The F5 criterion revised

The purpose of this work is to generalize part of the theory behind Faugère’s “F5” algorithm. This is one of the fastest known algorithms to compute a Gröbner basis of a polynomial ideal I generated by polynomials f₁,…,f_m. A major reason for this is what Faugère called the algorithm’s “new” criterion, and we call “the F5 criterion”; it provides a sufficient condition for a set of polynomials G to be a Gröbner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination.This paper introduces some new concepts that place the criterion in a more general setting: S-Gröbner bases and primitive S-irreducible polynomials. We use these to propose a new, simple algorithm based on a revised F5 criterion. The new concepts also enable us to remove various restrictions, such as proving termination without the requirement that f₁,…,f_m be a regular sequence.     

Termination of the F5 algorithm

The F5 algorithm, which calculates the Gröbner basis of an ideal generated by homogeneous polynomials, was proposed by Faugère in 2002; simultaneously, the correctness of this algorithm was proved under the condition of termination. However, termination itself was demonstrated only for a regular sequence of polynomials. In this paper, it is proved that the algorithm terminates for any input data. First, it is shown that if the algorithm does not terminate, it eventually generates two polynomials where the first is a reductor for the second. However, it is not argued that such a reduction is permitted by all the criteria introduced in F5. Next, it is shown that if such a pair exists, then there exists another pair for which the reduction is permitted by all the criteria, which is impossible.     

F[x]-lattice basis reduction algorithm and multisequence synthesis

By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field F. Its computational complexity is O(N2) operations in F where N is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomi-als is given. The set and exact number of all minimal polynomials are also described when F is a finite field.     

基于冗余零系数消除的F5改进算法

F5隐写分析算法利用收缩现象,比较剪裁后图像直方图和估计载体图像直方图的差异进行检测。针对该算法的特点,提出改进的F5算法,通过部分消除冗余零系数,提高嵌入率、防止收缩现象的发生。在标准图像集上的实验结果表明,改进算法改善了含密直方图的收缩现象,各检测参数与原始载体图像差别较小,可以有效抵抗F5隐写分析算法。     

针对F5隐写分析算法的FPGA实现

应用密钥来控制隐藏路径已成为一种趋势,随着消息长度的增加和密钥空间的增大,纯软件方式已不能满足隐写分析的实时性要求。针对依赖密钥的隐写算法F5,提出一种基于现场可编程门阵列(FPGA)的隐写分析方案。正确密钥与错误密钥产生嵌入位置的样本分布具有明显的差异,利用这一特性可以得到F5的正确密钥,从而实现密钥攻击。实验表明,消息长度超过2 000 bit时,该方案和软件攻击相比时间上能降低一个数量级。     

三元域上三次和四次剩余码的幂等生成元

有限域上高次剩余码的生成多项式都是多项式[xn-1]的因式。针对多项式[xn-1]在有限域上分解的困难性,给出了三元域[F3]上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解这些幂等生成元与[xn-1]最大公因式就可得到三次和四次剩余码生成多项式而不用分解[xn-1]。     

二元域上三次和四次剩余码的幂等生成元

有限域上高次剩余码的生成多项式都是多项式[xn-1]的因式。针对多项式[xn-1]在有限域上分解的困难性,给出了二元域[F2]上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解该幂等生成元与[xn-1]最大公因式就可得到三次和四次剩余码生成多项式而不用分解[xn-1]。     

F5隐写算法及其隐写分析研究

图像隐写分析是检测、提取和破坏隐写图像中秘密信息的技术,是信息安全领域的研究热点之一.由Westfeld提出的F5隐写算法是一种重要的图像隐写算法.分析了F5隐写算法及其隐写系统,讨论了一种针对F5隐写算法的隐藏检测方法,并给出了具体实现的算法.实验结果表明,F5算法采用矩阵编码,提高了嵌入效率.     

Anchoring and gliding of easy axis of 5CB on photoaligning PVCN‐F surface

Abstract— The photoaligning properties of the popular photoaligning material polyvinyl‐4(fluorocinnamate) (PVCN‐F) are presented. The aligning quality and azimuthal and zenithal anchoring energy were measured and the drift of the easy orientation axis (gliding effect) on the PVCN‐F surface, depending on UV exposure, was studied. Special attention is paid to unraveling the contribution of the adsorption liquid‐crystal molecules onto the aligning surface to the anchoring properties of PVCNF and measuring the drift of the easy orientation axis over the PVCN‐F surface. It is shown that a relatively weak azimuthal anchoring energy (W_az ～ 10^?7 ? 10^?5 J/m²) leads to strong drift of the easy axis in the azimuthal plane that was observed in a moderate (～0.1–0.3 T) magnetic field. A much stronger polar anchoring (W_zen ～ 10^?4 J/m²) allowed us to observe the essential gliding of the easy axis in the zenithal plane in a rather strong electric field (～5 V/μm).     

Generalization of the F5 algorithm for calculating Gröbner bases for polynomial ideals

This survey paper presents general approach to the well-known F5 algorithm for calculating Gröbner bases, which was created by Faugère in 2002.     

