Sub-additive topological pressure of proper maps

We introduce a natural extension of sub-additive topological pressure for a proper map of locally compact metric spaces and present a corresponding variational principle. As an application, for a class of sub-additive sequence, we describe a multi-fractal analysis of the entropy spectra of their generalized Birkhorff averages.     

Some properties of topological pressure of a semigroup of continuous maps

Based on the work of Ma and Wu,[9 Ma D, Wu M. Topological pressure and topological entropy of a semigroup of maps. Discrete Contin Dyn Syst. 2011;31:545–557.[Crossref], [Web of Science ®] , [Google Scholar]] some equivalent definitions of topological pressure of a semigroup of continuous maps are given and several of their basic properties are provided by using separated sets and spanning sets. We also answer an open problem of Bi? and Urbański.[19 Bi? A, Urbański M. Some remarks on topological entropy of a semigroup of continuous maps. Cubo. 2006;8:63–71. [Google Scholar]] That is, letting f_i, i = 2, … , k, be homeomorphisms acting on a compact metric space, G₁ = {id_X, f₂, … , f_k}, G^{? 1}₁ = {id_X, f^{? 1}₂, …, f_k^{? 1}} and letting G and G^?1 denote the semigroups generated by G₁ and G^{? 1}₁, respectively, we give an example showing that the topological entropy of G does not equal the topological entropy of G^?1.     

Variational principle for topological tail pressures with sub-additive upper semi-continuous potentials

The topological tail pressure and the conditional pressure are defined for sub-additive upper semi-continuous potentials via separated subsets and refining sequences of partitions in topological dynamical systems with finite topological entropy respectively. By proving the equivalence of the topological tail pressure and the conditional pressure with respect to the refining sequence of essential partitions, we present a variational principle for the topological tail pressure without any additional assumptions. The properties of the topological tail pressure including the power rule, the product rule and the natural extension are also discussed.     

The irregular set for maps with the specification property has full topological pressure

Let (X, d) be a compact metric space, f : X ? X be a continuous map with the specification property and ? : X ? ? a continuous function. We consider the set of points for which the Birkhoff average of ? does not exist (which we call the irregular set for ?) and show that this set is either empty or carries full topological pressure (in the sense of Pesin and Pitskel see, for example [Y.B. Pesin, Dimension Theory in Dimensional Systems: Contemporary Views and Applications, University of Chicago Press, Chicago, 1997]). We formulate various equivalent natural conditions on ? that completely describe when the latter situation holds and give examples of interesting systems to which our results apply but were not previously known. As an application, we show that for a suspension flow over a continuous map with specification, the irregular set carries full topological entropy.     

Topological pressure dimension for almost additive potentials

This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate fundamental properties of the topological pressure dimension for almost additive sequences. In particular, we study the relationships among different types of topological pressure dimension and identify an inequality relating them. Also, we show that the topological pressure dimension is always equal to or greater than 1 for certain special almost additive sequence.     

Variational principles for BS dimension of subsets

Using the Carathéodory structure, we redefine a new BS-dimension with packing method and prove some properties of this dimension, especially Bowen's equation. We also consider the relation between the new BS-dimension and BS-density which extend the variational principle to the new BS-dimension.     

拓扑关系与性质及其在空间推理中的应用

首先根据笔者以前的研究成果,给出了两个空间实体之间完备、唯一的拓扑关系形式化表达,进而论述了它们之间存在的性质。从这些性质出发,得出了相互间空间关系复合的结果。空间推理从广义上而言,是指从已知信息推导未知信息的理论和方法,据其使用的理论基础,可以分为代数推理和逻辑推理,空间复合的结果可以直接用于代数推理,又可以作为前提条件用于逻辑推理。     

层次离散熵及其在高压共轨喷油器故障诊断中的应用

随着非线性科学理论的飞速发展,信息熵方法已广泛应用于工程机械的故障诊断中.提出了层次分析和离散熵结合的层次离散熵(HDE),研究其参数变化对熵值计算精度和计算效率的影响,并与多尺度熵(MSE)、多尺度模糊熵(MFE)、多尺度离散熵(MDE)、层次样本熵(HSE)和层次模糊熵(HFE)进行对比研究,研究结果表明,HDE在...     

