Set invariance in control

The properties of positively invariant sets are involved in many different problems in control theory, such as constrained control, robustness analysis, synthesis and optimization. In this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems.

Local histogram based geometric invariant image watermarking

Compared with other existing methods, the feature point-based image watermarking schemes can resist to global geometric attacks and local geometric attacks, especially cropping and random bending attacks (RBAs), by binding watermark synchronization with salient image characteristics. However, the watermark detection rate remains low in the current feature point-based watermarking schemes. The main reason is that both of feature point extraction and watermark embedding are more or less related to the pixel position, which is seriously distorted by the interpolation error and the shift problem during geometric attacks. In view of these facts, this paper proposes a geometrically robust image watermarking scheme based on local histogram. Our scheme mainly consists of three components: (1) feature points extraction and local circular regions (LCRs) construction are conducted by using Harris-Laplace detector; (2) a mechanism of grapy theoretical clustering-based feature selection is used to choose a set of non-overlapped LCRs, then geometrically invariant LCRs are completely formed through dominant orientation normalization; and (3) the histogram and mean statistically independent of the pixel position are calculated over the selected LCRs and utilized to embed watermarks. Experimental results demonstrate that the proposed scheme can provide sufficient robustness against geometric attacks as well as common image processing operations. (C) 2010 Elsevier B.V. All rights reserved.

LEVEL SET输运方程的求解方法及其对气-液两相流运动界面数值模拟的影响

用数值模拟方法来研究气-液两相流动与传热现象是当今多相流领域的一个热门课题.由于两相流固有的复杂性,气-液两相流界面迁移现象的数值模拟一直是两相流研究中的一大难点.本文介绍了捕捉气-液两相流相界面运动的水平集方法(Level Set)及其研究进展,介绍了求解Level Set输运方程的3种方法,即一般差分格式、Superbee-TVD格式和Runge-Kutta法-5阶WENO组合格式.结合主流场的求解,分别用这3种方法对4种典型相界面在5种流场中的迁移特性进行了模拟计算,并对计算结果进行了比较和分析.结果表明,Runge-Kutta法-5阶WENO组合格式求解Level Set输运方程的效果最好,在以后的计算中将主要采用这种组合格式来进行气-液相界面输运方程的求解.

Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

On the invariant representation of spin tensors with applications

The invariant representation of the spin tensor defined as the rotation rate of a principal triad for a symmetric and non-degenerate tensor is derived on the basis of the general solution of a linear tensorial equation. The result can be naturally specified to study the. spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics. A remarkable formula which relates the generalized stress conjugate to the generalized strain in Hill's sense. to Cauchy stress, is obtained in invariant form through the work conjugate principle. Particularly, a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes of strain arc not fixed during deformation.

The Relationship between Decision Trees and the Scale of Train Data Set

Decision Trees need train samples in the train data set to get classification rules. If the number of train data was too small, the important information might be missed and thus the model could not explain the classification rules of data. While it is not affirmative that large scale of train data set can get well model. This Paper analysis the relationship between decision trees and the train data scale. We use nine decision tree algorithms to experiment the accuracy, complexity and robustness of decision tree algorithms. Some results are demonstrated.

Visual pattern recognition network: Its training algorithm and its optoelectronic architecture

A visual pattern recognition network and its training algorithm are proposed. The network constructed of a one-layer morphology network and a two-layer modified Hamming net. This visual network can implement invariant pattern recognition with respect to image translation and size projection. After supervised learning takes place, the visual network extracts image features and classifies patterns much the same as living beings do. Moreover we set up its optoelectronic architecture for real-time pattern recognition. (C) 1996 Optical Society of America

Two-step digit-set-restricted modified signed-digit addition-subtraction algorithm and its optoelectronic implementation

A novel, to our knowledge, two-step digit-set-restricted modified signed-digit (MSD) addition-subtraction algorithm is proposed. With the introduction of the reference digits, the operand words are mapped into an intermediate carry word with all digits restricted to the set {(1) over bar, 0} and an intermediate sum word with all digits restricted to the set {0, 1}, which can be summed to form the final result without carry generation. The operation can be performed in parallel by use of binary logic. An optical system that utilizes an electron-trapping device is suggested for accomplishing the required binary logic operations. By programming of the illumination of data arrays, any complex logic operations of multiple variables can be realized without additional temporal latency of the intermediate results. This technique has a high space-bandwidth product and signal-to-noise ratio. The main structure can be stacked to construct a compact optoelectronic MSD adder-subtracter. (C) 1999 Optical Society of America.

Parallel optical negabinary signed-digit computing: algorithm and optical implementation

Negabinary is a component of the positional number system. A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode. All the arithmetic operations can be performed with binary logic. By programming the binary reference bits, addition and subtraction can be realized in parallel with the same binary logic functions. This offers a technique to perform space-variant arithmetic-logic functions with space-invariant instructions. Multiplication can be performed in the tree structure and it is simpler than the modified signed-digit (MSD) counterpart. The parallelism of the algorithms is very suitable for optical implementation. Correspondingly, a general-purpose optical logic system using an electron trapping device is suggested. Various complex logic functions can be performed by programming the illumination of the data arrays without additional temporal latency of the intermediate results. The system can be compact. These properties make the proposed negabinary arithmetic-logic system a strong candidate for future applications in digital optical computing with the development of smart pixel arrays. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00803-X].

One-step digit-set-restricted modified signed-digit adder using an incoherent correlator based on a shared content-addressable memory

An efficient one-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In this technique, carry propagation is avoided by introducing reference digits to restrict the intermediate carry and sum digits to {1,0} and {0,1}, respectively. The proposed technique requires significantly fewer minterms and simplifies system complexity compared to the reported one-step MSD addition techniques. An incoherent correlator based on an optoelectronic shared content-addressable memory processor is suggested to perform the addition operation. In this technique, only one set of minterms needs to be stored, independent of the operand length. (C) 2002 society or Photo-Optical Instrumentation Engineers.

