Optimization of Random Feature Method in the High-Precision Regime

Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in terms of both accuracy and efficiency.Potentially,the optimization problem in the RFM is more difficult to solve than those that arise in traditional methods.Unlike the broader machine-learning research,which frequently targets tasks within the low-precision regime,our study focuses on the high-precision regime crucial for solving PDEs.In this work,we study this problem from the following aspects:(i)we analyze the coeffcient matrix that arises in the RFM by studying the distribution of singular values;(ii)we investigate whether the continuous training causes the overfitting issue;(ii)we test direct and iterative methods as well as randomized methods for solving the optimization problem.Based on these results,we find that direct methods are superior to other methods if memory is not an issue,while iterative methods typically have low accuracy and can be improved by preconditioning to some extent.

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Usefulness of the clip-flap method of endoscopic submucosal dissection: A randomized controlled trial

AIM To prospectively investigate the efficacy and safety of clipflap assisted endoscopic submucosal dissection(ESD) for gastric tumors.METHODS From May 2015 to October 2016, we enrolled 104 patients with gastric cancer or adenoma scheduled for ESD at Shiga University of Medical Science Hospital. We randomized patients into two subgroups using the minimization method based on location of the tumor(upper, middle or lower third of the stomach), tumor size(< 20 mm or > 20 mm) and ulcer status: ESD using an endoclip(the clip-flap group) and ESD without an endoclip(the conventional group). Therapeutic efficacy(procedure time) and safety(complication: Gastrointestinal bleeding and perforation) were assessed. RESULTS En bloc resection was performed in all patients. Four patients had delayed bleeding(3.8%) and two had perforation(1.9%). No significant differences in en bloc resection rate(conventional group: 100%, clip flap group: 100%), curative endoscopic resection rate(conventional group: 90.9%, clip flap group: 89.8%, P = 0.85), procedure time(conventional group: 70.8 ± 46.2 min, clip flap group: 74.7 ± 53.3 min, P = 0.69), area of resected specimen(conventional group: 884.6 ± 792.1 mm^2, clip flap group: 1006.4 ± 1004.8 mm^2, P = 0.49), delayed bleeding rate(conventional group: 5.5%, clip flap group: 2.0%, P = 0.49), or perforation rate(conventional group: 1.8%, clip flap group: 2.0%, P = 0.93) were found between the two groups. Lessexperienced endoscopists did not show any differences in procedure time between the two groups.CONCLUSION For patients with early-stage gastric tumors, the clipflap method has no advantage in efficacy or safety compared with the conventional method.

Randomized MILP framework for Securing Virtual Machines from Malware Attacks

Cloud computing involves remote server deployments with public net-work infrastructures that allow clients to access computational resources.Virtual Machines(VMs)are supplied on requests and launched without interactions from service providers.Intruders can target these servers and establish malicious con-nections on VMs for carrying out attacks on other clustered VMs.The existing system has issues with execution time and false-positive rates.Hence,the overall system performance is degraded considerably.The proposed approach is designed to eliminate Cross-VM side attacks and VM escape and hide the server’s position so that the opponent cannot track the target server beyond a certain point.Every request is passed from source to destination via one broadcast domain to confuse the opponent and avoid them from tracking the server’s position.Allocation of SECURITY Resources accepts a safety game in a simple format as input andfinds the best coverage vector for the opponent using a Stackelberg Equilibrium(SSE)technique.A Mixed Integer Linear Programming(MILP)framework is used in the algorithm.The VM challenge is reduced by afirewall-based controlling mechanism combining behavior-based detection and signature-based virus detection.The pro-posed method is focused on detecting malware attacks effectively and providing better security for the VMs.Finally,the experimental results indicate that the pro-posed security method is efficient.It consumes minimum execution time,better false positive rate,accuracy,and memory usage than the conventional approach.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

Exploration of the Impact Mechanism of Government Credibility Based on Variable Screening Method

Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. In recent years, researchers’ research on government credibility has mostly focused on exploring theories and mechanisms, with little empirical research on this topic. This article intends to apply variable selection models in the field of social statistics to the issue of government credibility, in order to achieve empirical research on government credibility and explore its core influencing factors from a statistical perspective. Specifically, this article intends to use four regression-analysis-based methods and three random-forest-based methods to study the influencing factors of government credibility in various provinces in China, and compare the performance of these seven variable selection methods in different dimensions. The research results show that there are certain differences in simplicity, accuracy, and variable importance ranking among different variable selection methods, which present different importance in the study of government credibility issues. This study provides a methodological reference for variable selection models in the field of social science research, and also offers a multidimensional comparative perspective for analyzing the influencing factors of government credibility.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

