A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.

Three-Dimensional Space Interpolation of Grey / Depth Image Sequence-A New Technique of Computer Graphics Synthesis

This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.

Three-Dimensional Generalized Inverse Matrix Rational Interpolation

In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.

Three-Dimensional Modeling of the Retinal Vascular Tree via Fractal Interpolation

In recent years,the three dimensional reconstruction of vascular structures in the field of medical research has been extensively developed.Several studies describe the various numerical methods to numerical modeling of vascular structures in near-reality.However,the current approaches remain too expensive in terms of storage capacity.Therefore,it is necessary to find the right balance between the relevance of information and storage space.This article adopts two sets of human retinal blood vessel data in 3D to proceed with data reduction in the first part and then via 3D fractal reconstruction,recreate them in a second part.The results show that the reduction rate obtained is between 66%and 95%as a function of the tolerance rate.Depending on the number of iterations used,the 3D blood vessel model is successful at reconstruction with an average error of 0.19 to 5.73 percent between the original picture and the reconstructed image.

A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

Three-dimensional cell-based strategies for liver regeneration

Liver regeneration and the development of effective therapies for liver failure remain formidable challenges in modern medicine.In recent years,the utilization of 3D cell-based strategies has emerged as a promising approach for addressing these urgent clinical requirements.This review provides a thorough analysis of the application of 3D cell-based approaches to liver regeneration and their potential impact on patients with end-stage liver failure.Here,we discuss various 3D culture models that incorporate hepatocytes and stem cells to restore liver function and ameliorate the consequences of liver failure.Furthermore,we explored the challenges in transitioning these innovative strategies from preclinical studies to clinical applications.The collective insights presented herein highlight the significance of 3D cell-based strategies as a transformative paradigm for liver regeneration and improved patient care.

The combined application of stem cells and three-dimensional bioprinting scaffolds for the repair of spinal cord injury

Spinal cord injury is considered one of the most difficult injuries to repair and has one of the worst prognoses for injuries to the nervous system.Following surgery,the poor regenerative capacity of nerve cells and the generation of new scars can make it very difficult for the impaired nervous system to restore its neural functionality.Traditional treatments can only alleviate secondary injuries but cannot fundamentally repair the spinal cord.Consequently,there is a critical need to develop new treatments to promote functional repair after spinal cord injury.Over recent years,there have been seve ral developments in the use of stem cell therapy for the treatment of spinal cord injury.Alongside significant developments in the field of tissue engineering,three-dimensional bioprinting technology has become a hot research topic due to its ability to accurately print complex structures.This led to the loading of three-dimensional bioprinting scaffolds which provided precise cell localization.These three-dimensional bioprinting scaffolds co uld repair damaged neural circuits and had the potential to repair the damaged spinal cord.In this review,we discuss the mechanisms underlying simple stem cell therapy,the application of different types of stem cells for the treatment of spinal cord injury,and the different manufa cturing methods for three-dimensional bioprinting scaffolds.In particular,we focus on the development of three-dimensional bioprinting scaffolds for the treatment of spinal cord injury.

Suitable region of dynamic optimal interpolation for efficiently altimetry sea surface height mapping

The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).

Research on Interpolation Method for Missing Electricity Consumption Data

Missing value is one of the main factors that cause dirty data.Without high-quality data,there will be no reliable analysis results and precise decision-making.Therefore,the data warehouse needs to integrate high-quality data consistently.In the power system,the electricity consumption data of some large users cannot be normally collected resulting in missing data,which affects the calculation of power supply and eventually leads to a large error in the daily power line loss rate.For the problem of missing electricity consumption data,this study proposes a group method of data handling(GMDH)based data interpolation method in distribution power networks and applies it in the analysis of actually collected electricity data.First,the dependent and independent variables are defined from the original data,and the upper and lower limits of missing values are determined according to prior knowledge or existing data information.All missing data are randomly interpolated within the upper and lower limits.Then,the GMDH network is established to obtain the optimal complexity model,which is used to predict the missing data to replace the last imputed electricity consumption data.At last,this process is implemented iteratively until the missing values do not change.Under a relatively small noise level(α=0.25),the proposed approach achieves a maximum error of no more than 0.605%.Experimental findings demonstrate the efficacy and feasibility of the proposed approach,which realizes the transformation from incomplete data to complete data.Also,this proposed data interpolation approach provides a strong basis for the electricity theft diagnosis and metering fault analysis of electricity enterprises.

