STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

基于Extrapolation Tikhonov正则化算法的重力数据三维约束反演

通过研究重力数据三维反演解的病态性,利用基于拉格朗日插值方法的Extrapolation Tikhonov正则化方法来解决反演中解的不唯一性和不稳定性问题,该方法最大限度的减少了因正则化参数的引入而在反演结果中介入的误差,同时详细讨论了基于三种选择原则的正则化双参数的具体选择方法,模型试算结果表明,与原Tikhonov方法相比,该方法提高了反演的拟合精度.其次,为了消除核函数随深度增加而快速衰减对反演结果的影响,本文改进了前人的重力数据三维反演深度加权函数,改进后的加权函数与原函数相比能更好的识别异常体底部密度分布特征,对于埋深较深的异常体具有较好的识别效果,更好的解决了由近地面趋肤效应作用引起的密度分布不均的问题.同时,利用上下限约束函数限制每一个立方体的密度差范围,并应用于多组人工合成模型.结果表明:该反演方法能准确地获得正演模型的预设参数范围和位置.

3D density inversion of gravity gradient data using the extrapolated Tikhonov regularization

We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations between calculated and observed data. We also use the depth weighting function based on the eigenvector of gravity gradient tensor to eliminate undesired effects owing to the fast attenuation of the position function. Model data suggest that the extrapolated Tikhonov regularization in conjunction with the depth weighting function can effectively recover the 3D distribution of density anomalies. We conduct density inversion of gravity gradient data from the Australia Kauring test site and compare the inversion results with the published research results. The proposed inversion method can be used to obtain the 3D density distribution of underground anomalies.

基于Power Extrapolation和Adaptive Method的网页评估新算法

Google的PageRank算法通过对超链接结构的分析,有效地提高了搜索结果的排序质量。PowerExtrapolation算法通过特征值直接求解马尔可夫超链接矩阵的主特征向量,但该算法的迭代次数与参数d的选择密切相关,而参数d的确定目前无明显规律可寻。另一方面,AdaptiveMethod通过将马尔可夫超链接矩阵稀疏化以达到节省迭代时间的目的。文章在PowerExtrapolation算法的基础上引入AdaptiveMethod,实验结果初步证明了新算法可以减少迭代运算的时间。

Extrapolated Tikhonov method and inversion of 3D density images of gravity data

Tikhonov regularization（TR） method has played a very important role in the gravity data and magnetic data process. In this paper, the Tikhonov regularization method with respect to the inversion of gravity data is discussed. and the extrapolated TR method（EXTR） is introduced to improve the fitting error. Furthermore, the effect of the parameters in the EXTR method on the fitting error, number of iterations, and inversion results are discussed in details. The computation results using a synthetic model with the same and different densities indicated that. compared with the TR method, the EXTR method not only achieves the a priori fitting error level set by the interpreter but also increases the fitting precision, although it increases the computation time and number of iterations. And the EXTR inversion results are more compact than the TR inversion results, which are more divergent. The range of the inversion data is closer to the default range of the model parameters, and the model features and default model density distribution agree well.

EXTRAPOLATION OF RF ECHO DATA BASED ON AR MODELING

Autoregressive (AR) modeling is applied to data extrapolation of radio frequency (RF) echo signals, and Burg algorithm, which can be computed in small amount and lead to a stable prediction filter, is used to estimate the prediction parameters of AR modeling. The complex data samples are directly extrapolated to obtain the extrapolated echo data in the frequency domain. The small rotating angle data extrapolation and the large rotating angular data extrapolation are considered separately in azimuth domain. The method of data extrapolation for the small rotating angle is the same as that in frequency domain, while the amplitude samples of large rotating angle echo data are extrapolated to obtain extrapolated echo amplitude, and the complex data of large rotating angle echo samples are extrapolated to get the extrapolated echo phase respectively. The calculation results show that the extrapolated echo data obtained by the above mentioned methods are accurate.

