Methods for Categorical Longitudinal Survey Data: Understanding Employment Status of Australian Women

Many variables that are of interest in social science research are nominal variables with two or more categories, such as employment status, occupation, political preference, or self-reported health status. With longitudinal survey data it is possible to analyse the transitions of individuals between different employment states or occupations (for example). In the statistical literature, models for analysing categorical dependent variables with repeated observations belong to the family of models known as generalized linear mixed models (GLMMs). The specific GLMM for a dependent variable with three or more categories is the multinomial logit random effects model. For these models, the marginal distribution of the response does not have a closed form solution and hence numerical integration must be used to obtain maximum likelihood estimates for the model parameters. Techniques for implementing the numerical integration are available but are computationally intensive requiring a large amount of computer processing time that increases with the number of clusters (or individuals) in the data and are not always readily accessible to the practitioner in standard software. For the purposes of analysing categorical response data from a longitudinal social survey, there is clearly a need to evaluate the existing procedures for estimating multinomial logit random effects model in terms of accuracy, efficiency and computing time. The computational time will have significant implications as to the preferred approach by researchers. In this paper we evaluate statistical software procedures that utilise adaptive Gaussian quadrature and MCMC methods, with specific application to modeling employment status of women using a GLMM, over three waves of the HILDA survey.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Relative dispersion of intravascular transit times during isolated human limb perfusions for recurrent melanoma

Aims We have characterized the relative dispersion of vascular and extravascular markers in the limbs of three patients undergoing isolated limb perfusions with the cytotoxic melphalan for recurrent malignant melanoma both before and after melphalan dosing. Methods A bolus of injectate containing [Cr-51] labelled red blood cells, [C-14]-sucrose and [H-3]-water was injected into an iliac or femoral artery and outflow samples collected at 1 s intervals by a fraction collector. The radioactivity due to each isotype was analysed by either gamma [Cr-51] or beta [C-14 and H-3] counting. The moments of the outflow fraction-time profiles were estimated by a nonparametric (numerical integration) method and a parametric model (sum of two inverse Gaussian functions). Results The availability, mean transit time and normalised variance (CV2) obtained for labelled red blood cells, sucrose and water were similar before and after melphalan dosing and with the two methods of calculation but varied between the patients. Conclusions The vascular space is not well-stirred but characterized by a CV2 similar that reported previously for in situ rat hind limb and rat liver perfusions. A flow-limited blood-tissue exchange was observed for the permeating indicators. Administration of melphalan did not influence the distribution characteristics of the indicators.

Model-Predicted Performance of Second-Trimester Down Syndrome Screening With Sonographic Prenasal Thickness

Objective. The purpose of this study was to estimate the Down syndrome detection and false-positive rates for second-trimester sonographic prenasal thickness (PT) measurement alone and in combination with other markers. Methods. Multivariate log Gaussian modeling was performed using numerical integration. Parameters for the PT distribution, in multiples of the normal gestation-specific median (MoM), were derived from 105 Down syndrome and 1385 unaffected pregnancies scanned at 14 to 27 weeks. The data included a new series of 25 cases and 535 controls combined with 4 previously published series. The means were estimated by the median and the SDs by the 10th to 90th range divided by 2.563. Parameters for other markers were obtained from the literature. Results. A log Gaussian model fitted the distribution of PT values well in Down syndrome and unaffected pregnancies. The distribution parameters were as follows: Down syndrome, mean, 1.334 MoM; log(10) SD, 0.0772; unaffected pregnancies, 0.995 and 0.0752, respectively. The model-predicted detection rates for 1%, 3%, and 5% false-positive rates for PT alone were 35%, 51%, and 60%, respectively. The addition of PT to a 4 serum marker protocol increased detection by 14% to 18% compared with serum alone. The simultaneous sonographic measurement of PT and nasal bone length increased detection by 19% to 26%, and with a third sonographic marker, nuchal skin fold, performance was comparable with first-trimester protocols. Conclusions. Second-trimester screening with sonographic PT and serum markers is predicted to have a high detection rate, and further sonographic markers could perform comparably with first-trimester screening protocols.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Identificação modal e simulação da resposta sísmica de barragens abóbada

