Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Ion-Beam Modified Terahertz GaAs Photoconductive Antenna

Ion-implanted photoconductive GaAs terahertz (THz) antennas were demonstrated to deliver both high-efficiency and high-power THz emitters, which are attributed to excellent carrier acceleration and fast carrier trapping for THz generations by analyzing ultrafast carrier dynamics at subpicosecond scale. The implantation distance at over 2.5 μm is deep enough to make defects (Ga vacancies, As Ga + …, etc.) quite few; hence, a few with good mobility similar to bare GaAs ensures excellent carrier acceleration in shallow distance <1.0 μm as photo carriers are generated by the pump laser. The implantation dosage is carefully optimized to make carrier trapping very fast, and screen effects by photo-generated carriers are significantly suppressed, which increases the THz radiation power of SI-GaAs antennas by two orders of magnitude. Under the same photo-excitation conditions (pump laser power, bias voltage), photocurrents from GaAs antennas with optimum conditions 300 keV, 5 × 1014 cm−2 for H implantation are decreased by two orders of magnitude; meanwhile, the THz radiation is enhanced by over four times, which means that the electrical-to-THz power conversion efficiency is improved by a factor of over 1600

Tensor Robust PCA with Nonconvex and Nonlocal Regularization

Tensor robust principal component analysis (TRPCA) is a promising way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular values equally. However, for real-world visual data, large singular values represent more signifiant information than small singular values. In this paper, we propose a nonconvex TRPCA (N-TRPCA) model based on the tensor adjustable logarithmic norm. Unlike TRPCA, our N-TRPCA can adaptively shrink small singular values more and shrink large singular values less. In addition, TRPCA assumes that the whole data tensor is of low rank. This assumption is hardly satisfied in practice for natural visual data, restricting the capability of TRPCA to recover the edges and texture details from noisy images and videos. To this end, we integrate nonlocal self-similarity into N-TRPCA, and further develop a nonconvex and nonlocal TRPCA (NN-TRPCA) model. Specifically, similar nonlocal patches are grouped as a tensor and then each group tensor is recovered by our N-TRPCA. Since the patches in one group are highly correlated, all group tensors have strong low-rank property, leading to an improvement of recovery performance. Experimental results demonstrate that the proposed NN-TRPCA outperforms some existing TRPCA methods in visual data recovery. The demo code is available at https://github.com/qguo2010/NN-TRPCA.Comment: 19 pages, 7 figure

MPR-Net:Multi-Scale Pattern Reproduction Guided Universality Time Series Interpretable Forecasting

Time series forecasting has received wide interest from existing research due to its broad applications and inherent challenging. The research challenge lies in identifying effective patterns in historical series and applying them to future forecasting. Advanced models based on point-wise connected MLP and Transformer architectures have strong fitting power, but their secondary computational complexity limits practicality. Additionally, those structures inherently disrupt the temporal order, reducing the information utilization and making the forecasting process uninterpretable. To solve these problems, this paper proposes a forecasting model, MPR-Net. It first adaptively decomposes multi-scale historical series patterns using convolution operation, then constructs a pattern extension forecasting method based on the prior knowledge of pattern reproduction, and finally reconstructs future patterns into future series using deconvolution operation. By leveraging the temporal dependencies present in the time series, MPR-Net not only achieves linear time complexity, but also makes the forecasting process interpretable. By carrying out sufficient experiments on more than ten real data sets of both short and long term forecasting tasks, MPR-Net achieves the state of the art forecasting performance, as well as good generalization and robustness performance

Surface Constraint of a Rational Interpolation and the Application in Medical Image Processing

Abstract : A new weighted bivariate blending rational spline with parameters is constructed based on function values of a function only. The interpolation is C1 in the whole interpolating region under the condition which free parameters is not limited. This study deals with the bounded property of the interpolation. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of surfaces. This rational interpolation with parameters is used in the medical image enhancement. The value of the interpolating function at any point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters. Using the surface control, the local enhancement of the image is implemented. The experimentations show that this algorithm is efficient

Constructing parametric quadratic curves

Abstract Constructing a parametric spline curve to pass through a set of data points requires assigning a knot to each data point. In this paper we discuss the construction of parametric quadratic splines and present a method to assign knots to a set of planar data points. The assigned knots are invariant under a ne transformations of the data points, and can be used to construct a parametric quadratic spline which reproduces parametric quadratic polynomials. Results of comparisons of the new method with several known methods are included