Choice of modelling technique for evaluating health care interventions

Economic evaluation, such as cost effectiveness analysis, provides a method for comparing healthcare interventions. These evaluations often use modelling techniques such as decision trees, Markov processes and discrete event simulations (DES). With the aid of examples from coronary heart disease, the use of these techniques in different health care situations is discussed. Guidelines for the choice of modelling technique are developed according to the characteristics of the health care intervention.The choice of modelling technique is shown to depend on the acceptance of the modelling technique, model ‘error’, model appropriateness, dimensionality and ease and speed of model development. Generally decision trees are suitable for acute interventions but they cannot model recursion and Markov models are suitable for simple chronic interventions. It is further recommended that population based models be used in order to provide health care outcomes for the likely cost, health benefits and cost effectiveness of the intervention. The population approach will complicate the construction of the model. DES will allow the modeller to construct more complex, dynamic and accurate systems but these may involve a corresponding increase in development time and expense. The modeller will need to make a judgement on the necessary complexity of the model in terms of interaction of individuals and model size and whether queuing for resources, resource constraints or the interactions between individuals are significant issues in the health care system.     

A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems

Inspired by the reduced basis approach and modern numerical multiscale methods, we present a new framework for an efficient treatment of heterogeneous multiscale problems. The new approach is based on the idea of considering heterogeneous multiscale problems as parametrized partial differential equations where the parameters are smooth functions. We then construct, in an offline phase, a suitable localized reduced basis that is used in an online phase to efficiently compute approximations of the multiscale problem by means of a discontinuous Galerkin method on a coarse grid. We present our approach for elliptic multiscale problems and discuss an a posteriori error estimate that can be used in the construction process of the localized reduced basis. Numerical experiments are given to demonstrate the efficiency of the new approach.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

A second-order finite element variational multiscale scheme for the fully discrete unsteady Navier–Stokes equations

In this report, we present and study a fully discrete finite element variational multiscale scheme for the unsteady incompressible Navier–Stokes equations where high Reynolds numbers are allowed. The scheme uses conforming finite element pairs for spatial discretization and a three-point difference formula for temporal discretization which is of second-order, where a stabilization term based on two local Gauss integrations is employed to stabilize the numerical scheme. We prove stability of the scheme, derive a priori error estimates for the fully discrete solution, and finally, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed numerical scheme.     

Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds

<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.     

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC) method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the offline stage,we construct a small number of reduced basis functions within each coarse grid block, which can then be used to approximate the multiscale finite element basis functions. In the online stage, we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid, without requiring the coarsest grid to resolve the smallestscale of the solution. We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients. Moreover, we provide convergence analysis of the proposed method. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.     

Modelling bubble rise and interaction with a glass surface

A theoretical model has been developed to analyse bubble rise in water and subsequent impact and bounce against a horizontal glass plate. The multiscale nature of the problem, where the bubble size is on the millimetre range and the film drainage process happens on the micrometre to nanometre scale requires the combined use of different modelling techniques. On the macro scale we solve the full Navier–Stokes equations in cylindrical coordinates to model bubble rise whereas modelling film drainage on the micro scale is based on lubrication theory because the film Reynolds number becomes much smaller than unity. Quantitative predictions of this model are compared with experimental data obtained using synchronised high-speed cameras. Video recording of bubble rise and bounce trajectories are combined with interferometry data to deduce the position and time-dependent thickness of the thin water film trapped between the deformed bubble and the glass plate. Bubble rise velocity indicated that the boundary condition at the bubble surface was tangentially immobile. Quantitative comparisons are presented for bubbles of different size to quantify similarities and differences.     

