Factoring Polynomials Over Local Fields

We describe an efficient new algorithm for factoring a polynomial Φ(x) over a fieldkthat is complete with respect to a discrete prime divisor. For every irreducible factorϕ (x) of Φ(x) this algorithm returns an integral basis fork[ x ] / ϕ(x)k[ x ] overk.     

由2次单参复解析多项式构造非线性迭代函数系

为了构造新形式的分形,提出利用单参复解析2次多项式映射构造非线性迭代函数系.首先构造出2次多项式复映射在参数平面上的1周期参数集合;然后在该集合上随机挑选2个以上的参数,由这些参数建立一组迭代映射,用这组迭代映射构造出一个由单参的2次复解析压缩映射构造的非线性压缩IFS迭代函数系;最后对迭代函数系中的一个迭代映射在平面上的压缩不动点连续迭代,构造出相应的奇怪吸引子或分形.实验结果表明,该方法可以用于大量构造平面上的奇怪吸引子或分形,图形结构新颖.     

一类有限域上的置换多项式

有限域上的置换多项式在科学工程中的多个领域有着广泛的应用,尤其应用于现代通讯、密码学等领域中。基于Zha等人在文献[23]中提出,当t为偶数时,有限域Fpⁿ上形如(xp^k－x+δ)^t+γx+βTr(x)的多项式是置换的,通过进一步研究,运用证明置换多项式的一般方法,将其改进为无论t为奇数或偶数,(xp^k+1－x^p+δ)^t+γx+βTr(x)形式的多项式在Fpⁿ上均是置换的。     

有限域上置换多项式的研究进展

AGW准则和分段方法是构造有限域上置换多项式的两种主要方法。介绍有限域上置换多项式在密码学和编码理论中的应用,总结利用AGW准则和分段方法构造有限域上置换多项式和逆置换的研究进展,阐述置换多项式存在的问题,并对下一步研究工作进行展望。     

Factoring Polynomials Over Finite Fields: A Survey

This survey reviews several algorithms for the factorization of univariate polynomials over finite fields. We emphasize the main ideas of the methods and provide an up-to-date bibliography of the problem.     

Computing GCDs of Polynomials over Algebraic Number Fields

Modular methods for computing the gcd of two univariate polynomials over an algebraic number field require a priori knowledge about the denominators of the rational numbers in the representation of the gcd. A multiplicative bound for these denominators is derived without assuming that the number generating the field is an algebraic integer. Consequently, the gcd algorithm of Langemyr and McCallum [J. Symbolic Computation8, 429 - 448, 1989] can now be applied directly to polynomials that are not necessarily represented in terms of an algebraic integer. Worst-case analyses and experiments with an implementation show that by avoiding a conversion of representation the reduction in computing time can be significant. A further improvement is achieved by using an algorithm for reconstructing a rational number from its modular residue so that the denominator bound need not be explicitly computed. Experiments and analyses suggest that this is a good practical alternative.     

Designing Quad‐dominant Meshes with Planar Faces

We study the combined problem of approximating a surface by a quad mesh (or quad‐dominant mesh) which on the one hand has planar faces, and which on the other hand is aesthetically pleasing and has evenly spaced vertices. This work is motivated by applications in freeform architecture and leads to a discussion of fields of conjugate directions in surfaces, their singularities and indices, their optimization and their interactive modeling. The actual meshing is performed by means of a level set method which is capable of handling combinatorial singularities, and which can deal with planarity, smoothness, and spacing issues.     

Factorization of Polynomials over Finite Fields and Characteristic Sequences

A new factorization algorithm for polynomials over finite fields was recently developed by the first author. For finite fields of characteristic 2, it is known from previous work that this algorithm has several advantages over the classical Berlekamp algorithm. In this paper we show that the linearization step in the new algorithm is feasible—in the sense that it can be carried out in polynomial time—for arbitrary finite fields, by using an approach based on decimation operators and characteristic linear recurring sequences. We also introduce a general principle for the linearization of the factorization problem for polynomials over finite fields.     

Pattern‐Based Quadrangulation for N‐Sided Patches

We propose an algorithm to quadrangulate an N‐sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch‐based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.     

Improved Corners with Multi‐Channel Signed Distance Fields

We propose an extension to the state‐of‐the‐art text rendering technique based on sampling a 2D signed distance field from a texture. This extension significantly improves the visual quality of sharp corners, which is the most problematic feature to reproduce for the original technique. We achieve this by using a combination of multiple distance fields in conjunction, which together provide a more thorough representation of the given glyph's (or any other 2D shape's) geometry. This multi‐channel distance field representation is described along with its application in shader‐based rendering. The rendering process itself remains very simple and efficient, and is fully compatible with previous monochrome distance fields. The introduced method of multi‐channel distance field construction requires a vector representation of the input shape. A comparative measurement of rendering quality shows that the error in the output image can be reduced by up to several orders of magnitude.     

Avoiding on‐screen metamerism in N‐primary displays

Abstract— The present paper describes a method for using more than three primaries in an additive‐primary display. The method ensures that each tristimulus specification can be produced in no more than one way, even if a non‐singular filter (i.e., one that does not reduce the dimensionality of color‐matching space) is interposed between the screen and the viewer. Starting with N primaries, the method uses only three at a time, but these may be composites — fixed linear combinations of the original N. As further insurance against on‐screen metamerism, a criterion on the primary spectra, based on the Binet‐Cauchy theorem, ensures that a triad of primaries keeps its right/left‐handed chromaticity ordering when a filter is interposed.     

