Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case

Adam is a commonly used stochastic optimization algorithm in machine learning. However, its convergence is still not fully understood, especially in the non-convex setting. This paper focuses on exploring hyperparameter settings for the convergence of vanilla Adam and tackling the challenges of non-ergodic convergence related to practical application. The primary contributions are summarized as follows: firstly, we introduce precise definitions of ergodic and non-ergodic convergence, which cover nearly all forms of convergence for stochastic optimization algorithms. Meanwhile, we emphasize the superiority of non-ergodic convergence over ergodic convergence. Secondly, we establish a weaker sufficient condition for the ergodic convergence guarantee of Adam, allowing a more relaxed choice of hyperparameters. On this basis, we achieve the almost sure ergodic convergence rate of Adam, which is arbitrarily close to $o(1/\sqrt{K})$. More importantly, we prove, for the first time, that the last iterate of Adam converges to a stationary point for non-convex objectives. Finally, we obtain the non-ergodic convergence rate of $O(1/K)$ for function values under the Polyak-Lojasiewicz (PL) condition. These findings build a solid theoretical foundation for Adam to solve non-convex stochastic optimization problems

A Parallel Feature-preserving Mesh Variable Offsetting Method with Dynamic Programming

Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and normal vector, a new calculation of offset position is proposed by using dynamic programming and quadratic programming, and the sharp feature can be preserved after offsetting. Instead of distance implicit field, a spatial coverage region represented by polyhedral for computing offsets is proposed. Our method can generate an offsetting model with smaller mesh size, and also can achieve high quality without gaps, holes, and self-intersections. Moreover, several acceleration techniques are proposed for the efficient mesh offsetting, such as the parallel computing with grid, AABB tree and rays computing. In order to show the efficiency and robustness of the proposed framework, we have tested our method on the quadmesh dataset, which is available at [https://www.quadmesh.cloud]. The source code of the proposed algorithm is available on GitHub at [https://github.com/iGame-Lab/PFPOffset]

Dual-Reference Source-Free Active Domain Adaptation for Nasopharyngeal Carcinoma Tumor Segmentation across Multiple Hospitals

Nasopharyngeal carcinoma (NPC) is a prevalent and clinically significant malignancy that predominantly impacts the head and neck area. Precise delineation of the Gross Tumor Volume (GTV) plays a pivotal role in ensuring effective radiotherapy for NPC. Despite recent methods that have achieved promising results on GTV segmentation, they are still limited by lacking carefully-annotated data and hard-to-access data from multiple hospitals in clinical practice. Although some unsupervised domain adaptation (UDA) has been proposed to alleviate this problem, unconditionally mapping the distribution distorts the underlying structural information, leading to inferior performance. To address this challenge, we devise a novel Sourece-Free Active Domain Adaptation (SFADA) framework to facilitate domain adaptation for the GTV segmentation task. Specifically, we design a dual reference strategy to select domain-invariant and domain-specific representative samples from a specific target domain for annotation and model fine-tuning without relying on source-domain data. Our approach not only ensures data privacy but also reduces the workload for oncologists as it just requires annotating a few representative samples from the target domain and does not need to access the source data. We collect a large-scale clinical dataset comprising 1057 NPC patients from five hospitals to validate our approach. Experimental results show that our method outperforms the UDA methods and achieves comparable results to the fully supervised upper bound, even with few annotations, highlighting the significant medical utility of our approach. In addition, there is no public dataset about multi-center NPC segmentation, we will release code and dataset for future research

STUDY ON ANTI-TUMOR EFFECT OF TOTAL GLYCOSIDES FROM RADIX PAEONIAE RUBRA IN S180 TUMOR-BEARING MICE

The objective of the paper was to study the anti-tumor effect of total glycosides from Radix paeoniae rubra in S180 tumor-bearing mice, and to preliminarily explore its mechanism of action. Mice were made into S180 solid tumor model, grouped and administered with the extracts; tumor inhibition rate was measured by harvesting the tumors, and serum IL-2 and IL-4 levels were measured by taking blood samples. Total glycosides of Radix paeoniae rubra significantly inhibited the growth of tumor cells in tumor-bearing organisms, enhanced the cytotoxic activity of NK cells, and increased the serum IL-2 and IL-4 levels. Total glycosides of Radix paeoniae rubra have some anti-tumor effect in vivo, which might have been accomplished through the regulation of the immune system