Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Using water balance models to approximate the effects of climate change on spring catchment discharge : Mt. Hanang, Tanzania

This project addresses the potential impacts of changing climate on dry-season water storage and discharge from a small, mountain catchment in Tanzania. Villagers and water managers around the catchment have experienced worsening water scarcity and attribute it to increasing population and demand, but very little has been done to understand the physical characteristics and hydrological behavior of the spring catchment. The physical nature of the aquifer was characterized and water balance models were calibrated to discharge observations so as to be able to explore relative changes in aquifer storage resulting from climate changes. To characterize the shallow aquifer supplying water to the Jandu spring, water quality and geochemistry data were analyzed, discharge recession analysis was performed, and two water balance models were developed and tested. Jandu geochemistry suggests a shallow, meteorically-recharged aquifer system with short circulation times. Baseflow recession analysis showed that the catchment behavior could be represented by a linear storage model with an average recession constant of 0.151/month from 2004-2010. Two modified Thornthwaite-Mather Water Balance (TMWB) models were calibrated using historic rainfall and discharge data and shown to reproduce dry-season flows with Nash-Sutcliffe efficiencies between 0.86 and 0.91. The modified TMWB models were then used to examine the impacts of nineteen, perturbed climate scenarios to test the potential impacts of regional climate change on catchment storage during the dry season. Forcing the models with realistic scenarios for average monthly temperature, annual precipitation, and seasonal rainfall distribution demonstrated that even small climate changes might adversely impact aquifer storage conditions at the onset of the dry season. The scale of the change was dependent on the direction (increasing vs. decreasing) and magnitude of climate change (temperature and precipitation). This study demonstrates that small, mountain aquifer characterization is possible using simple water quality parameters, recession analysis can be integrated into modeling aquifer storage parameters, and water balance models can accurately reproduce dry-season discharges and might be useful tools to assess climate change impacts. However, uncertainty in current climate projections and lack of data for testing the predictive capabilities of the model beyond the present data set, make the forecasts of changes in discharge also uncertain. The hydrologic tools used herein offer promise for future research in understanding small, shallow, mountainous aquifers and could potentially be developed and used by water resource professionals to assess climatic influences on local hydrologic systems.

The Blinder-Oaxaca decomposition for linear regression models

The counterfactual decomposition technique popularized by Blinder (1973, Journal of Human Resources, 436–455) and Oaxaca (1973, International Economic Review, 693–709) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. This article summarizes the technique and addresses several complications, such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new command called oaxaca is introduced, and examples illustrating its usage are given.

Some past decision theory models for euro construction model codes and for road drainage in Spain, and modest hints with multi-criteria methods for agro and environmental assurance

The authors are from UPM and are relatively grouped, and all have intervened in different academic or real cases on the subject, at different times as being of different age. With precedent from E. Torroja and A. Páez in Madrid Spain Safety Probabilistic models for concrete about 1957, now in ICOSSAR conferences, author J.M. Antón involved since autumn 1967 for euro-steel construction in CECM produced a math model for independent load superposition reductions, and using it a load coefficient pattern for codes in Rome Feb. 1969, practically adopted for European constructions, giving in JCSS Lisbon Feb. 1974 suggestion of union for concrete-steel-al.. That model uses model for loads like Gumbel type I, for 50 years for one type of load, reduced to 1 year to be added to other independent loads, the sum set in Gumbel theories to 50 years return period, there are parallel models. A complete reliability system was produced, including non linear effects as from buckling, phenomena considered somehow in actual Construction Eurocodes produced from Model Codes. The system was considered by author in CEB in presence of Hydraulic effects from rivers, floods, sea, in reference with actual practice. When redacting a Road Drainage Norm in MOPU Spain an optimization model was realized by authors giving a way to determine the figure of Return Period, 10 to 50 years, for the cases of hydraulic flows to be considered in road drainage. Satisfactory examples were a stream in SE of Spain with Gumbel Type I model and a paper of Ven Te Chow with Mississippi in Keokuk using Gumbel type II, and the model can be modernized with more varied extreme laws. In fact in the MOPU drainage norm the redacting commission acted also as expert to set a table of return periods for elements of road drainage, in fact as a multi-criteria complex decision system. These precedent ideas were used e.g. in wide Codes, indicated in symposia or meetings, but not published in journals in English, and a condensate of contributions of authors is presented. The authors are somehow involved in optimization for hydraulic and agro planning, and give modest hints of intended applications in presence of agro and environment planning as a selection of the criteria and utility functions involved in bayesian, multi-criteria or mixed decision systems. Modest consideration is made of changing in climate, and on the production and commercial systems, and on others as social and financial.

Frequency and temporal effects in linear optical quantum computing

Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be nonidealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a nondeterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing nonideal photon counters, which have finite bandwidth and time response.

Impact of potential models on adsorption of linear molecules on carbon black

In this paper, we investigate the effects of potential models on the description of equilibria of linear molecules (ethylene and ethane) adsorption on graphitized thermal carbon black. GCMC simulation is used as a tool to give adsorption isotherms, isosteric heat of adsorption and the microscopic configurations of these molecules. At the heart of the GCMC are the potential models, describing fluid-fluid interaction and solid-fluid interaction. Here we studied the two potential models recently proposed in the literature, the UA-TraPPE and AUA4. Their impact in the description of adsorption behavior of pure components will be discussed. Mixtures of these components with nitrogen and argon are also studied. Nitrogen is modeled a two-site plus discrete charges while argon as a spherical particle. GCMC simulation is also used for generating simulation mixture isotherms. It is found that co-operation between species occurs when the surface is fractionally covered while competition is important when surface is fully loaded.

