基于高维PDE投影恢复的低剂量CT重建方法

目的提出一种基于高维偏微分方程(PDE)投影恢复的低剂量CT重建方法。方法先将原始的投影数据映射到高维空间中,构造投影数据的高维表示,通过移动高维空间中的点来对高维表示进行更新,再使用偏微分方程对投影数据进行滤波,最后将恢复后的数据使用FBP算法重建出最终CT图像。结果在Shepp-Logan体模实验中,与FBP,PWLS-QM和TGV-WLS方法相比,新方法在相对均方根误差指标上分别降低了68.87%、50.15%和27.36%,结构相似性上分别提高了23.50%,8.83%和1.62%,特征相似性上分别提高了17.30%、2.71%和2.82%。在腹部临床数据实验中,与FBP,PWLS-QM和TGV-WLS方法相比,新方法在相对均方根误差中分别降低了42.09%、31.04%和21.93%,结构相似性上分别提高了18.33%、13.45%和4.63%,特征相似性上分别提高了3.13%、1.46%和1.10%。结论本研究提出的新方法在有效去除低剂量CT图像中的条形伪影和噪声的同时,可以保持图像的空间分辨率。

基于自适应神经网络的PDEs求解研究

针对当前基于神经网络的PDEs求解方法效率和精度均不够理想的缺陷,研究提出一种基于改进BP神经网络(BP neural network,BPNN)的PDEs求解模型。首先,参照自适应网格法来改进神经网络结构,构建自适应神经网络,改进模型的输出精度;其次,提出一种引入Levy飞行机制和鲸鱼优化算法(Whale optimization algorithm,WOA)的改进海鸥优化算法(Improved Seagull Optimization Algorithm,ISOA)来优化BPNN,寻找BPNN的最佳参数,提高模型的性能;基于上述内容,构建基于ISOA-BPNNPDEs智能求解模型。结果显示,该模型的F1值为95.74%,准确率达到97.96%,输出误差为0.021,优于当前最先进的两种PDEs求解模型。上述内容表明,研究构建的基于ISOA-BPNNPDEs智能求解模型能够高效、准确地实现PDEs求解,为PDEs求解研究提供了新的路径。

PDE4B专一性抑制剂选择性的起源

采用分子动力学模拟和结合自由能计算研究了PDE4B抑制剂选择性的起源.首先,探索了模拟时间、溶质介电常数、配体的电荷方案和结合自由能的计算方法对结合自由能预测值准确度的影响,确定最佳模拟条件为:模拟时间40~50 ns,溶质介电常数ε=2,采用MM/GBSA方法以及RESP配体电荷计算方案.接着,通过能量分解分析了抑制剂A33与PDE4B/PDE4D的相互作用,发现PDE4B酶上的Ile410、Gln443、Phe446和Phe506对抑制剂的选择性识别贡献较大.最后,通过位点突变方法探索了PDE4B的CR3螺旋上的Leu502残基对A33选择性所起的作用.当前的工作为设计高活性、高选择性的PDE4B抑制剂提供了有价值的结构与活性关系信息.

变分分数阶PDE的自适应图像保边缘去噪方法

为了优化图像去噪过程中的边缘保真问题,本文以ROF模型及其改进模型为基础,以分数阶变分偏微分方程方法为工具,通过构造自适应的边缘检测函数,提出了一种能更好地保护图像的边缘特征,有利于纹理细节保持和“阶梯效应”抑制的基于自适应分数阶变分PDE的图像去噪模型,并以标准图像测试了新模型的去噪效果。实验结果表明:与同类方法相比,新方法可以更加有效地提高图像的信噪比;从去噪前后的图像差可以看出,新方法在去噪的同时更好地保护了图像的边缘特征及纹理细节信息。文中提出的方法可以用于遥感成像、医学图像处理及地震图像处理等领域。

Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.

