A coherency function model of ground motion at base rock corresponding to strike-slip fault

At present, the method to study spatial variation of ground motions is statistic analysis based on dense array re-cords such as SMART-1 array, etc. For lacking of information of ground motions, there is no coherency function model of base rock and different style site. Spatial variation of ground motions in elastic media is analyzed by deterministic method in this paper. Taking elastic half-space model with dislocation source of fault, near-field ground motions are simulated. This model takes strike-slip fault and earth media into account. A coherency func-tion is proposed for base rock site.

Bessel Function and Damped Simple Harmonic Motion

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

MULTI-DIMENSIONAL GEOMETRIC BROWNIANMOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.

Numerical Green’s function method:Application to quantifying ground motion variations of M7 earthquakes

The concept of ＂numerical Green’s functions＂ （NGF or Green’s function database） is developed. The basic idea is： a large seismic fault is divided into subfaults of appropriate size, for which synthetic Green’s functions at the surface （NGF） are calculated and stored. Consequently, ground motions from arbitrary kinematic sources can be simulated, rapidly, for the whole fault or parts of it by superposition. The target fault is a simplified, vertical model of the Newport-Inglewood fault in the Los Angeles basin. This approach and its functionality are illustrated by investigating the variations of ground motions （e.g. peak ground velocity and synthetic seismograms） due to the source complexity. The source complexities are considered with two respects： hypocenter location and slip history. The results show a complex behavior, with dependence of absolute peak ground velocity and their variation on source process directionality, hypocenter location, local structure, and static slip asperity location. We concluded that combining effect due to 3-D structure and finite-source is necessary to quan- tify ground motion characteristics and their variations. Our results will facilitate the earthquake hazard assessment projects.

Research on motion compensation method based on neural network of radial basis function

The machining precision not only depends on accurate mechanical structure but also depends on motion compensation method. If manufacturing precision of mechanical structure cannot be improved, the motion compensation is a reasonable way to improve motion precision. A motion compensation method based on neural network of radial basis function(RBF) was presented in this paper. It utilized the infinite approximation advantage of RBF neural network to fit the motion error curve. The best hidden neural quantity was optimized by training the motion error data and calculating the total sum of squares. The best curve coefficient matrix was got and used to calculate motion compensation values. The experiments showed that the motion errors could be reduced obviously by utilizing the method in this paper.

Research on Key Technologies of Hand Function Rehabilitation Training Evaluation System Based on Leap Motion

This paper proposes an immersive training system for patients with hand dysfunction who can perform rehabilitation training independently. The system uses Leap Motion binocular vision sensors to collect human hand information, and uses the improved PCA (Principal Component Analysis) to perform data fusion on the real-time data collected by the sensor to obtain more hands with fewer principal components, and improve the stability and accuracy of the data. Immediately, the use of improved SVM (Support Vector Machine) and KNN (K-Nearest Neighbor Algorithm) for gesture recognition and classification is proposed to enable patients to perform rehabilitation training more effectively. Finally, the effective evaluation results of the rehabilitation effect of patients by the idea of AHP (Analytic Hierarchy Process) are taken as necessary reference factors for doctors to follow up treatment. Various experimental results show that the system has achieved the expected results and has a good application prospect.

Leap Motion-based virtual reality training for improving motor functional recovery of upper limbs and neural reorganization in subacute stroke patients

Virtual reality is nowadays used to facilitate motor recovery in stroke patients. Most virtual reality studies have involved chronic stroke patients; however, brain plasticity remains good in acute and subacute patients. Most virtual reality systems are only applicable to the proximal upper limbs （arms） because of the limitations of their capture systems. Nevertheless, the functional recovery of an affected hand is most difficult in the case of hemiparesis rehabilitation after a stroke. The recently developed Leap Motion controller can track the fine movements of both hands and fingers. Therefore, the present study explored the effects of a Leap Motion-based virtual reality system on subacute stroke. Twenty-six subacute stroke patients were assigned to an experimental group that received virtual reality training along with conventional occupational rehabilitation, and a control group that only received conventional rehabilitation. The Wolf motor func- tion test （WMFT） was used to assess the motor function of the affected upper limb; functional magnetic resonance imaging was used to measure the cortical activation. After four weeks of treatment, the motor functions of the affected upper limbs were significantly improved in all the patients, with the improvement in the experimental group being significantly better than in the control group. The action perfor- mance time in the WMFT significantly decreased in the experimental group. Furthermore, the activation intensity and the laterality index of the contralateral primary sensorimotor cortex increased in both the experimental and control groups. These results confirmed that Leap Motion-based virtual reality training was a promising and feasible supplementary rehabilitation intervention, could facilitate the recovery of motor functions in subacute stroke patients. The study has been registered in the Chinese Clinical Trial Registry （registration number： ChiCTR-OCH- 12002238）.