Error analysis of a fully discrete finite element variational multiscale method for time‐dependent incompressible Navier–Stokes equations

A finite element variational multiscale method based on two local Gauss integrations is applied to solve numerically the time‐dependent incompressible Navier–Stokes equations. A significant feature of the method is that the definition of the stabilization term is derived via two local Guass integrations at element level, making it more efficient than the usual projection‐based variational multiscale methods. It is computationally cheap and gives an accurate approximation to the quantities sought. Based on backward Euler and Crank–Nicolson schemes for temporal discretization, we derive error bounds of the fully discrete solution which are first and second order in time, respectively. Numerical tests are also given to verify the theoretical predictions and demonstrate the effectiveness of the proposed method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Comparative analysis of asynchronous cellular automata in stochastic pharmaceutical modelling

In pharmaceutical modelling, cellular automata have been used as an established tool to represent molecular changes through discrete structural interactions. The data quality provided by such modelling is found suitable for the early drug design phase where flexibility is paramount. While both synchronous (CA) and asynchronous (ACA) types of automata have been used, analysis of their nature and comparative influence on model outputs is lacking. In this paper, we outline a representative probabilistic CA for modelling complex controlled drug formulations and investigate its transition from synchronous to asynchronous update algorithms. The key investigation points include quantification of model dynamics through three distinct scenarios, parallelisation performance and the ability to describe different release phenomena, namely erosion, diffusion and swelling. The choice of the appropriate update mechanism impacts the perceived realism of the simulation as well as the applicability of large-scale simulations.     

Multiscale decision-making: Bridging organizational scales in systems with distributed decision-makers

Decision-making in organizations is complex due to interdependencies among decision-makers (agents) within and across organizational hierarchies. We propose a multiscale decision-making model that captures and analyzes multiscale agent interactions in large, distributed decision-making systems. In general, multiscale systems exhibit phenomena that are coupled through various temporal, spatial and organizational scales. Our model focuses on the organizational scale and provides analytic, closed-form solutions which enable agents across all organizational scales to select a best course of action. By setting an optimal intensity level for agent interactions, an organizational designer can align the choices of self-interested agents with the overall goals of the organization. Moreover, our results demonstrate when local and aggregate information exchange is sufficient for system-wide optimal decision-making. We motivate the model and illustrate its capabilities using a manufacturing enterprise example.     

Multiscale modeling of continuous fiber and fabric reinforced rubber components

Fabric or continuous fiber reinforced rubber components (e.g. tires, air springs, industrial hoses, conveyor belts or membranes) are underlying high deformations in application and show a complex, nonlinear material behavior. A particular challenge depicts the simulation of these composites. In this contribution we show the identification of the stress and strain distributions by using an uncoupled multiscale modeling method, see [1]. Within this method, two representation levels are described: One, the meso level, where all constituents of the composite are shown in a discrete manner by a representative volume element (RVE) and secondly, the macro level, where the structural behavior of the component is defined by a smeared anisotropic hyperelastic constitutive law. Uncoupled means that the RVE does not drive the macroscopic material behavior directly as in a coupled approach, where a RVE boundary value problem has to be solved at every integration point of the macro level. Thus an uncoupled approach leads to a tremendous reduction in numerical effort because the boundary value problem of a RVE just has to be solved at a point of interest, see [1]. However, the uncoupled scale transition has to fulfill the HILL–MANDEL condition of energetic equivalence of both scales. We show the calibration of material parameters for a given constitutive model for fiber reinforced rubber by fitting experimental data on the macro level. Additionally, we demonstrate the determination of effective properties of the yarns. Finally, we compare the energies of both scales in terms of compliance with the HILL–MANDEL condition by using the example of a biaxial loaded sample and discuss the consequences for the mesoscopic level. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The efficiency of health and education expenditures in the Philippines

This paper attempts to measure the efficiency of provinces in the Philippines in utilizing public resources for health and education where only 1% of the total budget is spent for health and 3% is allocated for education. With such budget constraints, it is important to examine the efficiency of spending on social services as small changes can have a major impact in achieving the Millennium Development Goals. Efficiency is defined as the deviation from the frontier which represents the maximum output attainable from each input level. This efficiency frontier is estimated using the data envelopment analysis, free disposal hull and Malmquist-DEA. We use expenditures for social services for input and primary and secondary enrollment rates, literacy rate per province, and life expectancy for outputs. An analysis of efficiency scores shows that provinces where the level of inequality is higher (as measured by the Gini coefficient) as well as those who receive a larger portion of their budget as grants are among the least efficient. This research can help in the budget allocation and rationalization among Philippine provinces.     

