ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation

In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two-dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid-like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid-like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.     

Three-dimensional immersed finite-element method for anisotropic magnetostatic/electrostatic interface problems with nonhomogeneous flux jump

Anisotropic diffusion is important to many different types of common materials and media. Based on structured Cartesian meshes, we develop a three-dimensional (3D) nonhomogeneous immersed finite-element (IFE) method for the interface problem of anisotropic diffusion, which is characterized by an anisotropic elliptic equation with discontinuous tensor coefficient and nonhomogeneous flux jump. We first construct the 3D linear IFE space for the anisotropic nonhomogeneous jump conditions. Then we present the IFE Galerkin method for the anisotropic elliptic equation. Since this method can efficiently solve interface problems on structured Cartesian meshes, it provides a promising tool to solve the physical models with complex geometries of different materials, hence can serve as an efficient field solver in a simulation on Cartesian meshes for related problems, such as the particle-in-cell simulation. Numerical examples are provided to demonstrate the features of the proposed method.     

两种多层穿梭车系统的性能比较分析

物流配送中心订单响应速度的加快,对订单拣选系统提出了更高的要求。多层穿梭车系统因其柔性强、效率高等特点,近年来得到了广泛应用。多层穿梭车系统具有两种形式--基于转载车和基于环形输送线,二者均可实现货物的快速拣选,但在系统吞吐量和订单完成周期方面存在差异,致使企业决策者难以进行系统选择。基于上述原因,本文比较两种多层穿梭车系统的性能差异。建立两个系统的开环排队网络模型,然后求解系统吞吐量、订单完成周期,通过仿真验证了排队论模型的准确性,通过试验对两种系统的性能进行对比分析。结果表明,系统吞吐量与层数、巷道数相关,层数越多,巷道数越少,转载车系统相对于环线系统优势越显著;订单完成周期与层数、订单到达率相关,层数越多,订单到达率越低,转载车系统相对于环线系统越具优势。     

Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes

This study proposes a method of constructing type II generalized angulated elements (GAEs II) Hoberman sphere mechanisms on the basis of deployment axes that intersect at one point. First, the constraint conditions for inserting n GAEs II into n deployment axes to form a loop are given. The angle constraint conditions of the deployment axes are obtained through a series of linear equations. Second, the connection conditions of two GAEs II loops that share a common deployable center are discussed. Third, a flowchart of constructing the generalized Hoberman sphere mechanism on the basis of deployment axes is provided. Finally, four generalized Hoberman sphere mechanisms based on a fully enclosed regular hexahedron, arithmetic sequence axes, orthonormal arithmetic sequence axes, and spiral-like axes are constructed in accordance with the given arrangement of deployment axes that satisfy the constraint conditions to verify the feasibility of the proposed method.     

A comparison of pivot selection techniques for permutation-based indexing

Recently, permutation based indexes have attracted interest in the area of similarity search. The basic idea of permutation based indexes is that data objects are represented as appropriately generated permutations of a set of pivots (or reference objects). Similarity queries are executed by searching for data objects whose permutation representation is similar to that of the query, following the assumption that similar objects are represented by similar permutations of the pivots. In the context of permutation-based indexing, most authors propose to select pivots randomly from the data set, given that traditional pivot selection techniques do not reveal better performance. However, to the best of our knowledge, no rigorous comparison has been performed yet. In this paper we compare five pivot selection techniques on three permutation-based similarity access methods. Among those, we propose a novel technique specifically designed for permutations. Two significant observations emerge from our tests. First, random selection is always outperformed by at least one of the tested techniques. Second, there is no technique that is universally the best for all permutation-based access methods; rather different techniques are optimal for different methods. This indicates that the pivot selection technique should be considered as an integrating and relevant part of any permutation-based access method.     

Finite-point method for efficient timing characterization of sequential elements

Timing characterization of sequential elements, such as latches and flip-flops, is one of the critical steps for timing closure in the pipelined design. Traditional characterization of setup and hold time constraints is computationally intensive, due to the demand on high accuracy in monitoring the operation failure. To improve the efficiency, this work proposes a finite-point based method for the characterization of setup and hold time constraints. The finite-point method identifies several critical data points in the non-linear curve of timing characteristics, and abstracts the essential setup/hold information from them. Moreover, compact models are derived for each point, further reducing the computation cost. The proposed method is general for all sequential elements in the standard cell library. It is comprehensively validated using benchmark circuits at 45 nm node. Experimental results demonstrate approximately 25× reduction in characterization time, with the prediction error in setup and hold time within 9% of FO₄ nominal delay, as compared to that of SPICE simulation results.