On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time

This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company’s portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company’s pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount c1 and when they are in the second class, the premium paid is a constant amount c2 such that c1 > c2. The nature of claims (low or high) is measured via random thresholds . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. .

Simulation of multi-support depth-varying earthquake ground motions within heterogeneous onshore and offshore sites

This paper presents a novel approach to model and simulate the multi-support depth-varying seismic motions（MDSMs） within heterogeneous offshore and onshore sites.Based on 1 D wave propagation theory,the three-dimensional ground motion transfer functions on the surface or within an offshore or onshore site are derived by considering the effects of seawater and porous soils on the propagation of seismic P waves.Moreover,the depth-varying and spatial variation properties of seismic ground motions are considered in the ground motion simulation.Using the obtained transfer functions at any locations within a site,the offshore or onshore depth-varying seismic motions are stochastically simulated based on the spectral representation method（SRM）.The traditional approaches for simulating spatially varying ground motions are improved and extended to generate MDSMs within multiple offshore and onshore sites.The simulation results show that the PSD functions and coherency losses of the generated MDSMs are compatible with respective target values,which fully validates the effectiveness of the proposed simulation method.The synthesized MDSMs can provide strong support for the precise seismic response prediction and performance-based design of both offshore and onshore large-span engineering structures.

Computation of Design Load and Motion for Floating Structures Navigating in Waves

Analytical and numerical investigation is made of the source potential for-floating structure with forward speed in waves. A particular form is selected for numerical applications, where the double integral of the Green function is transformed into the single one and the oscillation characteristics for integrands in the specific computation domain are treated numerically. A comparison of calculated examples with published data is given and it shows that the numerical simulation is satisfactory and the accuracy is adequate to engineering application.

Parameter Estimation for Blur Image Combining Defocus and Motion Blur using Cepstrum Analysis

The degraded parameters recognition is very important for the restoration of blurred images. There are two common types of blurs for most camera systems. One is the defocus blur due to the optical system's defocus phenomenon and the other is the motion blur due to the relative movement between the objectives and the camera. Compared with the recognition for the blurred image with only one blur model, the parameter estimation for the picture combining defocus and motion blur models is a more complicated mission. A method was proposed for computer to estimate the parameters of defocus blur and motion blur in cepstrum area simultaneously. According to characters of both blur models in the frequency domain, an adjustment approach was suggested in the frequency area and then convert to the cepstrum field to increase the accuracy of measurement.

Probability Distribution of the Hull Motion and Mooring Line Tension of Two Floating Systems

The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems.In general,the dynamic responses of offshore structures obey a Gaussian distribution,assuming that the structural system,and sea loads are linear or weakly nonlinear.However,mooring systems and wave loads are considerably nonlinear,and the dynamic responses of hull/mooring systems are non-Gaussian.In this study,the dynamic responses of two types of floaters,semi-submersible and spar platforms,and their mooring lines are computed using coupled dynamic analysis in the time domain.Herein,the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared.The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems.Then,the effects of water depth,wave parameters,and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion,and mooring line tension are investigated and discussed.A comparison of the statistical distributions of the responses with various probability density functions,including the Gamma,Gaussian,General Extreme Value,Weibull,and Gaussian Mixture Model(GMM)distributions,shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion,and mooring line tension responses.Furthermore,the GMM distribution has the best accuracy of response prediction.

RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS

The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.

Sloshing-Coupled Ship Motion Algorithm for Estimation of Slosh-Induced Pressures

The effect of coupling between sloshing and ship motions in the evaluation of slosh-induced interior pressures is studied. The coupling between sloshing loads and ship motions is modelled through a hybrid algorithm which combines a potential flow solution based on transient Green function for the external ship hydrodynamics with a viscous flow solution based on a multiphase interface capturing volume of fluid(VOF) technique for the interior sloshing motion. The coupled algorithm accounts for full nonlinear slosh forces while the external forces on the hull are determined through a blended scheme of linear radiationdiffraction with nonlinear Froude-Krylov and restoring forces. Consideration of this level of nonlinearities in ship motions is found to have non-negligible effects on the slosh-coupled responses and slosh-induced loads. A scheme is devised to evaluate the statistical measure of the pressures through long-duration simulation studies in extreme irregular waves. It is found that coupling significantly influences the tank interior pressures, and the differences in the pressures between coupled and uncoupled cases can be as much as 100% or more. To determine the RAO over the frequency range needed for the simulation studies in irregular waves, two alternative schemes are proposed, both of which require far less computational time compared to the conventional method of finding RAO at each frequency, and the merits of these are discussed.

