对称非线性系统的反馈解耦

本文用微分几何方法讨论具有对称性的非线性系统的反馈解耦问题,给出了问题可解的充要条件。从条件可以看出,我们的结果较不具对称性的情况简单,从而说明,具有对称性的系统不仅具有较好的系统结构,而且还具有其它一些较好的性质。     

基于频域共轭梯度算法的盲目图像恢复

在分析了目前各种算法存在的一些基本问题的基础上，提出了盲目图像恢复的频域共轭梯度算法，算法假设退化系统的点扩散函数具有圆对称性，并考虑图像的频域具有复共轭对称性，在频域里建立了新的优化判据；采用共轭梯度算法搜索判据，从而在有实际物理意义的区域中收敛于最优解；对光学成像系统常见的离焦、衍射模糊问题进行了仿真；用该算法实现了其退化图像的恢复，给出并分析了结果。     

可解的具有广义对称性的非线性系统的同构分解与可控性 *

本文讨论了一类具有广义对称性的非线性系统的同构分解及其可控性问题。首先提出了可解的具有广义对称性的系统的概念，然后推出了此类系统的以商系统为基本构造的分解形式，最后证明了此类系统可控笥在一定条件下可由分解后的系统的可控性来确定的结论，同时得到了相应的充要条件。     

一个交互式IC版图编辑系统的设计与现实

本文描述了一个交互式集成电路版图编辑系统的设计与实现。在系统实现中我们十分注意人机接口的设计,注重系统的实用性和使用的方便性,采用了一些新的思想和方法,使得本系统具有响应速度快,版图处理效率高,使用极其方便等显著特点。     

多方法修改错乱盘符

一般来说系统中的盘符是按照顺序进行排列的,硬盘分区在前,后面紧跟着是光驱或者移动的设备。但是实际情况并不是这样的,例如我们安装了双硬盘或者用PartitionMagic调整了硬盘分区都会出现盘符错乱的情况。盘符错乱会造成系统的一些问题,这是因为错乱的盘符号改变了路径会使得一些软     

高阶非完整系统的共形不变性与Noether守恒量

研究了高阶非完整系统的共形不变性与Noether守恒量,给出了与高阶非完整系统相应的完整系统的共形不变性的定义及其确定方程,通过系统共形不变性与Lie对称性的关系,推导出了系统运动方程具有共形不变性并且是Lie对称性的共形因子,利用限制方程和附加限制方程,给出了高阶非完整系统的弱Lie对称性和强Lie对称性的共形不变性,得到了共形不变性导致的Noether守恒量,举例说明了结果的应用.     

平面带群对称性图像的动力系统构图

探讨了动力系统迭代生成具有平面带群对称性彩色图像的一种新方法。把具有带群对称性混沌函数作为迭代函数系统,构造关于平面带群的不变函数,生成具有很强艺术效果的带群对称性图像。同时给出了该生成技术的理论基础。该方法为平面设计对称图像提供了一种新方法。     

关于数字图像压缩中小波基选择问题的探讨

针对数字图像压缩编码中最优小波基的选择问题,论证了双正交样条小波基的优点,并对其进行了推导.样条小波的导数连续性保证了小波基的光滑性,双正交对偶小波的对称性使得滤波器具有线性相位,可减小失真,保证重构图像的质量.     

轮换对称分块SVM图像重建算法及硬件实现

针对ECT系统SVM图像重建算法在处理大规模样本数据集时,成像精度不高及速度慢的问题,提出轮换对称分块支持向量机 RSPSVM 算法。算法对ECT系统模型进行具有轮换对称性的等面积剖分,使得通过一个单元即可得到同层其他所有单元的敏感度值;再选择性分块,形成可分别应用SVM 算法进行训练的小样本矩阵,用得出的决策函数进行样本预测;并采用FPGA硬件实现RSPSVM算法。图像重建实验结果表明,通过硬件实现的RSPSVM算法大大减少了执行时间,并提高了成像的精度。     

动力系统生成循环群和二面体群演化对称性图像

探讨从动力系统角度生成具有循环群、二面体群演化对称性图像的不变函数方法。把具有循环群、二面体群对称性演化函数作为迭代函数系统,构造相应的不变函数,生成具有很强艺术效果的循环群、二面体群演化对称性图像。该方法为平面设计对称图像提供了一种新方法。     

Improved group-theoretical method for eigenvalue problems of special symmetric structures,using graph theory

Group-theoretical methods for decomposition of eigenvalue problems of skeletal structures with symmetry employ the symmetry group of the structures and block-diagonalize their matrices. In some special cases, such decompositions can further be continued. This particularly happens when submatrices resulted from the decomposition process, correspond to substructures with new symmetrical properties which are not among the properties of the original structure. Thus, a group-theoretical method is not able to recognize such additional symmetry from the original problem. In this paper, an algorithm is presented based upon a combination of group-theoretical ideas and graph-methods. This algorithm identifies the cases where the structure has the potential of being further decomposed, and also finds the symmetry group, and subsequently the transformation which can further decompose the system. It is also possible to find out when the block-diagonalization is complete and no further decomposition is possible. This is particularly useful for large eigenvalue problems such as calculation of the buckling load or natural frequencies of vibrating systems with special symmetries.     

