Vertex Position Research Articles

Two-Year Progressive Cranial Changes Following the Melbourne Technique for Sagittal Craniosynostosis.

The Melbourne technique for total cranial vault remodeling aims to address all aspects of scaphocephaly in sagittal craniosynostosis. These features include anterior-posterior excessive length, anteriorly displaced vertex position, frontal bossing, vertex narrowing, and occipital bulleting. This study aimed to determine the progressive cranial changes that occur following the Melbourne technique for sagittal craniosynostosis. Retrospective review of 3-dimensional images collected preoperatively and postoperatively at 3 weeks, 3 months, 1 year, and 2 years. Tertiary care pediatric institution. Twenty-five patients with sagittal craniosynostosis. The Melbourne technique for total cranial vault remodeling. Head circumference, cephalic index, frontal bossing index, occipital bulleting index, vertex narrowing index, and vertex-nasion-opisthocranion (VNO) angle were evaluated. The cephalic index significantly increased postoperatively (P = .04) with a subsequent relapse at 3 months followed by progressively increased growth. The frontal bossing index significantly decreased postoperatively (P = .02) with a progressive decrease. The occipital bullet index had a relative decline postoperatively with relapse at 3 months, followed by a progressive decrease. The vertex narrowing index significantly decreased postoperatively (P < .001), with a plateau and slight relapse. The VNO angle showed a relative decline over time with a significant decrease by 1 year of age (P = .002). The Melbourne technique improved the cephalic index, frontal bossing, vertex narrowing, occipital bulleting, and vertex positioning at 2 years of age. Cephalic index and occipital bulleting showed slight relapse at 3 months, followed by progressive improvement over time.

Timing-based mass measurement of exotic long-lived particles at the FCC-ee

The very high luminosity run foreseen at the Z-pole for the FCC-ee will allow the detection in Z decays of new particles with very low couplings to the Standard Model. These particles can have measurable flight paths before they decay. If the timing and the position of the decay vertex can be measured with high precision, the mass of such particles can be measured by exploiting the constrained kinematics of an e+e- collider. The mass resolution achievable with this technique is studied through a detailed analysis in the framework of a parametrised simulation of the performance of the IDEA detector. The adopted benchmark model is the production of Heavy Neutral Leptons, which is one of the key channels for new physics discovery at the FCC-ee.

Performance Comparison of Vertex Block Descent and Position Based Dynamics Algorithms Using Cloth Simulation in Unity

This paper presents a comparative study of the Vertex Block Descent (VBD) and Position-Based Dynamics (PBD) algorithms, focusing on their performance in physical simulation tasks. Unity, a versatile physics engine, served as the simulation platform for the experiments. Among various types of physical simulations of deformable objects, fluids, and cloth dynamics, cloth simulations were chosen for implementation with both algorithms. The experimental setup ensured identical parameters, including time steps and movement behavior, for both algorithms across scenarios involving hanging, object-to-object collisions, and self-collisions. The results indicate that while the performance difference in frames per second (fps) between the two algorithms is negligible for simulations with a small number of nodes, the VBD algorithm consistently outperforms the PBD algorithm as the node count increases. Furthermore, this study provides practical guidelines for maintaining real-time performance, detailing the maximum node count each algorithm can support, while sustaining a minimum threshold of 30 fps, which is necessary for real-time applications. The comparison was conducted using CPU-based computation to establish a baseline for future studies in GPU-accelerated environments, where parallel processing is expected to further highlight the performance advantages of VBD. Future work will extend this research by evaluating additional physical simulation models, including the Mass-Spring System and Extended Position-Based Dynamics (XPBD), and developing optimizations to enhance the efficiency and scalability of these algorithms.

