Internal Edge Research Articles

Clade Size Statistics Under Ford’s α-Model

Given a labeled tree topology t of n taxa, consider a population P of k leaves chosen among those of t. The clade of P is the minimal subtree P^ of t containing P, and its size |P^| is provided by the number of leaves in the clade. We study distributive properties of the clade size variable |P^| considered over labeled topologies of size n generated at random in the framework of Ford’s α-model. Under this model, starting from the one-taxon labeled topology, a random labeled topology is produced iteratively by a sequence of α-insertions, each of which adds a pendant edge to either a pendant or internal edge of a labeled topology, with a probability that depends on the parameter α∈[0,1]. Different values of α determine different probability distributions over the set of labeled topologies of given size n, with the special cases α=0 and α=1/2 respectively corresponding to the Yule and uniform distributions. In the first part of the manuscript, we consider a labeled topology t of size n generated by a sequence of random α-insertions starting from a fixed labeled topology t∗ of given size k, and determine the probability mass function, mean, and variance of the clade size |P^| in t when P is chosen as the set of leaves of t inherited from t∗. In the second part of the paper, we calculate the probability that a set P of k leaves chosen at random in a Ford-distributed labeled topology of size n is monophyletic, that is, the probability that |P^|=k. Our investigations extend previous results on clade size statistics obtained for Yule and uniformly distributed labeled topologies.

Discrimination Model Construction for Non-Lactational Mastitis and Breast Cancer Based on Imaging Features.

Aims/Background The clinical presentation of non-lactational mastitis (NLM) shares similarities with some symptoms and examination results of breast cancer (BC), which can lead to misdiagnosis or delayed treatment. Current studies on breast lesions mostly focus on the diagnostic performance of a single imaging technique. This study aims to construct a discrimination diagnostic model for NLM and BC based on such imaging features as ultrasound and magnetic resonance imaging (MRI) and to validate the application value of the model, assisting clinicians in improving disease diagnosis and refining medical decisions. Methods This study is a retrospective analysis. Clinical data of 108 patients suspected of NLM based on imaging diagnosis, admitted to The First Affiliated Hospital with Nanjing Medical University between May 2018 and August 2023, were collected. Among them, 94 cases were pathologically confirmed as NLM and 14 cases as BC. Univariate and multivariate logistic regression analyses were performed on the patients' clinical data, ultrasound features, and MRI features to select the risk factors for discriminating NLM and BC, and construct a discrimination model. The discrimination performance of the model was analyzed with the receiver operating characteristic (ROC) curve, decision curve analysis (DCA), and calibration curve. Results In the NLM group, there were 24 cases of granulomatous lobular mastitis (25.53%) and 70 cases of plasma cell mastitis (74.47%). In the BC group, there were 2 cases of infiltrating ductal carcinoma, 2 cases of atypical hyperplasia, 3 cases of papillary carcinoma, and 7 cases of ductal carcinoma in situ. Age, internal blood flow, calcification, edge, enhancement characteristics, apparent diffusion coefficient (ADC) values, and time-intensity curve (TIC) type were independent factors for differentiating NLM and BC (p < 0.05). The ROC analysis showed that the area under the curve of the model for discriminating NLM and BC was 0.920. The DCA results showed that the model had high net benefits for discriminating NLM and BC. The calibration curve analysis showed that the model had good consistency with the actual diagnosis of NLM and BC, with a chi-square value of 4.545 and a p-value of 0.155 according to the Hosmer-Lemeshow test. Conclusion Age, internal blood flow, calcification, edge, enhancement characteristics, ADC, and TIC curve types are important factors in distinguishing NLM and BC, and the model based on the above characteristics to distinguish NLM and BC has a high net benefit in distinguishing the two.

MHD stability analysis against pressure and current-driven modes in the SMall Aspect Ratio Tokamak

Abstract Linear magnetohydrodynamic (MHD) simulations for the SMall Aspect Ratio Tokamak (SMART) have been carried out for the first time, for both positive (PT) and negative triangularity (NT) shaped plasmas using the MARS-F code. The MHD stability of projected SMART plasmas against internal kinks, infernal modes and edge peeling-ballooning modes have been analyzed for a wide range of realistic equilibria. A stabilization of internal kinks and infernal modes is observed when increasing the safety factor profile and reducing plasma beta. PT shaped plasmas are more stable against both internal kinks and infernal modes than their counterpart NT shaped plasmas. Toroidal flows have little impact on the MHD stability of the internal kinks, but they have a strong stabilizing effect on infernal modes, which can be further mitigated in NT shaped plasmas. The MHD stability of peeling-ballooning modes is reduced in NT shaped plasmas, as observed in conventional tokamaks.