Non‐Oriented MLS Gradient Fields

We introduce a new approach for defining continuous non‐oriented gradient fields from discrete inputs, a fundamental stage for a variety of computer graphics applications such as surface or curve reconstruction, and image stylization. Our approach builds on a moving least square formalism that computes higher‐order local approximations of non‐oriented input gradients. In particular, we show that our novel isotropic linear approximation outperforms its lower‐order alternative: surface or image structures are much better preserved, and instabilities are significantly reduced. Thanks to its ease of implementation (on both CPU and GPU) and small performance overhead, we believe our approach will find a widespread use in graphics applications, as demonstrated by the variety of our results.     

Approximating Free‐form Geometry with Height Fields for Manufacturing

We consider the problem of manufacturing free‐form geometry with classical manufacturing techniques, such as mold casting or 3‐axis milling. We determine a set of constraints that are necessary for manufacturability and then decompose and, if necessary, deform the shape to satisfy the constraints per segment. We show that many objects can be generated from a small number of (mold‐)pieces if slight deformations are acceptable. We provide examples of actual molds and the resulting manufactured objects.     

As‐Killing‐As‐Possible Vector Fields for Planar Deformation

Cartoon animation, image warping, and several other tasks in two‐dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, and its quality is determined by the type of distortion it introduces. In many applications, a desirable map is as isometric as possible. Finding such deformations, however, is a nonlinear problem, and most of the existing solutions approach it by minimizing a nonlinear energy. Such methods are not guaranteed to converge to a global optimum and often suffer from robustness issues. We propose a new approach based on approximate Killing vector fields (AKVFs), first introduced in shape processing. AKVFs generate near‐isometric deformations, which can be motivated as direction fields minimizing an “as‐rigid‐as‐possible” (ARAP) energy to first order. We first solve for an AKVF on the domain given user constraints via a linear optimization problem and then use this AKVF as the initial velocity field of the deformation. In this way, we transfer the inherent nonlinearity of the deformation problem to finding trajectories for each point of the domain having the given initial velocities. We show that a specific class of trajectories — the set of logarithmic spirals — is especially suited for this task both in practice and through its relationship to linear holomorphic vector fields. We demonstrate the effectiveness of our method for planar deformation by comparing it with existing state‐of‐the‐art deformation methods.     

Sliding mode control for N‐coupled reaction‐diffusion PDEs with boundary input disturbances

This paper develops the sliding mode control (SMC) design for N‐coupled reaction‐diffusion parabolic PDEs with boundary input disturbances. In order to reject the disturbances, the backstepping‐based boundary SMC law is constructed to steer the system trajectory to a suitable sliding surface and then maintain sliding motion on the surface thereafter, resulting in the exponential convergence to the zero equilibrium state. The well‐posedness of the closed‐loop system is established based on a detailed spectral analysis and Riesz basis generation. Finally, a simulation example is provided to illustrate the effectiveness of the SMC design.     

关于复杂FPGA设计的一些技巧

随着社会的发展,FPGA的应用将越来越广泛,其设计也必然将越来越复杂.作为设计人员来说,在今后的工作中会遇到更多的问题,从这个角度出发,提出了一些在设计中的技巧,最后给出了一个例子说明如何在实际中做到这点.     

Application of N‐step‐ahead NeuroControl on articulated manipulators

The N‐step‐ahead control method, called chain‐back‐propagation, is applied to articulated manipulators. The method is based on a pair of neural networks—the neural controller and the neural emulator—and focuses mainly in the appropriate design of the various global and chain‐local penalty functions and the convergence control limitations, needed for the on‐line training of the controller. No reference models or paths are needed for the implementation of the method, only set‐points. The results, compared to conventional proportional‐derivative (PD) control and to traditional one‐step‐ahead neural control, are quite satisfactory, indicating improved accuracy, faster response, and greater overall efficiency. © 2000 John Wiley & Sons, Inc.     

Stenciling: Designing Structurally‐Sound Surfaces with Decorative Patterns

We present a novel method to design shells with artistic cutouts in a manner that produces a stable final result. The process of stenciling, removing material with a fixed shape, is a particularly appealing way to introduce a decorative pattern into the design of architectural structures, furniture, or household objects. However, removing material can easily weaken an object to the point where its integrity is compromised, while purely functional distributions of cutouts lack the desired aesthetic component. We tackle this problem by combining aesthetics, stability, and material efficiency in an optimization that determines the distribution and scaling of these stencils in a way that complies as much as possible with both pattern and stability objectives. We demonstrate the capabilities of our system on examples from architecture, furniture design, and decorative items, and show how user interaction can be integrated to guide the aesthetics of the final result.     

High‐performance N‐thread software solutions for mutual exclusion

Software solutions for mutual exclusion developed over a 30‐year period, starting with complex ad hoc algorithms and progressing to simpler formal ones. While it is easy to dismiss software solutions for mutual exclusion, as this family of algorithms is antiquated and most platforms support atomic hardware instructions, there is still a need for these algorithms in threaded, embedded systems running on low‐cost processors lacking atomic instructions. While N‐thread solutions are usually short (10–25 lines of code), each is ingenious with exceptionally subtle aspects, often making it difficult to prove correctness or construct an implementation. This work examines correctness and performance of the implementations. An extensive survey of existing algorithms is presented, with explanations of the intuition behind the algorithms and how they work. Several errors were found and corrections made, as well as a few small improvements, in the existing algorithms; two new high‐performance algorithms were developed. Finally, a worst‐case high‐contention performance experiment is performed to compare the algorithms and contrast them with three common locks based on hardware atomic instructions. The results show our two new algorithms are highly competitive with an equivalent hardware lock (Mellor‐Crummey and Scott) over a range of 1–32 processors. Hence, threading is a viable alternative to event‐driven programming for complex embedded systems without atomic instructions. Copyright © 2014 John Wiley & Sons, Ltd.