Advantages of cluster analysis for multifunctional and intercrossing brain area distribution Evaluation by functional magnetic resonance imaging

BACKGROUND： Multiple linear regression, general linear test and calculation of correlation values are commonly used in studies of brain function using functional magnetic resonance imaging （fMRI）. However, there are some limitations in their applications. In non-signal data statistics, cluster analysis functions as a very mature method, but it is not reliable in signal data statistics. OBJECTIVE： To investigate the spatial distribution of complex function in brain areas during motor tasks by cluster analysis, and to compare this with multiple linear regression. DESIGN, TIME AND SETTING： Block design, performed at the MR laboratory of Guangzhou University of Chinese Medicine. PARTICIPANTS： Fifteen right-handed, healthy university students （10 males and 5 females, aged 19-21 years）. METHODS： fMRI was performed while the subjects performed a finger movement task with the right hand. The screen showed a gray hand, with red spots presented in a random order on one of the index, middle, ring and little fingers. The subjects were required to remember the sequence of the red spots on the display. After a delay of 14 seconds, the subjects tapped their fingers according to the order of the red spots, as soon as the red spots turned green. After an interval of 14 seconds, another sequence appeared. Every sequence lasted for 28 seconds, including preparation and execution phases. A total of nine sequences per subject were performed. The data were analyzed using deconvolution and cluster methods, and program ＂cluster＂ was used to statistically analyze the coordinate positions of deconvolution and cluster data. MAIN OUTCOME MEASURES： Brain activation maps by deconvolution and brain function maps by clustering of the maximum peak values; blood oxygenation level dependent curves by deconvolution; coordinates of peak values and activation volumes by the two methods. RESULTS： The deconvolution method could not integrate the brain activation maps during different tasks into one activation picture, which made it difficult to identify exactly the spatial distribution of various activities in certain brain areas. Cluster analysis, using maximum peak values, clearly showed brain areas of monofunction and multifunction, even complex function, and presented a clear spatial distribution of multiple functional movements. Using the command ＂clust＂ with the same parameters, the volumes of main brain activation areas were consistent, indicating the maximum peak values are completely reliable in contrast to the deconvolution method. CONCLUSION： Cluster analysis is conducive to the analysis of multifunctional complex areas. Clustering using maximum peak values is a reliable method. Brain areas, such as primary motor cortex, supplementary motor area, and posterior parietal cortex, are not monofunctional areas, but multifunctional, complex ones. The activation maps derived by deconvolution statistics are distributed in many maps, which are not convenient to determine the functional distribution of complex brain areas.

Reconfiguration of face expressions based on the discrete capture data of radial basis function interpolation

Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.

Surface motion of a semi-elliptical hill for incident plane SH waves

A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating is checked by boundary conditions, numerical results for and some conclusions are obtained. properties of very prolate hill. Accuracy of the solution surface motion of oblate and prolate hills are calculated,

Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System

It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.

Real-Time Hand Motion Parameter Estimation with Feature Point Detection Using Kinect

This paper presents a real-time Kinect- based hand pose estimation method. Different from model-based and appearance-based approaches, our approach retrieves continuous hand motion parameters in real time. First, the hand region is segmented from the depth image. Then, some specific feature points on the hand are located by the random forest classifier, and the relative displacements of these feature points are transformed to a rotation invariant feature vector. Finally, the system retrieves the hand joint parameters by applying the regression functions on the feature vectors. Experimental results are compared with the ground truth dataset obtained by a data glove to show the effectiveness of our approach. The effects of different distances and different rotation angles for the estimation accuracy are also evaluated.

Seismic hazard analysis of Tianjin area based on strong ground motion prediction

Taking Tianjin as an example, this paper proposed a methodology and process for evaluating near-fault strong ground motions from future earthquakes to mitigate earthquake damage for the metropolitan area and important engineering structures. The result of strong ground motion was predicted for Tianjin main faults by the hybrid method which mainly con- sists of 3D finite difference method and stochastic Green＇s function. Simulation is performed for 3D structures of Tianjin re- gion and characterized asperity models. The characterized asperity model describing source heterogeneity is introduced fol- lowing the fault information from the project of Tianjin Active Faults and Seismic Hazard Assessment. We simulated the worst case that two earthquakes separately occur. The results indicate that the fault position, rupture process and the sedi- mentary deposits of the basin significantly affect amplification of the simulated ground motion. Our results also demonstrate the possibility of practical simulating wave propagation including basin induced surface waves in broad frequency-band, for seismic hazard analysis near the fault from future earthquakes in urbanized areas.