In-situ coating and surface partial protonation co-promoting performance of single-crystal nickel-rich cathode in all-solid-state batteries

The poor electrochemical performance of all-solid-state batteries(ASSBs),which is assemblied by Ni-rich cathode and poly(ethylene oxide)(PEO)-based electrolytes,can be attributed to unstable cathodic interface and poor crystal structure stability of Ni-rich cathode.Several coating strategies are previously employed to enhance the stability of the cathodic interface and crystal structure for Ni-rich cathode.However,these methods can hardly achieve simplicity and high efficiency simultaneously.In this work,polyacrylic acid(PAA)replaced traditional PVDF as a binder for cathode,which can achieve a uniform PAA-Li(LixPAA(0<x≤1))coating layer on the surface of single-crystal LiNi_(0.83)Co_(0.12)Mn_(0.05)O_(2)(SC-NCM83)due to H^(+)/Li^(+)exchange reaction during the initial charging-discharging process.The formation of PAA-Li coating layer on cathode can promote interfacial Li^(+)transport and enhance the stability of the cathodic interface.Furthermore,the partially-protonated surface of SC-NCM83 casued by H^(+)/Li^(+)exchange reaction can restrict Ni ions transport to enhance the crystal structure stability.The proposed SC-NCM83-PAA exhibits superior cycling performance with a retention of 92%compared with that(57.3%)of SC-NCM83-polyvinylidene difluoride(PVDF)after 200 cycles.This work provides a practical strategy to construct high-performance cathodes for ASSBs.

THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE

This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).

基于Matlab PDE工具箱的土体冻结温度场模拟研究

分析并运用Matlab PDE tool模拟模型槽土体冻结的温度场并验证模拟值的准确性。首先,通过合理的边界假设,使三维的模型槽土体冻结热传导问题转化为二维空间;然后,运用Matlab PDE tool进行模拟并对比测温点的模拟温度和实测温度。结果表明:土体冻结中温度场导热可以通过Matlab PDE tool模拟,且操作简单易于掌握;测温点模拟值的准确性与测温点距边界距离和冻结时间有关。

Identification of partial differential equations from noisy data with integrated knowledge discovery and embedding using evolutionary neural networks

Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge.Specifically,the proposed method combines gene expression programming,one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms,with symbolic regression neural networks.These networks are designed to represent explicit functional expressions and optimize them with data gradients.In particular,the specifically designed neural networks can be easily transformed to physical constraints for the training data,embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification.The proposed method has been tested in four canonical PDE cases,validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.

PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

Wetting alternating with partial drying during grain filling increases lysine biosynthesis in inferior rice grain

Lysine content is a criterion of the nutritional quality of rice.Understanding the process of lysine biosynthesis in early-flowering superior grain(SG)and late-flowering inferior grain(IG)of rice would advance breeding and cultivation to improve nutritional quality.However,little information is available on differences in lysine anabolism between SG and IG and the underlying mechanism,and whether and how irrigation regimes affect lysine anabolism in these grains.A japonica rice cultivar was grown in the field and two irrigation regimes,continuous flooding(CF)and wetting alternating with partial drying(WAPD),were imposed from heading to the mature stage.Lysine content and activities of key enzymes of lysine biosynthesis,and levels of brassinosteroids(BRs)were lower in the IG than in the SG at the early grainfilling stage but higher at middle and late grain-filling stages.WAPD increased activities of these key enzymes,BR levels,and contents of lysine and total amino acids in IG,but not SG relative to CF.Application of 2,4-epibrassinolide to rice panicles in CF during early grain filling reproduced the effects of WAPD,but neither treatment altered the activities of enzymes responsible for lysine catabolism in either SG or IG.WAPD and elevated BR levels during grain filling increased lysine biosynthesis in IG.Improvement in lysine biosynthesis in rice should focus on IG.