Development of a toroidal soft x-ray imaging system and application for investigating three-dimensional plasma on J-TEXT

A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and located on the vacuum chamber wall at toroidal positionsφof 126.4°and 272.6°,respectively,while one set was established previously atφ=65.50.Each set of SXR arrays consists of three arrays viewing the plasma poloidally,and hence can be used separately to obtain SXR images via the tomographic method.The sawtooth precursor oscillations are measured by T-SXRI,and the corresponding images of perturbative SXR signals are successfully reconstructed at these three toroidal positions,hence providing measurement of the 3D structure of precursor oscillations.The observed 3D structure is consistent with the helical structure of the m/n=1/1 mode.The experimental observation confirms that the T-SXRI system is able to observe 3D structures in the J-TEXT plasma.

Intraoperative application of three-dimensional printed guides in total hip arthroplasty: A systematic review

BACKGROUND Acetabular component positioning in total hip arthroplasty(THA)is of key importance to ensure satisfactory post-operative outcomes and to minimize the risk of complications.The majority of acetabular components are aligned freehand,without the use of navigation methods.Patient specific instruments(PSI)and three-dimensional(3D)printing of THA placement guides are increasingly used in primary THA to ensure optimal positioning.AIM To summarize the literature on 3D printing in THA and how they improve acetabular component alignment.METHODS PubMed was used to identify and access scientific studies reporting on different 3D printing methods used in THA.Eight studies with 236 hips in 228 patients were included.The studies could be divided into two main categories;3D printed models and 3D printed guides.RESULTS 3D printing in THA helped improve preoperative cup size planning and post-operative Harris hip scores between intervention and control groups(P=0.019,P=0.009).Otherwise,outcome measures were heterogeneous and thus difficult to compare.The overarching consensus between the studies is that the use of 3D guidance tools can assist in improving THA cup positioning and reduce the need for revision THA and the associated costs.CONCLUSION The implementation of 3D printing and PSI for primary THA can significantly improve the positioning accuracy of the acetabular cup component and reduce the number of complications caused by malpositioning.

Integer multiple quantum image scaling based on NEQR and bicubic interpolation

As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

Computer-assisted three-dimensional individualized extreme liver resection for hepatoblastoma in proximity to the major liver vasculature

BACKGROUND The management of hepatoblastoma(HB)becomes challenging when the tumor remains in close proximity to the major liver vasculature(PMV)even after a full course of neoadjuvant chemotherapy(NAC).In such cases,extreme liver resection can be considered a potential option.AIM To explore whether computer-assisted three-dimensional individualized extreme liver resection is safe and feasible for children with HB who still have PMV after a full course of NAC.METHODS We retrospectively collected data from children with HB who underwent surgical resection at our center from June 2013 to June 2023.We then analyzed the detailed clinical and three-dimensional characteristics of children with HB who still had PMV after a full course of NAC.RESULTS Sixty-seven children diagnosed with HB underwent surgical resection.The age at diagnosis was 21.4±18.8 months,and 40 boys and 27 girls were included.Fifty-nine(88.1%)patients had a single tumor,39(58.2%)of which was located in the right lobe of the liver.A total of 47 patients(70.1%)had PRE-TEXT III or IV.Thirty-nine patients(58.2%)underwent delayed resection.After a full course of NAC,16 patients still had close PMV(within 1 cm in two patients,touching in 11 patients,compressing in four patients,and showing tumor thrombus in three patients).There were 6 patients of tumors in the middle lobe of the liver,and four of those patients exhibited liver anatomy variations.These 16 children underwent extreme liver resection after comprehensive preoperative evaluation.Intraoperative procedures were performed according to the preoperative plan,and the operations were successfully performed.Currently,the 3-year event-free survival of 67 children with HB is 88%.Among the 16 children who underwent extreme liver resection,three experienced recurrence,and one died due to multiple metastases.CONCLUSION Extreme liver resection for HB that is still in close PMV after a full course of NAC is both safe and feasible.This approach not only reduces the necessity for liver transplantation but also results in a favorable prognosis.Individualized three-dimensional surgical planning is beneficial for accurate and complete resection of HB,particularly for assessing vascular involvement,remnant liver volume and anatomical variations.