Differentiable Photon Mapping using Generalized Path Gradients

Photon mapping is a fundamental and practical Monte Carlo rendering technique for efficiently simulating global illumination effects, especially for caustics and specular-diffuse-specular (SDS) paths. In this paper, we present the first differentiable rendering method for photon mapping. The core of our method is a newly introduced concept named generalized path gradients. Based on the extended path space manifolds (EPSMs) [Xing et al. 2023], the generalized path gradients define the derivatives of the vertex positions and color contributions of a path with respect to scene parameters under given geometric constraints. By formalizing photon mapping as a path sampling technique through vertex merging [Georgiev et al. 2012] and incorporating a smooth differentiable density estimation kernel, we enable the differentiation of the photon mapping algorithms based on the theoretical results of generalized path gradients. Experiments demonstrate that our method is more effective than state-of-the-art physics-based differentiable rendering methods in inverse rendering applications involving difficult illumination paths, especially SDS paths.

Computing Hive Plots: A Combinatorial Framework

Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an axis and vertex positions on each axis were determined based on selected vertex attributes and the order of axes was prespecified. Here, we present a new framework focusing on combinatorial aspects of these drawings to extend the original hive plot idea and optimize visual properties such as the total edge length and the number of edge crossings in the resulting hive plots. Our framework comprises three steps: (1) partition the vertices into multiple groups, each corresponding to an axis of the hive plot; (2) optimize the cyclic axis order to bring more strongly connected groups near each other; (3) optimize the vertex ordering on each axis to minimize edge crossings. Each of the three steps is related to a well-studied, but NP-complete computational problem. We combine and adapt suitable exact and heuristic algorithmic approaches, implement them as an instantiation of our framework, and show in a case study how it can be applied in a practical setting. Furthermore, we conduct computational experiments to gain further insights regarding the algorithmic choices of our framework. The code of the implementation and a prototype web application can be found on OSF.

Exploring Mean Cordial Labeling Possible Combination Position of Vertices in Graphs: A Computational Approach

Objectives: We have developed the Python module of mean cordial labeling for the different types of graphs, like Path, Cycle, and Subdivision of Star graphs. We aim to identify the number of combination positions of vertices that satisfy the mean cordial labeling rules. We have found mathematical equations that describe the labeling behavior in these graphs. Methods: In this paper, a Python program was developed to find the mean cordial labeling of the Path, Cycle, and Subdivision of the Star graph. We have obtained the number of combination positions of vertex obeying the mean cordial labeling condition using this Python module. We have drawn the graph between the number of vertices and the number of combination positions of the vertex. Findings: We have found that the different graph types like Path, Cycle, and Subdivision of Star graph satisfy the mean cordial labeling condition. The result indicates that the number of combination positions of the Path and cycle graph fulfill the power equation Y=a*xb and the Subdivision of the Star graph meets the exponential growth equation Y=a*bx. Novelty: In this paper, a new method has been developed to find the number of combination position of varies graphs using the Python module. This computational approach will be useful to analyze the biological networking and protein-protein interaction study. Keywords: Mean Cordial, Path, Cycle, Subdivision of Star graph, Computational graph theory

Large-Strain Surface Modeling Using Plasticity.

Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. We give a new method to represent surfaces undergoing large spatially varying rotations and strains, based on differential geometry, and surface first and second fundamental forms. Methods that penalize the difference between the current shape and the rest shape produce sharp spikes under large strains, and variational methods produce wiggles, whereas our method naturally supports large strains and rotations without any special treatment. For stable and smooth results, we demonstrate that the deformed surface has to locally satisfy compatibility conditions (Gauss-Codazzi equations) on the first and second fundamental forms. We then give a method to locally modify the surface first and second fundamental forms in a compatible way. We use those fundamental forms to define surface plastic deformations, and finally recover output surface vertex positions by minimizing the surface elastic energy under the plastic deformations. We demonstrate that our method makes it possible to smoothly deform triangle meshes to large spatially varying strains and rotations, while meeting user constraints.

