复杂脑网络研究进展

复杂网络的研究方法是近年来对生物网络、社会网络及技术网络等真实网络进行研究的新兴方法.利用这一方法,可以从大脑皮层结构性网络、功能性网络以及效率性网络等不同角度着手对大脑的功能性分割和功能性整合两个主要功能进行研究,并进一步讨论其生长和发展演化,以期揭示支配大脑运作的规律.      

Reconciliation of size–density bivariate distributions over a separating node

Data reconciliation considers the restoration of mass balance among the noise prone measured data by way of component adjustments for the various particle size or particle density classes or assays over the separating node. In this paper, the method of Lagrange multipliers has been extended to balance bivariate feed and product size-density distributions of coal particles split from a settling column. The settling suspension in the column was split into two product fractions at 40% height from the bottom after a minute settling of homogenized suspension at start. Reconciliation of data assists to estimate solid flow split of particles to the settled stream as well as helps to calculate the profiles of partition curves of the marginal particle size or particle density distributions. In general, Lagrange multiplier method with uniform weighting of its components may not guarantee a smooth partition surface and thus the reconciled data needs further refinement to establish the nature of the surface. In order to overcome this difficulty, a simple alternative method of reconciling bivariate size-density data using partition surface concept is explored in this paper.     

An EEG study of brain connectivity dynamics at the resting state

We investigated the dynamical behavior of resting state functional connectivity using EEG signals. Employing a recently introduced methodology that considers the time variations of phase coupling among signals from different channels, a sequence of functional connectivity graphs (FCGs) was constructed for different frequency bands and analyzed based on graph theoretic tools. In the first stage of analysis, hubs were detected in the FCGs based on local and global efficiency. The probability of each node to be identified as a hub was estimated. This defined a topographic function that showed widespread distribution with prominence over the frontal brain regions for both local and global efficiency. Hubs consistent across time were identified via a summarization technique and found to locate over forehead. In the second stage of analysis, the modular structure of each single FCG was delineated. The derived time-dependent signatures of functional structure were compared in a systematic way revealing fluctuations modulated by frequency. Interestingly, the evolution of functional connectivity can be described via abrupt transitions between states, best described as short-lasting bimodal functional segregations. Based on a distance function that compares clusterings, we discovered that these segregations are recurrent. Entropic measures further revealed that the apparent fluctuations are subject to intrinsic constraints and that order emerges from spatially extended interactions.     

基于θ1方法的多体动力学数值算法研究

将结构动力学领域的\theta_1方法拓展到数值求解多体系统运动方程------微分--代数方 程(DAEs), 分别求解指标-3 DAEs形式的运动方程和指标-2超定DAEs (ODAEs)形式的运动方程. 通过数值算例验证了方法的有效性, 并得到\theta _1 方法中参数\theta _1的选取与数值耗散量之间的关系. 数值算例还说明对于同 一个多体系统, 采用指标-3的DAEs 描述时存在速度违约, 用指标-2的ODAEs描述时, 从计算机精度上讲, 位置和速度约束方程 同时满足, 并且\theta_1方法在求解非保守系统DAEs和ODAEs形式的运动方程时 都具有2阶精度. 最后\theta_1 方法与其他直接积分法求解DAEs和ODAEs形式运 动方程的CPU时间进行了比较.     

Transition of axial segregation patterns in a long rotating drum

Axial segreganon or a bidisperse mixture of particles in a long rotating drum is studied using the discrete element method. Simulation results show that particle interaction is responsible for axial segregation, the patterns of which are influenced by the end wall effect. Axial segregation patterns transform under competing influences of the end walls and the particle interaction forces. The two influential factors vary with various rotational speeds and end wall friction levels. The result is the transition of different axial segregation patterns： two large-particle bands at both ends, two small-particle bands at both ends, or a random segregation pattern where either a large-particle band or small-particle band may appear at either end.     

Reconciliation of size-density bivariate distributions over a separating node

Data reconciliation considers the restoration of mass balance among the noise prone measured data by way of component adjustments for the various particle size or particle density classes or assays over the separating node. In this paper, the method of Lagrange multipliers has been extended to balance bivariate feed and product size-density distributions of coal particles split from a settling column. The settling suspension in the column was split into two product fractions at 40% height from the bottom after a minute settling of homogenized suspension at start. Reconciliation of data assists to estimate solid flow split of particles to the settled stream as well as helps to calculate the profiles of partition curves of the marginal particle size or particle density distributions. In general, Lagrange multiplier method with uniform weighting of its components may not guarantee a smooth partition surface and thus the reconciled data needs further refinement to establish the nature of the surface. In order to overcome this difficulty, a simple alternative method of reconciling bivariate size-density data using partition surface concept is explored in this paper.     