Frontal Lobe Growth Impairment in Fetuses with Congenital Heart Disease Using Ultrasound Parameters; A Comparative Cross-Sectional Study

Abstract Background There is evidence; in neonates with critical congenital heart disease CHD, that the abnormal hemodynamics do not affect all brain regions similarly, with the frontal lobe growth being more severely impaired, especially in cases with univentricular heart anatomy. Aim and Objectives To assess whether fetuses with congenital heart disease (CHD) have smaller frontal brain areas compared with normal controls. Subjects and Methods This Cross-sectional study was conducted at Ain Shams University Maternity Hospital (Fetal Medicine unit). The study group included 280 women, 140 women whose fetuses are normal and the other 140 women whose fetuses suffered congenital heart disease using ultrasonography. Measuring the distance from the internal edge of the frontal bone to the posterior edge of the CSP (measured in-to-in), i.e the frontal lobe anteroposterior diameter (FAPD), which was assumed to be representative of the area of the frontal lobes; measuring of the occipitofrontal diameter (OFD), (also measured in-to-in), from the internal edge of the frontal bone to the internal edge of the occipital bone. The ratio of these two measurements, calculated as FAPD/OFD×100 and referred to as ‘FAPD/OFD ratio’, represents the reference index that was used in this investigation to assess the growth of the frontal component of the fetal brain in relation to the growth of the whole brain. Fetal echocardiography was done for both groups to assess the cardiac anomalies. Result There was a statistically significant difference between the studied groups regarding History of CHD. the FAPD/OFD ratio was significantly smaller in both the group of left-heart lesion or univentricular heart and the group of all other CHDs, compared with normal fetuses (P &amp;lt; 0.0001), with no statistically significant difference between the two CHD groups. There was no statistically significant difference between the studied groups regarding comparison between surgical history, co-morbidities and Correlation of frontal anteroposterior diameter (FAPD), occiptofrontal diamter (OFD) and FAPD/OFD ratio with the other studied parameters in all cases except in gestational age and CNS anomalies. Conclusion Fetuses with CHD have a shorter FAPD and a smaller FAPD/OFD ratio compared to normal fetuses. This impaired growth of the frontal area of the brain seems to occur in all types of CHD, regardless of their impact on the hemodynamics.

A macro BDM H-div mixed finite element on polygonal and polyhedral meshes

A BDM type of H(div) mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the H(div) subspace of the n-product ΠiPk(Ti)d space such that the divergence is a one-piece Pk−1 polynomial on the big polygon or polyhedron T. Here we assume the 2D polygon can be subdivided into triangles by connecting only one vertex with some vertices of the polygon. For the 3D polyhedron we assume it can be subdivided into tetrahedra, with no added vertex on subdividing its face-polygons, and with either no internal edge or one internal edge. Such mixed finite elements can be more economic on quadrilateral and hexahedral meshes, compared with the standard BDM mixed element on triangular and tetrahedral meshes. Numerical tests and comparisons with the triangular and tetrahedral BDM finite elements are provided.

Morphology's importance for farmland landscape pattern assessment and optimization: A case study of Jiangsu, China

Farmland landscape pattern (FLP) is critical in ensuring sustainable agricultural production. Amidst the challenge of increasingly fragmented FLP, accurate assessment and optimization strategies are essential. Traditional FLP assessment studies lack significance in ecological representation because they ignore landscape types and their characteristics and overlook changes in landscape details based on overall results. These factors lead to uncertain assessment outcomes. This study introduces a farmland landscape classification system based on morphological spatial pattern analysis to address this. Special attention is given to the internal core and external edge farmland landscape types, resulting in an innovative FLP assessment system being developed. The results of the Jiangsu Province reveal significant patchiness and marginalization of core farmland, particularly worsening from north to south. While recent trends show a slight improvement in the overall situation and effective perforation suppression, challenges persist with low-value FLP expansions in each agricultural zone. This study emphasizes integrating external edge farmland and overall pattern protection for optimal FLP. The improved assessment method identifies areas for scale improvement and fragmentation risks, offering valuable insights for permanent basic farmland policy. Overall, this study enriches the analytical framework of FLP from a morphological perspective, aiding in precise assessment and tailored optimization strategies.