Optimized Dual‐Volumes for Tetrahedral Meshes

AbstractConstructing well‐behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the de facto standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development of finite‐volume methods. In this paper, we place existing methods into a common construction, showing how their differences amount to the choice of simplex centers. These choices lead to satisfaction or breakdown of important properties: continuity with respect to vertex positions, positive semi‐definiteness of the implied Dirichlet energy, positivity of the mass matrix, and unbiased‐ness on regular grids. Based on this analysis, we propose a new method for constructing dual‐volumes which explicitly satisfy all of these properties via convex optimization.

Vertex Block Descent

We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational energy with maximized parallelism. This forms a physics solver that can achieve numerical convergence with unconditional stability and exceptional computation performance. It can also fit in a given computation budget by simply limiting the iteration count while maintaining its stability and superior convergence rate. We present and evaluate our method in the context of elastic body dynamics, providing details of all essential components and showing that it outperforms alternative techniques. In addition, we discuss and show examples of how our method can be used for other simulation systems, including particle-based simulations and rigid bodies.

Outpatient balloon catheter versus expectant management for post-term labor induction in nulliparous women: A randomized trial

BackgroundIncreased use of labor induction has renewed interest in outpatient cervical ripening. Post-term pregnancy (i.e., ≥41 weeks) is a specific situation of increased neonatal risk, including greater risk of perinatal death and adverse perinatal outcomes. While a high proportion of these patients will need induction, outpatient management of this specific population has never been studied. Therefore, our objective was to compare two policies of management of post term pregnancies: the use of a transcervical Foley catheter for outpatient cervical ripening compared with expectant management. MethodsMulticenter, randomized controlled open-label study comparing home induction with a Foley catheter versus expectant management. Inclusion criteria were nulliparous, live singleton fetus in a vertex position, post-term (at 41 + 4 days), requiring cervical ripening (Bishop score <6), intact membranes, and distance home-hospital within 40 min. The primary endpoint was change in Bishop score beetween randomization (41 + 4 days) and consultation (41 + 5 days). ResultsForty-five women were included: 21 in the home induction group and 24 in the control group. The study was stopped due to low recruitment. The difference in Bishop score increases one day after randomization approached significance (p = 0.055), with home induction showing a larger change compared with expectant management (Cohen's d = 0.60; 95 % confidence interval [CI] −0.002 to 1.21). Regarding change in Bishop score, 81 % of home induction group patients had a better score at 41 + 5 days versus 52.2 % in the control group (relative risk = 1.55; 95 %CI 0.99 to 2.15). ConclusionBy specifically evaluating home induction in nulliparous women with post term pregnancies, we observed a Bishop score improvement in the home induction group. These data support further evaluation of induction methods and birth experiences in a larger cohort of this population. Trial registrationThe study was registered under European policy (number EudraCT 2015-A01298–41) and on www.clinitrials.gov (number NCT02932319). Date of registration: 13/10/2016, Date of initial participant enrollment: 31/03/2017

Generating Baikal-GVD high energy cascade-like neutrino events with a GEANT4-based simulation toolkit

Abstract Using GEANT4 and Cosmic Ray Monte Carlo (CRMC) software packages, we developed a new simulation toolkit for astrophysical neutrino telescopes. By configuring the Baikal-GVD detector and comparing the vertex position and direction of incident particles, as well as the channel-by-channel signals, to the events detected by Baikal-GVD, we successfully generated 13 high-energy cascades neutrino events with the toolkit. Our analysis revealed a systematic offset between the reconstructed shower position and the true interaction position, with a distance close to the scale of the shower maximum of -0.64±1.32 m. The results of the linear fit between real data and simulation demonstrate reliable outcomes, indicating that the simulation toolkit is capable of studying the performance of astrophysical neutrino telescopes.