Recommendation system with minimized transaction data

This paper deals with the recommendation system in the so-called user-centric payment environment where users,i.e.,the payers,can make payments without providing self-information to merchants.This service maintains only the minimum purchase information such as the purchased product names,the time of purchase,the place of purchase for possible refunds or cancellations of purchases.This study aims to develop AI-based recommendation system by utilizing the minimum transaction data generated by the user-centric payment service.First,we developed a matrix-based extrapolative collaborative filtering algorithm based on open transaction data.The recommendation methodology was verified with the real transaction data.Based on the experimental results,we confirmed that the recommendation performance is satisfactory only with the minimum purchase information.

SnO_2-based solid solutions for CH_4 deep oxidation: Quantifying the lattice capacity of SnO_2 using an X-ray diffraction extrapolation method

A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M （M=Mn, Zr, Ti and Pb） molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3＋, Zr4＋, Ti4＋and Pb4＋cations are incorporated into the lattice of tetragonal rutile SnO2 to form a solid solution structure. As a consequence, the surface area and thermal stability of the catalysts are improved. Moreover, the oxygen species of the modified catalysts become easier to be reduced. Therefore, the oxidation activity over the catalysts was improved, except for the one modified by Pb oxide. Manganese oxide demonstrates the best promotional effects for SnO2. Using an X‐ray diffraction extrapolation method, the lattice capacity of SnO2 for Mn2O3 was 0.135 g Mn2O3/g SnO2, which indicates that to form stable solid solution, only 21%Sn4＋cations in the lattice can be maximally replaced by Mn3＋. If the amount of Mn3＋cations is over the capacity, Mn2O3 will be formed, which is not favorable for the activity of the catalysts. The Sn rich samples with only Sn‐Mn solid solution phase show higher activity than the ones with excess Mn2O3 species.

A Composite Approach of Radar Echo Extrapolation Based on TREC Vectors in Combination with Model-Predicted Winds

Extending the lead time of precipitation nowcasts is vital to improvements in heavy rainfall warning, flood mitigation, and water resource management. Because the TREC vector （tracking radar echo by correlation） represents only the instantaneous trend of precipitation echo motion, the approach using derived echo motion vectors to extrapolate radar reflectivity as a rainfall forecast is not satisfactory if the lead time is beyond 30 minutes. For longer lead times, the effect of ambient winds on echo movement should be considered. In this paper, an extrapolation algorithm that extends forecast lead times up to 3 hours was developed to blend TREC vectors with model-predicted winds. The TREC vectors were derived from radar reflectivity patterns in 3 km height CAPPI （constant altitude plan position indicator） mosaics through a cross-correlation technique. The background steering winds were provided by predictions of the rapid update assimilation model CHAF （cycle of hourly assimilation and forecast）. A similarity index was designed to determine the vertical level at which model winds were applied in the extrapolation process, which occurs via a comparison between model winds and radar vectors. Based on a summer rainfall case study, it is found that the new algorithm provides a better forecast.

Application of Multi-Scale Tracking Radar Echoes Scheme in Quantitative Precipitation Nowcasting

A new radar echo tracking algorithm known as multi-scale tracking radar echoes by cross-correlation （MTREC） was developed in this study to analyze movements of radar echoes at different spatial scales. Movement of radar echoes, particularly associated with convective storms, exhibits different characteristics at various spatial scales as a result of complex interactions among meteorological systems leading to the formation of convective storms. For the null echo region, the usual correlation technique produces zero or a very small magnitude of motion vectors. To mitigate these constraints, MTREC uses the tracking radar echoes by correlation （TREC） technique with a large ＂box＂ to determine the systematic movement driven by steering wind, and MTREC applies the TREC technique with a small ＂box＂ to estimate small-scale internal motion vectors. Eventually, the MTREC vectors are obtained by synthesizing the systematic motion and the small-scale internal motion. Performance of the MTREC technique was compared with TREC technique using case studies： the Khanun typhoon on 11 September 2005 observed by Wenzhou radar and a squall-line system on 23 June 2011 detected by Beijing radar. The results demonstrate that more spatially smoothed and continuous vector fields can be generated by the MTREC technique, which leads to improvements in tracking the entire radar reflectivity pattern. The new multi-scMe tracking scheme was applied to study its impact on the performance of quantitative precipitation nowcasting. The location and intensity of heavy precipitation at a 1-h lead time was more consistent with quantitative precipitation estimates using radar and rain gauges.