Lightweight dynamic symmetry breaking

Symmetries in constraint problems present an opportunity for reducing search. This paper presents Lightweight Dynamic Symmetry Breaking, an automatic symmetry breaking method that is efficient enough to be used as a default, since it never yields a major slowdown while often giving major performance improvements. This is achieved by automatically exploiting certain kinds of symmetry that are common, can be compactly represented, easily and efficiently processed, automatically detected, and lead to large reductions in search. Moreover, the method is easy to implement and integrate in any constraint system. Experimental results show the method is competitive with the best symmetry breaking methods without risking poor performance.     

Metric-Driven RoSy Field Design and Remeshing

Designing rotational symmetry fields on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces with user-defined field topologies. The user has full control of the number, positions, and indexes of the singularities (as long as they are compatible with necessary global constraints), the turning numbers of the loops, and is able to edit the field interactively. We formulate N-RoSy field construction as designing a Riemannian metric such that the holonomy along any loop is compatible with the local symmetry of N-RoSy fields. We prove the compatibility condition using discrete parallel transport. The complexity of N-RoSy field design is caused by curvatures. In our work, we propose to simplify the Riemannian metric to make it flat almost everywhere. This approach greatly simplifies the process and improves the flexibility such that it can design N-RoSy fields with single singularity and mixed-RoSy fields. This approach can also be generalized to construct regular remeshing on surfaces. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing. Furthermore, based on our remeshing results with high global symmetry, we generate Celtic knots on surfaces directly.     

A template-based approach for the generation of abstractable and reducible models of featured networks

We investigate the relationship between symmetry reduction and inductive reasoning when applied to model checking networks of featured components. Popular reduction techniques for combatting state space explosion in model checking, like abstraction and symmetry reduction, can only be applied effectively when the natural symmetry of a system is not destroyed during specification. We introduce a property which ensures this is preserved, open symmetry. We describe a template-based approach for the construction of open symmetric Promela specifications of featured systems. For certain systems (safely featured parameterised systems) our generated specifications are suitable for conversion to abstract specifications representing any size of network. This enables feature interaction analysis to be carried out, via model checking and induction, for systems of any number of featured components. In addition, we show how, for any balanced network of components, by using a graphical representation of the features and the process communication structure, a group of permutations of the underlying state space of the generated specification can be determined easily. Due to the open symmetry of our Promela specifications, this group of permutations can be used directly for symmetry reduced model checking.The main contributions of this paper are an automatic method for developing open symmetric specifications which can be used for generic feature interaction analysis, and the novel application of symmetry detection and reduction in the context of model checking featured networks.We apply our techniques to a well known example of a featured network – an email system.     

Identification in the presence of symmetry: oscillator networks

It is well known that the presence of symmetry in the equations of a dynamical system has a profound effect on the resulting behavior. This note examines how this effect is manifested in the corresponding parameter identification problem. Our work shows that standard ideas such as persistent excitation in a trajectory can be explained by symmetry. Moreover, by understanding how symmetry affects the dynamics, it may be possible to obtain sufficient information to achieve full identification even when typical trajectories are not persistently exciting. Alternately, our analysis shows how properly interpreting the output of the identification process can give useful information even if full identification is not possible     

Breaking symmetries in graph search with canonizing sets

There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration. We also demonstrate the application of a generalization of our approach to fully-interchangeable matrix search problems.     

A new method for solving boundary value problems for partial differential equations

This paper proposes a symmetry–iteration hybrid algorithm for solving boundary value problems for partial differential equations. First, the multi-parameter symmetry is used to reduce the problem studied to a simpler initial value problem for ordinary differential equations. Then the variational iteration method is employed to obtain its solution. The results reveal that the proposed method is very effective and can be applied for other nonlinear problems.     

Harmonic Functions for Rotational Symmetry Vector Fields

Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D vector fields, but it is applicable in 2D. Given the finite symmetry group G of a symmetry vector field v (x) on a 3D domain Ω, we formulate the harmonic function h(s) as a stationary point of group G. Using the real spherical harmonic (SH) bases, we showed the coefficients of the harmonic functions are an eigenvector of the SH rotation matrices corresponding to group G. Instead of solving eigen problems to obtain the eigenvector, we developed a forward constructive method based on orthogonal group theory. The harmonic function found by our method is not only invariant under G, but also expressive and can distinguish different rotations with respect to G. At last, we demonstrate some vector field design results with tetrahedron‐symmetry, cube‐symmetry and dodecahedron‐symmetry groups.     

Controlled Lagrangians and the stabilization of mechanical systems.I. The first matching theorem

We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane     

Analysis of emergent symmetry breaking in collective decision making

We investigate a simulated multi-agent system (MAS) that collectively decides to aggregate at an area of high utility. The agents’ control algorithm is based on random agent–agent encounters and is inspired by the aggregation behavior of honeybees. In this article, we define symmetry breaking, several symmetry breaking measures, and report the phenomenon of emergent symmetry breaking within our observed system. The ability of the MAS to successfully break the symmetry depends significantly on a local-neighborhood-based threshold of the agents’ control algorithm that determines at which number of neighbors the agents stop. This dependency is analyzed and two macroscopic features are determined that significantly influence the symmetry breaking behavior. In addition, we investigate the connection between the ability of the MAS to break symmetries and the ability to stay flexible in a dynamic environment.