未知环境中基于视觉的增量式拓扑建模及导航

针对未知环境提出并实现了一个新的基于摄像机视觉的增量式拓扑建模及导航系统.该系统包括自然路标提取、建模与定位、地图及路标库管理、规划4个主要部分.采用局部显著图像区域构造自然路标,并利用隐马尔科夫模型(HMM)建模当前场景中所获得路标间的关系,构造拓扑顶点.为提高定位精度,设计了最大后验概率(MAP)的学习策略.设计了基于竞争学习的路标管理机制,采用简单的最短路径算法在拓扑图上进行路径规划.该系统支持在线增量式建模,利用局部图像特征及其关系表示环境,定位算法简洁有效,辅以路标管理使之能够适应大规模环境导航任务.实验结果表明该系统路标提取稳定、位置识别率高、定位精确,能够保证机器人在未知环境中的安全导航.     

Product platform design through clustering analysis and information theoretical approach

An effectively designed product platform is vital to the final product family derived from it. A product platform design consists of platform configuration to decide which variables to make common across the product family and to determining the optimal values for platform and scaling variables for all product variants. Many existing product family design methods assume a given platform configuration, i.e. the platform variables are specified a priori by designers. However, selecting the right combination of common and scaling variables is not trivial. Most approaches are single-platform methods, in which design variables are either shared across all product variants or not at all. While in multiple-platform design, platform variables can have special value with regard to a subset of product variants within the product family, offering opportunities for superior overall design. This paper proposes a quantitative method for scale-based multiple-platform design using clustering analysis and Shannon's Entropy theory. Optimization methods are used to design the product family by holding the values of platform variables constant and to find the best values of the scaling variables. An information theoretical approach is used to help select platform variables based on the clustering analysis of individually designed products. Validity analysis is performed to determine the optimal settings for platform variables. Local clustering is further performed on each platform variable, to establish subsets of variants such that variants within a subset are more similar to each other than they are to variants in other subsets and a common value is used to represent the various values of variants in each subset. A case study is used to illustrate the process of the proposed method, and the design solutions are compared with that found by other methods given in previous literature. The comparison results verified that the multiple-platform design can lead to superior solutions of product family.     

The entropic basis of collective behaviour

We identify a unique viewpoint on the collective behaviour of intelligent agents. We first develop a highly general abstract model for the possible future lives these agents may encounter as a result of their decisions. In the context of these possibilities, we show that the causal entropic principle, whereby agents follow behavioural rules that maximize their entropy over all paths through the future, predicts many of the observed features of social interactions among both human and animal groups. Our results indicate that agents are often able to maximize their future path entropy by remaining cohesive as a group and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of possible future paths. We derive social interaction rules that are consistent with maximum entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber''s law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus–response mechanism and providing a novel basis for the common assumption of linearly additive ‘social forces’ in simulation studies of collective behaviour.     

Flammability limits of isobutane and its mixtures with various gases

Flammability limits of isobutane and five kinds of binary mixtures of isobutane were measured by the ASHRAE method. Propane, nitrogen, carbon dioxide, chloroform, and HFC-125 (1,1,1,2,2-pentafluoroethane) were used as the counter part gases in the mixtures. The observed data were analyzed using the equations based on Le Chatelier's formula. The flammability limits of mixtures with propane were well explained by the original Le Chatelier's formula. The flammability limits of mixtures with nitrogen and the ones with carbon dioxide were adequately analyzed by the extended Le Chatelier's formula. It was found that the extended Le Chatelier's formula is also applicable to the flammability limits of mixtures with chloroform and HFC-125.     

A superconvergent point interpolation method (SC‐PIM) with piecewise linear strain field using triangular mesh

A superconvergent point interpolation method (SC‐PIM) is developed for mechanics problems by combining techniques of finite element method (FEM) and linearly conforming point interpolation method (LC‐PIM) using triangular mesh. In the SC‐PIM, point interpolation methods (PIM) are used for shape functions construction; and a strain field with a parameter α is assumed to be a linear combination of compatible stains and smoothed strains from LC‐PIM. We prove theoretically that SC‐PIM has a very nice bound property: the strain energy obtained from the SC‐PIM solution lies in between those from the compatible FEM solution and the LC‐PIM solution when the same mesh is used. We further provide a criterion for SC‐PIM to obtain upper and lower bound solutions. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained using the present SC‐PIM; (2) there exists an α_exact∈(0, 1) at which the SC‐PIM can produce the exact solution in the energy norm; (3) for any α∈(0, 1) the SC‐PIM solution is of superconvergence, and α=0 is an easy way to obtain a very accurate and superconvergent solution in both energy and displacement norms; (4) a procedure is devised to find a α_prefer∈(0, 1) that produces a solution very close to the exact solution. Copyright © 2008 John Wiley & Sons, Ltd.     