Three-dimensional numerical analysis of plant-soil hydraulic interactions on pore water pressure of vegetated slope under different rainfall patterns

Understanding the pore water pressure distribution in unsaturated soil is crucial in predicting shallow landslides triggered by rainfall,mainly when dealing with different temporal patterns of rainfall intensity.However,the hydrological response of vegetated slopes,especially three-dimensional(3D)slopes covered with shrubs,under different rainfall patterns remains unclear and requires further investigation.To address this issue,this study adopts a novel 3D numerical model for simulating hydraulic interactions between the root system of the shrub and the surrounding soil.Three series of numerical parametric studies are conducted to investigate the influences of slope inclination,rainfall pattern and rainfall duration.Four rainfall patterns(advanced,bimodal,delayed,and uniform)and two rainfall durations(4-h intense and 168-h mild rainfall)are considered to study the hydrological response of the slope.The computed results show that 17%higher transpiration-induced suction is found for a steeper slope,which remains even after a short,intense rainfall with a 100-year return period.The extreme rainfalls with advanced(PA),bimodal(PB)and uniform(PU)rainfall patterns need to be considered for the short rainfall duration(4 h),while the delayed(PD)and uniform(PU)rainfall patterns are highly recommended for long rainfall durations(168 h).The presence of plants can improve slope stability markedly under extreme rainfall with a short duration(4 h).For the long duration(168 h),the benefit of the plant in preserving pore-water pressure(PWP)and slope stability may not be sufficient.

Influence of sampling on three-dimensional surface shape measurement

In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.

Three-dimensional visualization technology for guiding one-step percutaneous transhepatic cholangioscopic lithotripsy for the treatment of complex hepatolithiasis

BACKGROUND Biliary stone disease is a highly prevalent condition and a leading cause of hospitalization worldwide.Hepatolithiasis with associated strictures has high residual and recurrence rates after traditional multisession percutaneous transhepatic cholangioscopic lithotripsy(PTCSL).AIM To study one-step PTCSL using the percutaneous transhepatic one-step biliary fistulation(PTOBF)technique guided by three-dimensional(3D)visualization.METHODS This was a retrospective,single-center study analyzing,140 patients who,between October 2016 and October 2023,underwent one-step PTCSL for hepatolithiasis.The patients were divided into two groups:The 3D-PTOBF group and the PTOBF group.Stone clearance on choledochoscopy,complications,and long-term clearance and recurrence rates were assessed.RESULTS Age,total bilirubin,direct bilirubin,Child-Pugh class,and stone location were similar between the 2 groups,but there was a significant difference in bile duct strictures,with biliary strictures more common in the 3D-PTOBF group(P=0.001).The median follow-up time was 55.0(55.0,512.0)days.The immediate stone clearance ratio(88.6%vs 27.1%,P=0.000)and stricture resolution ratio(97.1%vs 78.6%,P=0.001)in the 3D-PTOBF group were significantly greater than those in the PTOBF group.Postoperative complication(8.6%vs 41.4%,P=0.000)and stone recurrence rates(7.1%vs 38.6%,P=0.000)were significantly lower in the 3D-PTOBF group.CONCLUSION Three-dimensional visualization helps make one-step PTCSL a safe,effective,and promising treatment for patients with complicated primary hepatolithiasis.The perioperative and long-term outcomes are satisfactory for patients with complicated primary hepatolithiasis.This minimally invasive method has the potential to be used as a substitute for hepatobiliary surgery.

Three-dimensional stability calculation method for high and large composite slopes formed by mining stope and inner dump in adjacent open pits

The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.

Study of three-dimensional spatial diffuse discharge in contact electrode structure applied to air purification

In this work,based on the role of pre-ionization of the non-uniform electric field and its effect of reducing the collisional ionization coefficient,a diffuse dielectric barrier discharge plasma is formed in the open space outside the electrode structure at a lower voltage by constructing a three-dimensional non-uniform spatial electric field using a contact electrode structure.The air purification study is also carried out.Firstly,a contact electrode structure is constructed using a three-dimensional wire electrode.The distribution characteristics of the spatial electric field formed by this electrode structure are analyzed,and the effects of the non-uniform electric field and the different angles of the vertical wire on the generation of three-dimensional spatial diffuse discharge are investigated.Secondly,the copper foam contact electrode structure is constructed using copper foam material,and the effects of different mesh sizes on the electric field distribution are analyzed.The results show that as the mesh size of the copper foam becomes larger,a strong electric field region exists not only on the surface of the insulating layer,but also on the surface of the vertical wires inside the copper foam,i.e.,the strong electric field region shows a three-dimensional distribution.Besides,as the mesh size increases,the area of the vertical strong electric field also increases.However,the electric field strength on the surface of the insulating layer gradually decreases.Therefore,the appropriate mesh size can effectively increase the discharge area,which is conducive to improving the air purification efficiency.Finally,a highly permeable stacked electrode structure of multilayer wire-copper foam is designed.In combination with an ozone treatment catalyst,an air purification device is fabricated,and the air purification experiment is carried out.

Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.