Gaussian Shape Research Articles (Page 1)

Herniation, rotation, looping, and retraction of the midgut occur sequentially during midgut morphogenesis. Recent studies have demonstrated the importance of mechanical forces arising from the differential growth between the midgut and mesentery in the formation of small intestinal loops. However, the roles of mechanics and differential growth in the overall process remain unclear. In this study, we developed a computational model of midgut morphogenesis based on continuum mechanics. We showed that the protrusion, rotation, and retraction of the midgut can emerge sequentially because of temporal changes in differential growth. The midgut was modeled as a hyperelastic tube with a Gaussian shape. The differential growth of the midgut and mesentery was modeled by the spatial variation in spontaneous plastic deformation. The hyperelastic tube developed a protrusion by compression-induced deformation, suggesting that other external forces are not necessary for midgut herniation prior to rotation. Appropriate differential growth induced a rotation of the tube. A less-growing mesentery attempts to face inward to minimize the tensile forces, which causes tube twisting and results in midgut rotation. Excess differential growth may cause the retraction of the midgut before the formation of small intestinal loops. The results of this study will serve as reference in future studies on embryology and tissue engineering.

Rendering animatable and realistic hand avatars is pivotal for enhancing user experiences in human-centered AR/VR applications. While recent initiatives have utilized neural radiance fields to forge hand avatars with lifelike appearances, these methods are often hindered by high computational demands and the necessity for extensive training views. In this paper, we introduce GaussianHand, the first Gaussian-based real-time 3D rendering approach that enables efficient free-view and free-pose hand avatar animation from sparse view images. Our approach encompasses two key innovations. We first propose Hand Gaussian Blend Shapes that effectively models hand surface geometry while ensuring consistent appearance across various poses. Second, we introduce the Neural Residual Skeleton, equipped with Residual Skinning Weights, designed to rectify inaccuracies involved in Linear Blend Skinning deformations due to geometry offsets. Experiments demonstrate that our method not only achieves far more realistic rendering quality with as few as 5 or 20 training views, compared to the 139 views required by existing methods, but also excels in efficiency, achieving up to 125 frames per second for real-time rendering and remarkably surpassing recent methods.

Advanced therapy medicinal products (ATMPs), especially effective against cancer, remain costly due to their reliance on genetically modified T cells. Contamination during production is a major concern, as traditional quality control methods involve samplings, which can themselves introduce contaminants. It is therefore necessary to develop methods for detecting contamination without sampling and, if possible, in real time. In this article, we present a white light spectroscopy method that makes this possible. It is based on shape analysis of the absorption spectrum, which evolves from an approximately Gaussian shape to a shape modified by the 1/λ component of bacterial absorption spectra when contamination develops. A warning value based on this shape descriptor is proposed. It is demonstrated that a few hours are sufficient to detect contamination and trigger an alarm to quickly stop the production. This time-saving should reduce the cost of these new drugs, making them accessible to as many people as possible. This method can be used regardless of the type of contaminants, provided that the shape of their absorption spectrum is sufficiently different from that of pure T cells so that the shape descriptor is efficient.

Abstract Biaxial wheel polishing has the advantages of high processing flexibility, high removal rate, and excellent surface quality. As a sub-aperture polishing method, the shape stability of the removal function plays a crucial role in both computational convergence and accuracy preservation for subsequent applications to computer-controlled optical surfacing (CCOS). However, the anomalous removal function due to improper selection of process parameters during machining hinders the further application of the process. Therefore, this paper investigates the mechanism of shape evolution of the removal function by biaxial wheel polishing. Single-point material removal experiments were carried out based on a biaxial wheel polishing device. The results show that an increase in compression amounts causes the shape of the removal function to evolve from the Gaussian shape to the plateau and w-shape and that different particle sizes and concentrations of the polishing solution affect the trend of this shape evolution. This study explains this evolution mechanism based on the abrasive grain loading characteristics, and the experimental results are of guiding significance for the selection of process parameters for biaxial wheel polishing.

