Symbolic Dynamic Patterns of Written Exchanges: Hierarchical Structures in an Electronic Problem Solving Group

A spontaneous scientific creative problem solving discussion, which had transpired across a listserver, was captured and content-analyzed according to two protocols. One protocol centered on social interaction and the second pertained to problem completion behavior. Data were analyzed for topological entropy and dimensional complexity with a hierarchical variation of the symbolic dynamics procedure that was first introduced by Guastello, Hyde, and Odak (1998). The principal findings were that (1) There was a greater prevalence of clarification and initiating (particularly creative) behaviors compared to a real-time creative problem solving episode; they were presumably liberated by the unblocking effect that tends to characterize computer-assisted group discussions. (2) There were complex responses containing up to five conversational elements as identified by a Social Interaction scoring system. (3) The two different scoring protocols produced different indicators of string length and entropy. The content of those patterns, which are, in principle, decomposed orbits, is discussed.     

Multistable switching series in chaotic nets

Examples of conscious and interpretable responses that have two or more forms alternating to the same stimuli have been known for centuries, and methods of describing how such situations arise have evolved in biological science. When switches between transient, perceptual or cognitive responses can occur and are mixed serially within time series exhibiting local terminal stability, then patterns arise where psychological data series are too brief to analyse empirically, and neurophysiological data and mathematical simulation are necessary. Modelling such conditions can be approached by using one modified Markov matrix, which we illustrate if we allow some singularities to exist in the dynamics. As soon as networks cease to be homogeneous and have a number of attractors present and operate with different local structures, then one or more response patterns may potentially exist at the same time. The patterns may be addressed within the behavioural dynamics by incorporating in turn very short transients that can be voluntary or involuntary, in sensory and cognitive data. Related software work for modelling, employing hierarchical Dirichlet structures projected into hidden Markov matrices is noted.     

The game of futsal as an adaptive process

Some researchers have described team sports as complex, open, and hierarchical systems. This study aimed to investigate and describe how the game of futsal could be characterized as a dynamic adaptive process. One game, which included participation by two amateur teams, was analyzed by examining players' individual (space occupied, skills with and without ball) and collective actions (attacks and defenses). Data were collected through time-continuum notation, and were analyzed through frequencies and clustering, using trend analysis and multiple comparisons, and Ward's minimum variance method with Euclidean distance, respectively. Results revealed four attack patterns for each team, with four defense patterns for one (Blue), and seven for the other (Red), and they showed within-pattern variability. All were performed in an unpredictable manner, with no absolute correspondence between attacks and defenses. The futsal game as an adaptive process was characterized by changing intra- and inter-patterns.     

A fast 3D dual boundary element method based on hierarchical matrices

In this paper a fast solver for three-dimensional BEM and DBEM is developed. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. Special algorithms are developed to deal with crack problems within the context of DBEM. The structure of DBEM matrices has been efficiently exploited and it has been demonstrated that, since the cracks form only small parts of the whole structure, the use of hierarchical matrices can be particularly advantageous. Test examples presented show that, with the proposed technique, substantial increase in number of elements over the crack surfaces leads only to moderate increases in memory storage and solution time.     

Operant behavior of rats under fixed-interval reinforcement schedules: a dynamical analysis via the extended return map

The extended-return-map was employed to analyze the inter-response time data of operant experiments using fixed-interval schedules and food reinforcement. After intensive training over numerous sessions, rats gradually developed several types of temporal patterns of lever pressing behaviors, which were visualized through different patterns of data point distributions in the extended-return-map. Analyses with randomly shuffled data sets confirmed that these patterns depended on the sequential order of the inter-response time data, indicating that they reflected dynamics of the behavior. A procedure was developed to quantify the difference between patterns in the extended-return-maps, thus, enabling the comparison between sessions, and between animals. Simulations suggested that, in addition to the two-state break-and-burst responding, both multiple switches of behavioral states during the inter-reinforcement periods and the acceleration of lever pressing rate should be taken into consideration for the dynamics found in the data.     