Trabalho Final de Mestrado elaborado no Laboratório Nacional de Engenharia Civil (LNEC) para a obtenção do grau de Mestre em Engenharia Civil pelo Instituto Superior de Engenharia de Lisboa no âmbito do protocolo de cooperação ente o ISEL e o LNEC

Analysis of parity between protein-based electrophoretic methods for the characterization of oral Candida species

Electrophoretic studies of multilocus-enzymes (MLEE) and whole-cell protein (SDS-PAGE) were carried out in order to evaluate the parity between different methods for the characterization of five Candida species commonly isolated from oral cavity of humans by numerical taxonomy methods. The obtained data revealed that sodium dodecyl sulfate polyacrylamide gel electrophoresis is more efficient in grouping strains in their respective species while MLEE has much limited resolution in organizing all strains in their respective species-specific clusters. MLEE technique must be regarded for surveys in which just one species of Candida is involved.

Segmentation and grid generation for numerical simulations of vad connections with patient-specific data

Objectives: We are interested in the numerical simulation of the anastomotic region comprised between outflow canula of LVAD and the aorta. Segmenta¬tion, geometry reconstruction and grid generation from patient-specific data remain an issue because of the variable quality of DICOM images, in particular CT-scan (e.g. metallic noise of the device, non-aortic contrast phase). We pro¬pose a general framework to overcome this problem and create suitable grids for numerical simulations.Methods: Preliminary treatment of images is performed by reducing the level window and enhancing the contrast of the greyscale image using contrast-limited adaptive histogram equalization. A gradient anisotropic diffusion filter is applied to reduce the noise. Then, watershed segmentation algorithms and mathematical morphology filters allow reconstructing the patient geometry. This is done using the InsightToolKit library (www.itk.org). Finally the Vascular Model¬ing ToolKit (www.vmtk.org) and gmsh (www.geuz.org/gmsh) are used to create the meshes for the fluid (blood) and structure (arterial wall, outflow canula) and to a priori identify the boundary layers. The method is tested on five different patients with left ventricular assistance and who underwent a CT-scan exam.Results: This method produced good results in four patients. The anastomosis area is recovered and the generated grids are suitable for numerical simulations. In one patient the method failed to produce a good segmentation because of the small dimension of the aortic arch with respect to the image resolution.Conclusions: The described framework allows the use of data that could not be otherwise segmented by standard automatic segmentation tools. In particular the computational grids that have been generated are suitable for simulations that take into account fluid-structure interactions. Finally the presented method features a good reproducibility and fast application.

CR1Dmod: A Matlab program to model 1D complex resistivity effects in electrical and electromagnetic surveys

We have constructed a forward modelling code in Matlab, capable of handling several commonly used electrical and electromagnetic methods in a 1D environment. We review the implemented electromagnetic field equations for grounded wires, frequency and transient soundings and present new solutions in the case of a non-magnetic first layer. The CR1Dmod code evaluates the Hankel transforms occurring in the field equations using either the Fast Hankel Transform based on digital filter theory, or a numerical integration scheme applied between the zeros of the Bessel function. A graphical user interface allows easy construction of 1D models and control of the parameters. Modelling results are in agreement with other authors, but the time of computation is less efficient than other available codes. Nevertheless, the CR1Dmod routine handles complex resistivities and offers solutions based on the full EM-equations as well as the quasi-static approximation. Thus, modelling of effects based on changes in the magnetic permeability and the permittivity is also possible.

