In clinical research, it is sometimes desirable to dichotomize a continuous variable so that the information expressed using a dichotomous variable is more straightforward for clinicians to interpret and communicate w...
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In clinical research, it is sometimes desirable to dichotomize a continuous variable so that the information expressed using a dichotomous variable is more straightforward for clinicians to interpret and communicate with patients. The distribution of the continuous variable can differ between two populations defined by a disease case status. Under such a scenario, the dichotomization process can be based on distributions of the continuous variable in two distinct populations. The resulting dichotomous variable can be used as an endpoint in future studies. Even though dichotomization has not been extensively studied, dichotomization has been commonly carried out in clinical trials. We developed a methodology for determining the optimal cutoff point based on maximizing the correlation between the two populations and the dichotomous variable. In some real-world scenarios where outcome status in samples from two populations is not completely identified, we recommend using EM method to first estimate the parameters associated with the two populations before applying the proposed method to find the optimal cutoff point. In addition, we have investigated the performance of the proposed method for several common distributions (e.g., normal, log-normal and exponential distribution) of the continuous variable. Finally, we applied the proposed methods to a varicella vaccine example.
A novel multifluid plasma model is developed, based on the finite-volume method,with a fourth-order accurate algorithm and solution-adaptive mesh refinement inspace and time. Previously, the order of accuracy of the m...
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A novel multifluid plasma model is developed, based on the finite-volume method,with a fourth-order accurate algorithm and solution-adaptive mesh refinement inspace and time. Previously, the order of accuracy of the multifluid plasma modelwas verified and the solutions to common plasma test cases were *** the present work, the multifluid plasma model is applied to solve complextest cases involving discontinuities and shocks. Discussion is thus focused onmethods of numerical stabilization and strategies with adaptive mesh *** results show improvements to solution stability and as much as an order ofmagnitude improvement in compute time due to adaptive mesh refinement
The paper deals with a method of solution of a nonlinear integro-differential static string equation. The accuracy of the method is discussed. The numerical examples are given.
The paper deals with a method of solution of a nonlinear integro-differential static string equation. The accuracy of the method is discussed. The numerical examples are given.
This work is devoted to the development of a numerical algorithm for the system of kinetic equations corresponding to the formation of the Ti-TxCy composite with the prospect of subsequent using of this algorithm in t...
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This work is devoted to the development of a numerical algorithm for the system of kinetic equations corresponding to the formation of the Ti-TxCy composite with the prospect of subsequent using of this algorithm in the model of the technology of the synthesis of composites. In this Ti-C system, irreversible phases can appear under certain conditions typical of composite synthesis. No theoretical works are available however, that would model the synthesis of composites and consider chemical stages eventuating in nonequilibrium phase composition. The present work uses a multistage kinetic model of the formation of nonstoichiometric titanium carbide at a preset temperature. Reaction rates are assumed to be dependent on concentration by the mass action law. Additionally, the reaction rate retardation typical of solid-state reactions is presented with the aid of a special function. This results in nonlinear kinetic equations. The paper suggests an iteration algorithm for numerical embodiment of the kinetic model, as well as its special variants corresponding to different initiation conditions and initial data. Depending on the temperature and time of the synthesis, the final product contains the carbides TiC, Ti2C, Ti3C2, and TiC2 in various proportions. Among the irreversible carbides, the most stable one is TiC2. Taking into account the retardation of the reactions by the layer of products in the kinetic functions only extends the time necessary for conversions.
A survey of all global time-dependent MHD simulations is presented. The survey includes a discussion of the physical situations simulated by the respective authors as well as the numerical algorithms employed. Finally...
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A survey of all global time-dependent MHD simulations is presented. The survey includes a discussion of the physical situations simulated by the respective authors as well as the numerical algorithms employed. Finally a discussion of the advantages enjoyed by certain numerical schemes and the problems that a researcher will very likely encounter if he should undertake construction of such codes is presented.
In this paper, a new algorithm for a cubic spline fit with equally spaced data points and given end conditions is described. It provides a new understanding of how a spline fit works and possesses the following comput...
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In this paper, a new algorithm for a cubic spline fit with equally spaced data points and given end conditions is described. It provides a new understanding of how a spline fit works and possesses the following computational advantages: 1) It can solve large size problems (virtually unlimited). 2) The accuracy can be realistically controlled based on the characteristics of data. 3) The computation time-is linearly proportional to the size of the problem. 4) It can handle a localized fit. 4) It can handle a localizd. The new algorithm is particularly suitable to be implemented in minicomputers for cutting surfaces by numerically controlled machines and for other applications.
In this study, the undrained mechanical behavior of saturated completely decomposed granite (CDG) with different weathering degrees is investigated. To this end, a series of consolidation undrained (CU) triaxial compr...
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In this study, the undrained mechanical behavior of saturated completely decomposed granite (CDG) with different weathering degrees is investigated. To this end, a series of consolidation undrained (CU) triaxial compression tests are conducted on saturated CDG, and the effects of weathering degree on the main undrained mechanical properties are analyzed. Based on the experimental results, a poromechanical model is then established with the concept of effective plastic stress in a poroplasticity framework. Plastic distortion is described using a particular yield surface and a nonassociated plastic potential, which are both functions of the effective plastic stress and a subtly unified smooth hardening/softening variable. As an original contribution, an enhanced semi-implicit return mapping (ESRM) algorithm is developed to integrate the proposed model. This algorithm is based on a semi-implicit return mapping procedure and is combined with a new adaptive substepping technique. The model is subsequently implemented and validated by comparing the numerical simulation results with the experimental data. The main undrained mechanical characteristics of saturated CDG with different weathering degrees are well reproduced. A discussion follows regarding the parameter sensitivity analysis and robustness of the ESRM algorithm. Interestingly, the high accuracy of the ESRM algorithm is almost step-size independent, and the computational efficiency is also greatly improved.
An analytical representation of the general solution to a finite-difference system describing transport in a periodic medium is found. On the basis of this representation, an efficient numerical algorithm is developed...
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An analytical representation of the general solution to a finite-difference system describing transport in a periodic medium is found. On the basis of this representation, an efficient numerical algorithm is developed for solving some boundary value problems of transport in a multilayered medium.
It shows how the high pressure electric gas discharge plasma near to the local thermodynamic equilibrium point can be modeled. Partial differential equations with variable coefficients and non-linear source terms are ...
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It shows how the high pressure electric gas discharge plasma near to the local thermodynamic equilibrium point can be modeled. Partial differential equations with variable coefficients and non-linear source terms are solved using the finite element method.
We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Z(d)-Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannu...
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We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Z(d)-Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat (ESAIM Math. Model. Numer. Anal. (2021) 55 37-55). We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.
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