The Ackermann function. a theoretical,computational, and formula manipulative study

Ackermann's function is of highly recursive nature and of two arguments. It is here treated as a class of functions of one argument, where the other argument defines the member of the class. The first members are expressed with elementary functions, the higher members with a hierarchy of primitive recursive functions. The number of calls of the function needed in a straightforward recursive computation is given for the first members. The maximum depth in the recursion during the evaluation is investigated.Results from tests with the Ackermann function of recursive procedure implementations in ALGOL-60, ALGOL W, PL/I and SIMULA-67 on IBM 360/75 and CD 6600 are given.A SYMBAL formula manipulating program, that automatically solves recurrence relations for the first members of the function class and for the number of calls needed in their straightforward computation, is given.The Ackermann rating of programming languages is discussed.     

一种适用于大型阵列的递推干扰抑制算法

天线阵列在雷达与卫星通信中有着广泛的应用,它可以通过波束形成来抑制干扰.对于具有较多阵元数的大型阵列,普通的波束形成算法计算量很高.本文给出一种适用于大型阵列的递推干扰抑制算法,它是在波束空间分解最大信干噪比准则下基于干扰矢量进行变维递推处理,所需递推步数为干扰数,且每步递推中数据矩阵的维数很小,因而所需的总计算量较低.阵元数越多该递推算法的计算效率越高.仿真结果表明,该递推算法可以有效实现干扰抑制.     

A PGM framework for recursive modeling of players in simple sequential Bayesian games

We consider the situation where two agents try to solve each their own task in a common environment. In particular, we study simple sequential Bayesian games with unlimited time horizon where two players share a visible scene, but where the tasks (termed assignments) of the players are private information. We present an influence diagram framework for representing simple type of games, where each player holds private information. The framework is used to model the analysis depth and time horizon of the opponent and to determine an optimal policy under various assumptions on analysis depth of the opponent. Not surprisingly, the framework turns out to have severe complexity problems even in simple scenarios due to the size of the relevant past. We propose two approaches for approximation. One approach is to use Limited Memory Influence Diagrams (LIMIDs) in which we convert the influence diagram into a set of Bayesian networks and perform single policy update. The other approach is information enhancement, where it is assumed that the opponent in a few moves will know your assignment. Empirical results are presented using a simple board game.     

A Non-Cyclic Prefixed SFBC-SCFDE System Based on a Recursive Algorithm of Joint Channel Estimation and Data Detection

We propose a non-cyclic prefixed Single carrier frequency-domain equalization （SCFDE） system with Space-frequency block codes （SFBC）. The transmitted signals in proposed system are composed of Singlecarrier （SC） information sequences derived from SFBC and training sequences, both of which have been placed in an alternate order without any Cyclic prefix （CP） before each SC information sequence. Furthermore, a recursire algorithm of Joint channel estimation and data detection （recursive-JCEDD） is proposed for system receiver. Simulation results show that the proposed non-cyclic prefixed SFBC-SCFDE system based on the recursive-JCEDD algorithm has better Bit error rate （BER） performance than traditional cyclic prefixed SFBC-SCFDE, Space-time block-coded SCFDE （STBC-SCFDE） and STBC-OFDM systems with some common channel estimation algorithms.     

Recursive residual atrous spatial pyramid pooling network for single image deraining

In recent years, removing rain streaks from a single image has been a significant issue for outdoor vision tasks. In this paper, we propose a novel recursive residual atrous spatial pyramid pooling network to directly recover the clear image from rain image. Specifically, we adopt residual atrous spatial pyramid pooling (ResASPP) module which is constructed by alternately cascading a ResASPP block with a residual block to exploit multi-scale rain information. Besides, taking the dependencies of deep features across stages into consideration, a recurrent layer is introduced into ResASPP to model multi-stage processing procedure from coarse to fine. For each stage in our recursive network we concatenate the stage-wise output with the original rainy image and then feed them into the next stage. Furthermore, the negative SSIM loss and perceptual loss are employed to train the proposed network. Extensive experiments on both synthetic and real-world rainy datasets demonstrate that the proposed method outperforms the state-of-the-art deraining methods.     

