Advancements in Numerical Solutions:Fractal Runge-Kutta Approach to Model Time-Dependent MHD Newtonian Fluid with Rescaled Viscosity on Riga Plate

Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical solutions.This study presents an innovative computational approach to tackle these difficulties.The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic(MHD)Newtonian fluid with rescaled viscosity flow on Riga plates.An efficient computational scheme is proposed for handling fractal timedependent problems in flow phenomena.The scheme is comprised of three stages and constructed using three different time levels.The stability of the scheme is shown by employing the Fourier series analysis to solve scalar problems.The scheme’s convergence is guaranteed for a time fractal partial differential equations system.The scheme is applied to the dimensionless fractal heat and mass transfer model of incompressible,unsteady,laminar,Newtonian fluid with rescaled viscosity flow over the flat and oscillatory Riga plates under the effects of spaceand temperature-dependent heat sources.The first-order back differences discretize the continuity equation.The results show that skin friction local Nusselt number declines by raising the coefficient of the temperature-dependent term of heat source and Eckert number.The numerical simulations provide valuable insights into fluid dynamics,explicitly highlighting the influence of the temperature-dependent coefficient of the heat source and the Eckert number on skin friction and local Nusselt number.

A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

Understanding and modeling flows over porous layers are of great industrial significance.To accurately solve the turbulent multi-scale flows on complex configurations,a rescaling algorithm designed for turbulent flows with the Chapman-Enskog analysis is proposed.The mesh layout and the detailed rescaling procedure are also introduced.Direct numerical simulations(DNSs)for a turbulent channel flow and a porous walled turbulent channel flow are performed with the three-dimensional nineteen-velocity(D3Q19)multiple-relaxation-time(MRT)lattice Boltzmann method(LBM)to validate the accuracy,adaptability,and computational performance of the present rescaling algorithm.The results,which are consistent with the previous DNS studies based on the finite difference method and the LBM,demonstrate that the present method can maintain the continuity of the macro values across the grid interface and is able to adapt to complex geometries.The reasonable time consumption of the rescaling procedure shows that the present method can accurately calculate various turbulent flows with multi-scale and complex configurations while maintaining high computational efficiency.

Accelerating SAGE algorithm in PET image reconstruction by rescaled block-iterative method

A new method to accelerate the convergent rate of the space-alternatinggeneralized expectation-maximization (SAGE) algorithm is proposed. The new rescaled block-iterativeSAGE (RBI-SAGE) algorithm combines the RBI algorithm with the SAGE algorithm for PET imagereconstruction. In the new approach, the projection data is partitioned into disjoint blocks; eachiteration step involves only one of these blocks. SAGE updates the parameters sequentially in eachblock. In experiments, the RBI-SAGE algorithm and classical SAGE algorithm are compared in theapplication on positron emission tomography (PET) image reconstruction. Simulation results show thatRBI-SAGE has better performance than SAGE in both convergence and image quality.

基于Rescaled Hinge损失函数的多子支持向量机

针对多分类学习模型性能会受异常值影响的问题,提出基于Rescaled Hinge损失函数的多子支持向量机(RHMBSVM)。首先,该方法通过引入有界、非凸的Rescaled Hinge损失函数来构建相应的优化问题;然后,利用共轭函数理论将优化问题作等价变换;最后,使用变量交替策略形成一个迭代算法来求解非凸优化问题,该方法在求解的过程中可自动调节每个样本点的惩罚权重,从而削弱了异常值对K个超平面的影响,增强了鲁棒性。使用5折交叉验证的方法进行数值实验,实验结果表明,在数据集无异常值的情况下,该方法的正确率比多子支持向量机(MBSVM)提升了1.11个百分点,比基于Rescaled Hinge损失函数的鲁棒支持向量机(RSVM-RHHQ)提升了0.74个百分点;在数据集有异常值的情况下,该方法的正确率比MBSVM提升了2.10个百分点,比RSVM-RHHQ提升了1.47个百分点。实验结果证明了所提方法在解决有异常值的多分类问题上的鲁棒性。