Compatibility of divertor detachment and ELM suppression in DIII-D high- βp plasmas with ITER-similar shape

Integration of transient and steady-state divertor heat fluxes control with a high-performance core is necessary for future fusion reactors. In recent DIII-D high- βp experiments, divertor detachment and simultaneous edge localized mode (ELM) suppression are demonstrated while the plasma confinement quality is maintained high in ITER-similar shape. By optimizing the neon injection in high- βp scenario with ITER-similar shape, deep detachment and ELM suppression are achieved with a high-performance core ( βN ∼ 2.8, βp ∼ 2.3) at q95 ∼ 7.5. Partial divertor detachment and suppression of large ELMs are achieved at q95 ∼ 6. The stability analyses suggest that with low neon injection, the density pedestal becomes higher and steeper and the Ti profile also increases, therefore the increased edge pressure and higher current density destabilize the Peeling-Ballooning mode (PBM), which would lead to a large ELM collapse. With strong neon gas puffing, the significantly reduced pedestal pressure and current density, due to the degraded Te pedestal, lead to the stabilization of PBM and ELMs are suppressed. For both cases, the coupling between the large radius internal transport barrier (ITB) and edge pedestal is the key reason for maintaining high global performance. The formation of large radius ITB compensates for pedestal degradation. Such results could provide an attractive scenario to well control the transient and steady-state heat flux onto the divertor plates while maintaining good plasma performance, which is an important step toward the steady-state operation of future fusion reactors.

Simulated deep CT characterization of liver metastases with high-resolution filtered back projection reconstruction

Early diagnosis and accurate prognosis of colorectal cancer is critical for determining optimal treatment plans and maximizing patient outcomes, especially as the disease progresses into liver metastases. Computed tomography (CT) is a frontline tool for this task; however, the preservation of predictive radiomic features is highly dependent on the scanning protocol and reconstruction algorithm. We hypothesized that image reconstruction with a high-frequency kernel could result in a better characterization of liver metastases features via deep neural networks. This kernel produces images that appear noisier but preserve more sinogram information. A simulation pipeline was developed to study the effects of imaging parameters on the ability to characterize the features of liver metastases. This pipeline utilizes a fractal approach to generate a diverse population of shapes representing virtual metastases, and then it superimposes them on a realistic CT liver region to perform a virtual CT scan using CatSim. Datasets of 10,000 liver metastases were generated, scanned, and reconstructed using either standard or high-frequency kernels. These data were used to train and validate deep neural networks to recover crafted metastases characteristics, such as internal heterogeneity, edge sharpness, and edge fractal dimension. In the absence of noise, models scored, on average, 12.2% (α=0.012\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.012$$\\end{document}) and 7.5% (α=0.049)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.049)$$\\end{document} lower squared error for characterizing edge sharpness and fractal dimension, respectively, when using high-frequency reconstructions compared to standard. However, the differences in performance were statistically insignificant when a typical level of CT noise was simulated in the clinical scan. Our results suggest that high-frequency reconstruction kernels can better preserve information for downstream artificial intelligence-based radiomic characterization, provided that noise is limited. Future work should investigate the information-preserving kernels in datasets with clinical labels.

Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization

The lung is one of the most vital organs in the human body, and its condition is closely correlated with overall health. Electrical impedance tomography (EIT), as a biomedical imaging technique, often produces low-quality reconstructed images due to its inherent ill-posedness in solving the inverse problem. To address this issue, this paper proposes a soft-threshold region segmentation algorithm with a relaxation factor. This algorithm segments the reconstructed lung images into internal regions, edge regions, and background regions, resulting in clearer boundaries in the reconstructed images. This facilitates the intuitive identification of regions of interest by healthcare professionals. Additionally, this segmentation algorithm is suitably combined with a dimension-reduced Tikhonov regularization algorithm. By utilizing the joint capabilities of these algorithms, the partition points belonging to the background region can be excluded from the sought grayscale vector, thereby improving the ill-posedness of the image reconstruction process and enhancing the quality of image reconstruction. Finally, a 16-electrode human lung EIT simulation model is established for the thoracic region and verified through simulation. Experimental validation is conducted using a human lung tank simulation platform to further demonstrate the effectiveness of the proposed method.