Solubility in compressible polymers: Beyond the regular solution theory

The age-old idea of “like dissolves like” requires a notion of “likeness” that is hard to quantify for polymers. We revisit the concepts of pure component cohesive energy density c^P and mutual cohesive energy density c₁₂ so that they can be extended to polymers. We recognize the inherent limitations of c₁₂ due to its very definition, which is based on the assumption of no volume of mixing (true for incompressible systems), one of the assumptions in the random mixing approximation (RMA); no such limitations are present in the identification of c^P. We point out that the other severe restriction on c₁₂ is the use of pure components in its definition because of which c₁₂ is not merely controlled by mutual interactions. Another quantity as a measure of mutual cohesive energy density that does not suffer from the above limitations of c₁₂ is introduced. It reduces to c₁₂ in the RMA limit. We are able to express in terms of c₁₂ and pure component c^P’s. We also revisit the concept of the internal pressure and its relationship with the conventional and the newly defined cohesive energy densities. In order to investigate volume of mixing effects, we introduce two different mixing processes in which volume of mixing remains zero. We then carry out a comprehensive reanalysis of various quantities using a recently developed recursive lattice theory that has been tested earlier and has been found to be more accurate than the conventional regular solution theory such as the Flory-Huggins theory for polymers. In the RMA limit, our recursive theory reduces to the Flory-Huggins theory or its extension for a compressible blend. Thus, it supersedes the Flory-Huggins theory. Consequently, the conclusions based on our theory are more reliable and should prove useful.     

基于累积量的递归最小二乘算法研究

从基于累积量的均方误差（ＣＭＳＥ）准则,本文推导了一种基于累积量的递归最小二乘（ＣＲＬＳ）算法．并从信号检验和估计的角度对三阶ＣＲＩＳ算法中出现的加权求和系数给出的一种物理解释,以说明其抗高斯噪声的机理．本文提出应根据三种不同条件下信号的最优估计来确定最佳窗口函数的原则,并进一步证明了在极大似（ＭＬ）和线性均方（ＬＭＳ）估计意义下的最佳窗口都是矩形窗而非Ｄｅｌｏｐｏｕｌｏｓ和Ｇｉａｎｎａｋｉｓ建议的Ｈａｍｍｉｎｇ窗~［３］。仿真实验证实：ＣＲＬＳ算法采用矩形窗确定比采用Ｈａｍｍｉｎｇ窗具有更上的结果偏差。     

On a Class of Recursively Enumerable Sets

We define a class of so-called ∑(n)-sets as a natural closure of recursively enumerable sets W_n under the relation “∈” and study its properties.     

基于遗传算法的递归式MTI滤波器的设计

递归式MTI滤波器从理论上讲几乎可以合成任意形状的频率响应函数,因而具有很广的应用范围。为了能够灵活设计出满足系统要求的递归式MTI滤波器,提出了一种设计方法。该方法以遗传算法(GA)的基本思想为基础,利用滤波器的改善因子、通带宽度和通带波纹来构成适应函数,并用GA来加快参量搜索速度和获取全局近似最优解。实验仿真设计了两种典型的递归式MTI滤波器,结果证明该方法是一种有效的设计方法,它可以灵活而快速地设计出所需要的滤波器。     

Least squares based and gradient based iterative identification for Wiener nonlinear systems

This paper derives a least squares-based and a gradient-based iterative identification algorithms for Wiener nonlinear systems. These methods separate one bilinear cost function into two linear cost functions, estimating directly the parameters of Wiener systems without re-parameterization to generate redundant estimates. The simulation results confirm that the proposed two algorithms are valid and the least squares-based iterative algorithm has faster convergence rates than the gradient-based iterative algorithm.