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

The state of in situ stress is a crucial parameter in subsurface engineering,especially for critical projects like nuclear waste repository.As one of the two ISRM suggested methods,the overcoring(OC)method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test.However,such customary independent analysis of individual OC tests,known as no pooling,is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method.To address this problem,a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests,which are usually available in OC measurement campaigns.Hence,this paper presents a Bayesian partial pooling(hierarchical)model for combined analysis of adjacent OC tests.We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden.The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests,and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling,particularly for those unreliable no pooling stress estimates.A further model comparison shows that the partial pooling model also gives better predictive performance,and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Preoperative albumin-bilirubin score and liver resection percentage determine postoperative liver regeneration after partial hepatectomy

BACKGROUND The success of liver resection relies on the ability of the remnant liver to regenerate.Most of the knowledge regarding the pathophysiological basis of liver regeneration comes from rodent studies,and data on humans are scarce.Additionally,there is limited knowledge about the preoperative factors that influence postoperative regeneration.AIM To quantify postoperative remnant liver volume by the latest volumetric software and investigate perioperative factors that affect posthepatectomy liver regenera-tion.METHODS A total of 268 patients who received partial hepatectomy were enrolled.Patients were grouped into right hepatectomy/trisegmentectomy(RH/Tri),left hepa-tectomy(LH),segmentectomy(Seg),and subsegmentectomy/nonanatomical hepatectomy(Sub/Non)groups.The regeneration index(RI)and late rege-neration rate were defined as(postoperative liver volume)/[total functional liver volume(TFLV)]×100 and(RI at 6-months-RI at 3-months)/RI at 6-months,respectively.The lower 25th percentile of RI and the higher 25th percentile of late regeneration rate in each group were defined as“low regeneration”and“delayed regeneration”.“Restoration to the original size”was defined as regeneration of the liver volume by more than 90%of the TFLV at 12 months postsurgery.RESULTS The numbers of patients in the RH/Tri,LH,Seg,and Sub/Non groups were 41,53,99 and 75,respectively.The RI plateaued at 3 months in the LH,Seg,and Sub/Non groups,whereas the RI increased until 12 months in the RH/Tri group.According to our multivariate analysis,the preoperative albumin-bilirubin(ALBI)score was an independent factor for low regeneration at 3 months[odds ratio(OR)95%CI=2.80(1.17-6.69),P=0.02;per 1.0 up]and 12 months[OR=2.27(1.01-5.09),P=0.04;per 1.0 up].Multivariate analysis revealed that only liver resection percentage[OR=1.03(1.00-1.05),P=0.04]was associated with delayed regeneration.Furthermore,multivariate analysis demonstrated that the preoperative ALBI score[OR=2.63(1.00-1.05),P=0.02;per 1.0 up]and liver resection percentage[OR=1.02(1.00-1.05),P=0.04;per 1.0 up]were found to be independent risk factors associated with volume restoration failure.CONCLUSION Liver regeneration posthepatectomy was determined by the resection percentage and preoperative ALBI score.This knowledge helps surgeons decide the timing and type of rehepatectomy for recurrent cases.

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.

A Cu-Pd alloy catalyst with partial phase separation for the electrochemical CO_(2) reduction reaction

Cu catalysts can convert CO_(2) through an electrochemical reduction reaction into a variety of useful carbon-based products.However,this capability provides an obstacle to increasing the selectivity for a single product.Herein,we report a simple fabrication method for a Cu-Pd alloy catalyst for use in a membrane electrode assembly(MEA)-based CO_(2) electrolyzer for the electrochemical CO_(2) reduction reaction(ECRR)with high selectivity for CO production.When the composition of the Cu-Pd alloy catalyst was fabricated at 6:4,the selectivity for CO increased and the production of multi-carbon compounds and hydrogen is suppressed.Introducing a Cu-Pd alloy catalyst with 6:4 ratio as the cathode of the MEAbased CO_(2) electrolyzer showed a CO faradaic efficiency of 92.8%at 2.4 V_(cell).We assumed that these results contributed from the crystal planes on the surface of the Cu-Pd alloy.The phases of the Cu-Pd alloy catalyst were partially separated through annealing to fabricate a catalyst with high selectivity for CO at low voltage and C_(2)H_4 at high voltage.The results of CO-stripping testing confirmed that when Cu partially separates from the lattice of the Cu-Pd alloy,the desorption of~*CO is suppressed,suggesting that C-C coupling reaction is favored.