A self-adaptive edge matching method based on mean shift and its application in video tracking

A self-adaptive edge matching method based on mean shift adjustment is proposed in this paper. Such method uses the local mode seeking character of mean shift to adjust the edge information of each model to a stable state before matching, which can effectively avoid the deviation problem of traditional method and raise the successful matching rate. Furthermore, the interfering vector with a self-adaptive coefficient is proposed to optimise the matching performance in complex background. Compared with a pre-set constant coefficient, the self-adapted coefficient has a better perception of background edge complexity so as to control the initial adjusting position more rationally, and thus increases the robustness and accuracy of matching. This matching method is applied in an improved particle filtering tracking framework, and experimental results prove the validity and rationality of the theoretical analysis, and show that the proposed matching method performs a robust and efficient tracking.     

Derivatives of maximum‐entropy basis functions on the boundary: Theory and computations

In this paper, we obtain explicit expressions to evaluate the derivatives of maximum‐entropy (max‐ent) basis function on the boundary of a convex domain. In the max‐ent formulation, the basis functions are obtained by maximizing a concave functional subjected to linear constraints (reproducing conditions). In doing so, it is found that the Lagrange multipliers blow up when x ∈ ?Ω, and the expressions for the derivatives of the max‐ent basis functions in Ω are of an indeterminate form for points on ?Ω. We appeal to l'Hôpital's rule to derive expressions to determine the derivatives of the basis functions. We consider the Shannon entropy functional and the relative entropy functional with different choices of the prior weight function. The first‐order derivatives of all basis functions are bounded. In contrast, on an irregular grid with a certain nodal spacing, some of the second derivatives of the basis functions are unbounded on the boundary. Necessary and sufficient conditions on the priors to obtain bounded Lagrange multipliers are established. Optimal convergence rates for fourth‐order problems are demonstrated for a Galerkin approach with a quadratically complete partition‐of‐unity enriched max‐ent approximation.Copyright © 2013 John Wiley & Sons, Ltd.     

The d'Alembert–Lagrange principal equations and applications to floating flexible systems

This paper addresses the dynamics and quasi‐statics of floating flexible structures as well as extensions to unconstrained substructures and partitions of coupled mechanical systems. The principal solution is defined as the state of self‐equilibrated forces obtained as the particular solution of the rigid motion and interface equilibrium equations. This solution is independent of the stress–strain constitutive properties as well as of the compatibility equations. For statically determinate systems, the principal solution is the final force solution. For statically indeterminate systems, the correction due to flexibility and compatibility is orthogonal to the principal solution. The formulation is done in the context of d'Alembert's principle, which supplies the d'Alembert–Lagrange principal equations for floating bodies. These are obtained by summation of virtually working forces and moments acting on the floating systems. Applications of this approach are demonstrated on a set of dynamic and quasi‐static example problems of increasing generality. Linkage to variational principles with an interface potential is eventually discussed as providing the theoretical foundation for handling interacting semi‐discrete subsystems linked by node‐collocated Lagrange multipliers. Copyright © 2008 John Wiley & Sons, Ltd.     

神经美学在用户研究领域的研究现状及展望

目的 探索神经美学研究中用户的情感认知与脑活动规律、脑电成分间的关联,对非侵入性测量方法的3个主要研究方向进行分类梳理及总结,提出神经美学在用户研究领域发展的3个方向。方法 从当下量化美学的需求出发,阐述神经美学的产生发展、相关概念、研究方法;从审美偏好、意象认知、用户体验3个方向,交叉对比现有国内外学者的研究,对神经美学在用户研究领域的应用进行分类讨论;对神经美学的理论研究和应用实例文献进行讨论,提出了实验设计可行性、数据采集精准度、研究方法普适性3个维度中可能存在的问题。结论 神经美学的产生发展是美学与实证科学并行、融合的结果,在用户情感需求的驱动下,促进效能提升、优化美学计算、扩展应用范围将成为神经美学在用户研究领域的重要研究方向。     

高压水射流破碎胎面胶的脆化效应与胶粉形成

采用霍布金森压杆试验模拟子午线轮胎胎面胶的破碎回收过程,分析高压水射流冲击下胎面胶材料受力及响应状态,试验表明材料存在韧脆转变现象,进而发生脆性断裂。橡胶断口与胶粉微观形貌表明,裂纹扩展区呈现典型的放射状脆性断面形貌,并形成大量与胶粉尺寸匹配的平整光滑区域,直接验证了脆性断裂的存在并阐述其发生过程。然后利用应力波传播判据和脆断力学分析解释了胎面胶材料出现脆化效应的原因。对材料韧脆转变的影响因素进行分析后可知,高压水射流冲击过程中,材料质点变形速度远大于韧脆转变临界速度,在力学性能上表现为断裂应力小于屈服应力,致使材料发生脆性断裂并形成精细胶粉。