The Application of Shape Gradient for the Incompressible Fluid in Shape Optimization

This paper is concerned with the numerical simulation for shape optimization of the Stokes flow around a solid body. The shape gradient for the shape optimization problem in a viscous incompressible flow is evaluated by the velocity method. The flow is governed by the steady-state Stokes equations coupled with a thermal model. The structure of continuous shape gradient of the cost functional is derived by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. A gradient-type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose, and the proposed algorithm is feasible and effective

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

summary:The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique

Testing for Treatment Effect in Covariate-Adaptive Randomized Clinical Trials with Generalized Linear Models and Omitted Covariates

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two sample t-test for treatment effect is typically conservative, in the sense that the actual test size is smaller than the nominal level. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method

Efficient Match Pair Retrieval for Large-scale UAV Images via Graph Indexed Global Descriptor

SfM (Structure from Motion) has been extensively used for UAV (Unmanned Aerial Vehicle) image orientation. Its efficiency is directly influenced by feature matching. Although image retrieval has been extensively used for match pair selection, high computational costs are consumed due to a large number of local features and the large size of the used codebook. Thus, this paper proposes an efficient match pair retrieval method and implements an integrated workflow for parallel SfM reconstruction. First, an individual codebook is trained online by considering the redundancy of UAV images and local features, which avoids the ambiguity of training codebooks from other datasets. Second, local features of each image are aggregated into a single high-dimension global descriptor through the VLAD (Vector of Locally Aggregated Descriptors) aggregation by using the trained codebook, which remarkably reduces the number of features and the burden of nearest neighbor searching in image indexing. Third, the global descriptors are indexed via the HNSW (Hierarchical Navigable Small World) based graph structure for the nearest neighbor searching. Match pairs are then retrieved by using an adaptive threshold selection strategy and utilized to create a view graph for divide-and-conquer based parallel SfM reconstruction. Finally, the performance of the proposed solution has been verified using three large-scale UAV datasets. The test results demonstrate that the proposed solution accelerates match pair retrieval with a speedup ratio ranging from 36 to 108 and improves the efficiency of SfM reconstruction with competitive accuracy in both relative and absolute orientation