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.

Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System

In order to improve the efficiency of the Ocean Variational Assimilation System （OVALS）, which has been widely used in various applications, an improved OVALS （OVALS2） is developed based on the recursive filter （RF） algorithm. The first advantage of OVALS2 is that memory storage can be substantially reduced in practice because it implicitly computes the background error covariance matrix; the second advantage is that there is no inversion of the background error covariance by preconditioning the control variable. For comparing the effectiveness between OVALS2 and OVALS, a set of experiments was implemented by assimilating expendable bathythermograph （XBT） and ARGO data into the Tropical Pacific circulation model. The results show that the efficiency of OVALS2 is much higher than that of OVALS. The computational time and the computer storage in the assimilation process were reduced by 83% and 77%, respectively. Additionally, the corresponding results produced by the RF are almost as good as those obtained by OVALS. These results prove that OVALS2 is suitable for operational numerical oceanic forecasting.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

Assimilation of Total Lightning Data Using the Three-Dimensional Variational Method at Convection-Allowing Resolution

A large number of observational analyses have shown that lightning data can be used to indicate areas of deep convection. It is important to assimilate observed lightning data into numerical models, so that more small-scale information can be incorporated to improve the quality of the initial condition and the subsequent forecasts. In this study, the empirical relationship between flash rate, water vapor mixing ratio, and graupel mixing ratio was used to adjust the model relative humidity, which was then assimilated by using the three-dimensional variational data assimilation system of the Weather Research and Forecasting model in cycling mode at 10-min intervals. To find the appropriate assimilation time-window length that yielded significant improvement in both the initial conditions and subsequent forecasts, four experiments with different assimilation time-window lengths were conducted for a squall line case that occurred on 10 July 2007 in North China. It was found that 60 min was the appropriate assimilation time-window length for this case, and longer assimilation window length was unnecessary since no further improvement was present. Forecasts of 1-h accumulated precipitation during the assimilation period and the subsequent 3-h accumulated precipitation were significantly improved compared with the control experiment without lightning data assimilation. The simulated reflectivity was optimal after 30 min of the forecast, it remained optimal during the following 42 min, and the positive effect from lightning data assimilation began to diminish after 72 min of the forecast. Overall,the improvement from lightning data assimilation can be maintained for about 3 h.

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 Sound Source Location Algorithm for Subsea Leakage Using Hydrophone

Leakages from subsea oil and gas equipment cause substantial economic losses and damage to marine ecosystem,so it is essential to locate the source of the leak.However,due to the complexity and variability of the marine environment,the signals collected by hydrophone contain a variety of noises,which makes it challenging to extract useful signals for localization.To solve this problem,a hydrophone denoising algorithm is proposed based on variational modal decomposition(VMD)with grey wolf optimization.First,the average envelope entropy is used as the fitness function of the grey wolf optimizer to find the optimal solution for the parameters K andα.Afterward,the VMD algorithm decomposes the original signal parameters to obtain the intrinsic mode functions(IMFs).Subsequently,the number of interrelationships between each IMF and the original signal was calculated,the threshold value was set,and the noise signal was removed to calculate the time difference using the valid signal obtained by reconstruction.Finally,the arrival time difference is used to locate the origin of the leak.The localization accuracy of the method in finding leaks is investigated experimentally by constructing a simulated leak test rig,and the effectiveness and feasibility of the method are verified.

Variational Reconstruction and Simulation Experiments of Sea Surface Wind Field for Ocean Data Buoy

The sea surface wind field is an important physical parameter in oceanography and meteorology.With the continuous refinement of numerical weather prediction,air-sea interface materials,energy exchange,and other studies,three-dimensional(3D)wind field distribution at local locations on the sea surface must be measured accurately.The current in-situ observation of sea surface wind parameters is mainly achieved through the installation of wind sensors on ocean data buoys.However,the results obtained from this single-point measurement method cannot reflect wind field distribution in a vertical direction above the sea surface.Thus,the present paper proposes a theoretical framework for the optimal inversion of the 3D wind field structure variation in the area where the buoy is located.The variation analysis method is first used to reconstruct the wind field distribution at different heights of the buoy,after which theoretical analysis verification and numerical simulation experiments are conducted.The results indicate that the use of variational methods to reconstruct 3D wind fields is significantly effective in eliminating disturbance errors in observations,which also verifies the correctness of the theoretical analysis of this method.The findings of this article can provide a reference for the layout optimization design of wind measuring instruments in buoy observation systems and also provide theoretical guidance for the design of new observation buoys in the future.

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.

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.

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.

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.

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems

The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem.

Variational Learned Talking-Head Semantic Coded Transmission System

Video transmission requires considerable bandwidth,and current widely employed schemes prove inadequate when confronted with scenes featuring prominently.Motivated by the strides in talkinghead generative technology,the paper introduces a semantic transmission system tailored for talking-head videos.The system captures semantic information from talking-head video and faithfully reconstructs source video at the receiver,only one-shot reference frame and compact semantic features are required for the entire transmission.Specifically,we analyze video semantics in the pixel domain frame-by-frame and jointly process multi-frame semantic information to seamlessly incorporate spatial and temporal information.Variational modeling is utilized to evaluate the diversity of importance among group semantics,thereby guiding bandwidth resource allocation for semantics to enhance system efficiency.The whole endto-end system is modeled as an optimization problem and equivalent to acquiring optimal rate-distortion performance.We evaluate our system on both reference frame and video transmission,experimental results demonstrate that our system can improve the efficiency and robustness of communications.Compared to the classical approaches,our system can save over 90%of bandwidth when user perception is close.