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Abstract. Stiffness excitation is one of the important excitations for the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear system. Accurate calculation of the gear meshing stiffness is of great significance to investigating dynamic characteristics of the VH-CATT cylindrical gear system. Firstly, based on the forming theory of the modified tooth surface, the modified tooth surface equation of the VH-CATT cylindrical gear was deduced, and the 3D reconstruction was realised. Next, the load tooth contact analysis (LTCA) model of the VH-CATT cylindrical gear was developed to calculate the meshing stiffness of the VH-CATT cylindrical gear, and it was verified by the finite-element calculation. Finally, the influence of the load and modification parameters on the VH-CATT cylindrical gear stiffness was investigated. Research shows that the stiffness calculation method of the VH-CATT cylindrical gear based on LTCA is accurate. The meshing stiffness of the VH-CATT cylindrical gear in the double-tooth meshing area is large, and the meshing stiffness of the VH-CATT cylindrical gear in the single-tooth meshing area is small. The stiffness of the VH-CATT cylindrical gear increases with an increase in the load and cutter inclination angle, the stiffness of the VH-CATT cylindrical gear only in the double-tooth meshing area decreases with an increase in the parabolic coefficient, and the stiffness of the VH-CATT cylindrical gear increases with a decrease in the blade parabolic vertex position value. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising design.

Neutral Facial Rigging from Limited Spatiotemporal Meshes

Manual facial rigging is time-consuming. Traditional automatic rigging methods lack either 3D datasets or explainable semantic parameters, which makes it difficult to retarget a certain 3D expression to a new face. To address the problem, we automatically generate a large 3D dataset containing semantic parameters, joint positions, and vertex positions from a limited number of spatiotemporal meshes. We establish an expression generator based on a multilayer perceptron with vertex constraints from the semantic parameters to the joint positions and establish an expression recognizer based on a generative adversarial structure from the joint positions to the semantic parameters. To enhance the accuracy of key facial area recognition, we add local vertex constraints for the eyes and lips, which are determined by the 3D masks computed by the proposed projection-searching algorithm. We testthe generation and recognition effects on a limited number of publicly available Metahuman meshes and self-collected meshes. Compared with existing methods, our generator has the shortest generation time of 14.78 ms and the smallest vertex relative mean square error of 1.57 × 10−3, while our recognizer has the highest accuracy of 92.92%. The ablation experiment verifies that the local constraints can improve the recognition accuracy by 3.02%. Compared with other 3D mask selection methods, the recognition accuracy is improved by 1.03%. In addition, our method shows robust results for meshes of different levels of detail, and the rig has more dimensions of semantic space. The source code will be made available if this paper is accepted for publication.

Structural properties and aromaticity of rare-earth doped tin cluster anion: MSn9− (M = Sc, Y, La)

Doping rare earth elements into clusters can significantly improve the performance and application value of the materials. The structure, bonding properties, stability, and aromaticity of MSn9− (M = Sc, Y, La) have been investigated using density-functional theory. The global minimum structure of these clusters is determined to be the addition of a triangle to the vertex position of a pentagonal bipyramid. Ab initio molecular dynamics simulations are used to demonstrate the thermal stability of the structure. Bonding analyses indicate the presence of ionic bonding and covalent bonding. Iso-chemical shielding surfaces and the gauge-including magnetically induced currents indicate that MSn9− clusters are significantly aromatic. This study provides a comprehensive understanding of tin-based nanomaterials, which is important for their design and synthesis.

Nulliparas at Term with Premature Rupture of Membranes and an Unfavorable Cervix: Labor Induction with Prostaglandin or Oxytocin? A Retrospective Matched Case Study