Mechanosensing of substrate stiffness regulates focal adhesions dynamics in cell

Cell mechanical recognition of extracellular matrix determines the cell activities and functions. Focal adhesions are part of the cell mechanosensing machinery and, operating at the very dynamic interface between cell and extracellular matrix, can operate this recognition and trigger conformational, functional and behavioral modification of the cell. To investigate how the dynamic of assembly and disassembly of focal adhesion are influenced by the substrate mechanics we developed a novel procedure. The analysis consists of the over time tracking of focal adhesion structures in a stable cell line of NIH/3T3 expressing fluorescent pmKate2-paxillin. From collected signals and by their autocorrelation we evaluated the average lifetime and assembly rate of focal adhesion as function of substrate stiffness. Further, by signals cross-correlation we obtained information about the mechanical nature of cytoskeleton and its network. This quantitative approach to focal adhesion dynamics characterization was presented in this study as an investigation tool for cell mechanobiology.     

一种结构动力时程分析的积分求微方法

传统采用微分求积(differential quadrature,DQ)法求解动力问题时都是以位移响应作为基本未知量,而将速度响应和加速度响应表示为位移响应的加权和的形式.如此做法需要处理线性方程组或者矩阵方程(Sylvester方程)才能求得动力响应,导出的算法一般为有条件稳定算法.本文利用动力响应的Duhamel积分解,逆用DQ原理,提出了一种计算卷积的高精度显式算法.该算法可以逐时段地求解出动力时程响应,当各时段内DQ节点分布完全一致时,仅须进行一次Vandermonde矩阵求逆计算即可应用于各个时段,一次性获得时段内多个时刻的位移响应值,因而具有计算效率高的优点.通过分析动力方程积分格式,证明本文动力算法传递矩阵的谱半径恒等于1,因而该算法具有无条件稳定特性,且计算过程中不会产生数值耗散. 本文算法的数值精度取决于分析时段内布置的DQ节点数量$N$,具有$N-1$阶代数精度.实际操作时可以取10个甚至更多的DQ节点数,从而获得比较高的数值精度.      

Approximate yield criteria for anisotropic metals with prolate or oblate voidsCritères macroscopiques pour des métaux plastiques anisotropes contenant des cavités non sphériques

Following the study of Gologanu et al. (1997) which has extended the well-known approach of Gurson (1975), we propose approximate yield criteria for anisotropic plastic voided metals containing non spherical cavities. The plastic anisotropy of the matrix is described by means of Hill's quadratic criterion. The procedure to establish the closed form expression of approximate macroscopic criteria, in which void shape and plastic anisotropic effects are included, is detailed. The new criteria allow us to recover existing results in the cases of spherical and cylindrical voids in an Hill type plastic matrix. Moreover, they agree with previous criteria for non spherical voids in an isotropic plastic matrix. Finally, for validation purposes, we provide, in the general case of non spherical cavities in the anisotropic matrix, a comparison with the numerical exact two field criteria. To cite this article: V. Monchiet et al., C. R. Mecanique 334 (2006).     

Understanding neuromotor strategy during functional upper extremity tasks using symbolic dynamics

The ability to model and quantify brain activation patterns that pertain to natural neuromotor strategy of the upper extremities during functional task performance is critical to the development of therapeutic interventions such as neuroprosthetic devices. The mechanisms of information flow, activation sequence and patterns, and the interaction between anatomical regions of the brain that are specific to movement planning, intention and execution of voluntary upper extremity motor tasks were investigated here. This paper presents a novel method using symbolic dynamics (orbital decomposition) and nonlinear dynamic tools of entropy, self-organization and chaos to describe the underlying structure of activation shifts in regions of the brain that are involved with the cognitive aspects of functional upper extremity task performance. Several questions were addressed: (a) How is it possible to distinguish deterministic or causal patterns of activity in brain fMRI from those that are really random or non-contributory to the neuromotor control process? (b) Can the complexity of activation patterns over time be quantified? (c) What are the optimal ways of organizing fMRI data to preserve patterns of activation, activation levels, and extract meaningful temporal patterns as they evolve over time? Analysis was performed using data from a custom developed time resolved fMRI paradigm involving human subjects (N=18) who performed functional upper extremity motor tasks with varying time delays between the onset of intention and onset of actual movements. The results indicate that there is structure in the data that can be quantified through entropy and dimensional complexity metrics and statistical inference, and furthermore, orbital decomposition is sensitive in capturing the transition of states that correlate with the cognitive aspects of functional task performance.     