基于张量建模和进化K均值聚类的社区检测方法

很多传统社区检测方法大多局限于单关系网络,适用性和准确性均较弱。针对此问题,提出了一种针对多关系网络的社区检测方法。首先,为进行多关系网络建模,使用了三阶邻接张量,其中张量的每个切片表示与参与者之间一种类型的关系相对应的邻接矩阵。从数据表示的角度,将多关系网络解读为三阶张量利于将因子分解方法作为学习方法使用。然后,应用RESCAL分解作为关系学习的工具,从而揭示参与者的唯一隐性表征。最后,在上一步得到的结果上应用进化K均值聚类算法,以确定多维度上的社区结构。在一个合成数据集和两个公开数据集上进行实验。实验结果表明,与基于上下文信息的社区检测(CICD)方法、Memetic方法和局部谱聚类(LSC)方法相比,所提方法的纯度最少提高了5个百分点,重叠归一化互信息(ONMI)最少提高了2个百分点,F得分最少提高了3个百分点,并且验证了该方法具有较快的收敛速度。

An Improved Control Algorithm for High-order Nonlinear Systems with Unmodelled Dynamics

In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance （e,g., asymptotical stability） and reducing the control effort. By introducing a new reseating transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs all improved output-feedback controller. The output-feedback controller guarantees the globally asymptotieal stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and resealing transformation parameter are obtained to effectively reduce the control effort.

Linear synchronization and circuit implementation of chaotic system with complete amplitude control

Although chaotic signals are considered to have great potential applications in radar and communication engineering, their broadband spectrum makes it difficult to design an applicable amplifier or an attenuator for amplitude conditioning. Moreover, the transformation between a unipolar signal and a bipolar signal is often required. In this paper, a more intelligent hardware implementation based on field programmable analog array （FPAA） is constructed for chaotic systems with complete amplitude control. Firstly, two chaotic systems with complete amplitude control are introduced, one of which has the property of offset boosting with total amplitude control, while the other has offset boosting and a parameter for partial control. Both cases can achieve complete amplitude control including amplitude rescaling and offset boosting. Secondly, linear synchronization is established based on the special structure of chaotic system. Finally, experimental circuits are constructed on an FPAA where the predicted amplitude control is realized through only two independent configurable analog module （CAM） gain values.

Translocalization and Social Rescaling:Case Studies of Linguistic Landscapes in Guangzhou

Languages and linguistic resources transport from one locality to another,adapting to the norms,customs,and regulations of a new locality.This process involves translocalization.Translocalization emphasizes the movement of linguistic resources against the backdrop of globalization and the combination or reframing of resources from different localities.This research explores the extent to which translocalization is reflected by the linguistic landscapes of three distinct commercial areas in Guangzhou,China.It goes on to discuss how translocalization works together with social rescaling to incur the movement of linguistic resources and to result in distinct linguistic landscapes of the three commercial areas.It concludes that some languages or linguistic resources,such as English,pinyin and traditional Chinese writing,are transported to local contexts for the purpose of rescaling,whereas other languages or dialects,like Cantonese,might gradually lose their function of rescaling and retain its function in indexing local identity and solidarity.This study calls for more attention to the local resources and contexts in linguistic landscape studies.It argues for the indexical function of linguistic resources in social rescaling and city planning.

An rescaled range analysis on the characteristics of coal seam development in the Eastern depression of the Liaohe Basin

The characteristics of coal seam development,and the prospects of a favorable coal-forming area,were evaluated for the Liaohe Basin located in China.The Number 3 and Number 9 coal seam thickness series from 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined by a rescaled range analysis.The results indicate that the Hurst exponents of the Number 3 and Number 9 coal seam thickness series are 0.69 and 0.68,respectively.This suggests the presence of persistence.As the bore spacing increases the Hurst exponent of the Number 3 series gradually decreases（H changes from 0.69 to 0.52） and shifts from persistence to randomness.The Hurst exponent of the Number 9 thickness data gradually increases（H changes from 0.68 to 0.91） and always shows the characteristic of persistence.A combination of geological characteristics and the series data allow the conclusion that it is more suitable for the Number 9 coal seam to form in the Northeastern part of the Eastern depression than the Number 3 coal seam.

