Multi-slice Spiral CT Three-dimensional Portography in Portal Vein Tumor Thrombus of Hepatic Cancer

Objective: To study the clinical significance of multi-slice spiral CT 3-dimensional (3D) portography in portal vein tumor thrombosis of hepatocellular cacinoma.Methods: 57 cases undergoing 3D portography were collected, of which 6 cases were normal, 5 cases were subjected to cirrhosis and hypertension of portal vein, 42 cases had portal tumor thrombus of hepatic cancer, and the remaining 4 cases showed lymph node enlargment in hilar of liver. All data of the patients came from conventional multi-slice spiral CT double phase of liver. Contrast media was 1.5–2 ml/kg with the injection rate being 2.5–3 ml/s. Axis and 3D portography was analyzed and compared in 42 cases of portal tumor thrombus of hepatic cancer.Results: According to portal tumor thrombus position, 42 cases were fallen into three categories: left (13 cases), right (20 cases), main (9 cases) of potal vein. There was no difference between axis and 3D portography in displaying portal tumor thrombus of hepatic cancer (P>0.05), but 3D portography showing collateral branches was better than axis portography after main portal vein thrombus.Conclusion: Multi-slice spiral CT 3D portography can display the position and types of portal tumor thrombus of hepatic cancer. 3D combined with axis portography can better evaluate the portal tumor thrombus of hepatic cancer and guide to select the therapies. Key words portal vein - tumor thrombus - multi-slice CT - 3 dimension imaging

Large Time Behavior of Solutions for General Navier-Stokes Systems in Multi-Dimension

Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in several space dimensions.

Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.

Hausdorff Dimension of Multi-Layer Neural Networks

This elucidation investigates the Hausdorff dimension of the output space of multi-layer neural networks. When the factor map from the covering space of the output space to the output space has a synchronizing word, the Hausdorff dimension of the output space relates to its topological entropy. This clarifies the geometrical structure of the output space in more details.

Multi-state Information Dimension Reduction Based on Particle Swarm Optimization-Kernel Independent Component Analysis

The precision of the kernel independent component analysis( KICA) algorithm depends on the type and parameter values of kernel function. Therefore,it's of great significance to study the choice method of KICA's kernel parameters for improving its feature dimension reduction result. In this paper, a fitness function was established by use of the ideal of Fisher discrimination function firstly. Then the global optimal solution of fitness function was searched by particle swarm optimization( PSO) algorithm and a multi-state information dimension reduction algorithm based on PSO-KICA was established. Finally,the validity of this algorithm to enhance the precision of feature dimension reduction has been proven.

Multi-dimensional scattering properties diagnosis system of scale aircraft model in an anechoic chamber

Aiming at the concept of ＂diagnosis＂, a simple and effective broadband radar cross section （RCS） measurement system is constructed, and some multi-dimensional scattering properties diagnosis techniques are presented based on the system. Firstly, a stepped-frequency signal is employed to achieve high range resolution, combining with a variety of signal processing tech- niques. Secondly, cross-range resolution is gained with a rotating table, and the high-resolution two-dimensional （2-D） imaging of the scale model is obtained by the microwave imaging theory. Finally, two receiving antennas with a small distance in altitude are used, and the three-dimensional （3-D） height distribution of scattering points on the scale model is extracted from the phase of images. Some typical bodies and a scale aircraft model are diagnosed in an anechoic chamber. The experimental results show that, after scaling with a metal sphere, the accurate one- dimensional （l-D） RCS pattern of the model is obtained, and it has a large dynamic range. When the bandwidth of the transmitting signal is 4 GHz, the resolution of the 2-D image can reach to 0.037 5 m. The 3-D height distribution of scattering points is given by interferometric measurement. This paper provides a feasible way to obtain high-precision scattering properties parameters of the scale aircraft model in a conventional rectangular anechoic chamber.

ON MULTI-DIMENSIONAL SONIC-SUBSONIC FLOW

In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional （n ≥ 2） Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy Hloc^-1（Ω） compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional （n ≥ 2） Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension （n ≥ 3）.

Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise

Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.

MSSTNet:Multi-scale facial videos pulse extraction network based on separable spatiotemporal convolution and dimension separable attention

Background The use of remote photoplethysmography(rPPG)to estimate blood volume pulse in a noncontact manner has been an active research topic in recent years.Existing methods are primarily based on a singlescale region of interest(ROI).However,some noise signals that are not easily separated in a single-scale space can be easily separated in a multi-scale space.Also,existing spatiotemporal networks mainly focus on local spatiotemporal information and do not emphasize temporal information,which is crucial in pulse extraction problems,resulting in insufficient spatiotemporal feature modelling.Methods Here,we propose a multi-scale facial video pulse extraction network based on separable spatiotemporal convolution(SSTC)and dimension separable attention(DSAT).First,to solve the problem of a single-scale ROI,we constructed a multi-scale feature space for initial signal separation.Second,SSTC and DSAT were designed for efficient spatiotemporal correlation modeling,which increased the information interaction between the long-span time and space dimensions;this placed more emphasis on temporal features.Results The signal-to-noise ratio(SNR)of the proposed network reached 9.58dB on the PURE dataset and 6.77dB on the UBFC-rPPG dataset,outperforming state-of-the-art algorithms.Conclusions The results showed that fusing multi-scale signals yielded better results than methods based on only single-scale signals.The proposed SSTC and dimension-separable attention mechanism will contribute to more accurate pulse signal extraction.

