PFP train spectrum. Finally, in vivo measurements of physiological PFP signals of normal volunteers are presented. Results of simulations and analysis of signals recorded from human subjects support the mathematical model's prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal. Evidence is presented to show that ignoring these IPI statistics will affect the interpretation of the spectrum.

A model of magnetoelasticity based on the differential susceptibility, the stress effective magnetic field and stress demagnetization in conjunction with appropriate rules of hysteresis is presented and compared to experimental data for high strength steels for several magnetoelastic processes, including (Mathematical Expression Omitted) where symbols indicate the order of application and removal of stress and field. We observe a decrease in stress effectiveness and define a saturation anisotropy factor which decreases from unity in the Rayleigh region to less than one half for our values of stress and field. The model also predicts the stressed saturate hysteresis loop and equilibrium near the anhysteretic curve and enables understanding of the Villari reversal of magnetoelastic sensitivity.

Modern robust control synthesis techniques aim at providing robustness with respect to uncertainty in the form of both additive noise and plant perturbations. On the other hand, the most popular system identification methods assume that all uncertainty is in the form of additive noise. This has hampered the application of robust control methods to practical problems. This paper begins to address the gap between the models used in control synthesis and those obtained from identification experiments by considering the connection between uncertain models and data. The model validation problem addressed here is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard [H.sub.infinity]/[mu] framework models. A necessary condition for such a model to describe an experimental datum is obtained. Furthermore, for a large class of models, in the robust control framework, this condition is computable as the solution of a quadratic optimization problem.

A method for modeling turbulent particle dispersion is evaluated for computational speed. The method diminishes sampling requisites and gives the lowest computational shot noise. The technique produces numerical results that are comparable with those derived from direct-modeling. In deriving the formula for the turbulent dispersion, the effect of each turbulent eddy on the succeeding dispersions was sent through the following eddies.

The effectiveness of two-equation turbulence models to forecast the behavior of separated flows is evaluated. Turbulent flow from a backward-facing step is studied to verify disputed claims about the models' capability. Results show that forecasting errors are introduced because of computational complexities encountered in analyzing the turbulence. The utilization of an isotropic eddy viscosity led to erroneous forecasts of Reynolds stress variations. The K-epsilon model gives good results for the backward-facing step problem if an anisotropic eddy viscosity with a correct value is used.

A mathematical model was developed to calculate optimal sterilization temperatures. The value for the processing temperature was mathematically derived from the following considered variables: product heating rate, surface heat transfer coefficient, initial food temperature , heating medium come-up time z-value for quality factor and sterilizing value. The initial temperature and heating medium come-up time had the least significance in the equation.

Accident prediction models or the before-and-after study approach is commonly used to estimate the reduction in number of accidents resulting from highway improvements. The highway improvement evaluation results will depend on the approach used, if the two approaches do not yield the same number of accidents reduced. This study computed the accident reductions on two-lane rural highways in Illinois using: (1) Mathematical models for accident frequency prediction; and (2) a before-and-after study with control sites. Accident data for two years before and two years after the improvements were collected. One linear and three multiplicative form models were used to fit the accident data collected from 51 projects with a total length of 349 mi. The linear models were found to be as good as, and in some cases even better than, the multiplicative models in explaining the variation of accident frequency in both before and after conditions. The linear models indicated a stronger correlation between accident frequency, traffic volume, and roadway geometry than the multiplicative models for an ADT range of 500-5,000. This finding is contrary to that of Boyce et al. (1988) and Zegeer et al. (1987a), which recommended the multiplicative models over the linear models. The before-and-after study with control sites estimated accident reductions 1.40-2.06 times higher than those of the linear model., Estimating accident reductions on highways involves the use of either mathematical models or before-and-after studies with control sites. A comparative study on these two approaches was conducted with data supplied by the Illinois Department of Transportation. Mathematical modeling, which is based on the relationship between variables such as average daily traffic, accident frequency and roadway geometry, is most effectively used in sensitivity analysis. Before-and-after studies give precise results depending on how well the control sites simulate actual highway improvements.

This Monte Carlo study examined the accuracy of 6 validity generalization (VG) procedures when the procedures were applied without a set of assumed artifact distributions. Because in most cases the relevance of the artifact distributions is difficult if not impossible to establish, it is important to investigate the accuracy of VG procedures when these are based only on available data. The study showed that VG procedures that are based on the available data are accurate, if the usual VG assumptions are met and the selection ratio is not too small. When there was little or no variability in the selection ratio across situations, the TSA1 procedure (Raju & Burke, 1983) was the most accurate. For conditions in which there is variability in the selection ratio, we recommend Hedge's procedure (Hedges, 1988).

The corrected Miller-tucker-Zemlin subtour elimination constraints for the capacitated vehicle routing problem are presented.

Authors G. Kaiblinger-Grujin, H. Kosina and S. Selberherr have proposed a model to explain the experimentally observed dependence of the low-field electron mobility in n-type silicon on dopant species. However, a scrutiny of their model presents a number of questionable aspects. Further, when their model is modified to relieve it from its original inconsistencies, it is unable to account for the dependence of the electron mobility on dopant species.

A model is proposed for the pricing of US-type interest rate bond options for pure Gaussian processes factors that integrates the impact of skewness and kurtosis in the distribution of bond option price interest rates. The proposed model extends existing literature on such pricing models to pricing under Poisson-Gaussian processes in the Heath-Jarrow-Morton structure. It then allows the impact of skewness and kurtosis to be incorporated in the pricing of interest rate derivative securities.

Most compact and non-compact optimization schemes which have been developed are limited to central difference algorithms which result in stability problems that must be addressed through the use of filters or explicit dissipation terms. An optimized upwind dispersion-relation-preserving finite difference scheme has been developed to enhance the quality of the numerical solution of short waves without adding an explicit artificial damping term to the finite difference equations. The proposed scheme is discussed.