Chinese herbal medicine Xinfeng Capsule in treatment of rheumatoid arthritis:study protocol of a multicenter randomized controlled trial

BACKGROUND： Rheumatoid arthritis （RA）, as a common systemic inflammatory autoimmune disease, affects approximately 1 in 100 individuals. Effective treatment for RA is not yet available because current research does not have a clear understanding of the etiology and pathogenesis of RA. Xinfeng Capsule, a patent Chinese herbal medicine, has been used in the treatment of RA in recent years. Despite its reported clinical efficacy, there are no large-sample, multicenter, randomized trials that support the use of Xinfeng Capsule for RA. Therefore, we designed a randomized, double-blind, multicenter, placebo-controlled trial to assess the efficacy and safety of Xinfeng Capsule in the treatment of RA. METHODS AND DESIGN： This is a 12-week, randomized, placebo-controlled, double-blind, multicenter trial on the treatment of RA. The participants will be randomly assigned to the experimental group and the control group at a ratio of 1：1. Participants in the experimental group will receive Xinfeng Capsule and a pharmaceutical placebo （imitation leflunomide）. The control group will receive leflunomide and an herbal placebo （imitation Xinfeng Capsule）. The American College of Rheumatology （ACR） Criteria for RA will be used to measure the efficacy of the Xinfeng Capsule. The primary outcome measure will be the percentage of study participants who achieve an ACR 20% response rate （ACR20）, which will be measured every 4 weeks after randomization. Secondary outcomes will include the ACR50 and ACR70 responses, the side effects of the medications, the Disease Activity Score 28, RA biomarkers, quality of life, and X-rays of the hands and wrists. The first four of the secondary outcomes will be measured every 4 weeks and the others will be measured at baseline and after 12 weeks of treatment. DISCUSSION： The result of this trial will help to evaluate whether Xinfeng Capsule is effective and safe in the treatment of RA. TRIAL REGISTRATION： This trial has been registered in ClinicalTrials.gov. The identifier is N CT01774877.

Numerical simulation of solitary and random wave propagation through vegetation based on VOF method

A vertical two-dimensional numerical model has been applied to solving the Reynolds Averaged Navier- Stokes （RANS} equations in the simulation of current and wave propagation through vegetated and non- vegetated waters. The k-e model is used for turbulence closure of RANS equations. The effect of vegeta- tion is simulated by adding the drag force of vegetation in the flow momentum equations and turbulence model. To solve the modified N-S equations, the finite difference method is used with the staggered grid system to solver equations. The Youngs＇ fractional volume of fluid （VOF） is applied tracking the free sur- face with second-order accuracy. The model has been tested by simulating dam break wave, pure current with vegetation, solitary wave runup on vegetated and non-vegetated channel, regular and random waves over a vegetated field. The model reasonably well reproduces these experimental observations, the model- ing approach presented herein should be useful in simulating nearshore processes in coastal domains with vegetation effects.

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

The vibroimpact systems with bilateral barriers are often encountered in practice.However,the dynamics of the vibroimpact system with bilateral barriers is full of challenges.Few closed-form solutions were obtained.In this paper,we propose a novel method for random vibration analysis of single-degree-of-freedom(SDOF)vibroim-pact systems with bilateral barriers under Gaussian white noise excitations.A periodic approximate transformation is employed to convert the equations of the motion to a con-tinuous form.The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov(FPK)equation.The closed-form station-ary probability density function(PDF)of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow.Finally,the versatility of the proposed approach is demonstrated by its application to two typical examples.Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

DYNAMIC CHARACTERISTIC ANALYSIS OF FUZZY-STOCHASTIC TRUSS STRUCTURES BASED ON FUZZY FACTOR METHOD AND RANDOM FACTOR METHOD

A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh＇s quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable＇s moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.