Analysis of Multi-Scale Fractal Dimension for Image Interpolation

This article presents a novel image interpolation based on rational fractal fimction. The rational function has a simple and explicit expression. At the same time, the fi＇actal interpolation surface can be defined by proper parameters. In this paper, we used the method of ＇covering blanket＇ combined with multi-scale analysis; the threshold is selected based on the multi-scale analysis. Selecting different parameters in the rational function model, the texture regions and smooth regions are interpolated by rational fractal interpolation and rational interpolation respectively. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance compared with the state-of-the-art interpolation algorithms, especially in image details and texture features.

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.

Scalable Temporal Dimension Preserved Tensor Completion for Missing Traffic Data Imputation With Orthogonal Initialization

Dear Editor,This letter puts forward a novel scalable temporal dimension preserved tensor completion model based on orthogonal initialization for missing traffic data(MTD)imputation.The MTD imputation acts directly on accessing the traffic state,and affects the traffic management.

Multi-Scale X-Ray Imaging Technologies for Rechargeable Batteries

The rapid advancement in electric vehicles and electrochemical energy storage technology has raised the demands placed on rechargeable batteries.It is essential to comprehend the operational principles and degradation mechanisms of batteries across multiple scales to propel the research on rechargeable batteries for the next generation forward.Microstructure,phase information,and lattice of energy materials in both two dimensions and three dimensions can be intuitively obtained through the utilization of x-ray imaging techniques.Additionally,x-ray imaging technology is increasingly gaining attention due to its non-destructive nature and high penetrative capability,enabling in situ experiments and multi-scale spatial resolution.In this review,we initially overview the basic principles and characteristics of several key x-ray imaging technologies.Each x-ray imaging technology is tailored to specific application scenarios.Furthermore,examples of multi-scale implementations of x-ray imaging technologies in the field of rechargeable batteries are discussed.This review is anticipated to augment the comprehension of readers for x-ray imaging techniques as well as to stimulate the development of novel concepts and approaches in rechargeable battery research.

Publisher’s Note:“Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions”[Matter Radiat.Extremes 9, 067802 (2024)]

This article was originally published online on 30 August 2024.Due to a production error,as originally published the author list was not in its intended order.All online versions of this article were corrected on 9 September 2024 and it appears correctly in print.AIP Publishing apologizes for this error.

Three-dimensional Model Analysis of Electric Field Excited by Multi-circuit Intersecting Overhead Transmission Lines

This work is carried out to predict the special distribution of electric field induced by multi-circuit intersecting overhead high-voltage (HV) transmission lines (TLs) within a large range without any expensive and time-consuming computation. The two main parts of the presented methodology are 1) setting up a three-dimensional (3D) model to calculate the electric field based on combining ca- tenary equations with charge simulation method and 2) calculating the hybrid electric field excited by multi-circuit intersecting TLs using coordinate transformation and superposition technique. Examples of different TLs configurations, including a 220 kV single-circuit hori- zontally configured TLs, a 500 kV single-circuit triangularly configured TLs and a combination of the 220 kV TLs and the 550 kV TLs, are illustrated to verify the validity of this methodology. A more complicatal configurations, including a 500 kV double-circuit TLs and two 220 kV single-circuit horizontally configured TLs, are also calculated. Conclusions were drawn from the simulation: 1) The presented 3D model outperforms 2D models in describing the electric field distribution generated by practical HV TLs with sag and span. 2) Coordinate trans- formation and superposition technique considerably simplify the electric field computation for multi-circuit TLs configurations, which makes it possible to deal with complex engineering problems. 3) The electric field in the area covered by multiple intersecting overhead TLs is distorted and the hybrid electric field strength in some partial region increases so sharply that it might exceed the admissible value. 4) The configuration parameters of the TLs and the spatial configuration of multi-circuit TLs, for instance, the height of TLs, the length of span and the intersection angle of multiple circuits, influence the strength and the distribution of hybrid electric field. The influence regularities sum- marized in this paper can be referred by future TL designs to meet the electromagnetic environmental protection regulations.

Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions

We study radiative transfer in participating binary stochastic mixtures in two dimensions(2D)by developing an accurate and efficient simulation tool.For two different sets of physical parameters,2D benchmark results are presented,and it is found that the influence of the stochastic mixture on radiative transfer is clearly parameter-dependent.Our results confirm that previous multidimensional results obtained in different studies are basically consistent,which is interpreted in terms of the relationship between the photon mean free path l_(p)and the system size L.Nonlinear effects,including those due to scattering and radiation-material coupling,are also discussed.To further understand the particle size effect,we employ a dimensionless parameter l_(p)/L,from which a critical particle size can be derived.On the basis of further 2D simulations,we find that an inhomogeneous mix is obtained for l_(p)/L>0.1.Furthermore,2D material temperature distributions reveal that self-shielding and particle-particle shielding of radiation occur,and are enhanced when l_(p)/L is increased.Our work is expected to provide benchmark results to verify proposed homogenized models and/or other codes for stochastic radiative transfer in realistic physical scenarios.

An Exploration of the Three Dimensions and Epochal Strengths of Building a Human Community With a Shared Future

The idea of a human community with a shared future was proposed by the Communist Party of China(CPC)Central Committee with Comrade Xi Jinping at its core for the future development of human beings to face up to the most important question in today's world:“What is happening to the world and what should we do?”It profoundly answers the question of the world,history,and the times.The theory of a human community with a shared future is an innovative theory with a multidimensional formation logic that guides humanity toward continually seeking common interests and values.This paper dives into the profound motivations behind building a human community with a shared future from historical,cultural,and practical dimensions and analyzes its epochal value from both domestic and international perspectives.This not only helps exert China's role in the international community,contributing Chinese strength to the construction of a peaceful,stable,and prosperous human society,but also enhances the influence of the idea of a human community with a shared future in the international community,accelerating the building of a human community with a shared future that considers the legitimate concerns of all countries,and aiding in solving the crises facing the world.

Hausdorff Dimension of Range and Graph for General Markov Processes

We establish the Hausdorff dimension of the graph of general Markov processes on Rd based on some probability estimates of the processes staying or leaving small balls in small time.In particular,our results indicate that,for symmetric diffusion processes(withα=2)or symmetricα-stable-like processes(withα∈(0,2))on Rd,it holds almost surely that dimH GrX([0,1])=1{α<1}+(2−1/α)1{α≥1,d=1}+(d∧α)1{α≥1,d≥2}.We also systematically prove the corresponding results about the Hausdorff dimension of the range of the processes.

Multi-dimension Aspiration Control Mode in Phacoemulsification

Purpose: Multi-dimension aspiration control mode was put forward in this study.Accuracy of multi-dimension aspiration control model was compared to simple traditional pedal control model.Methods: Induced by high aspiration pressure (200～250 mmHg), hard nucleus (≥Grade Ⅲ ) of senile cataract was chopped before phacoemulsification in 170 patients (174 eyes). Ninety-one patients (94 eyes) accepted multi-dimension aspiration control model in which aspiration direction, distance and targets prevention were adjusted by phaco-tip besides traditional pedal control. Another 79 patients (80 eyes) were compared as reviewed group, aspiration of which was controlled simply by traditional pedal control. Postcapsular rupture rates (PCRR) were compared between two groups.Results: Multi-dimension control model could make the terminal effects cooperate with phacoemulsification more precisely and protect post capsular from damage (x2 =5.41, P ＜ 0.02).Conclusion: Multi-dimension control model could improve the accuracy of aspiration effects and protect postcapsular from damage.

Multi-surrogate framework with an adaptive selection mechanism for production optimization

Data-driven surrogate models that assist with efficient evolutionary algorithms to find the optimal development scheme have been widely used to solve reservoir production optimization problems.However,existing research suggests that the effectiveness of a surrogate model can vary depending on the complexity of the design problem.A surrogate model that has demonstrated success in one scenario may not perform as well in others.In the absence of prior knowledge,finding a promising surrogate model that performs well for an unknown reservoir is challenging.Moreover,the optimization process often relies on a single evolutionary algorithm,which can yield varying results across different cases.To address these limitations,this paper introduces a novel approach called the multi-surrogate framework with an adaptive selection mechanism(MSFASM)to tackle production optimization problems.MSFASM consists of two stages.In the first stage,a reduced-dimensional broad learning system(BLS)is used to adaptively select the evolutionary algorithm with the best performance during the current optimization period.In the second stage,the multi-objective algorithm,non-dominated sorting genetic algorithm II(NSGA-II),is used as an optimizer to find a set of Pareto solutions with good performance on multiple surrogate models.A novel optimal point criterion is utilized in this stage to select the Pareto solutions,thereby obtaining the desired development schemes without increasing the computational load of the numerical simulator.The two stages are combined using sequential transfer learning.From the two most important perspectives of an evolutionary algorithm and a surrogate model,the proposed method improves adaptability to optimization problems of various reservoir types.To verify the effectiveness of the proposed method,four 100-dimensional benchmark functions and two reservoir models are tested,and the results are compared with those obtained by six other surrogate-model-based methods.The results demonstrate that our approach can obtain the maximum net present value(NPV)of the target production optimization problems.