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High-order schemes are essential for high-fidelity aerodynamic simulations. To enhance computational efficiency while maintaining the adaptability of high-order schemes across various flow regions, this study proposes a simplified discontinuity-detection method based on the scale sensor. It operates prior to the reconstruction algorithm. In smooth regions, common weights are applied for all governing equations, whereas in multi-scale regions, the scheme adaptively switches between schemes with varying dispersion properties. By integrating these novel techniques with a computationally efficient smoothness indicator within the TENO framework, the schemes called FTENO and its optimized version are constructed. Comparative analyses of several typical benchmark cases demonstrate the superior comprehensive performance in efficiency and multi-scale resolution of the proposed schemes.

Recently, leveraging on the development of end-to-end convolutional neural networks, deep stereo matching networks have achieved remarkable performance far exceeding traditional approaches. However, state-of-the-art stereo frameworks still have difficulties at finding correct correspondences in texture-less regions, detailed structures, small objects and near boundaries, which could be alleviated by geometric clues such as edge contours and corresponding constraints. To improve the quality of disparity estimates in these challenging areas, we propose an effective multi-task learning network, EdgeStereo, composed of a disparity estimation branch and an edge detection branch, which enables end-to-end predictions of both disparity map and edge map. To effectively incorporate edge cues, we propose the edge-aware smoothness loss and edge feature embedding for inter-task interactions. It is demonstrated that based on our unified model, edge detection task and stereo matching task can promote each other. In addition, we design a compact module called residual pyramid to replace the commonly-used multi-stage cascaded structures or 3-D convolution based regularization modules in current stereo matching networks. By the time of the paper submission, EdgeStereo achieves state-of-art performance on the FlyingThings3D dataset, KITTI 2012 and KITTI 2015 stereo benchmarks, outperforming other published stereo matching methods by a noteworthy margin. EdgeStereo also achieves comparable generalization performance for disparity estimation because of the incorporation of edge cues.

Roller coaster is one of the attractions to the public. The design of roller coaster plays an important role for the smoothness and safety of each roller coaster rail. This research is about designing a smooth roller coaster rail loop using extended cubic uniform B-spline method as one of the alternative in designing a smooth roller coaster rail. Two-dimensional design of roller coaster rail loop is form by using extended cubic uniform B-spline with degree 3, 4 and 5 and shape parameter, λ= 0.5, and 1. Then, three-dimensional cubic B-spline is formed by using sweep surface which is translation method. The loop is analysed by the distance between curve and control polygon. Moreover, the G-felt with the different radius of the loop has been calculated. The value of G-felt for each method used will be compared to the G-felt value of the original roller coaster. The result from this research showed that by using extended cubic B-spline method degree 4, λ = 0.5 is the best way to design roller coaster rail because it has the best G-force value compared to others designs.

As aerospace intelligent assembly advances, robotic path planning becomes critical for production efficiency. Traditional algorithms like APF and RRT lack search efficiency and path smoothness in complex, high-precision environments, failing to meet modern assembly demands. This paper proposes an APF-RRT-based algorithm that modifies node generation probability using the potential field force, directing the search toward the goal. Path optimization occurs through pruning and quasi-uniform B-spline interpolation. Simulations in 2D and 3D environments confirm the algorithm’s effectiveness by demonstrating superior path length reduction and smoothness, thereby offering a robust solution for aerospace assembly tasks.

In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the T${\\bar {\\rm T}}$T¯ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at θ = 0. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.

We present early results regarding the morphological and structural properties of galaxies seen with the James Webb Space Telescope (JWST) at z > 3 in the Early Release Observations toward the SMACS 0723 cluster field. Using JWST we investigate, for the first time, the optical morphologies of a significant number of z > 3 galaxies with accurate photometric redshifts in this field to determine the form of galaxy structure in the relatively early universe. We use visual morphologies and Morfometryka measures to perform quantitative morphology measurements, both parametric with light profile fitting (Sérsic indices) and nonparametric (concentration, asymmetry, and smoothness (CAS) values). Using these, we measure the relative fraction of disk, spheroidal, and peculiar galaxies at 3 < z < 8. We discover the surprising result that at z > 1.5 disk galaxies dominate the overall fraction of morphologies, with a factor of ∼10 relative higher number of disk galaxies than seen by the Hubble Space Telescope at these redshifts. Our visual morphological estimates of galaxies align closely with their locations in CAS parameter space and their Sérsic indices.

Borel and symmetric Borel derivatives are generalized derivatives defined through local averages of difference quotients. Distributional point values, in the sense of Łojasiewicz and its symmetric variants, are a classical way of describing the local value of a distribution. This paper connects these two ideas. Writing \\(T_f\\) for the regular distribution generated by \\(f\\), we prove that finite first and second symmetric Borel derivatives give symmetric distributional point values of \\(T_f'\\) and \\(T_f''\\), respectively. For the first symmetric derivative, Borel smoothness is used as a sufficient condition to pass from the symmetric point value to the full Łojasiewicz point value. We also prove that the one-sided Borel derivatives determine the right and left distributional point values of \\(T_f'\\), and that the ordinary Borel derivative gives the full point value when the two one-sided averages agree. Examples show why the second-order symmetric result cannot be strengthened automatically.

We study functions introduced by Buhmann. The exact exponent of smoothness of these functions is obtained and the problem of positivity of their Hankel transforms is analyzed.

The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions due to the large design matrix it requires. The Highly Adaptive Ridge (HAR) has been proposed as a related ridge-regularized analogue. Building on both procedures, we introduce the Principal Component Highly Adaptive Lasso (PCHAL) and Principal Component Highly Adaptive Ridge (PCHAR). These estimators use an outcome-blind principal-component reduction of the HAL basis, offering substantial computational gains over HAL while achieving empirical performance comparable to HAL and HAR. We also describe an early-stopped gradient descent variant, which provides a convenient form of smooth spectral regularization without explicitly selecting a hard principal-component cutoff. Finally, we uncover that under special circumstances, the HAL kernel is identical to the covariance function of Brownian motion.