Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

T2-weighted imaging-based radiomic-clinical machine learning model for predicting the differentiation of colorectal adenocarcinoma

BACKGROUND The study on predicting the differentiation grade of colorectal cancer(CRC)based on magnetic resonance imaging(MRI)has not been reported yet.Developing a non-invasive model to predict the differentiation grade of CRC is of great value.AIM To develop and validate machine learning-based models for predicting the differ-entiation grade of CRC based on T2-weighted images(T2WI).METHODS We retrospectively collected the preoperative imaging and clinical data of 315 patients with CRC who underwent surgery from March 2018 to July 2023.Patients were randomly assigned to a training cohort(n=220)or a validation cohort(n=95)at a 7:3 ratio.Lesions were delineated layer by layer on high-resolution T2WI.Least absolute shrinkage and selection operator regression was applied to screen for radiomic features.Radiomics and clinical models were constructed using the multilayer perceptron(MLP)algorithm.These radiomic features and clinically relevant variables(selected based on a significance level of P<0.05 in the training set)were used to construct radiomics-clinical models.The performance of the three models(clinical,radiomic,and radiomic-clinical model)were evaluated using the area under the curve(AUC),calibration curve and decision curve analysis(DCA).RESULTS After feature selection,eight radiomic features were retained from the initial 1781 features to construct the radiomic model.Eight different classifiers,including logistic regression,support vector machine,k-nearest neighbours,random forest,extreme trees,extreme gradient boosting,light gradient boosting machine,and MLP,were used to construct the model,with MLP demonstrating the best diagnostic performance.The AUC of the radiomic-clinical model was 0.862(95%CI:0.796-0.927)in the training cohort and 0.761(95%CI:0.635-0.887)in the validation cohort.The AUC for the radiomic model was 0.796(95%CI:0.723-0.869)in the training cohort and 0.735(95%CI:0.604-0.866)in the validation cohort.The clinical model achieved an AUC of 0.751(95%CI:0.661-0.842)in the training cohort and 0.676(95%CI:0.525-0.827)in the validation cohort.All three models demonstrated good accuracy.In the training cohort,the AUC of the radiomic-clinical model was significantly greater than that of the clinical model(P=0.005)and the radiomic model(P=0.016).DCA confirmed the clinical practicality of incorporating radiomic features into the diagnostic process.CONCLUSION In this study,we successfully developed and validated a T2WI-based machine learning model as an auxiliary tool for the preoperative differentiation between well/moderately and poorly differentiated CRC.This novel approach may assist clinicians in personalizing treatment strategies for patients and improving treatment efficacy.

An improved global-direction stencil based on the face-area-weighted centroid for the gradient reconstruction of unstructured finite volume methods

The accuracy of unstructured finite volume methods is greatly influenced by the gradient reconstruction, for which the stencil selection plays a critical role. Compared with the commonly used face-neighbor and vertex-neighbor stencils, the global-direction stencil is independent of the mesh topology, and characteristics of the flow field can be well reflected by this novel stencil. However, for a high-aspect-ratio triangular grid, the grid skewness is evident, which is one of the most important grid-quality measures known to affect the accuracy and stability of finite volume solvers. On this basis and inspired by an approach of using face-area-weighted centroid to reduce the grid skewness, we explore a method by combining the global-direction stencil and face-area-weighted centroid on high-aspect-ratio triangular grids, so as to improve the computational accuracy. Four representative numerical cases are simulated on high-aspect-ratio triangular grids to examine the validity of the improved global-direction stencil. Results illustrate that errors of this improved methods are the lowest among all methods we tested, and in high-mach-number flow, with the increase of cell aspect ratio, the improved global-direction stencil always has a better stability than commonly used face-neighbor and vertex-neighbor stencils. Therefore, the computational accuracy as well as stability is greatly improved, and superiorities of this novel method are verified.

Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

Hybrid C a rrie r S prea d Based on 4-Weighted T ra nsform Spectrum System Fractional Fourier

Spread Spectrum （SS） is a promising technique to resist interference in wireless communication system In order to further improve this capability, this paper proposes a Hybrid Carrier （HC） SS system, combining 4-Weighted Fractional Fourier Transform （4-WFRFT） with SS technique. In this HC-SS system, due to the property of 4- WFRFT, the signal energy of proposed system is distributed on the time-frequency plane more evenly and symmmetrically, compared with the existing Single-Cartier （SC） and Multi-Carrier （MC） spread spectrum systems. In the selective channel, the proposed method can split the interference to a more broad range in order to reduce the influence, resulting in the better system perforrmnce. In addition, proposed system can be seen as the convergence of the existing SS techniques, which is a main feature in future.