Background: Induction of labor (IOL) in nulliparas with premature rupture of membranes (PROM) and an unfavorable cervix at term poses challenges. Our study sought to investigate the impact of prostaglandin E2 (PGE2) compared to oxytocin on the duration of IOL in this specific group of parturients. Methods: This was retrospective matched-case study. All nulliparas with term PROM who underwent induction between January 2006 to April 2023 at Shaare Zedek Medical Center were identified. Cases induced by either PGE2 or oxytocin were matched by the following criteria: (1) time from PROM to IOL; (2) modified Bishop score prior to IOL ≤ 5; (3) newborn birthweight; and (4) vertex position. The primary outcome was time from IOL to delivery. Results: Ninety-five matched cases were identified. All had a modified Bishop score ≤ 5. Maternal age (26 ± 4.7 years old, p = 0.203) and gestational age at delivery (38.6 ± 0.6, p = 0.701) were similar between the groups. Matched factors including time from PROM to IOL (23.5 ± 19.2 versus 24.3 ± 21.4 p = 0.780), birth weight of the newborn (3111 g versus 3101 g, p = 0.842), and occiput anterior position (present on 98% in both groups p = 0.687) were similar. Time from IOL to delivery was significantly shorter by 3 h and 36 min in the group induced with oxytocin than in the group induced with PGE2 (p = 0.025). Within 24 h, 55 (58%) of those induced with PGE2 delivered, compared to 72 (76%) of those induced with oxytocin, (p = 0.033). The cesarean delivery rates [18 (19%) versus 17 (18%)], blood transfusion rates [2 (2%) versus 3 (3%)], and Apgar scores (8.8 versus 8.9) were similar between the groups (PGE2 versus oxytocin, respectively), p ≥ 0.387. Conclusions: Induction with oxytocin, among nulliparas with term PROM and an unfavorable cervix, was associated with a shorter time from IOL to delivery and a higher rate of vaginal delivery within 24 h, with no difference in short-term maternal or neonatal adverse outcomes.

Optimum design of Chinese solar greenhouses for maximum energy availability

Given the aging of greenhouse facility, there is a need for investigating the transformation of existing greenhouses to maximize solar energy utilization. In this study, Chinese solar greenhouse (CSG) in the Beijing area served as an optimized prototype. A mathematical model was established to determine the range of CSG vertex positions. Then, a 3D dynamic simulation model was developed to optimize greenhouse structure and determine the lighting roof shape that offers better light and temperature environments. The structural safety of CSG steel skeletons was assessed and designed using finite element software. The optimized greenhouse significantly improved the indoor climate, particularly in light environment. Compared to the original greenhouse, the average captured solar energy of the optimized CSG increased by 5.4 MJ m−2, and the average temperature increased by 3.1 °C. The maximum differences in solar radiation and temperature among various lighting roof shapes are 4.8 % and 6.1 %, respectively. Furthermore, the optimized CSG steel skeletons met the requirements for structural stability. The payback period of CSG optimization was about 1.6 years. These methods and findings provide valuable design strategies for upgrading old greenhouses and can be further applied in different regions.

Face presentation at term: incidence, risk factors and influence on maternal and neonatal outcomes.

The incidence, diagnosis, management and outcome of face presentation at term were analysed. A retrospective, gestational age-matched case-control study including 27 singletons with face presentation at term was conducted between April 2006 and February 2021. For each case, four women who had the same gestational age and delivered in the same month with vertex position and singletons were selected as the controls (control group, n = 108). Conditional logistic regression was used to assess the risk factors of face presentation. The maternal and neonatal outcomes of the face presentation group were followed up. The incidence of face presentation at term was 0.14‰. After conditional logistic regression, the two factors associated with face presentation were high parity (adjusted odds ratio [aOR] 2.76, 95% CI 1.19-6.39)] and amniotic fluid index > 18cm (aOR 2.60, 95% CI 1.08-6.27). Among the 27 cases, the diagnosis was made before the onset of labor, during the latent phase of labor, during the active phase of labor, and during the cesarean section in 3.7% (1/27), 40.7% (11/27), 11.1% (3/27) and 44.4% (12/27) of cases, respectively. In one case of cervical dilation with a diameter of 5cm, we innovatively used a vaginal speculum for rapid diagnosis of face presentation. The rate of cesarean section and postpartum haemorrhage ≥ 500ml in the face presentation group was higher than that of the control group (88.9% vs. 13.9%, P < 0.001, and 14.8% vs. 2.8%, P = 0.024), but the Apgar scores were similar in both sets of newborns. Among the 27 cases of face presentation, there were three cases of adverse maternal and neonatal outcomes, including one case of neonatal right brachial plexus injury and two cases of severe laceration of the lower segment of the uterus with postpartum haemorrhage ≥ 1000ml. Face presentation was rare. Early diagnosis is difficult, and thus easily neglected. High parity and amniotic fluid index > 18cm are risk factors for face presentation. An early diagnosis and proper management of face presentation could lead to good maternal and neonatal outcomes.