神经系统疾病与认知动力学(II): 神经振荡与认知动力学

大脑神经系统具有从慢到快多种不同的振荡节律, 这些节律振荡被认为参与了大脑多种功能的实现, 其中高频的伽马同步振荡被认为与大脑的认知功能最为相关. 本文阐述了生物学实验方面关于伽马振荡及其功能的研究进展, 并针对实验中伽马振荡的频率敏感依赖于外部刺激特征的现象, 综述了基于神经网络模型进行变频伽马振荡及其认知功能的动力学建模研究工作, 解释了视觉刺激调控的变频率伽马振荡动力学产生机理, 提出了基于同步抑制增强全局放电率对比度的神经认知机制. 研究成果有助于理解神经系统同步振荡的产生机理及其认知作用, 为大脑认知原理以及类脑智能的研究奠定基础.      

神经动力学研究进展和若干思考

神经动力学是动力学与控制学科的基础性分支,属于力学与脑科学、智能科学的国际前沿交叉学科领域,主要是通过动力学与控制的基本理论和方法,建立合理的模型来探究神经系统电生理动力学行为和脑认知功能的机理.近年来,国内外学者在神经动力学的基础研究方面取得了显著成果,包括神经元和神经元网络动力学行为的深入研究、大脑不同功能结构的建模分析以及神经疾病关联脑区的网络动力学建模与控制等.本文首先对国内外神经动力学研究领域取得的进展做了较全面的概括分析,特别是给出了建模方面的发展历程.进而,基于解析生物神经网络及其动力学的研究成果,对神经动力学未来的研究方向提出了一些思考展望,期望神经动力学的研究将助力具备较强可解释性和泛化能力的类脑智能原理和方法的突破及在重大工程中的应用.     

Oscillations and global attractivity in models of hematopoiesis

LetP(t) denote the density of mature cells in blood circulation. Mackey and Glass (1977) have proposed the following equations:

神经系统信息处理和异常功能的复杂动力学

神经系统通过电活动实现信息处理及生物功能,电活动的节律和时空行为是功能的动力学表征.神经电生理实验结合理论模型,借助于分岔揭示了外界激励、参数和噪声调控下的周期、混沌和随机等多样性的节律模式及其节律的复杂转迁规律,揭示了感觉神经对信息(如血压压力信号和痛觉信息)的节律编码机制,揭示了突触噪声扩大脑神经元的信息传递能力并对能力强弱进行了分类,结果可用于提高信息检测能力和指导镇痛;借助于单神经元节律的动力学——如分岔和簇放电节律的快慢动力学——解释了网络功能异常的时空行为,如药物调控脑皮层的螺旋波/癫痫和慢抑制耦合调控的运动网络的同步转迁/运动模式异常,结果给出了调控系统功能的途径;通过大数据分析获得自闭症患者的脑功能网络的时空行为特征——症状相关脑区的同步活动降低,给出了用于诊断的潜在指标.通过新实验发现、新建理论模型、新分析方法和新观点阐释,揭示了神经系统的复杂动力学,认识和解释了神经系统的信息处理机制和异常生物功能/疾病,具有重要科学意义和潜在应用价值.     

弹性力学的复变量数值流形方法

数值流形方法通过引入数学和物理双重网格,将插值域和积分域分别定义在两个不同的覆盖上来完成系统能量泛函积分运算. 当采用高阶函数构造位移函数时,广义节点自由度将大大增加. 在求解系统的平衡方程中,运算量是与自由度的三次方成正比的,因此数值流形方法的计算量是较大的. 为此,在复变量理论的基础上,采用一维基函数建立二维问题的逼近试函数,然后将其应用于弹性力学的数值流形方法,提出了复变量数值流形方法,推导了弹性力学的复变量数值流形方法的公式. 与传统的数值流形方法相比,复变量数值流形方法具有计算量小、精度高的优点.      

Higher-order accurate implicit time integration schemes for transport problems

The present paper is concerned with the numerical solution of transient transport problems by means of spatial and temporal discretization methods. The generalized initial boundary value problem of various nonlinear transport phenomena like heat transfer or mass transport is discretized in space by p-finite elements. After finite element discretization, the resulting first-order semidiscrete balance has to be solved with respect to time. Next to the classical generalized-α integration method predicated on the Newmark approach and the evaluation at a generalized midpoint also implicit Runge–Kutta time integration schemes, are presented. Both families of finite difference-based integration schemes are derived for general first-order problems. In contrast to the above-mentioned algorithms, temporal discontinuous and continuous Galerkin methods evaluate the balance equation not at a selected time instant within the timestep, but in an integral sense over the whole time step interval. Therefore, the underlying semidiscrete balance and the continuity of the primary variables are weakly formulated within time steps and between time steps, respectively. Continuous Galerkin methods are obtained by the strong enforcement of the continuity condition as special cases. The introduction of a natural time coordinate allows for the application of standard higher-order temporal shape functions of the p-Lagrange type and the well-known Gau?–Legendre quadrature of associated time integrals. It is shown that arbitrary order accurate integration schemes can be developed within the framework of the proposed temporal p-Galerkin methods. Selected benchmark analyses of calcium diffusion demonstrate the properties of all three methods with respect to non-smooth initial or boundary conditions. Furthermore, the robustness of the present time integration schemes is also demonstrated for the highly nonlinear reaction–diffusion problem of calcium leaching, including the pronounced changes of the reaction term and non-smooth changes of Dirichlet boundary conditions of calcium dissolution.     