Community detection with Greedy Modularity disassembly strategy

Community detection recognizes groups of densely connected nodes across networks, one of the fundamental procedures in network analysis. This research boosts the standard but locally optimized Greedy Modularity algorithm for community detection. We introduce innovative exploration techniques that include a variety of node and community disassembly strategies. These strategies include methods like non-triad creating, feeble, random as well as inadequate embeddedness for nodes, as well as low internal edge density, low triad participation ratio, weak, low conductance as well as random tactics for communities. We present a methodology that showcases the improvement in modularity across the wide variety of real-world and synthetic networks over the standard approaches. A detailed comparison against other well-known community detection algorithms further illustrates the better performance of our improved method. This study not only optimizes the process of community detection but also broadens the scope for a more nuanced and effective network analysis that may pave the way for more insights as to the dynamism and structures of its functioning by effectively addressing and overcoming the limitations that are inherently attached with the existing community detection algorithms.

Characteristics of annular surface dielectric barrier discharge with microsecond pulse under water-covered condition.

Surface dielectric barrier discharge (SDBD) has wide applications in flow control, wastewater treatment, and biomedicine. The dielectric surface of an SDBD actuator is generally attached to the water droplets during applications. Thus far, only a few studies have been conducted on the effects of water covering the dielectric surface on the discharge characteristics of SDBD. Therefore, the effects of water droplets on the discharge of an SDBD actuator based on a repetitive microsecond pulse power supply were investigated in this study. The results show that a filament micro-discharge channel forms between the light and dark regions at the internal edge of the SDBD high-voltage electrode and develops toward the center of the dielectric surface in the region without water droplet coverage. SDBD in the water-covered region was divided into two stages. This paper compares the electrical characteristics of SDBD with and without water droplet, and explores the electric field distortion effect of water droplet endpoints through 3D simulation.Based on the theories of water droplet polarization and gas discharge, the effects of water droplets on plasma development and surface charge accumulation under water-covered condition were analyzed. The water droplet plays a similar role as a "secondary electrode" during the discharge process.

Fracture analysis of Brazilian circular hole disk under mixed mode loading

The paper presents an investigation into a Brazilian disk specimen featuring a concentric circular hole, accompanied by two internal edge radial cracks. By introducing rotations of the cracks relative to the vertical axis, a combination of fracture modes I and II is induced. Employing the finite element method, we compute stress intensity factors related to fracture modes I and II, alongside T-stresses, while varying geometric parameters such as inner and outer diameters, crack length-to-ring width ratio, and crack inclination angle. Experimental analyses of ebonite's fracture toughness in the mixed mode are conducted, subjecting samples to static loading until complete failure. Each test provides the angle at which crack initiation occurs and the corresponding critical load. Three distinct fracture criteria - the generalized maximum tangential stress criterion (GMTS), extended maximum tangential strain criterion (EMTSN), and generalized strain energy density (GSED) criterion - are employed to predict fracture direction and critical load. The outcomes exhibit good correspondence between experimental critical loads and theoretical predictions.

Cheese-like Ti3C2 for enhanced hydrogen storage

MXenes are highly promising in efficient Mg-based hydrogen storage but their activity is insufficient due to the low efficiency of active sites. Here, for the first time, we propose a facile oxidation-etching-oxidation strategy to expose and optimize abundant internal active sites in a typical MXene (Ti3C2), avoiding additional introduction of active metal sites or complex structural optimization. The obtained cheese-like Ti3C2 with Ti/TiO2 activity sites enriched at the edge of through holes exhibits much better performance in terms of dehydrogenation temperature (from 190 °C) as well as rate in initial 10 min at 250 °C (0.37 wt%/min) than ordinary Ti3C2 when applied in Mg-based hydrogen storage. Compared to ordinary Ti3C2, the dehydrogenation temperature is 60 °C decreased and rate increases to 2-fold, respectively. This work elucidates that significantly enhanced hydrogen storage performance of MXenes can be realized by exposing abundant internal edge active sites via a facile oxidation-etching-oxidation strategy.