NON-STANDARD GALERKIN METHODS OF HIGH ACCURACY FOR PARABOLIC PROBLEMS

In this paper we employ the Petrov Galerkin method for the parabolic problems to get the finite element approximate solution of high accuracy by means of the interpolation postprocessing, extrapolation and defect correction techniques.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

Feasibility study of computed vs measured high b-value(1400 s/mm2) diffusion-weighted MR images of the prostate

AIM: To evaluate the impact of computed b = 1400 s/mm2(C-b1400) vs measured b = 1400 s/mm2(M-b1400) diffusion-weighted images(DWI) on lesion detection rate, image quality and quality of lesion demarcation using a modern 3T-MR system based on a small-field-of-view sequence(sFOV). METHODS: Thirty patients(PSA: 9.5 ± 8.7 ng/mL; 68 ± 12 years) referred for magnetic resonance imaging(MRI) of the prostate were enrolled in this study. All measurements were performed on a 3T MR system.For DWI, a single-shot EPI diffusion sequence(b = 0, 100, 400, 800 s/mm2) was utilized. C-b1400 was cal-culated voxelwise from the ADC and diffusion images. Additionally, M-b1400 was acquired for evaluation and comparison. Lesion detection rate and maximum lesion diameters were obtained and compared. Image quality and quality of lesion demarcation were rated accord-ing to a 5-point Likert-type scale. Ratios of lesion-to-bladder as well as prostate-to-bladder signal intensity(SI) were calculated to estimate the signal-to-noise-ratio(SNR). RESULTS: Twenty-four lesions were detected on M-b1400 images and compared to C-b1400 images. C-b1400 detected three additional cancer suspicious lesions. Overall image quality was rated significantly better and SI ratios were significantly higher on C-b1400(2.3 ± 0.8 vs 3.1 ± 1.0, P < 0.001; 5.6 ± 1.8 vs 2.8 ± 0.9, P < 0.001). Comparison of lesion size showed no significant differences between C- and M-b1400(P = 0.22). CONCLUSION: Combination of a high b-value extrap-olation and sFOV may contribute to increase diagnostic accuracy of DWI without an increase of acquisition time, which may be useful to guide targeted prostate biopsies and to improve quality of multiparametric MRI(mMRI) especially under economical aspects in a pri-vate practice setting.

Insights on the use of biosimilars in the treatment of inflammatory bowel disease

Biologic therapy, such as those that target tumor necrosis factor(TNF) signaling, has proven to be an efficacious method of treatment for patients with inflammatory bowel disease(IBD) with regards to symptom management and mucosal healing. However, the rising prevalence of IBD worldwide and the everincreasing burden of biologic pharmaceuticals in the health care industry is alarming for insurance companies, clinicians, and patients. The impending patent expiry and the relatively high costs of biologics, particularly anti-TNF agents, have paved the way for biosimilar development for IBD. The United States Food and Drug Administration defines a biosimilar as a biological product that is highly similar to its reference medicinal product, with no clinically meaningful differences in terms of safety, purity, and potency. The hope with biosimilars is that their entry into the market will be able to drive competition between pharmaceutical companies to reduce prices like that of the generic market, and that access to appropriate biologic treatments for IBD patients is increased in the long-term. Yet, there are challenging issues such as indication extrapolation and interchangeability that are still being debated in the field of IBD and must be addressed in future issued guidance. This review will discuss the issues and implications concerning the use of biosimilar therapy for IBD.