SYMPLECTIC ANALYSIS FOR WAVE PROPAGATION OF HIERARCHICAL HONEYCOMB STRUCTURES

Wave propagation in two-dimensional hierarchical honeycomb structures with twoorder hierarchy is investigated by using the symplectic algorithm. By applying the variational principle to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectic eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications.     

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.     

A General Solution of the Duffing Equation

In this paper, we describe the application of the elliptic balance method (EBM) to obtain a general solution of the forced, damped Duffing equation by assuming that the modulus of the Jacobian elliptic functions are slowly varying as a function of time. From this solution, the maximum transient and steady-state amplitudes will be determined for large nonlinearities and positive damping. The amplitude–time response curves obtained from our elliptic balance approximate solution are in good agreement with those obtained from the numerical integration solution over the selected time interval.     

Mechanistic Model of Steady-State Two-Phase Flow in Porous Media Based on Ganglion Dynamics

Recent experimental work has shown that the pore-scale flow mechanism during steady-state two-phase flow in porous media is ganglion dynamics (GD) over a broad and practically significant range of the system parameters. This observation suggests that our conception and theoretical treatment of fractional flow in porous media need careful reconsideration. Here is proposed a mechanistic model of steady-state two-phase flow in those cases where the dominant flow regime is ganglion dynamics. The approach is based on the ganglion population balance equations in combination with a microflow network simulator. The fundamental information on the cooperative flow behavior of the two fluids at the scale of a few hundred pores is expressed through the system factors, which are functions of the system parameters and are calculated using the simulator. These system factors are utilized by the population balance equations to predict the macroscopic behavior of the process. The dependence of the conventional relative permeability coefficients not only on the wetting fluid saturation S_wbut also on the capillary number, Ca, the viscosity ratio the wettability (⁰ a, ⁰ r), the coalescence factor, Co, as well as the porous medium geometry and topology is explained and predicted on a mechanistic basis. Sample calculations have been performed for steady-state fully developed (SSFD) and steady-state nonfully developed (SSnonFD) flow conditions. The number distributions of the moving and the stranded ganglia, the mean ganglion size, the fraction of the nonwetting fluid in the form of mobile ganglia, the ratio of the conventional relative permeability coefficients and the fractional flows are studied as functions of the system parameters and are correlated with the flow phenomena at pore level and the system factors.     

Network analysis and the connectopathies: current research and future approaches

Complex network analysis has been applied to capture the structure and functional dynamics of the brain. These studies have revealed normal and abnormal network topologies. Network differences are observed in conditions such as Alzheimer's disease, Schizophrenia, Depression and ADHD. Such findings suggest that a number of different pathologies have sufficiently similar features that the term 'connectopathies' has been introduced to describe these common topological characteristics. This paper examines the evidence for network properties and failures found in certain disorders, concluding with a brief discussion of maps and the Human Connectome Project's value to understanding brain disorders and dynamics.     

Chemically induced swelling of hydrogels

We consider a continuum model for chemically induced volume transitions in hydrogels. Consistent with experimental observations, the model allows for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the model involves a supplemental interfacial equation imposing configurational force balance. We present a hybrid eXtended-Finite-Element/Level-Set Method for obtaining approximate solutions to the governing equations of the model. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued to engineer hydrogels with optimal response times.     

Approximating equations of a plane gas flow and their integration

It is known that the nonlinear system of equations of plane steady isentropic potential gas flow can be linearized and transformed to a single equivalent linear differential equation of second order. For the case of a perfect gas this equation has the form [1]

$$\begin{gathered} \frac{{1 - \tau ^2 }}{{\tau ^2 (1 - \alpha \tau ^2 )}} \frac{{\partial ^2 \Phi }}{{\partial \theta ^2 }} + \frac{{\partial ^2 \Phi }}{{\partial \tau ^2 }} + \frac{{\tau (1 - \tau ^2 )}}{{\tau ^2 (1 - \alpha \tau ^2 )}} \frac{{\partial \Phi }}{{\partial \tau }} = 0, \hfill \\ (\tau = w/c_k , w = \sqrt {u^2 + \upsilon ^2 } , \alpha = (\gamma - 1)/(\gamma + 1); \gamma = c_p /c_\upsilon ). (0.1) \hfill \\ \end{gathered} $$