Modeling the Batch Sedimentation of Calcium Carbonate Particles in Laboratory Experiments-A Systematic Approach.

The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistical indicators. The model used for demonstration has a theoretical basis combined with an empirical component to account for the effect of the particle concentrations and their state of aggregation. The values of the numerical parameters obtained are related to the characteristic dimensions of the aggregates and their mass-length fractal dimensions.

Randomizing a clinical trial in neuro-degenerative disease.

The paper studies randomization rules for a sequential two-treatment, two-site clinical trial in Parkinson's disease. An important feature is that we have values of responses and five potential prognostic factors from a sample of 144 patients similar to those to be enrolled in the trial. Analysis of this sample provides a model for trial analysis. The comparison of allocation rules is made by simulation yielding measures of loss due to imbalance and of potential bias. A major novelty of the paper is the use of this sample, via a two-stage algorithm, to provide an empirical distribution of covariates for the simulation; sampling of a correlated multivariate normal distribution is followed by transformation to variables following the empirical marginal distributions. Six allocation rules are evaluated. The paper concludes with some comments on general aspects of the evaluation of such rules and provides a recommendation for two allocation rules, one for each site, depending on the target number of patients to be enrolled.

On the Design of Aqueous Emulsions of Colophony Resin.

Companies regularly face market pressure to develop products faster but they also need to simultaneously incorporate technological constraints, sustainability trends, and customer requirements into their designs, which requires the use of systematic procedures. Firms that exploit natural resources and convert them into high-value products are among them. However, the literature on the application of such systematic approaches to products of this type remains scarce, as they often requrire extensive experimental plans involving the testing and optimization of multiple formulations. Here, we propose a systematic approach to the design of pine-resin-in-water emulsions, which can be used to fabricate pressure-sensitive adhesives. The strategy is customer-centric in the sense that the customers' specifications are integrated into the decision-making tool used to assess the quality of the formulations obtained through experiments. This tool uses loss functions to assess satisfaction with individual quality characteristics and multi-attribute decision-making methods to integrate them into an overall quality metric. Our framework is aligned with industrial practices and consists of three sequential stages: (i) screening of primary factors; (ii) optimization of secondary factors; and (iii) assessment of the experimental repeatability of the formulations. In each of these stages, the decision-making tool is used to "drive" the process of finding the optimal formulation.

Using rheological monitoring to determine the gelation kinetics of chitosan-based systems.

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) [1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) - approximately of first order -, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.

Optimal design of multiple-objective Lot Quality Assurance Sampling (LQAS) plans.

Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique.

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D-, A- and E-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.