Analysis of linear elastic wave propagation in piping systems by a combination of the boundary integral equations method and the finite element method

The combined methodology of boundary integral equations and finite elements is formulated and applied to study the wave propagation phenomena in compound piping systems consisting of straight and curved pipe segments with compact elastic supports. This methodology replicates the concept of hierarchical boundary integral equations method proposed by L. I. Slepyan to model the time-harmonic wave propagation in wave guides, which have components of different dimensions. However, the formulation presented in this article is tuned to match the finite element format, and therefore, it employs the dynamical stiffness matrix to describe wave guide properties of all components of the assembled structure. This matrix may readily be derived from the boundary integral equations, and such a derivation is superior over the conventional derivation from the transfer matrix. The proposed methodology is verified in several examples and applied for analysis of periodicity effects in compound piping systems of several alternative layouts.     

气体动理学统一算法的隐式方法研究

目前的气体动理学统一算法(unified gas kinetic scheme, 简称UGKS) 在求解高速流动问题时的计算效率,难以满足求解复杂工程问题的需求. 为了提高该算法的计算效率, 本文对模型方程的对流项和碰撞项进行了隐式处理, 并针对UGKS 界面通量与演化时间相关的特点, 引入了演化时间平均界面通量, 通过对控制方程矩阵进行近似LU 分解(lower-upper decomposition), 实现了隐式UGKS. 不同来流马赫数的圆柱绕流算例测试表明, 只要演化时间选取得当, 隐式方法可以得到与显式方法完全相同的结果, 且计算效率可以提高1~2 个量级.      

Experimental and computational models for three-dimensional crack-fiber interactions

This study sheds light on the small-scale interaction of a three-dimensional matrix crack with a fiber. The experiments with a model brittle-matrix/brittle-fiber system record the three-dimensional growth history of an initially penny-shaped fracture which quasi-statically propagates toward and around a cylindrical inclusion. Crack growth histories are obtained by hydraulically fracturing a cement matrix with embedded glass rods. These experimentally determined crack patterns support micromechanical computational simulations which were conducted using a three-dimensional surface integral method. The implications for tailoring interfacial friction to increase the crack resistance of brittle materials (e.g., ceramic matrix/ceramic fiber composites) are discussed.     

Monte Carlo Simulation of Contaminant Transport: I. Long-range Correlations in Fracture Conductivity

We develop a network model of fractures, and use the model to study transport of contaminants by groundwater through natural geological media. The fractures are narrow rectangular channels between large flat parallel plates, which are embedded in the surrounding rock matrix. The fracture-permeabilities and the fracture-widths are obtained from both uniform and fBm distributions. The pressure distribution in the network, and subsequently the velocity of groundwater in each channel, is obtained. The transport problem in an individual fracture is solved in Laplace space using the realized groundwater velocities and network mass conservation. The transform space solutions are then inverted to real time using a fast and efficient inversion algorithm. Monte Carlo simulations are then carried out by repeating the above procedure for a large number of realizations. The main focus of this study is to explore the effects correlated fracture-permeabilities and fracture-widths have on the transport of contaminants. While the primary transport mechanism is convection, we also study such processes as adsorption onto the fracture surface, and radioactive decay. We show how these phenomena, individually and in combination with one another, affect the overall transport process. In addition, we investigate the nature of the mixing zone, and discuss how these results can be helpful in developing remediation techniques for a contaminated site.     