High-resolution algorithm based on temporal-spatial extrapolation

To enhance the resolution of parameter estimation with limited samples received by a short passive array, an iterative nonparametric algorithm for estimating the frequencies and direction-of-arrivals （DOAs） of signals is proposed. The cost function is constructed using 12-norm Gaussian entropy combined with an additional constraint, 12-norm constraint or linear constraint. By minimizing the cost functions in the temporal and the spatial dimensions using corresponding iteration algorithms respectively, the sparse discrete Fourier transforms （DFTs） of temporal and spatial samples are obtained to represent the extrapolated sequences with much larger sizes than the original samples. Then frequency and angle estimates are obtained by performing the traditional simple methods on the extrapolated sequences. It is shown that the proposed algorithm offers increased resolution and significantly reduced sidelobes compared with the periodogram and beamforming based methods. And it achieves high precision compared with the high-resolution method with lower computational burden. Some numerical simulations and real data processing results are presented to verify the effectiveness of the method.

Maximum Probabilistic and Dynamic Traffic Load Effects onShort-to-Medium Span Bridges

The steadily growing traffic load has resulted in lots of bridge collapse events over the past decades, especiallyfor short-to-medium span bridges. This study investigated probabilistic and dynamic traffic load effects on shortto-medium span bridges using practical heavy traffic data in China. Mathematical formulations for traffic-bridgecoupled vibration and probabilistic extrapolation were derived. A framework for extrapolating probabilistic anddynamic traffic load effect was presented to conduct an efficient and accurate extrapolation. An equivalent dynamicwheel load model was demonstrated to be feasible for short-to-medium span bridges. Numerical studies of twotypes of simply-supported bridges were conducted based on site-specific traffic monitoring data. Numerical resultsshow that the simulated samples and fitting lines follow a curve line in the Gumbel distribution coordinate system. Itcan be assumed that dynamic traffic load effects follow Gaussian distribution and the extreme value follows Gumbeldistribution. The equivalent probabilistic amplification factor is smaller than the individual dynamic amplificationfactor, which might be due to the variability of individual samples. Eurocode 1 is the most conservative specificationon vehicle load models, followed by the BS5400 specification. The D60-2015 specification in China and ASSHTOspecification provide lower conservative traffic load models.

BEM+Born series modeling schemes for wave propagation and their convergence analysis

This paper formulates two different boundary-element＋Born series schemes for wave propagation simulation in multilayered media by incorporating a Born series and boundary integral equations. The first scheme directly decomposes the resulting boundary integral equation matrix into the self-interaction operators associated with each boundary itself and the extrapolation operators expressing cross-interactions between different boundaries in a subregion. For the second scheme, the matrix dimension is firstly reduced to a half by the elimination of the traction field in the equations. The resulting new matrix can also be split into the self-interaction matrices associated each subregion itself and the extrapolation matrices interpreting cross-interactions between different subregions in a whole model. Both the numerical schemes avoid the inversion of the relatively much larger boundary integral equation matrix of a full-waveform BE method and hence save computing time and memory greatly. The two schemes are validated by calculating synthetic seismograms for a homogeneous layered model, compared with the full-waveform BE numerical solution. Numerical experiments indicate that both the BEM＋Born series modeling schemes are valid and effective. The tests also confirm that the second modeling scheme has a faster convergence in comparison with the first one.

ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.

High-resolution digital beamforming of UWB signals based on Carathéodory representation for delay compensation and array extrapolation

To realize high-resolution digital beamforming(DBF)of ultra-wideband(UWB) signals, we propose a DBF method based on Carath ′eodory representation for delay compensation and array extrapolation. Delay compensation by Carath ′eodory representation could achieve high interpolation accuracy while using the single channel sampling technique. Array extrapolation by Carath ′eodory representation reformulates and extends each snapshot, consequently extends the aperture of the original uniform linear array(ULA) by several times and provides a better realtime performance than the existing aperture extrapolation utilizing vector extrapolation based on the two dimensional autoregressive(2-D AR) model. The UWB linear frequency modulated(LFM) signal is used for simulation analysis. Simulation results demonstrate that the proposed method is featured by a much higher spatial resolution than traditional DBF methods and lower sidelobes than using Lagrange fractional filters.

WAVE FIELD EXTRAPOLATION IN VISCOELASTIC MEDIUM AND VARIABLE FOCUS METHOD TO SEPARATE SEISMIC COMPOUND WAVE

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