Variational Neural Inference Enhanced Text Semantic Communication System

Recently,deep learning-based semantic communication has garnered widespread attention,with numerous systems designed for transmitting diverse data sources,including text,image,and speech,etc.While efforts have been directed toward improving system performance,many studies have concentrated on enhancing the structure of the encoder and decoder.However,this often overlooks the resulting increase in model complexity,imposing additional storage and computational burdens on smart devices.Furthermore,existing work tends to prioritize explicit semantics,neglecting the potential of implicit semantics.This paper aims to easily and effectively enhance the receiver's decoding capability without modifying the encoder and decoder structures.We propose a novel semantic communication system with variational neural inference for text transmission.Specifically,we introduce a simple but effective variational neural inferer at the receiver to infer the latent semantic information within the received text.This information is then utilized to assist in the decoding process.The simulation results show a significant enhancement in system performance and improved robustness.

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.

Computed tomography three-dimensional reconstruction in the diagnosis of bleeding small intestinal polyps:A case report

BACKGROUND Computed tomography(CT)small bowel three-dimensional(3D)reconstruction is a powerful tool for the diagnosis of small bowel disease and can clearly show the intestinal lumen and wall as well as the outside structure of the wall.The horizontal axis position can show the best adjacent intestinal tube and the lesion between the intestinal tubes,while the coronal position can show the overall view of the small bowel.The ileal end of the localization of the display of excellent,and easy to quantitative measurement of the affected intestinal segments,the sagittal position for the rectum and the pre-sacral lesions show the best,for the discovery of fistulae is also helpful.Sagittal view can show rectal and presacral lesions and is useful for fistula detection.It is suitable for the assessment of inflammatory bowel disease,such as assessment of disease severity and diagnosis and differential diagnosis of the small bowel and mesenteric space-occupying lesions as well as the judgment of small bowel obstruction points.CASE SUMMARY Bleeding caused by small intestinal polyps is often difficult to diagnose in clinical practice.This study reports a 29-year-old male patient who was admitted to the hospital with black stool and abdominal pain for 3 months.Using the combination of CT-3D reconstruction and capsule endoscopy,the condition was diagnosed correctly,and the polyps were removed using single-balloon enteroscopyendoscopic retrograde cholangiopancreatography without postoperative complications.CONCLUSION The role of CT-3D in gastrointestinal diseases was confirmed.CT-3D can assist in the diagnosis and treatment of gastrointestinal diseases in combination with capsule endoscopy and small intestinal microscopy.

Research on Quantitative Identification of Three-Dimensional Connectivity of Fractured-Vuggy Reservoirs

The fractured-vuggy carbonate oil resources in the western basin of China are extremely rich.The connectivity of carbonate reservoirs is complex,and there is still a lack of clear understanding of the development and topological structure of the pore space in fractured-vuggy reservoirs.Thus,effective prediction of fractured-vuggy reservoirs is difficult.In view of this,this work employs adaptive point cloud technology to reproduce the shape and capture the characteristics of a fractured-vuggy reservoir.To identify the complex connectivity among pores,fractures,and vugs,a simplified one-dimensional connectivity model is established by using the meshless connection element method(CEM).Considering that different types of connection units have different flow characteristics,a sequential coupling calculation method that can efficiently calculate reservoir pressure and saturation is developed.By automatic history matching,the dynamic production data is fitted in real-time,and the characteristic parameters of the connection unit are inverted.Simulation results show that the three-dimensional connectivity model of the fractured-vuggy reservoir built in this work is as close as 90%of the fine grid model,while the dynamic simulation efficiency is much higher with good accuracy.

Application of three-dimensional speckle tracking technique in measuring left ventricular myocardial function in patients with diabetes

BACKGROUND Diabetic cardiomyopathy is considered as a chronic complication of diabetes mellitus(DM).Therefore,early detection of left ventricular systolic function(LVSF)damage in DM is essential.AIM To explore the use of the three-dimensional speckle tracking technique(3D-STI)for measuring LVSF in DM patients via meta-analysis.METHODS The electronic databases were retrieved from the initial accessible time to 29 April 2023.The current study involved 9 studies,including 970 subjects.We carried out this meta-analysis to estimate myocardial function in DM compared with controls according to myocardial strain attained by 3D-STI.RESULTS Night articles including 970 subjects were included.No significant difference was detected in the left ventricular ejection fraction between the control and the diabetic group(P>0.05),while differences in global longitudinal strain,global circumferential strain,global radial strain,and global area strain were markedly different between the controls and DM patients(all P<0.05).CONCLUSION The 3D-STI could be applied to accurately measure early LVSF damage in patients with DM.