Special Cases in Optimization Problems for Stationary Linear Closed-Loop Systems

Consideration is given to problems of solving the algebraic Riccati equation (ARE)—J-factorization of matrix polynomials and J-factorization of rational matrices—to which traditional solution algorithms are not applicable. In this connection, solution algorithms for these problems are discussed where the eigenvalues of the Hamiltonian matrix corresponding to the ARE and the zeros of matrix polynomials are located on the imaginary axis. Moreover, a procedure is set forth for asymptotic expansion of a stabilizing solution of the ARE in the neighborhood of a point at which the ARE has no stabilizing solution. It is shown how this expansion can be used for constructing canonical J-factorization of matrix polynomials that is nearly a noncanonical J-factorization. It is pointed out that the algorithms described can be implemented with the help of MATLAB routines     

A geometry-based framework for modeling the complexity of origami folding

This paper presents a quantitative framework to analyze the complexity of folding origami structures from flat membranes. Extensive efforts have realized intricate origami patterns with desired functions such as mechanical properties, packaging efficiency, and deployment behavior. However, the complexity associated with the manufacturing or folding of origami patterns has not been explored. Understanding how difficult origami structures are to make, and how much time they require to form is crucial information to determining the practical feasibility of origami designs and future applications such as robotic origami assembly in space. In this work, we develop this origami complexity metric by modeling the geometric properties and crease formation of the origami structure, from which it outputs crease and pattern complexity values and a prediction of the time to complete the pattern assembly, based on the characteristics of the operator. The framework is experimentally validated by fabricating various Miura-ori origami paper models.     

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque （SL） hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.     

An approach to the study of dynamics of work motivation using the diary method

This study is concerned with work motivation as a dynamic process. Twenty workers kept a motivation diary over a period of several weeks. Using a PDA they recorded their level of motivation, self-efficacy beliefs and perceived instrumentality with respect to the task being carried out. The time series obtained were analyzed using common procedures in the study of dynamic systems in order to determine whether motivation followed linear or nonlinear patterns. The results revealed highly nonlinear dynamics for the different variables studied. The implications of these findings are discussed and questions are raised regarding the basic assumptions underlying current theories and models of motivation, for example, the assumptions of linearity and stability.     

基于H - Matrices的结构特征值问题加速研究

提出遗传双重互易法,利用遗传矩阵结构（Hierarchical Matrices , H - Matrices）加速双重互易边界元法（DRBEM）结构特征值问题分析过程并压缩数据存储。通过自适应交叉拟合算法对遗传矩阵中的相容子块使用低阶秩块拟合,减少参与矩阵运算数据规模,降低计算消耗的内存空间。针对规模和效率的不同计算环境要求提出两种求解优化策略,即完全遗传双重互易法(PHDM)和混合遗传双重互易法(MHDM),以求针对性提高数值计算效果。数值算例验证了所提方法的效率以及数据压缩效果。     

A Statistical Representation of the Matrix�CFracture Transfer Function for Porous Media

In this article, the authors present a matrix?Cfracture transfer function where the statistical variation in geometric properties of the matrix blocks is considered. Several particular representations with hypothetical probability density functions (PDFs) for matrix block size distributions are presented, including: (a) the single-value distribution (the limiting case); (b) the uniform distribution; (c) the Gamma distribution; and (d) an approximate representation for arbitrary PDFs. An example using experimental data from the literature, along with the single-block based transfer function developed in this study, is presented demonstrating how the statistical procedure proposed in this text can be applied in practice. It is shown with this example that significant relative errors can be introduced when the statistical variance is ignored. Furthermore, two existing dual-porosity models, the Lim and Aziz model and the Zimmerman et al. model, are also considered using the experimental data. It is shown that considerable relative errors can be introduced with these two models when the effect of statistical variance is not taken into account.