Tool wear assessment when drilling AISI H13 tool steel multilayered claddings

Laser cladding is a layer-by-layer metal deposition technique often used to deposit high-quality metallic coatings on poorly performant metal alloy surfaces. Nevertheless, to reach the desired surface finish and geometrical tolerances, machining operations after laser cladding may become necessary, whose performances can be significantly affected by the deposition parameters. While the outcomes of milling operations carried out on multi-layered claddings in terms of tool wear and surface integrity have been recently investigated, the same is not available in literature in case of drilling, which is particularly challenging when the drilling operation intersects several layers. In this paper, C45 steel substrates were laser cladded with multiple AISI H13 tool steel layers using different powder size and laser power. The laser cladded samples were characterized on the basis of their microstructural features and micro-hardness. Afterward, drilling trials were conducted on these samples to evaluate the drill bit wear. The effect of the laser cladded-induced microstructure on the tool wear was then assessed at varying deposition parameters. Moreover, the quality of the drilled holes in terms of hole internal surface roughness and hole edge contour was investigated and related to the tool wear. The obtained results showed that, when drilling laser cladded AISI H13 tool steel, the microstructural features induced by the deposition process significantly affect the tool wear and, in turn, the hole quality.

Multi-Scale Feature Fusion Network for Low-Dose CT Denoising.

Computed tomography (CT) is an imaging technique extensively used in medical treatment, but too much radiation dose in a CT scan will cause harm to the human body. Decreasing the dose of radiation will result in increased noise and artifacts in the reconstructed image, blurring the internal tissue and edge details. To get high-quality CT images, we present a multi-scale feature fusion network (MSFLNet) for low-dose CT (LDCT) denoising. In our MSFLNet, we combined multiple feature extraction modules, effective noise reduction modules, and fusion modules constructed using the attention mechanism to construct a horizontally connected multi-scale structure as the overall architecture of the network, which is used to construct different levels of feature maps at all scales. We innovatively define a composite loss function composed of pixel-level loss based on MS-SSIM-L1 and edge-based edge loss for LDCT denoising. In short, our approach learns a rich set of features that combine contextual information from multiple scales while maintaining the spatial details of denoised CT images. Our laboratory results indicate that compared with the existing methods, the peak signal-to-noise ratio (PSNR) value of CT images of the AAPM dataset processed by the new model is 33.6490, and the structural similarity (SSIM) value is 0.9174, which also achieves good results on the Piglet dataset with different doses. The results also show that the method removes noise and artifacts while effectively preserving CT images' architecture and grain information.

Effects of the spatial patterns of urban parks on public satisfaction: evidence from Shanghai, China.

Urban parks need to meet the growing demand for activities vital to residents' well-being and urban development. A holistic understanding of public satisfaction with urban parks is a prerequisite for improving management. The spatial patterns and composition of urban parks vary greatly, and the objective of this study is to comprehensively investigate public satisfaction with urban parks and the impact of their structure. With the metropolis of Shanghai, China, as an example, we employed 111,814 social media data sets for 50 urban park sites to quantify public satisfaction via the long short-term memory model. We analyzed the internal, boundary and external dimensions of spatial patterns and described the internal landscape patterns from the perspectives of size, heterogeneity, aggregation, shape, diversity and landscape elements. Moreover, we used all-subset regression and hierarchical partitioning to quantify the relationship and mechanism of action between spatial patterns and public satisfaction. The results indicate that the mean value of public satisfaction with urban parks was 0.716 (ranging from 0 to 1), which is generally positive or neutral. Satisfaction was influenced by the internal, boundary, and external spatial patterns of urban parks. The independent contribution rates of external transportation facility density (51.49%) and internal edge density (48.51%) to satisfaction. We highlight the roles of spatial patterns, especially the degree of external transportation convenience and the edge density of urban parks at the landscape level. The findings provide guidance and recommendations for the planning and design of public satisfaction-oriented urban parks. The online version contains supplementary material available at 10.1007/s10980-023-01615-z.