Computational homogenization for heterogeneous cohesive layers incorporating size effects

A numerical framework is presented for the multiscale modelling of material layers that possess a both heterogeneous and microstructured mesostructure. The material layer is represented as a cohesive interface on the macro level, while on the meso level micromorphic representative volume elements are used. A computational homogenization approach for the cohesive material layers has been proposed to solve this nonlinear multiscale problem numerically. The present framework is particularly well suited for the modelling of damage and failure, as the micromorphic RVE is well known for its regularizing character. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A two‐level variational multiscale method for incompressible flows based on two local Gauss integrations

In this article, a two‐level variational multiscale method for incompressible flows based on two local Gauss integrations is presented. We solve the Navier–Stokes problem on a coarse mesh using finite element variational multiscale method based on two local Gauss integrations, then seek a fine grid solution by solving a linearized problem on a fine grid. In computation, we use the two local Gauss integrations to replace the projection operator without adding any variables. Stability analysis is performed, and error estimates of the method are derived. Finally, a series of numerical experiments are also given, which confirm the theoretical analysis and demonstrate the efficiency of the new method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Recent models in data envelopment analysis: Theory and applications

A critical review of the recent models of data envelopment analysis (DEA) is attempted here. Three new lines of approach involving dynamic changes in parameters, the error correction models and a stochastic sensitivity analysis are discussed in some detail. On the applications side, two new formulations are presented and discussed, e.g. a model of technical change and a cost frontier for testing economies of scale and adjustment due to risk factors. Thus the critical review of recent DEA models of productivity measurement provides new insight into the frontier of research in this field.     

A generic environment for modelling future launch operations—GEM-FLO: a success story in generic modelling

Several NASA programs have been established to study and improve the current launch capability to meet the need for more aggressive space exploration in the future. Numerous launch systems have been proposed by different government and commercial organizations with the potential goal of replacing the Space Shuttle. NASA must evaluate new designs and technologies with the objective of improving upon today's Shuttle cost, performance, and turnaround time, before the government or commercial organizations pursue the large undertaking of a new launch system. To address this issue, the Generic Simulation Environment for Modelling Future Launch Operations (GEM-FLO) was developed to accurately predict processing turnaround times and other effectiveness criteria and support making key business and program decisions. GEM-FLO utilizes a generic modelling paradigm to provide a single platform for modelling different designs, which helped significantly cut the cost of these studies. This paper documents a success story in generic simulation modelling.     

A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

We present an “a posteriori” error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro‐to‐micro formulation, where the macroscopic physical problem is discretized in a macroscopic finite element space, and the missing macroscopic data are recovered on‐the‐fly using the solutions of corresponding microscopic problems. We propose a new framework that allows to follow the concept of the (single‐scale) dual‐weighted residual method at the macroscopic level in order to derive a posteriori error estimates in quantities of interests for multiscale problems. Local error indicators, derived in the macroscopic domain, can be used for adaptive goal‐oriented mesh refinement. These error indicators rely only on available macroscopic and microscopic solutions. We further provide a detailed analysis of the data approximation error, including the quadrature errors. Numerical experiments confirm the efficiency of the adaptive method and the effectivity of our error estimates in the quantities of interest. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics

This paper is an introduction to the modelling of viscoelastic fluids,with an emphasis on micromacro(or multiscale) models.Some elements of mathematical and numerical analysis are provided.These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop "Stress Tensor E?ects on Fluid Mechanics" in January 2010.