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Two different ‘a posteriori’ error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive mesh refinement for 2D and 3D electrostatic problems are also analyzed with numerical test results. The post‐processing method employs an improved solution to estimate the error, whereas the gradient of field method utilizes the gradient of the field solution for estimating the ‘a posterior’ error. The gradient of field method is computationally inexpensive, since it solves a local problem on a patch of elements. The error estimates are tested by solving a set of self‐adjoint boundary value problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.

This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method.

The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P₁-P₀-P₁ which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution.

The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.

The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.

This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems.

The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems.

The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis.

An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results.

The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

Proposes an automatic adaptive meshing scheme. Error in strain energy is directly obtained through strain energy density function (SED). Versatility of this function, in comparison with that of others, is looked at in detail. Mesh enrichment method consists of a series of h‐refinement steps and concludes with a single p‐refinement step. Adds that an examination of the accuracy of the element used in the refinement procedure is made. This scheme has been implemented in ZATILAN, a FE code developed in the Department of the Mechanical Engineering of the University of the Basque Country.

This study aims to find the usefulness of the customized surgical osteotomy guide (CSOG) for accurate mandibular tumor resection for boosting the accuracy of prefabricated customized implant fixation in mandibular reconstructions.

In all, 30 diseased mandibular RP models (biomodels) were allocated for the study (for experimental group [n = 15] and for control group [n = 15]). To reconstruct the mandible with customized implant in the experimental group, CSOGs and in control group, no CSOG were used for accurate tumor resections. In control group, only preoperative virtual surgical planning (VSP) and reconstructed RP mandible model were used for the reference. Individually each patient’s preoperative mandibular reconstructions data of both the groups were superimposed to the preoperative VSP of respective patient by registering images with the non-surgical side of the mandible. In both the groups, 3D measurements were taken on the reconstructed side and compared the preoperative VSP and postoperative reconstructed mandible data. The sum of the differences between pre and postoperative data was considered as the total error. This procedure was followed for both the groups and compared the obtained error between the two groups using statistical analysis.

The use of CSOG for accurate tumor resection and exact implant fixation in mandibular reconstruction produced a smaller total error than without using CSOG.

The results showed that, benefits provided with the use of CSOG in mandibular reconstruction justified its use over the without using CSOG, even in free hand tumor resection using rotating burr.

This article surveys recent developments in the evaluation of point and density forecasts in the context of forecasts made by vector autoregressions. Specific emphasis is placed on highlighting those parts of the existing literature that are applicable to direct multistep forecasts and those parts that are applicable to iterated multistep forecasts. This literature includes advancements in the evaluation of forecasts in population (based on true, unknown model coefficients) and the evaluation of forecasts in the finite sample (based on estimated model coefficients). The article then examines in Monte Carlo experiments the finite-sample properties of some tests of equal forecast accuracy, focusing on the comparison of VAR forecasts to AR forecasts. These experiments show the tests to behave as should be expected given the theory. For example, using critical values obtained by bootstrap methods, tests of equal accuracy in population have empirical size about equal to nominal size.

Estimating parameters of constrained optimization models in a consistent way requires a different set of methods than what is available in a typical econometric toolkit. We identify three complications likely to arise in this context, and suggest solutions to those complications: (i) the bi-level programming character, (ii) ill-posedness, and (iii) derivation of estimator properties. The solutions suggested involve a combination of numerical techniques and utilization of out-of-sample information through Bayesian techniques. The proposed framework is also suitable for typical empirical problems arising in trade analysis such as the estimation of trade equilibrium models and data balancing exercises.

We develop a Bayesian approach for modeling brain activation and connectivity from functional magnetic resonance image (fMRI) data. Our approach simultaneously estimates local hemodynamic response functions (HRFs) and activation parameters, as well as global effective and functional connectivity parameters. Existing methods assume identical HRFs across brain regions, which may lead to erroneous conclusions in inferring activation and connectivity patterns. Our approach addresses this limitation by estimating region-specific HRFs. Additionally, it enables neuroscientists to compare effective connectivity networks for different experimental conditions. Furthermore, the use of spike and slab priors on the connectivity parameters allows us to directly select significant effective connectivities in a given network.

We include a simulation study that demonstrates that, compared to the standard generalized linear model (GLM) approach, our model generally has higher power and lower type I error and bias than the GLM approach, and it also has the ability to capture condition-specific connectivities. We applied our approach to a dataset from a stroke study and found different effective connectivity patterns for task and rest conditions in certain brain regions of interest (ROIs).