Spontaneous combustion influenced by surface methane drainage and its prediction by rescaled range analysis

This study established numerical modeling using COMSOLTMto examine the influence of horizontal location and drainage ability of surface borehole on spontaneous combustion in longwall working face gob. Rescaled Range Analysis(R/S analysis) was employed to investigate the chaos characteristic of N_2/O_2 ratio from a surface borehole in 10416 working face gob, Yangliu Colliery, China. The simulation results show that there is always a circular ‘‘dissipation zone" around the drainage borehole and an elliptic ‘‘spontaneous combustion zone" in deep gob. Little influence was found on spontaneous combustion zone on the intake side of the gob but the width of spontaneous combustion zone in middle gob is enlarged, while the depth of spontaneous combustion zone near the return side is reduced. The R/S analysis indicates that the influence of surface borehole on spontaneous combustion can be divided into two stages by the chaos feature of N_2/O_2: safety drainage stage and spontaneous combustion initiating stage. It can be concluded that the methane drainage from gob through surface borehole can intervene in the distribution of spontaneous combustion zone in gob and the chaos feature of N_2/O_2 from surface borehole can effectively reflect coal spontaneous combustion condition in gob.

The Effects of Land Surface Process Perturbations in a Global Ensemble Forecast System

Atmospheric variability is driven not only by internal dynamics, but also by external forcing, such as soil states, SST, snow, sea-ice cover, and so on. To investigate the forecast uncertainties and effects of land surface processes on numerical weather prediction, we added modules to perturb soil moisture and soil temperature into NCEP＇s Global Ensemble Forecast System （GEFS）, and compared the results of a set of experiments involving different configurations of land surface and atmospheric perturbation. It was found that uncertainties in different soil layers varied due to the multiple timescales of interactions between land surface and atmospheric processes. Perturbations of the soil moisture and soil temperature at the land surface changed sensible and latent heat flux obviously, as compared to the less or indirect land surface perturbation experiment from the day-to-day forecasts. Soil state perturbations led to greater variation in surface heat fluxes that transferred to the upper troposphere, thus reflecting interactions and the response to atmospheric external forcing. Various verification scores were calculated in this study. The results indicated that taking the uncertainties of land surface processes into account in GEFS could contribute a slight improvement in forecast skill in terms of resolution and reliability, a noticeable reduction in forecast error, as well as an increase in ensemble spread in an under-dispersive system. This paper provides a preliminary evaluation of the effects of land surface processes on predictability. Further research using more complex and suitable methods is needed to fully explore our understanding in this area.

一种张量分解的知识图谱推理优化算法

随着信息爆炸,知识图谱推理算法在社会网络、生物信息学等许多领域都有着重要应用。现有RESCAL张量分解的知识图谱推理算法仅从信息论或数值分析角度进行了张量分解,未充分考虑知识图谱数据的复杂性。因此,基于RESCAL张量分解,对于知识图谱推理问题,提出了一种改进的优化算法,称为KLLS*-RESCAL算法。该算法通过融合相对熵与平方差设置新的损失函数,从信息论与数值分析两个角度进行张量分解,综合考虑知识图谱数据的复杂性。实验结果表明,在知识图谱推理中,KLLS*-RESCAL算法相对于其他RESCAL算法具有更高的预测准确率。

On Symmetry Flows of Noncommutative Kadomtsev-Petviashvili Hierarchy

We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.

Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin–Huxley neurons

The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.

Resizable, Rescalable and Free-Style Visualization of Hierarchical Clustering and Bioinformatics Analysis

Graphical representation of hierarchical clustering results is of final importance in hierarchical cluster analysis of data. Unfortunately, almost all mathematical or statistical software may have a weak capability of showcasing such clustering results. Particularly, most of clustering results or trees drawn cannot be represented in a dendrogram with a resizable, rescalable and free-style fashion. With the “dynamic” drawing instead of “static” one, this research works around these weak functionalities that restrict visualization of clustering results in an arbitrary manner. It introduces an algorithmic solution to these functionalities, which adopts seamless pixel rearrangements to be able to resize and rescale dendrograms or tree diagrams. The results showed that the algorithm developed makes clustering outcome representation a really free visualization of hierarchical clustering and bioinformatics analysis. Especially, it possesses features of selectively visualizing and/or saving results in a specific size, scale and style (different views).