一种基于量化表修改的F5隐写方法

IQTM-F5方法在高嵌入比情况下,DCT系数直方图统计特性会被破坏。针对该问题,利用新的信息嵌入策略并结合IQTM-F5方法中采用的修改后量化表,提出一种保持DCT系数直方图统计特性的F5隐写方法。实验结果表明,该方法能够取得与IQTM-F5方法近似的信息隐藏容量和嵌入效率,隐秘图像具有更高的图像质量,并且抗直方图统计分析攻击的能力更强。     

基于F5负载均衡技术的网上选课平台

针对基于云南财经大学现有的网络条件,着力探索改善网络选课过程中大并发量处理的策略,主张利用F5_BIG_IP LTM设备搭建网络和服务器负载均衡,以解决在实时选课过程中处理大量学生并发访问选课平台可能引起的服务器过载不能响应学生的请求问题.该架构能够在实际使用过程中很好的解决大并发量的拥堵问题,并且负载均衡技术为对日益增涨的Web应用服务提供了一种可靠稳定的架构,为网上实时处理大并发量访问拥堵问题提供了一种参考方案.     

Automatic Generation of Numerical Redundancies for Non-Linear Constraint Solving

In this paper we present a framework for the cooperation of symbolic and propagation-based numerical solvers over the real numbers. This cooperation is expressed in terms of fixed points of closure operators over a complete lattice of constraint systems. In a second part we instantiate this framework to a particular cooperation scheme, where propagation is associated to pruning operators implementing interval algorithms enclosing the possible solutions of constraint systems, whereas symbolic methods are mainly devoted to generate redundant constraints. When carefully chosen, it is well known that the addition of redundant constraint drastically improve the performances of systems based on local consistency (e.g. Prolog IV or Newton). We propose here a method which computes sets of redundant polynomials called partial Gröbner bases and show on some benchmarks the advantages of such computations.     

Cartesian control of redundant robots

This article presents a Cartesian-space position/force controller for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F ? R ^m and robot actuator torque T ? R ⁿ(for redundant robots, m < n). The underdetermined nature of the F → T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F → T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F→T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.     

冗余磁盘阵列RAID5性能损失研究

冗余磁盘阵列虽然引入了容错机制使得磁盘阵列的数据可靠性得到了很大的提高，但同时也引起性能不降。而且随着磁盘数量的增加，磁盘失效的概率将明显增大，当单个磁盘失效后，虽然此时磁盘阵列数据并未矢失，且仍能服务于系统的请量此时磁盘阵列是带“病”工作，处于一种降级模式，本文对冗余磁盘阵列ＲＡＩＤ５进行了队列建模和仿真计算，提出了性能损失率的概念，并作为评价磁盘阵列性能损失的衡量指标。计算结果分析表明，ＲＡＩ     

基于多特征支持向量回归的F5定量隐密分析研究

针对现有F5定量隐密分析方法仅考虑直方图收缩导致定量估计误差较大的问题,提出了一种新的基于多特征支持向量回归(SVR)的定量隐密分析算法.算法通过最大似然估计拟合DCT系数分布模型的参数,利用参数的相对变化量来反映嵌入机制对直方图的修改,并使用共生矩阵描述F5算法对图像像素间相关性的破坏.在确定特征与嵌入量之间的函数关系时,算法采用SVR在高维空间中进行拟合,从而估计待测图像的容量.实验表明,该算法可以对F5算法的嵌入量进行有效估计,而且估计效果要优于已有的算法.     

The impact of display angles on the legibility of Sans-Serif 5 × 5 capitalized letters

This paper introduced a laboratory study on quantifying the impact of display angles 0.0°–90.0° on the legibility of Sans-Serif 5 × 5 Capitalized Letters C, D, E, F, H, K, N, P, R, U, V, and Z, commonly used for acuity tests. This study addressed three issues not tackled in the previous studies, including (a) extremely large incident angles 82.8°–90°, (b) multiple letters other than a single letter E previously used, and (c) the interference of people's normal reading habit on legibility evaluation. A total of 20 young college students with Snellen acuity 20/20 or better and normal color vision participated in this experiment. They were asked to read viewing materials presented at 15 display angles. This study derived two equations and modified an existing legibility index to correct the interference of people's normal reading habit on legibility evaluation at extreme oblique display angles.     

SoftSig: Software-Exposed Hardware Signatures for Code Analysis and Optimization

Many code analysis techniques for optimization, debugging, and parallelization must perform runtime disambiguation of address sets. Hardware signatures support such operations efficiently and with low complexity. SoftSig exposes hardware signatures to software through instructions that control which addresses to collect and which to disambiguate against. The Memoise algorithm demonstrates SoftSig's versatility by detecting and eliminating redundant function calls.     

基于F5多链路负载均衡技术在校园网中的应用

目前大部分国内高校的出口链路已经有多种选择,出口带宽也逐年提高,而针对校外访问校园网内部各种资源的研究与应用实践不多,该文对基于F5的多链路接入负载均衡技术在校园网外部访问校园网内资源方式的应用做了研究和实践。     

Combined 5 x 2 cv F test for comparing supervised classification learning algorithms

Dietterich (1998) reviews five statistical tests and proposes the 5 x 2 cv t test for determining whether there is a significant difference between the error rates of two classifiers. In our experiments, we noticed that the 5 x 2 cv t test result may vary depending on factors that should not affect the test, and we propose a variant, the combined 5 x 2 cv F test, that combines multiple statistics to get a more robust test. Simulation results show that this combined version of the test has lower type I error and higher power than 5 x 2 cv proper.