A Discretize-then-Optimize Approach to PDE-Constrained Shape Optimization

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a smooth manifold, termed the manifold of planar triangular meshes. The latter can be endowed with a complete Riemannian metric, which allows large mesh deformations without jeopardizing mesh quality; see R. Herzog and E. Loayza-Romero, Math. Comput. 92 (2022) 1-50. Nonetheless, the discrete shape optimization problem of finding optimal vertex positions does not, in general, possess a globally optimal solution. To overcome this ill-possedness, we propose to add a mesh quality penalization term to the objective function. This allows us to simultaneously render the shape optimization problem solvable, and keep track of the mesh quality. We prove the existence of a globally optimal solution for the penalized problem and establish first-order necessary optimality conditions independently of the chosen Riemannian metric. Because of the independence of the existence results of the choice of the Riemannian metric, we can numerically study the impact of different Riemannian metrics on the steepest descent method. We compare the Euclidean, elasticity, and a novel complete metric, combined with Euclidean and geodesic retractions to perform the mesh deformation.

Analysing detail preserving capabilities of bilateral, laplacian and taubin mesh filtering methods

Mesh filtering of surfaces is crucial for noise reduction, feature preservation, and mesh simplification in graphics, visualization, and computer vision. In this paper, the detail preservation capacities of 3 frequently used filters, i.e., Bilateral, Laplacian, and Taubin mesh filters, in mesh filtering have been thoroughly examined by experiments conducted on 4 different test meshes. While the Bilateral filter excels in preserving sharp features due to its integration of geometric proximity with intensity similarity, the Laplacian filter prioritizes smoothness by averaging neighboring vertex positions, and the Taubin filter offers a balanced approach by merging attributes of both Laplacian and high-pass filters. The Bilateral filter's primary strength lies in its ability to maintain sharp features on a mesh, ensuring that intricate details are preserved by considering both the spatial closeness and intensity similarity of vertices. The Laplacian filter, although effective in achieving mesh smoothness, has the propensity to excessively smooth out sharp and defining features, potentially causing a loss of critical details in the processed mesh. The Taubin filter integrates the best of both worlds, ensuring smoothness without excessive mesh shrinkage; however, it might not excel in feature preservation as effectively as the Bilateral filter or smooth as uniformly as the Laplacian filter, making it a middle-ground option for certain applications. The statistical analysis of the experimental results has shown that the Taubin method is statistically a more successful mesh filtering method for the test sets used in this paper.

FILLING GAPS BETWEEN MESHES OF TREE CROWN AND TREE TRUNK BASED ON BOUNDARY CONSTRAINTS AND COORDINATE PROJECTION FOR 3D TREE MODELLING

Abstract. In order to reconstruct high-quality 3D tree models, trunks and crowns could be reconstructed using appropriate methods separately and merged together. During this process, gaps will appear after tree models are spliced, which will affect the models' topological connectivity and visual effects. In this paper, a gap-repair algorithm for tree mesh models based on boundary restriction and coordinates projection is proposed. The algorithm first extracts all the holes in the tree trunk meshes and crown meshes and matched them according to their relative positions. Then, the gaps in the tree meshes are identified. After that, based on the projection of the hole vertices from 3D space to 2D space, the relative positions of the hole vertices were determined, and vertex connection and surface addition were carried out to generate a 2-manifold patch. Finally, the patch was refined to keep its density of vertices similar to the surrounding meshes. Real 3D Tree meshes of different species were used to conduct experiments, and the quality of the repaired tree models are evaluated qualitatively and quantitatively. Experimental results revealed that the proposed algorithm could fill gaps in tree meshes quickly and effectively, so as to achieve the topology connection and smooth transition between the trunk and crown meshes.