Efficient two-step digit-set-restricted modified signed-digit algorithm based on optoelectronic shared content-addressable memory

A two-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In the proposed addition algorithm, carry propagation is avoided by using reference digits to restrict the intermediate MSD carry and sum digits into {(1) over bar ,0} and {0, 1}, respectively. The algorithm requires only 12 minterms to generate the final results, and no complementarity operations for nonzero outputs are involved, which simplifies the system complexity significantly. An optoelectronic shared content-addressable memory based on an incoherent correlator is used for experimental demonstration. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

Efficient two-step digit-set-restricted modified signed-digit algorithm based on optoelectronic shared content-addressable memory

A two-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In the proposed addition algorithm, carry propagation is avoided by using reference digits to restrict the intermediate MSD carry and sum digits into {(1) over bar ,0} and {0, 1}, respectively. The algorithm requires only 12 minterms to generate the final results, and no complementarity operations for nonzero outputs are involved, which simplifies the system complexity significantly. An optoelectronic shared content-addressable memory based on an incoherent correlator is used for experimental demonstration. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

蔷薇类的分子系统学研究—兼论系统发育基因组学的原理和方法(以SET基因超家族为例)

分子系统发育分析的主要任务包括：（1）帮助建立生命之树（tree of life）;（2）追踪基因和基因家族（gene family）的起源和进化, 以获知基因在进化过程中的功能分化和伴随发生的重要分子事件（key molecular events）和形态性状的关键创新（key innovation）。这两个方面在本研究中都有所涉及。对于前者，选用植物线粒体matR基因重建被子植物蔷薇类群的系统发育关系;对于后者，则以SET基因超家族为例，探讨其在真核生物中的进化分类以及与功能多样性的关系。 I 蔷薇类的分子系统学 蔷薇类（rosids）是基于分子数据建立的被子植物的主要分支之一，包含13个目，大约三分之一的被子植物物种。两个主要蔷薇类内部分支是豆类fabids（包含7个目）和锦葵类malvids（包含3个目）。然而，这两个分支内部，以及这两个分支与蔷薇类基部类群，包括牻牛儿苗目（Geraniales）、桃金娘目（Myrtales）和流苏子目（Crossosomatales）之间的关系大多是不清楚的。本研究中，我们选取174个物种来代表72个蔷薇类（rosids）的科，利用两个数据集，即线粒体matR单基因数据集和包括线粒体matR基因、两个质体基因(rbcL、 atpB)和一个核基因(18S rDNA) 的4基因数据集，重建蔷薇类在科以上分类阶元水平的系统发育关系。同时，还对线粒体matR基因的进化特征和用于大尺度系统发育分析的适合度和潜力进行了评价。 线粒体matR单基因数据支持malvids和大多数蔷薇类目的单系性质，然而，豆类（fabids）成员没有形成一个分支，其COM亚支，包括卫矛目（Celastrales）、酢浆草目（Oxalidales）、金虎尾目（Malpighiales）和蒜树科（Huaceae），分辨为锦葵类（malvids）的姐妹群。这个关系在最近根据花结构特征曾被提出过，但从未在之前的分子系统发育分析中得到分辨。4基因数据集支持首先是牻牛儿苗目（Geraniales），接着是桃金娘目（Myrtales）作为蔷薇类（rosids）的最基部的分支;流苏子目（Crossosomatales）是锦葵类（malvids）姐妹群，以及蔷薇类（rosids）的核心部分包括豆类（fabids），锦葵类（malvids）和流苏子目（Crossosomatales）。线粒体matR基因的进化特征分析显示，与两个叶绿体基因(rbcL 和atpB)比较，同义替代速率约是它们的1/4，而非同义替代速率接近于自身的同义替代速率，表明matR 基因具有松弛的选择压力。线粒体matR基因相对慢速的进化使非同源相似（homoplasious）突变减少，提高了系统发育信息的质量，同时，松弛的选择压力使非同义替代数量增加，弥补了慢速进化导致的系统发育信息数量不足的缺陷，这两个方面的结合使线粒体matR基因非常适用于被子植物在科以上水平的系统发育研究。 II SET基因超家族的系统发育基因组学分析 SET基因超家族基因编码含有SET结构域的蛋白，在真核生物中，SET-domain蛋白一般是多结构域（multi-domain）的。SET-domain蛋白具有对组蛋白H3和H4的N末端尾部进行赖氨酸残基甲基化修饰的酶活性;从异染色质形成到基因转录，甲基化的组蛋白广泛影响染色质水平的基因调控。依据SET结构域一级序列的相似性和结构域组织（domain architecture）特征，目前，SET-domain基因超家族被划分为4-7个家族。由于这些划分或者使用动物或者使用植物SET基因，只有少数其它类群的物种加入分析，因此这样的划分可能是不完整的。本研究采用系统发育基 因组学方法（phylogenomic approach），在真核生物范围内广泛取样，期望获得相对完整的SET-domain基因家族的 进化分类方案，在此基础上加深理解SET-domain基因的进化机制和功能多样性。 在提取了17个物种，代表5个真核超群的SET蛋白序列基础上，系统发育分析结合“结构域组织特征”鉴别了9个SET基因家族，其中一个是新的SET基因家族。以前的SET8和Class VI家族,及SMYD和SUV4-20家族分别合并为一个家族。大部分家族在进化过程中发生了2次以上的基因重复事件，通过获得不同的结构域产生具有不同功能的新基因。一个SET基因家族在进化过程中推测发生了从脊椎动物祖先向盘基网柄菌（Dictyostelium discoideum）的水平基因转移。