An Assessment ofFatigue Strength of Load Carrying Welded Joints with Lack of Penetration

On yleisesti tiedossa, että väsyttävän kuormituksen alaisena olevat hitsatut rakenteet rikkoutuvat juuri hitsausliitoksista. Täyden tunkeuman hitsausliitoksia sisältävien rakenteiden asiantunteva suunnittelu janykyaikaiset valmistusmenetelmät ovat lähes eliminoineet väsymisvauriot hitsatuissa rakenteissa. Väsymislujuuden parantaminen tiukalla täyden tunkeuman vaatimuksella on kuitenkin epätaloudellinen ratkaisu. Täyden tunkeuman hitsausliitoksille asetettavien laatuvaatimuksien on määriteltävä selkeät tarkastusohjeet ja hylkäämisperusteet. Tämän diplomityön tarkoituksena oli tutkia geometristen muuttujien vaikutusta kuormaa kantavien hitsausliitosten väsymislujuuteen. Huomio kiinnitettiin pääasiassa suunnittelumuuttujiin, joilla on vaikutusta väsymisvaurioiden syntymiseen hitsauksen juuren puolella. Nykyiset määräykset ja standardit, jotka perustuvat kokeellisiin tuloksiin; antavat melko yleisiä ohjeita hitsausliitosten väsymismitoituksesta. Tämän vuoksi muodostettiin kokonaan uudet parametriset yhtälöt sallitun nimellisen jännityksen kynnysarvon vaihteluvälin, ¿¿th, laskemiseksi, jotta vältettäisiin hitsausliitosten juuren puoleiset väsymisvauriot. Lisäksi, jokaiselle liitostyypille laskettiin hitsin juuren puolen väsymisluokat (FAT), joita verrattiin olemassa olevilla mitoitusohjeilla saavutettuihin tuloksiin. Täydentäviksi referensseiksi suoritettiin useita kolmiulotteisia (3D) analyysejä. Julkaistuja kokeellisiin tuloksiin perustuvia tietoja käytettiin apuna hitsausliitosten väsymiskäyttäytymisen ymmärtämiseksi ja materiaalivakioiden määrittämiseksi. Kuormaa kantavien vajaatunkeumaisten hitsausliitosten väsymislujuus määritettiin käyttämällä elementtimenetelmää. Suurimman pääjännityksen kriteeriä hyödynnettiin murtumiskäyttäytymisen ennakoimiseksi. Valitulle hitsatulle materiaalille ja koeolosuhteille murtumiskäyttäytymistä mallinnettiin särön kasvunopeudella da/dN ja jännitysintensiteettikertoimen vaihteluvälillä, 'K. Paris:n yhtälön numeerinen integrointi suoritettiin FRANC2D/L tietokoneohjelmalla. Saatujen tulosten perusteella voidaan laskea FAT tutkittavassa tapauksessa. ¿¿th laskettiin alkusärön jännitysintensiteettikertoimen vaihteluvälin ja kynnysjännitysintensiteettikertoimen, 'Kth, perusteella. ¿Kth arvoa pienemmällä vaihteluvälillä särö ei kasva. Analyyseissäoletuksena oli hitsattu jälkikäsittelemätön liitos, jossa oli valmis alkusärö hitsin juuressa. Analyysien tulokset ovat hyödyllisiä suunnittelijoille, jotka tekevät päätöksiä koskien geometrisiä parametreja, joilla on vaikutusta hitsausliitosten väsymislujuuteen.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Desenvolvimento e aplicação de células eletroquímicas em camada delgada

Theoretical and practical aspects concerning construction and use of a thin layer electrochemical cell are presented. Construction was realized by a simple technic and geometry was optimized in order to minimize the problems of electrical resistance. A well known redox system was studied ((Fe(III)(CN)6(3-)/Fe(II)(CN) 6(4-)) using two experimental methods, cyclic voltammetry and pulse chronopotentiometry. A numerical integration based-program was developed to calculate the voltammetric current in case of nernstian and non-nernstian behaviours and a diffusional model was used to treat the chronopotentiometric data. Thermodynamic (potential, concentration) and kinetic parameters (diffusion coefficient) were successfully determined for the redox system studied in this work.

