Using partial correlation to enhance structural equation modeling of functional MRI data

In functional magnetic resonance imaging (fMRI) data analysis, effective connectivity investigates the influence that brain regions exert on one another. Structural equation modeling (SEM) has been the main approach to examine effective connectivity. In this paper, we propose a method that, given a set of regions, performs partial correlation analysis. This method provides an approach to effective connectivity that is data driven, in the sense that it does not require any prior information regarding the anatomical or functional connections. To demonstrate the practical relevance of partial correlation analysis for effective connectivity investigation, we reanalyzed data previously published [Bullmore, Horwitz, Honey, Brammer, Williams, Sharma, 2000. How good is good enough in path analysis of fMRI data? NeuroImage 11, 289–301]. Specifically, we show that partial correlation analysis can serve several purposes. In a pre-processing step, it can hint at which effective connections are structuring the interactions and which have little influence on the pattern of connectivity. As a post-processing step, it can be used both as a simple and visual way to check the validity of SEM optimization algorithms and to show which assumptions made by the model are valid, and which ones should be further modified to better fit the data.     

The kinetic equation and the equation of momentum transfer for a plasma

An attempt is made to derive a simple form of the collision integral of the kinetic equation for a plasma, by using Rostoker’s equation which expresses the pair correlation function in terms of the distribution functions of the particles, and the conditional probability of one particle shielding the other. The conditional probability function is assumed to be given by its equilibrium value. By taking first order velocity-moment of the resulting kinetic equation, the equation of momentum transfer has been obtained.     

Analysis of the radiative transfer equation with highly assymetric phase function

This paper considers a scalar radiative transfer problem with high scattering anisotropy. Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal, which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2+ is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.     

Trial function method and exact solutions to the generalized nonlinear Schrodinger equation with time-dependent coefficient

In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.     

579 nm外腔式拉曼激光器传输耦合方程的数值计算

 为了提高以KGd(WO4)2晶体为拉曼介质的外腔式拉曼激光器的输出功率和转化效率,采用面积求和法编制matlab计算程序,对该激光器的传输耦合方程进行数值求解。计算得到了一至三阶斯托克斯光输出光强随时间的变化规律和受激拉曼散射的弛豫振荡过程。得出：拉曼谐振腔输出耦合镜对一阶斯托克斯光的反射率越高,拉曼谐振腔内的一阶斯托克斯光功率密度就越高,越有利于泵浦光向二阶斯托克斯光的转换。     

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.     

一层非球形粒子散射的标量辐射传输迭代解的求逆

给出了一层有下垫反射面的非球形粒子散射的标量辐射传输方程一、二阶迭代解,推导了相函数各阶Legendre展开系数与随机小椭球粒子相函数的对应关系,提出了一层随机小椭球粒子介电常数和单位面积粒子数的迭代反演方法.通过两次各方位角上双站散射测量,反演随机小椭球粒子的介电常数和单位面积粒子数.本方法比现有文献的一些反演方法易于实现,可应用于颗粒性复合材料介电与结构特性以及地表背景参数的反演研究 关键词： 辐射传输方程 迭代解 反演 相函数 介电常数     

Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 keV photon energy range. Diffuse radiation field are calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms n, n² and (∂n/∂x_k) where n is photon phase density and x_k=(hν/kT_e), in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation I^MB[1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at τ=0 and reflected radiation τ=τ_max are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.     

An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation

An efficient and robust method based on the complex-variable-differentiation method (CVDM) is proposed to reconstruct the distribution of optical parameters in two-dimensional participating media. An upwind-difference discrete-ordinate formulation of the time-domain radiative transfer equation is well established and used as forward model. The regularization term using generalized Gaussian Markov random field model is added in the objective function to overcome the ill-posed nature of the radiative inverse problem. The multi-start conjugate gradient method was utilized to accelerate the convergence speed of the inverse procedure. To obtain an accurate result and avoid the cumbersome formula of adjoint differentiation model, the CVDM was employed to calculate the gradient of objective function with respect to the optical parameters. All the simulation results show that the CVDM is efficient and robust for the reconstruction of optical parameters.     

A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging

During the last few years a quite large number of fluorescence molecular imaging applications have been reported in the literature, as one of the most challenging aspects in medical imaging is to “see” a tumor embedded into tissue, which is a turbid medium, by using fluorescent probes for tumor labeling. However, the forward solvers, required for the successful convergence of the inverse problem, are still lacking accuracy and time feasibility. Moreover, initialization of these solvers may be proven even more difficult than solving the inverse problem itself. This paper describes in depth a coupled radiative transfer equation and diffusion approximation model for solving the forward problem in fluorescence imaging. The theoretical confrontation of these solvers comprises the model deployment, its Galerkin finite elements approximation and the domain discretization scheme. Finally, a new optical properties mapping algorithm, based on super-ellipsoid models, is implemented, providing a fully automated simulation target construction within feasible time.     