Effects of rock properties on specific cutting energy in linear cutting of sandstones by picks

Specific cutting energy (SE) has been widely used to assess the rock cuttability for mechanical excavation purposes. Some prediction models were developed for SE through correlating rock properties with SE values. However, some of the textural and compositional rock parameters i.e. texture coefficient and feldspar, mafic, and felsic mineral contents were not considered. The present study is to investigate the effects of previously ignored rock parameters along with engineering rock properties on SE. Mineralogical and petrographic analyses, rock mechanics, and linear rock cutting tests were performed on sandstone samples taken from sites around Ankara, Turkey. Relationships between SE and rock properties were evaluated using bivariate correlation and linear regression analyses. The tests and subsequent analyses revealed that the texture coefficient and feldspar content of sandstones affected rock cuttability, evidenced by significant correlations between these parameters and SE at a 90% confidence level. Felsic and mafic mineral contents of sandstones did not exhibit any statistically significant correlation against SE. Cementation coefficient, effective porosity, and pore volume had good correlations against SE. Poisson's ratio, Brazilian tensile strength, Shore scleroscope hardness, Schmidt hammer hardness, dry density, and point load strength index showed very strong linear correlations against SE at confidence levels of 95% and above, all of which were also found suitable to be used in predicting SE individually, depending on the results of regression analysis, ANOVA, Student's t-tests, and R2 values. Poisson's ratio exhibited the highest correlation with SE and seemed to be the most reliable SE prediction tool in sandstones.

Effects of rock properties on specific cutting energy in linear cutting of sandstones by picks

Specific cutting energy (SE) has been widely used to assess the rock cuttability for mechanical excavation purposes. Some prediction models were developed for SE through correlating rock properties with SE values. However, some of the textural and compositional rock parameters i.e. texture coefficient and feldspar, mafic, and felsic mineral contents were not considered. The present study is to investigate the effects of previously ignored rock parameters along with engineering rock properties on SE. Mineralogical and petrographic analyses, rock mechanics, and linear rock cutting tests were performed on sandstone samples taken from sites around Ankara, Turkey. Relationships between SE and rock properties were evaluated using bivariate correlation and linear regression analyses. The tests and subsequent analyses revealed that the texture coefficient and feldspar content of sandstones affected rock cuttability, evidenced by significant correlations between these parameters and SE at a 90% confidence level. Felsic and mafic mineral contents of sandstones did not exhibit any statistically significant correlation against SE. Cementation coefficient, effective porosity, and pore volume had good correlations against SE. Poisson's ratio, Brazilian tensile strength, Shore scleroscope hardness, Schmidt hammer hardness, dry density, and point load strength index showed very strong linear correlations against SE at confidence levels of 95% and above, all of which were also found suitable to be used in predicting SE individually, depending on the results of regression analysis, ANOVA, Student's t-tests, and R-2 values. Poisson's ratio exhibited the highest correlation with SE and seemed to be the most reliable SE prediction tool in sandstones.

Error models for mode mismatch in linear optics quantum computing

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.

Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data

2000 Mathematics Subject Classification: 62H12, 62P99

Improved models for estimating temporal changes in carbon sequestration in above-ground biomass of mixed-species environmental plantings

Plantings of mixed native species (termed 'environmental plantings') are increasingly being established for carbon sequestration whilst providing additional environmental benefits such as biodiversity and water quality. In Australia, they are currently one of the most common forms of reforestation. Investment in establishing and maintaining such plantings relies on having a cost-effective modelling approach to providing unbiased estimates of biomass production and carbon sequestration rates. In Australia, the Full Carbon Accounting Model (FullCAM) is used for both national greenhouse gas accounting and project-scale sequestration activities. Prior to undertaking the work presented here, the FullCAM tree growth curve was not calibrated specifically for environmental plantings and generally under-estimated their biomass. Here we collected and analysed above-ground biomass data from 605 mixed-species environmental plantings, and tested the effects of several planting characteristics on growth rates. Plantings were then categorised based on significant differences in growth rates. Growth of plantings differed between temperate and tropical regions. Tropical plantings were relatively uniform in terms of planting methods and their growth was largely related to stand age, consistent with the un-calibrated growth curve. However, in temperate regions where plantings were more variable, key factors influencing growth were planting width, stand density and species-mix (proportion of individuals that were trees). These categories provided the basis for FullCAM calibration. Although the overall model efficiency was only 39-46%, there was nonetheless no significant bias when the model was applied to the various planting categories. Thus, modelled estimates of biomass accumulation will be reliable on average, but estimates at any particular location will be uncertain, with either under- or over-prediction possible. When compared with the un-calibrated yield curves, predictions using the new calibrations show that early growth is likely to be more rapid and total above-ground biomass may be higher for many plantings at maturity. This study has considerably improved understanding of the patterns of growth in different types of environmental plantings, and in modelling biomass accumulation in young (<25. years old) plantings. However, significant challenges remain to understand longer-term stand dynamics, particularly with temporal changes in stand density and species composition. © 2014.