Kitaev formula for periodic, quasicrystal, and fractal Floquet topological insulators

Topological insulators are attracting researchers to reveal related fundamental physics, whose fractal versions are expanding topological physics into the fractal regime. The fractal topological systems, however, show a challenge to the Kitaev formula, because it leads to a noninteger Chern number. The Chern number within the band gap oscillates more and more actively as the system size increases. We uncover that such a challenge should be attributed to the coupling, brought about by the lattice fractalization, between the internal and external edge states. To confirm this, examples of periodic, quasicrystal, and fractal Floquet topological insulators are compared with each other by analyzing the topological edge states and local Chern markers. The sum of the local Chern markers on all the edges of the fractal lattice presents a fractional power relation with the system size, reflecting the fractalization of the topological edge states. We reveal that once such a coupling is shut down, the Kitaev formula would once again result in integers.

Dynamic iris inner edge location method based on distance-regularized level set

Iris localization is an important part of iris recognition. Aiming at the influence of irregular pupil circle and illumination inequality in dynamic iris localization in actual scene, a dynamic iris inner edge location method based on distance regularized level set model was proposed. According to the geometric features of iris, the pupil and iris are coarsely located through the secondary projection of binary image, and the initial contour of evolution of horizontal set is determined. Accurate positioning of the inner edge of iris is achieved by the improved distance regularized level set model of edge indicator function. Iris images Database were respectively experimented with this paper and another improved distance regularized level set model, and the positioning effect was evaluated by using the Jakard similarity coefficient. The results show that the distance regularized level set model based dynamic iris internal edge localization algorithm proposed in this paper can significantly reduce the number of iterations and positioning time of the localization algorithm on the basis of ensuring the positioning accuracy,which provides a theoretical basis and technical reference for the application of iris recognition technology.

Analysis of regional large-gradient land subsidence in the Alto Guadalentín Basin (Spain) using open-access aerial LiDAR datasets

Land subsidence associated with groundwater overexploitation in the Alto Guadalentín Basin (Spain) aquifer system has been detected during the last decades. In this work, for the first time, we propose a new point cloud differencing methodology to detect land subsidence at basin scale, based on the multiscale model-to-model cloud comparison (M3C2) algorithm. This method is applied to two open-access airborne LiDAR datasets acquired in 2009 and 2016, respectively. First the internal edge connection errors in the different flight lines were addressed by means of a smoothing point cloud method. LiDAR datasets capture information from ground and non-ground points. Therefore, a method combining gradient filtering and cloth simulation filtering (CSF) algorithms was applied to remove non-ground points. The iterative closest point (ICP) algorithm was used for point cloud registration of both point clouds exhibiting a very stable and robust performance. The results show that vertical deformation rates are up to −14 cm/year in the basin from 2009 to 2016, in agreement with the displacement reported by previous studies. LiDAR results have been compared to the velocity measured by continuous GNSS stations and an InSAR dataset. For the GNSS-LiDAR and InSAR-LiDAR comparison, we computed a common 100 × 100 m grid in order to assess any similarities and discrepancies. The results show a good agreement between the vertical displacements obtained from the three different surveying techniques. Furthermore, LiDAR results were compared with the distribution of compressible soil thickness showing a clear relationship. The study underlines the potential of open-access and non-customized LiDAR to monitor the distribution and magnitude of vertical deformations in areas prone to be affected by groundwater-withdrawal-induced land subsidence.

Predicted optimization of β N limit for steady-state scenario with double transport barriers in HL-2M tokamak

The equilibria of the HL-2M tokamak, designed for steady-state operation with reversed magnetic shear and double transport barriers, are calculated using TOQ code, and the linear ideal magnetohydrodynamic (MHD) stability of the equilibria is investigated using GATO code. To improve the beta () limit, the MHD stability of the equilibria with different heights of internal transport barrier (ITB) and edge transport barrier (ETB) is simulated. The simulation results indicate that the ITB drives low globalized modes while the ETB drives high edge localized modes, and thus a moderate barrier height ratio is beneficial to MHD stability. By adjusting the heights of both barriers with different plasma shapes, as well as different locations and widths of ITBs, optimal equilibria with improved MHD stability are achieved, which always have a moderate barrier height ratio unless the ITB is extremely wide or very close to the edge. In ideal-wall conditions, when the ITB is wide enough or very close to the edge, limits could exceed six, or even reach seven in some special cases. Increasing elongation and triangularity, broadening the ITB, as well as moving the ITB to a large minor radius, can contribute to the optimization of the limit, especially when combined with the stabilizing effect from an ideal wall.