Numerical proper reparametrization of space curves and surfaces

Simplifying rational parametrizations of surfaces is a basic problem in CAD (computer-aided design). One important way is to reduce their tracing index, called proper reparametrization. Most existing proper reparametrization work is symbolic, yet in practical environments the surfaces are usually given with perturbed coefficients hence need a numerical technique of reparametrization considering the intrinsic properness of the perturbed surfaces. We present algorithms for reparametrizing a numerically rational space curve or surface. First, we provide an efficient way to find a parametric support transformation and compute a reparametrization with proper parametric support. Second, we develop a numerical algorithm to further reduce the tracing index, where numerical techniques such as sparse interpolation and approximated GCD computations are involved. We finally provide the error bound between the given rational curve/surface and our reparametrization result.Ministerio de Ciencia, Innovación y Universidade

On computational tools for Bayesian data analysis

While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte Carlo methods and more recently Approximate Bayesian Computation techniques have considerably increased the potential for Bayesian applications and they have also opened new avenues for Bayesian inference, first and foremost Bayesian model choice.Comment: This is a chapter for the book "Bayesian Methods and Expert Elicitation" edited by Klaus Bocker, 23 pages, 9 figure

Monotonic regression based on Bayesian P-splines: an application to estimating price response functions from store-level scanner data

Generalized additive models have become a widely used instrument for flexible regression analysis. In many practical situations, however, it is desirable to restrict the flexibility of nonparametric estimation in order to accommodate a presumed monotonic relationship between a covariate and the response variable. For example, consumers usually will buy less of a brand if its price increases, and therefore one expects a brand's unit sales to be a decreasing function in own price. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for a brand of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response function considerably

Bayesian computational methods

In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions. Of course, this chapter is only a terse introduction to the problems and solutions related to Bayesian computations. For more complete references, see Robert and Casella (2004, 2009), or Marin and Robert (2007), among others. We also restrain from providing an introduction to Bayesian Statistics per se and for comprehensive coverage, address the reader to Robert (2007), (again) among others.Comment: This is a revised version of a chapter written for the Handbook of Computational Statistics, edited by J. Gentle, W. Hardle and Y. Mori in 2003, in preparation for the second editio

On Functional Decomposition of Multivariate Polynomials with Differentiation and Homogenization

In this paper, we give a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which are proposed by Ye, Dai, Lam (1999) and Faug$\mu$ere, Perret (2006, 2008, 2009). We show that a degree proper functional decomposition for a set of randomly decomposable quartic homogenous polynomials can be computed using the algorithm with high probability. This solves a conjecture proposed by Ye, Dai, and Lam (1999). We also propose a conjecture such that the decomposition for a set of polynomials can be computed from that of its homogenization with high probability. Finally, we prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space. Combining these results together, we prove that the algorithm can compute a degree proper decomposition for a set of randomly decomposable quartic polynomials with probability one when the base field is of characteristic zero, and with probability close to one when the base field is a finite field with sufficiently large number under the assumption that the conjeture is correct

Numerical proper reparametrization of parametric plane curves

We present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. More precisely, given a tolerance ϵ>0 and a rational parametrization P of a plane curve C with perturbed float coefficients, we present an algorithm that computes a parametrization Q of a new plane curve D such that Q is an ϵ –proper reparametrization of D. In addition, the error bound is carefully discussed and we present a formula that measures the “closeness” between the input curve C and the output curve D

Investigation of IGES for CAD/CAE data transfer

In a CAD/CAE facility there is always the possibility that one may want to transfer the design graphics database from the native system to a non-native system. This may occur because of dissimilar systems within an organization or a new CAD/CAE system is to be purchased. The Initial Graphics Exchange Specification (IGES) was developed in an attempt to solve this scenario. IGES is a neutral database format into which the CAD/CAE native database format can be translated to and from. Translating the native design database format to IGES requires a pre-processor and transling from IGES to the native database format requires a post-processor. IGES is an artifice to represent CAD/CAE product data in a neutral environment to allow interfacing applications, archive the database, interchange of product data between dissimilar CAD/CAE systems, and other applications. The intent here is to present test data on translating design product data from a CAD/CAE system to itself and to translate data initially prepared in IGES format to various native design formats. This information can be utilized in planning potential procurement and developing a design discipline within the CAD/CAE community

Effect of Cyclic Loadings on the Shear Strength and Reinforcement Slip of RC Beams

Numerous studies of the response of reinforced concrete members under cyclic loadings, many of which have been summarized and have indicated that, in general, the flexural strength of under-reinforced beams remains unimpaired under cyclic loadings consisting of a reasonable number of cycles. However, there is a body of evidence indicating that their shear strength may suffer under such loadings. The first objective of the current study is to construct an accurate 2D shell finite element model of reinforced concrete beams under cyclic loadings. The second objective is carrying out a parametric study on reinforced concrete beams, using the suggested 2D shell model.  The objective of this study was to observe the effect of the stirrup spacing, steel-to-concrete bond properties on the performance of reinforced concrete beams under cyclic loadings. For this purpose, an efficient and accurate finite element model was established taking into account the compression and tensile softening introducing damage in the concrete material, the Baushinger effect using nonlinear isotropic/kinematic hardening in the steel and an adequate bond-slip law for the concrete–steel interface. The simulated results of numerical models were verified by experimental results available in literature in order to validate the proposed model, including hysteretic curves, failure modes, crack pattern and debonding failure mode. The model provided a strong tool for investigating the performances of reinforced concrete beam. The results showed that: Cyclic loadings may change the failure mode of the beam to bond failure even though it has sufficient bond length to resist static loadings. So that under cyclic loadings additional anchorage length must be taken, cyclic loadings also influence the ductility and peak load for beams fail in shear. All these topics are of the utmost importance to RC behaviour to be considered by construction codes

Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models

Structured additive regression provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix