GF(2~N)上线性化多项式根的存在性

给出了判断有限域上某元素为线性化多项式根的方法。在此基础上,将线性化多项式根的求解问题归结为有限域上简单方程的求解,使得可以方便地用计算机求解线性化多项式的根。     

边缘识别的二维正交多项式拟合及结构变形检测

数字图像中边缘附近的灰度是沿边缘方向和跨边缘方向二维变化的,以前边缘识别的多项式拟合大多采用跨边缘方向的一维拟合。介绍一种采用二维正交多项式进行边缘识别的新方法,由于二维拟合更符合边缘附近小区域内像素灰度二维变化的实际,因此拟合结果优于一维拟合。在进行拟合时,利用正交多项式的正交性将优化方程对角化,避免求逆或解方程,没有多项式拟合优化方程的病态问题,采用高阶多项式拟合可以提高拟合精度。对生成图像的边缘识别结果表明,二维正交多项式拟合识别边缘的精度和稳定性较好。简支梁模型试验表明,采用正交多项式边缘拟合方法检测梁的静变形,图像变形检测精度在0.1像素之内,适当选择图像采集设备和采集范围,点检测精度与传统检测方法的精度相当,边缘检测属线状高密度检测,检测范围远大于传统方法。     

The Use of Legendre Polynomial Expansions in Solving Optimal Control Problems in the Space l 2

A method for solving a class of general deterministic optimal control problems is presented here. The method consists of relating the functions involved in the problem to sequences and then converting the problem to one which deals with these sequences alone. The function-sequence correspondence is defined by representing each function by its Legendre polynomial expansion and then relating the function to the sequence of coefficients in this expansion. After this is done, the problem is converted to one in l ²; by determining the equivalents in l ²; of differentiation, inner multiplication, and multiplication.

The resulting problem in l ²; is a non-linear programming problem which consists of an infinite array of equations, inequalities, and expressions, each of which involves infinite polynomial expressions. To solve a problem of this type it must be approximated by a finite non-linear programming problem. After this is done various methods can bo used for solving the final problem.     

On the Ranks and Kernels Problem for Perfect Codes

A construction is proposed which, for n large enough, allows one to build perfect binary codes of length n and rank r, with kernel of dimension k, for any admissible pair (r, k) within the limits of known bounds.     

On peer-to-peer (P2P) content delivery

In both academia and industry, peer-to-peer (P2P) applications have attracted great attentions. P2P applications such as Napster, Gnutella, FastTrack, BitTorrent, Skype and PPLive, have witnessed tremendous success among the end users. Unlike a client-server based system, peers bring with them serving capacity. Therefore, as the demand of a P2P system grows, the capacity of the network grows, too. This enables a P2P application to be cheap to build and superb in scalability. In this paper, we survey the state of the art of the research and the development of P2P content delivery application. Using examples of the deployed P2P applications and research prototypes, we survey the best practices in P2P overlay building and P2P scheduling. We hope that the information may help the readers to build a reliable, robust P2P content delivery application.

On the Automatizability of Polynomial Calculus

We prove that Polynomial Calculus and Polynomial Calculus with Resolution are not automatizable, unless W[P]-hard problems are fixed parameter tractable by one-side error randomized algorithms. This extends to Polynomial Calculus the analogous result obtained for Resolution by Alekhnovich and Razborov (SIAM J. Comput. 38(4):1347–1363, 2008).     

一个关于Hamilton环（路）的多项式时间算法

该研究为Hamilton环路（道路）问题设计出了一个多项式时间算法,论证了它的正确性。根据该算法编制了程序,进行了大量的实例计算。文章公布了主要研究方法、过程、实验数据,以及粗略的算法步骤。详细的算法步骤和证明将在随后的论文中发表。由于Hamilton环路（道路）为著名的NP完全问题,而作者认为自己已彻底解决了NP复杂问题。     

Existence Theorems for Nonconvex Problems of Variational Calculus

A solution to a variational calculus problem is studied under the conditions of integrant convexity. The existence theorem is proved. As an example, a function is given, which satisfies all the conditions of the theorem but is not convex.     

On the Complexity of Polynomial Recurrence Sequences

We consider recurrence sequences over the set of integers with generating functions being arbitrary superpositions of polynomial functions and the sg function, called polynomial recurrence sequences. We define polynomial-register (PR) machines, close to random-access machines. We prove that computations on PR machines can be modeled by polynomial recurrence sequences. On the other hand, computation of elements of a polynomial recurrence sequence can be implemented using a suitable PR machine.     

On the Dynamic Semantics and the Timing Behavior of Ravenscar Kernels

Mature research advances in scheduling theory show that carefully-crafted concurrent computational models permit static analysis of real-time behavior. This evidence enables designers to consider using suitable forms of explicit concurrency to model the inherent concurrency of real-time systems. The Ravenscar Profile, a specifically tailored subset of the Ada 95 tasking model, defines a compact and efficient concurrent computational model, especially suited for the development of high integrity, high efficiency real-time systems.Ravenscar runtimes can be implemented by small, efficient, reliable and certifiable kernels. At least two such implementations already exist and are being industrially deployed. The simplicity and intrinsic determinism of Ravenscar kernels facilitate the definition of metrics that cater for very accurate characterization of the dynamic behavior of the runtime and of the execution time of its primitives. Accurate runtime metrics enable forms of response time analysis that minimize the pessimism in the prediction of the runtime influence on the application. This is especially useful for concurrent systems that exhibit significant dependency on runtime support services. This paper recalls the motivations of the Ravenscar Profile, outlines the definition of it and formulates a precise characterisation of the associated runtime metrics.     

Polynomial Time Approximation Schemes for Some Dense Instances of NP-Hard Optimization Problems

We survey recent results on the existence of polynomial time approximation schemes for some dense instances of NP-hard combinatorial optimization problems. We indicate some inherent limits for the existence of such schemes for some other dense instances of optimization problems. We also go beyond the dense optimization problems and show how other approximation problems can be solved by using dense techniques. Received October 30, 1997; revised June 25, 1999, and April 17, 2000.     

(l,d)-模体识别问题的遗传优化算法

转录因子结合位点识别在基因表达调控过程中起着重要的作用.文中提出了一种贝叶斯模型驱动的模体识别的遗传优化算法GOBMD(Genetic Optimization with Bayesian Model for Motif Discovery).GOBMD首先使用一个基于位置加权散列的投影过程,将输入序列中的l-mers投影到k维(k相似文献   

Combining DC Algorithms (DCAs) and Decomposition Techniques for the Training of Nonpositive–Semidefinite Kernels

Today, decomposition methods are one of the most popular methods for training support vector machines (SVMs). With the use of kernels that do not satisfy Mercer's condition, new techniques must be designed to handle nonpositive–semidefinite kernels resulting to this choice. In this work we incorporate difference of convex (DC functions) optimization techniques into decomposition methods to tackle this difficulty. The new approach needs no problem modification and we show that the only use of a truncated DC algorithms (DCAs) in the decomposition scheme produces a sufficient decrease of the objective function at each iteration. Thanks to this property, an asymptotic convergence proof of the new algorithm is produced without any blockwise convexity assumption on the objective function. We also investigate a working set selection rule using second-order information for sequential minimal optimization (SMO)-type decomposition in the spirit of DC optimization. Numerical results show the robustness and the efficiency of the new methods compared with state-of-the-art software.      

On the Existence of Epipolar Matrices

This paper considers the foundational question of the existence of a fundamental (resp. essential) matrix given m point correspondences in two views. We present a complete answer for the existence of fundamental matrices for any value of m. We disprove the widely held beliefs that fundamental matrices always exist whenever \(m \le 7\). At the same time, we prove that they exist unconditionally when \(m \le 5\). Under a mild genericity condition, we show that an essential matrix always exists when \(m \le 4\). We also characterize the six and seven point configurations in two views for which all matrices satisfying the epipolar constraint have rank at most one.     

Existence of (cheap) minimal norm controllers

It is shown that the spectral norm of the closed-loop system matrix is minimized if a special type of minimum variance control is applied. Furthermore, a sufficient condition is derived for the existence of a controller which, with less control effort than this minimum variance controller, obtains the same minimal closed-loop norm.