Investigating the neural basis for fMRI-based functional connectivity in a blocked design: application to interregional correlations and psycho-physiological interactions

This paper investigates how well different kinds of fMRI functional connectivity analysis reflect the underlying interregional neural interactions. This is hard to evaluate using real experimental data where such relationships are unknown. Rather, we use a biologically realistic neural model to simulate both neuronal activities and multiregional fMRI data from a blocked design. Because we know how every element in the model is related to every other element, we can compare functional connectivity measurements across different spatial and temporal scales. We focus on (1) psycho-physiological interaction (PPI) analysis, which is a simple brain connectivity method that characterizes the activity in one brain region by the interaction between another region's activity and a psychological factor, and (2) interregional correlation analysis. We investigated the neurobiological underpinnings of PPI using simulated neural activities and fMRI signals generated by a large-scale neural model that performs a visual delayed match-to-sample task. Simulated fMRI data are generated by convolving integrated synaptic activities (ISAs) with a hemodynamic response function. The simulation was done under three task conditions: high-attention, low-attention and a control task ('passive viewing'). We investigated how biological and scanning parameters affect PPI and compared these with functional connectivity measures obtained using correlation analysis. We performed correlational and PPI analyses with three types of time-series data: ISA, fMRI and deconvolved fMRI (which yields estimated neural signals) obtained using a deconvolution algorithm. The simulated ISA can be considered as the 'gold standard' because it represents the underlying neural activity. Our main findings show (1) that evaluating the change in an interregional functional connection using the difference in regression coefficients (as is essentially done in the PPI method) produces results that better reflect the underlying changes in neural interrelationships than does evaluating the functional connectivity difference as a change in correlation coefficient; (2) that using fMRI and deconvolved fMRI data led to similar conclusions in the PPI-based functional connectivity results, and these generally agreed with the nature of the underlying neural interactions; and (3) the functional connectivity correlation measures often led to different conclusions regarding significance for different scanning and hemodynamic parameters, but the significances of the PPI regression parameters were relatively robust. These results highlight the way in which neural modeling can be used to help validate the inferences one can make about functional connectivity based on fMRI data.     

用变换方程测量窄带阿秒超紫外线XUV脉冲的强度时间结构

阿秒超紫外线(extreme ultra-violet, XUV)与飞秒超短激光脉冲共同激发惰性气体原子产生光电子，其终态能量与光电子产生时刻即激光相位有关. 介绍光电子的激光相位确定法，并利用光电子能谱本身(其比例谱)，计算出待测窄带XUV脉冲的强度时间结构. 研究表明，在与激光线性极化方向成0°或180°方向测量得到的光电子能谱动态范围大，容易解谱. XUV脉冲的时间宽度的测量范围为半个激光振荡周期，时间分辨率主要取决于测量系统的时间晃动和控制精度. 关键词： 光电子能谱 相位确定法 变换方程 脉冲强度时间结构     

Bayer滤波型彩色相机调制传递函数测量方法

Bayer滤波型彩色相机广泛应用于航天遥感、空间对地观测、环境监测等领域.由于Bayer滤波片造成彩色相机相比黑白相机在像质方面进一步退化,如何对Bayer滤波型彩色相机成像性能全频段综合评价是目前亟待解决的问题.调制传递函数(MTF)是相机成像性能综合评价的关键指标,传统调制传递函数测量方法无法实现对Bayer滤波型彩色相机MTF全频段高精度测量.为了解决这个问题,本文提出了一种采用旋转刀口靶测量彩色相机调制传递函数的方法.理论方面,推导了Bayer滤波型彩色相机调制传递函数测量理论模型,仿真分析了刃函数采样率和刀口刃边倾斜角度误差对调制传递函数测量精度的影响,并给出了计算算法.实验方面,对彩色相机R,G,B三基色调制传递函数权重因子进行了实验定标,并搭建了基于条纹板和旋转刀口靶的彩色相机调制传递函数测量试验装置.采用旋转刀口靶法和条纹靶板法测量彩色相机MTF结果在耐奎斯特频率f_c处极差为0.061,在空间频率f_c/2处极差为0.043,试验结果验证了所提方法的有效性.     

Optical transfer function of an optical system with a vortex phase mask in the presence of primary aberrations

The impact of primary aberrations on the optical transfer function of an optical system with a vortex phase mask has been investigated in detail. The optical transfer function of such a system becomes negative in a certain frequency range even in the absence of aberrations, a feature different from the case of an optical system in which center of the point spread function is bright.     

Computational modeling of MR flow imaging by the lattice Boltzmann method and Bloch equation

In this work, a computational model of magnetic resonance (MR) flow imaging is proposed. The first model component provides fluid dynamics maps by applying the lattice Boltzmann method. The second one uses the flow maps and couples MR imaging (MRI) modeling with a new magnetization transport algorithm based on the Eulerian coordinate approach. MRI modeling is based on the discrete time solution of the Bloch equation by analytical local magnetization transformations (exponential scaling and rotations).     

Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems.     

Green function solution of the Boltzmann transport equation for semiconducting thin film with rough boundaries

In this study the Green function solution of the Boltzmann transport equation on semiconducting thin film with irregular walls has been applied for the first time. The effects of electron scattering caused by these irregularities on the electrical conductivity have been investigated. First of all by using coordinate transformations, the irregularities on the walls have been transferred into the volume and in this way the both surfaces have been brought into flat forms. By taking two models, Gaussian and exponential, for random potential energy term contained in the transformed Hamiltonian as the perturbation, the resistivity results have been calculated and compared with the ones obtained from the methods widely known in the literature. The Boltzmann transport equation has been solved in relaxation time approximation for the irregular walled system in the case of no magnetic field.     

Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus

Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode(CCM) operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.     

Construction of a Langevin model from time series with a periodical correlation function: Application to wind speed data

A Langevin-type equation for stochastic processes with a periodical correlation function is introduced. A procedure of reconstruction of the equation from time series is proposed and verified on simulated data. The method is applied to geophysical time series–hourly time series of wind speed measured in northern Italy–constructing the macroscopic model of the phenomenon.     

广义Helmholtz方程的Green函数及旋波介质色散关系的另一求解方法

运用并矢法求解广义Helmholtz方程,结合Fourier变换、留数定理等数学处理,给出方程的并矢Green函数解析表达式;并进一步就旋波介质给出其中色散关系的另外一种求解方法．