SEMI-WEIGHT FUNCTION METHOD ON COMPUTATION OF STRESS INTENSITY FACTORS IN DISSIMILAR MATERIALS

Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.

Comparison of Diagnostic Effects of T2-Weighted Imaging,DWI,SWI,and DTI in Acute Cerebral Infarction

Objective:To achieve precision medicine,the use of imaging methods to help the clinical detection of cerebral infarction is conducive to the clinical development of a treatment plan and increase of the cure rate and improvement of the prognosis of patients.Methods:In this work,T2-weighted imaging(T2WI),diffusion-weighted imaging(DWI),susceptibility-weighted imaging(SWI),and diffusion tensor imaging(DTI)examinations were performed on 34 patients with clinically diagnosed cerebral infarction to measure the difference in signal intensity between the lesion and its mirror area and make a comparative analysis by means of the Student-Newman-Keuls method.Results:The detection rate of T2WI was 79%(27/34),the detection rate of DWI was 97%(33/34),the detection rate of SWI was 88%(30/34),and the detection rate of DTI was 94%(32/34).Conclusion:The imaging performance was in the order DWI>DTI>SWI>T2WI for the diagnosis of cerebral infarction,and combined imaging is better than single imaging.

A Review on Sources,Extractions and Analysis Methods of a Sustainable Biomaterial:Tannins

Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly to substitute petroleum-based products.They are a definite class of sustainable materials of the forestry industry.They have been in operation for hundreds of years to manufacture leather and now for a growing number of applications in a variety of other industries,such as wood adhesives,metal coating,pharmaceutical/medical applications and several others.This review presents the main sources,either already or potentially commercial of this forestry by-materials,their industrial and laboratory extraction systems,their systems of analysis with their advantages and drawbacks,be these methods so simple to even appear primitive but nonetheless of proven effectiveness,or very modern and instrumental.It constitutes a basic but essential summary of what is necessary to know of these sustainable materials.In doing so,the review highlights some of the main challenges that remain to be addressed to deliver the quality and economics of tannin supply necessary to fulfill the industrial production requirements for some materials-based uses.

A comparison study on structure-function relationship of polysaccharides obtained from sea buckthorn berries using different methods:antioxidant and bile acid-binding capacity

In this study,the structural characters,antioxidant activities and bile acid-binding ability of sea buckthorn polysaccharides(HRPs)obtained by the commonly used hot water(HRP-W),pressurized hot water(HRP-H),ultrasonic(HRP-U),acid(HRP-C)and alkali(HRP-A)assisted extraction methods were investigated.The results demonstrated that extraction methods had significant effects on extraction yield,monosaccharide composition,molecular weight,particle size,triple-helical structure,and surface morphology of HRPs except for the major linkage bands.Thermogravimetric analysis showed that HRP-U with filamentous reticular microstructure exhibited better thermal stability.The HRP-A with the lowest molecular weight and highest arabinose content possessed the best antioxidant activities.Moreover,the rheological analysis indicated that HRPs with higher galacturonic acid content and molecular weight showed higher viscosity and stronger crosslinking network(HRP-C,HRP-W and HRP-U),which exhibited stronger bile acid binding capacity.The present findings provide scientific evidence in the preparation technology of sea buckthorn polysaccharides with good antioxidant and bile acid binding capacity which are related to the structure affected by the extraction methods.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Light-Weighted Decision Support Framework for Selecting Cloud Service Providers

Multi-criteria decision making(MCDM)is a technique used to achieve better outcomes for some complex business-related problems,whereby the selection of the best alternative can be made in as many cases as possible.This paper proposes a model,the multi-criteria decision support method,that allows both service providers and consumers to maximize their profits while preserving the best matching process for resource allocation and task scheduling.The increasing number of service providers with different service provision capabilities creates an issue for consumers seeking to select the best service provider.Each consumer seeks a service provider based on various preferences,such as price,service quality,and time to complete the tasks.In the literature,the problem is viewed from different perspectives,such as investigating how to enhance task scheduling and the resource allocation process,improve consumers’trust,and deal with network problems.This paper offers a novel model that considers the preferences of both service providers and consumers to find the best available service provider for each consumer.First,the model adopts the best-worst method(BWM)to gather and prioritize tasks based on consumers’and service providers’preferences.Then,the model calculates and matches similarities between the sets of tasks from the consumer’s side with the sets of tasks from the provider’s side to select the best service provider for each consumer using the two proposed algorithms.The complexity of the two algorithms is found to be O(n3).

Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.

Deciphering gastric inflammation-induced tumorigenesis through multi-omics data and AI methods

Gastric cancer(GC), the fifth most common cancer globally, remains the leading cause of cancer deaths worldwide. Inflammation-induced tumorigenesis is the predominant process in GC development;therefore, systematic research in this area should improve understanding of the biological mechanisms that initiate GC development and promote cancer hallmarks. Here, we summarize biological knowledge regarding gastric inflammation-induced tumorigenesis, and characterize the multi-omics data and systems biology methods for investigating GC development. Of note, we highlight pioneering studies in multi-omics data and state-of-the-art network-based algorithms used for dissecting the features of gastric inflammation-induced tumorigenesis, and we propose translational applications in early GC warning biomarkers and precise treatment strategies. This review offers integrative insights for GC research, with the goal of paving the way to novel paradigms for GC precision oncology and prevention.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method

In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP un-certainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20%are added to these original factors for con-structing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron(MLP),support vector machine(SVM)and random forest(RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2)With the proportions of random errors increasing from 5%to 20%,the LSP uncertainty increases continuously.(3)The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4)The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5)The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide sus-ceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors.

Assessment the Optimal Effect of Time of Repetition: Extrinsic Pulse Parameter on Gd-DTPA Enhanced, Spin-Echo T1-Weighted MR Images under Low Magnetic Field Strength

The contrast agent concentration, the time of repetition (TR) and magnetic field strength are significant parameters that influence for the accurate signal intensity (SI) in quantitative Magnetic Resonance Imaging (MRI). Therefore, this study was conducted to investigate and refine the dependence and the optimal effect of Time of Repetition (TR) on the relationship between signal intensity and Gd-DTPA (Gadolinium-diethylene-triaminepenta-acetic acid) concentration, after applying two-dimensional (2D) Spin Echo (SE) pulse sequence under low-field MRI. In addition to that, the optimal concentration of Gd-DTPA at given sequence parameters at low-field MRI was also evaluated. A water-filled phantom was constructed for a range of Gd-DTPA concentrations (0 - 6 mmol/L) and the mean signal intensities (SIs) were assessed in the defined region of interest on T1-weighted images with different TR values (40 - 2000 ms). The generated signal-concentration curves for Gd-DTPA revealed that increasing TR was associated with the increase of the overall SIs and the maximum relationship between SI to concentration. Moreover, the required Gd-DTPA concentration to produce the maximum SI was associated to decrease with the increase of TR. In addition to this, the application of beyond 100 ms TR values in this study with relatively higher concentrations (beyond 1 - 2 mmol/L) has resulted predominantly non-linear patterns in the signal-concentration curves and it appears the saturation or decay of the SIs due to T2 effect. From these results, it can be suggested that the selection of relatively lower Gd-DTPA concentration ( mmol/L) with less than 800 ms (<800 ms) TR values can produce a better linear relationship between the concertation and SIs in T1-weighted SE low field contrast-enhanced MRI. Furthermore, this study also outlined the significance and necessity of the optimization of TR in SE sequence in low field MRI prior to a particular examination.

Experimental study on secondary air mixing along the bed height in a circulating fluidized bed with a multitracer-gas method

A multitracer-gas method was proposed to study the secondary air(SA)mixing along the bed height in a circulating fluidized bed(CFB)using carbon monoxide(CO),oxygen(O_(2)),and carbon dioxide(CO_(2))as tracer gases.Experiments were carried out on a cold CFB test rig with a cross-section of 0.42 m×0.73 m and a height of 5.50 m.The effects of superficial velocity,SA ratio,bed inventory,and particle diameter on the SA mixing were investigated.The results indicate that there are some differences in the measurement results obtained using different tracer gases,wherein the deviation between CO and CO_(2) ranges from 42%to 66%and that between O_(2) and CO_(2) ranges from 45%to 71%in the lower part of the fluidized bed.However,these differences became less pronounced as the bed height increased.Besides,the high solid concentration and fine particle diameter in the CFB may weaken the difference.The measurement results of different tracer gases show the same trends under the variation of operating parameters.Increasing superficial velocity and SA ratio and decreasing particle diameter result in better mixing of the SA.The effect of bed inventory on SA mixing is not monotonic.