Computational methods for tactical simulations

Tämä taktiikan tutkimus keskittyy tietokoneavusteisen simuloinnin laskennallisiin menetelmiin, joita voidaan käyttää taktisen tason sotapeleissä. Työn tärkeimmät tuotokset ovat laskennalliset mallit todennäköisyyspohjaisen analyysin mahdollistaviin taktisen tason taistelusimulaattoreihin, joita voidaan käyttää vertailevaan analyysiin joukkue-prikaatitason tarkastelutilanteissa. Laskentamallit keskittyvät vaikuttamiseen. Mallit liittyvät vahingoittavan osuman todennäköisyyteen, jonka perusteella vaikutus joukossa on mallinnettu tilakoneina ja Markovin ketjuina. Edelleen näiden tulokset siirretään tapahtumapuuanalyysiin operaation onnistumisen todennäköisyyden osalta. Pienimmän laskentayksikön mallinnustaso on joukkue- tai ryhmätasolla, jotta laskenta-aika prikaatitason sotapelitarkasteluissa pysyisi riittävän lyhyenä samalla, kun tulokset ovat riittävän tarkkoja suomalaiseen maastoon. Joukkueiden mies- ja asejärjestelmävahvuudet ovat jakaumamuodossa, eivätkä yksittäisiä lukuja. Simuloinnin integroinnissa voidaan käyttää asejärjestelmäkohtaisia predictor corrector –parametreja, mikä mahdollistaa aika-askelta lyhytaikaisempien taistelukentän ilmiöiden mallintamisen. Asemallien pohjana ovat aiemmat tutkimukset ja kenttäkokeet, joista osa kuuluu tähän väitöstutkimukseen. Laskentamallien ohjelmoitavuus ja käytettävyys osana simulointityökalua on osoitettu tekijän johtaman tutkijaryhmän ohjelmoiman ”Sandis”- taistelusimulointiohjelmiston avulla, jota on kehitetty ja käytetty Puolustusvoimien Teknillisessä Tutkimuslaitoksessa. Sandikseen on ohjelmoitu karttakäyttöliittymä ja taistelun kulkua simuloivia laskennallisia malleja. Käyttäjä tai käyttäjäryhmä tekee taktiset päätökset ja syöttää nämä karttakäyttöliittymän avulla simulointiin, jonka tuloksena saadaan kunkin joukkuetason peliyksikön tappioiden jakauma, keskimääräisten tappioiden osalta kunkin asejärjestelmän aiheuttamat tappiot kuhunkin maaliin, ammuskulutus ja radioyhteydet ja niiden tila sekä haavoittuneiden evakuointi-tilanne joukkuetasolta evakuointisairaalaan asti. Tutkimuksen keskeisiä tuloksia (kontribuutio) ovat 1) uusi prikaatitason sotapelitilanteiden laskentamalli, jonka pienin yksikkö on joukkue tai ryhmä; 2) joukon murtumispisteen määritys tappioiden ja haavoittuneiden evakuointiin sitoutuvien taistelijoiden avulla; 3) todennäköisyyspohjaisen riskianalyysin käyttömahdollisuus vertailevassa tutkimuksessa sekä 4) kokeellisesti testatut tulen vaikutusmallit ja 5) toimivat integrointiratkaisut. Työ rajataan maavoimien taistelun joukkuetason todennäköisyysjakaumat luovaan laskentamalliin, kenttälääkinnän malliin ja epäsuoran tulen malliin integrointimenetelmineen sekä niiden antamien tulosten sovellettavuuteen. Ilmasta ja mereltä maahan -asevaikutusta voidaan tarkastella, mutta ei ilma- ja meritaistelua. Menetelmiä soveltavan Sandis -ohjelmiston malleja, käyttötapaa ja ohjelmistotekniikkaa kehitetään edelleen. Merkittäviä jatkotutkimuskohteita mallinnukseen osalta ovat muun muassa kaupunkitaistelu, vaunujen kaksintaistelu ja maaston vaikutus tykistön tuleen sekä materiaalikulutuksen arviointi.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.