A study was conducted to develop a rapid non-destructive ultrasonic technique for evaluating the decomposition of fish. Thus, the efficacy of a semi-empirical equation that was developed to link the ultrasonic velocity of fish tissue to its composition at any temperature was investigated using fillets from the Atlantic cod, Atlantic mackerel, Atlantic salmon, Channel catfish and Sole flounder. Results indicate that ultrasonic velocity measurements may be useful for evaluating the composition of fish.

We consider an on-line string matching problem in which we find all the occurrences of a pattern of in characters in a text of n characters, where all the characters of the pattern are available before processing while the characters of the text are input one after the other. We propose a space-time optimal parallel algorithm for this problem using a neural network approach. This algorithm uses in McCulloch-Pitts neurons connected as a linear array. It processes every input character of the text in one step and hence it requires at most n iteration steps. Index Terms - Algorithms, neural network, string matching.

Game theory can be utilized as a basis for the modelling of the political economy and agricultural economics. The game theory can also be utilized for the analysis of complex household and organizations in commercial agriculture. The application of game theory to the New International Trade Theory (NITT) in connection with the New Growth Theory led to the formation of a more comprehensive framework or model for the NITT.

Pascal Lavergne's criticisms on the use of R2 in probability models are erroneous and his transformed model is not applicable in processes with varied unconditional mean values. The percentage variation of dependent variables is overstated by conventional measures of R2 due to the shifting of the unconditional mean. The unconditional mean of the dependent variable is inappropriately treated as a constant by the R2 causing biased conventional R2 measures.

Ana M. McGuirk and Paul Driscoll's criticisms on the use of R2 in the selection of probability models was erroneous. McGuirk and Driscoll stated that R2 levels are low in probability models but misspecified models produce high R2 levels. However, their comments on the use of R2 are trivial due to their erroneous interpretation of R2 measures including conditional and unconditional probability distributions. Furthermore, the consistency problems that they detected based on their simulations are non-existent.

Background: Many mathematical models have investigated the impact of expanding access to antiretroviral therapy (ART) on new HIV infections. Comparing results and conclusions across models is challenging because models have addressed slightly different questions and have reported different outcome metrics. This study compares the predictions of several mathematical models simulating the same ART intervention programmes to determine the extent to which models agree about the epidemiological impact of expanded ART. Methods and Findings: Twelve independent mathematical models evaluated a set of standardised ART intervention scenarios in South Africa and reported a common set of outputs. Intervention scenarios systematically varied the CD4 count threshold for treatment eligibility, access to treatment, and programme retention. For a scenario in which 80% of HIV- infected individuals start treatment on average 1 y after their CD4 count drops below 350 cells/µl and 85% remain on treatment after 3 y, the models projected that HIV incidence would be 35% to 54% lower 8 y after the introduction of ART, compared to a counterfactual scenario in which there is no ART. More variation existed in the estimated long-term (38 y) reductions in incidence. The impact of optimistic interventions including immediate ART initiation varied widely across models, maintaining substantial uncertainty about the theoretical prospect for elimination of HIV from the population using ART alone over the next four decades. The number of person-years of ART per infection averted over 8 y ranged between 5.8 and 18.7. Considering the actual scale-up of ART in South Africa, seven models estimated that current HIV incidence is 17% to 32% lower than it would have been in the absence of ART. Differences between model assumptions about CD4 decline and HIV transmissibility over the course of infection explained only a modest amount of the variation in model results. Conclusions: Mathematical models evaluating the impact of ART vary substantially in structure, complexity, and parameter choices, but all suggest that ART, at high levels of access and with high adherence, has the potential to substantially reduce new HIV infections. There was broad agreement regarding the short-term epidemiologic impact of ambitious treatment scale-up, but more variation in longer term projections and in the efficiency with which treatment can reduce new infections. Differences between model predictions could not be explained by differences in model structure or parameterization that were hypothesized to affect intervention impact. Please see later in the article for the Editors' Summary., Introduction There has recently been increasing interest in expanding provision of antiretroviral therapy (ART) as a tool for reducing the spread of HIV in generalised epidemics in sub-Saharan Africa [1-5]. [...]

Byline: Mihaela Popescu, Stein Tore Johansen This paper sets out to investigate parameters that determine flow-induced vibrations in flexible, corrugated pipes. A central element in this paper is a mathematical model that describes the phenomenon. The presented model is designed to capture the aero-acoustic wave behaviour of gas that flows in a corrugated pipe, exploring the feedback analysis. This model involves the coupling between the large-scale acoustic behaviour in a pipe and a line of self-excited oscillators representing vortex excitation caused by flow over corrugations.

Byline: Schalk W.P. Cloete, Jacques J. Eksteen, Steven M. Bradshaw A full-scale, three-dimensional, transient mathematical model for application to gas-stirred ladles was developed. Multiphase aspects were accounted for by employing the Lagrangian Discrete Phase Model (DPM) in describing the bubble plume and the Eulerian Volume of Fluid (VOF) model for tracking the free surface of the melt. The standard k-ε (SKE) model was used for modelling turbulence. Further research is required to refine the turbulence modelling approach, but validation experiments showed that the present approach yielded accurate information on bulk fluid flow and mixing in the ladle. The resulting model is easily generalised and computationally efficient.

Byline: Y. Zhao, S.A. Billings, D. Coca An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models is introduced. Simulation examples are employed to find appropriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed and the parameters of the model are investigated.

An occupational choice model that corrects for occupational choice misclassification and errors in occupation-specific work experience measurement is presented. Results show that ignoring occupational choice misclassification cause biases, affecting findings from empirical occupational choice models. The applications of the new occupational choice model are discussed.