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

Prediction and calculation for new energy development

Some important questions for new energy development were discussed, such as the prediction and calculation of sea surface temperature, ocean wave, offshore platform price, typhoon track, fire status, vibration due to earthquake, energy price, stock market’s trend and so on with the fractal methods (including the four ones of constant dimension fractal, variable dimension fractal, complex number dimension fractal and fractal series) and the improved rescaled range analysis (R/S analysis).

Forecasting Diabetes Patients Attendance at Al-Baha Hospitals Using Autoregressive Fractional Integrated Moving Average (ARFIMA) Models

Diabetes has become a concern in the developed and developing countries with its growing number of patients reported to the ministry of health records. This paper discusses the use of the Autoregressive Fractional Moving Average (ARFIMA) technique to modeling the diabetes patient’s attendance at Al-Baha hospitals using monthly time series data. The data used in the analysis of this paper are monthly readings of diabetes patients data covered the period January 2006-December 2016. The data were collected from the General Directorate of Health Affairs, Al-Baha region. The autoregressive fractional moving average approach was applied to the data through the model identification, estimation, diagnostic checking and forecasting. Hurst test results and ACF confirmed that there is a long memory behavior in diabetic patient’s data. Also, the fractional difference to diabetes series data revealed that (d = 0.44). Moreover, unit root tests indicated that the fractional difference of diabetes series level is stationary. Furthermore, according to AIC and BIC of model selection criteria ARFIMA (1, 0.44, 0) model shown the smallest values, hence this model was chosen as an adequate represents the data. Also, a diagnostic check confirmed that ARFIMA was appropriate and highly recommended in modeling and forecasting this type of data.

Urban Transition Dynamics in the Regional Rescaling of the Pearl River Delta Area:a Qualitative Approach

The Pearl River Delta region has been the hub of urban vibrancy and boom ever since the country’s opening up and devolution reforms.However,the political and economic institutions of the cities in this region are so different and complicated that they pose great challenges to the integration of the whole region.This study takes one prominent experiment of urban expansion,Hengqin in Zhuhai,as a case study to investigate how institutional innovations are forged and managed to boost urban development and transitions towards sustainable growth and regional integration.We adopt a multi-level perspective framework to analyze Hengqin’s urban transition.Government archives,master plans,various documents and interviews with government officials,planners,residents,and businesses from Zhuhai,Hong Kong,and Macao are chosen as sources of the analysis,which delineates the complex interactions from a variety of stakeholders.Despite difficulties in the early days,Hengqin is now transitioning quickly,although still confronted with inter-scalar challenges.A better understanding of the governance and economic innovations that have taken place,and the investment-driven development strategies involved,will help shed light on the urban transition of other similar city regions.

Numerical Study on Viscous Fingering Using Electric Fields in a Hele-Shaw Cell

We investigate the nonlinear dynamics of amoving interface in aHele-Shaw cell subject to an in-plane applied electric field.We develop a spectrally accurate numerical method for solving a coupled integral equation system.Although the stiffness due to the high order spatial derivatives can be removed using a small scale decomposition technique,the long-time simulation is still expensive since the evolving velocity of the interface drops dramatically as the interface expands.We remove this physically imposed stiffness by employing a rescaling scheme,which accelerates the slow dynamics and reduces the computational cost.Our nonlinear results reveal that positive currents restrain finger ramification and promote the overall stabilization of patterns.On the other hand,negative currents make the interface more unstable and lead to the formation of thin tail structures connecting the fingers and a small inner region.When no fluid is injected,and a negative current is utilized,the interface tends to approach the origin and break up into several drops.We investigate the temporal evolution of the smallest distance between the interface and the origin and find that it obeys an algebraic law(t∗−t)b,where t∗is the estimated pinch-off time.