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This paper investigates the production of nanoparticles via detonation. To extract valuable knowledge regarding this route, a phenomenological model of the process is developed and simulated. This framework integrates the mathematical description of the detonation with a model representing the particulate phenomena. The detonation process is simulated using a combination of a thermochemical code to determine the Chapman–Jouguet (C-J) conditions, coupled with an approximate spatially homogeneous model that describes the radial expansion of the detonation matrix. The conditions at the C-J point serve as initial conditions for the detonation dynamic model. The Mie–Grüneisen Equation of State (EoS) is used, with the "cold curve" represented by the Jones–Wilkins–Lee Equation of State. The particulate phenomena, representing the formation of metallic oxide nanoparticles from liquid droplets, are described by a Population Balance Equation (PBE) that accounts for the coalescence and coagulation mechanisms. The variables associated with detonation dynamics interact with the kernels of both phenomena. The numerical approach employed to handle the PBE relies on spatial discretization based on a fixed-pivot scheme. The dynamic solution of the models representing both processes is evolved with time using a Differential-Algebraic Equation (DAE) implicit solver. The strategy is applied to simulate the production of alumina nanoparticles from Ammonium Nitrate Fuel Oil aluminized emulsions. The results show good agreement with the literature and experience-based knowledge, demonstrating the tool's potential in advancing understanding of the detonation route. [ABSTRACT FROM AUTHOR]

We consider optimal designs for clinical trials when response variance depends on treatment and covariates are included in the response model. These designs are generalizations of Neyman allocation, and commonly employed in personalized medicine where external covariates linearly affect the response. Very often, these designs aim at maximizing the amount of information gathered but fail to assure ethical requirements. We analyze compound optimal designs that maximize a criterion weighting the amount of information and the reward of allocating the patients to the most effective/least risky treatment. We develop a general representation for static (a priori) allocation and propose a semidefinite programming (SDP) formulation to support their numerical computation. This setup is extended assuming the variance and the parameters of the response of all treatments are unknown and an adaptive sequential optimal design scheme is implemented and used for demonstration. Purely information theoretic designs for the same allocation have been addressed elsewhere, and we use them to support the techniques applied to compound designs. [ABSTRACT FROM AUTHOR]

We study optimal designs for clinical trials when the value of the response and its variance depend on treatment and covariates are included in the response model. Such designs are generalizations of Neyman allocation, commonly used in personalized medicine when external factors may have differing effects on the response depending on subgroups of patients. We develop theoretical results for D-, A-, E- and D$_{\rm{A}}$ A-optimal designs and construct semidefinite programming (SDP) formulations that support their numerical computation. D-, A-, and E-optimal designs are appropriate for efficient estimation of distinct properties of the parameters of the response models. Our formulation allows finding optimal allocation schemes for a general number of treatments and of covariates. Finally, we study frequentist sequential clinical trial allocation within contexts where response parameters and their respective variances remain unknown. We illustrate, with a simulated example and with a redesigned clinical trial on the treatment of neuro-degenerative disease, that both theoretical and SDP results, derived under the assumption of known variances, converge asymptotically to allocations obtained through the sequential scheme. Procedures to use static and sequential allocation are proposed. [ABSTRACT FROM AUTHOR]

Explicit models representing the response variables as functions of the control variables are standard in virtually all scientific fields. For these models, there is a vast literature on the optimal design of experiments (ODoE) to provide good estimates of the parameters with the use of minimal resources. Contrarily, the ODoE for implicit models is more complex and has not been systematically addressed. Nevertheless, there are practical examples where the models relating the response variables, the parameters and the factors are implicit or hardly convertible into an explicit form. We propose a general formulation for developing the theory of the ODoE for implicit algebraic models to specifically find continuous local designs. The treatment relies on converting the ODoE problem into an optimization problem of the nonlinear programming (NLP) class which includes the construction of the parameter sensitivities and the Cholesky decomposition of the Fisher information matrix. The NLP problem generated has multiple local optima, and we use global solvers, combined with an equivalence theorem from the theory of ODoE, to ensure the global optimality of our continuous optimal designs. We consider D- and A-optimality criteria and apply the approach to five examples of practical interest in chemistry and thermodynamics. for this article are available online. [ABSTRACT FROM AUTHOR]

We consider the dependence on the measurement schedule of optimal experiments for kinetic parameters when the rates are temperature-dependent and follow the Arrhenius law. We compare three different approaches using the D-optimality criterion: (1) a locally optimal design based on a sequence of four batches where the process is observed at a single time; (2) two batches carried out at constant temperature where the process is observed at a pre-defined grid of times; and (3) a single batch where the temperature profile is optimal regarding the amount of information extracted and the process is observed at a pre-defined grid of times. An extension of the generalized equivalence theorem of optimal experimental design provides insight into the structure of the designs we find. The local D-optimality of the designs obtained is validated using the extended theorem for the latter two approaches. [ABSTRACT FROM AUTHOR]

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors. Published by Elsevier Inc.)

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., (© 2019 International Biometric Society.)

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.

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.