Numerical investigations on mechanical characteristics and failure mechanism of outwash deposits based on random meso-structures using discrete element method

Outwash deposit is a unique type of geological materials, and its features such as heterogeneity, discontinuity and nonlinearity determine the complexity of mechanical characteristics and failure mechanism. In this work, random meso-structure of outwash deposits was constructed by the technique of computer random simulation based on characteristics of its meso-structure in the statistical sense and some simplifications, and a series of large direct shear tests on numerical samples of outwash deposits with stone contents of 15%, 30%, 45% and 60% were conducted using the discrete element method to further investigate its mechanical characteristics and failure mechanism under external load. The results show that the deformation characteristics and shear strength of outwash deposits are to some extent improved with the increase of stone content, and the shear stress–shear displacement curves of outwash deposits show great differences at the post-peak stage due to the random spatial distribution and content of stones. From the mesoscopic view, normal directions of contacts between "soil" and "stone" particles undergo apparent deflection as the shear displacement continues during the shearing process, accompanying redistribution of the magnitude of contact forces during the shearing process. For outwash deposits, the shear zone formed after shear failure is an irregular stripe due to the movements of stones near the shear zone, and it expands gradually with the increase of stone content. In addition, there is an approximately linear relation between the mean increment of internal friction angle and the stone content lying between 30% and 60%, and a concave nonlinear relation between the mean increment of cohesion and stone content, which are in good agreement with the existing research results.

Modeling habitat suitability of range plant species using random forest method in arid mountainous rangelands

Mountainous rangelands play a pivotal role in providing forage resources for livestock, particularly in summer, and maintaining ecological balance. This study aimed to identify environmental variables affecting range plant species distribution, ecological analysis of the relationship between these variables and the distribution of plants, and to model and map the plant habitats suitability by the Random Forest Method(RFM) in rangelands of the Taftan Mountain, Sistan and Baluchestan Province, southeastern Iran. In order to determine the environmental variables and estimate the potential distribution of plant species, the presence points of plants were recorded by using systematic random sampling method(90 points of presence) and soils were sampled in 5 habitats by random method in 0–30 and 30–60 cm depths. The layers of environmental variables were prepared using the Kriging interpolation method and Geographic Information System facilities. The distribution of the plant habitats was finally modelled and mapped by the RFM. Continuous maps of the habitat suitability were converted to binary maps using Youden Index(?) in order to evaluate the accuracy of the RFM in estimation of the distribution of species potentialhabitat. Based on the values of the area under curve(AUC) statistics, accuracy of predictive models of all habitats was in good level. Investigating the agreement between the predicted map, generated by each model, and actual maps, generated from fieldmeasured data, of the plant habitats, was at a high level for all habitats, except for Amygdalus scoparia habitat. This study concluded that the RFM is a robust model to analyze the relationships between the distribution of plant species and environmental variables as well as to prepare potential distribution maps of plant habitats that are of higher priority for conservation on the local scale in arid mountainous rangelands.

Infinitesimal dividing modeling method for dual suppliers inventory model with random lead times

As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.

Neumann stochastic finite element method for calculating temperature field of frozen soil based on random field theory

To study the effect of uncertain factors on the temperature field of frozen soil, we propose a method to calculate the spatial average variance from just the point variance based on the local average theory of random fields. We model the heat transfer coefficient and specific heat capacity as spatially random fields instead of traditional random variables. An analysis for calculating the random temperature field of seasonal frozen soil is suggested by the Neumann stochastic finite element method, and here we provide the computational formulae of mathematical expectation, variance and variable coefficient. As shown in the calculation flow chart, the stochastic finite element calculation program for solving the random temperature field, as compiled by Matrix Laboratory （MATLAB） sottware, can directly output the statistical results of the temperature field of frozen soil. An example is presented to demonstrate the random effects from random field parameters, and the feasibility of the proposed approach is proven by compar- ing these results with the results derived when the random parameters are only modeled as random variables. The results show that the Neumann stochastic finite element method can efficiently solve the problem of random temperature fields of frozen soil based on random field theory, and it can reduce the variability of calculation results when the random parameters are modeled as spatial- ly random fields.

Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Response of train-bridge system under intensive seismic excitation by random vibration method

Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation,the intensity of which is larger than 7,acts in train-bridge system.Firstly,the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established,where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom,while the single-span simple supported bridge subsystem is composed of 102D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support.Secondly,Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system.The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method,respectively solved by precise integral method and Newmark-βmethod through the inter-system iterative procedure.Finally,the results are compared with the case under the weak seismic excitation,and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution.In a high probability,the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.

Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD AND ITS VERIFICATION FOR EFFECTIVE PROPERTIES OF COMPOSITE MATERIALS

The present study aims at developing a new method-RandomMicrostructure Finite Element Method (RMFEM) for the effectiveproperties of com- Posite materials. In this method, a randommicrostructure Model is used to simulate the microstructure of thereal composite materials. The physical fields in such a randomMicrosturucture model under specified boundary and initial Conditionsare analyzed by finite element method.