Radiance field methods such as 3D Gaussian Splatting (3DGS) allow easy reconstruction from photos, enabling free-viewpoint navigation. Nonetheless, pose estimation using Structure from Motion and 3DGS optimization can still each take between minutes and hours of computation after capture is complete. SLAM methods combined with 3DGS are fast but struggle with wide camera baselines and large scenes. We present an on-the-fly method to produce camera poses and a trained 3DGS immediately after capture. Our method can handle dense and wide-baseline captures of ordered photo sequences and large-scale scenes. To do this, we first introduce fast initial pose estimation, exploiting learned features and a GPU-friendly mini bundle adjustment. We then introduce direct sampling of Gaussian primitive positions and shapes, incrementally spawning primitives where required, significantly accelerating training. These two efficient steps allow fast and robust joint optimization of poses and Gaussian primitives. Our incremental approach handles large-scale scenes by introducing scalable radiance field construction, progressively clustering 3DGS primitives, storing them in anchors, and offloading them from the GPU. Clustered primitives are progressively merged, keeping the required scale of 3DGS at any viewpoint. We evaluate our solution on a variety of datasets and show that it can provide on-the-fly processing of all the capture scenarios and scene sizes we target. At the same time our method remains competitive - in speed, image quality, or both - with other methods that only handle specific capture styles or scene sizes.

Abstract. 3D Gaussian Splatting (3DGS) is an innovative solution for explicit point-based 3D representation where each point is represented as a Gaussian distribution. Using calibrated images and sparse point cloud for initialization, the scene is reconstructed by optimizing the Gaussian position, orientation, shape and appearance. In this contribution, we present a comprehensive overview of 3DGS methods available on complimentary radiance field reconstruction platforms namely, the original 3DGS implementation as reference, Splatfacto, 3DGS-MCMC and 3DGS-LumaAI to address a broader audience in industry and non-technical users as well. Being an indispensable part of our environment, we are particularly interested in vegetation since the irregular and complex shape of plants and trees, especially dense foliage can challenge the 3D reconstruction. We evaluate the geometric accuracy and completeness in two real-world scenarios, one occlusion-free indoor and one outdoor scenario where the object of interest is placed behind vegetation to investigate how the methods can reconstruct the underlying geometry behind occlusion. To investigate if 3DGS methods can challenge traditional and state-of-the-art 3D reconstruction approaches we compare the results with Multi-View Stereo (MVS) and Neural Radiance Fields (NeRFs). The evaluation is based on point cloud comparison against a ground truth mesh. Just behind MVS, the original 3DGS implementation achieves second best accuracy results outperforming NeRFs in both scenarios, making it the most accurate 3DGS method. 3DGS-MCMC achieves the best and third best completeness for each scenario respectively, making it competitive with MVS and NeRFs in real-world setting. Moreover, we demonstrate 3DGS ability to reliably reconstruct the geometry behind vegetation occlusion indicating the potential for large-scale forestry applications, allowing canopy reconstruction, biomass estimation and agricultural monitoring.

We study oscillons in a real scalar field theory in a (3+1)-dimensional AdS space with global coordinates. The initial configuration is given by a Gaussian shape with an appropriate core size as in Minkowski spacetime. The solution exhibits a long lifetime. In particular, since the AdS space can be seen as a box, the recurrence phenomenon can be observed under suitable conditions. In particular, as the AdS radius decreases, one can see a transition from a metastable oscillon to a stable oscillatory solution. Finally, we discuss some potential applications of the oscillon in the context of AdS/CFT duality.

Objective.Breath-hold (BH) is a promising approach for proton therapy of moving targets, but multiple BHs per field are needed to compensate for long irradiation time. In pencil beam scanning therapy, two factors define the treatment delivery time: the beam-on time and the dead time, which is the time required for energy-layer and spot-position adjustments. This study examines the interplay of various spot-reduction techniques to decrease delivery time without sacrificing robustness or plan quality.Approach.We created treatment plans for a cohort of 12 non-small cell lung cancer patients, combining a range modulator (RM) that broadens the Bragg peak into a Gaussian shape with three different spot placement algorithms (SPA):a fixed grid-based spot placement technique, an energy-dependent grid-based on the beam's size in air and water, and two types of optimization: a conventional and a spot suppression (SS.) optimization. These configurations were compared in terms of plan quality and clinical acceptability.Main results.RM combined with a fixed grid, leads to the best performance regarding plan quality and robustness. All SPAs reduce treatment time similarly. The SS. optimization reduces the number of spots but does not impact the treatment time. Given the time efficiency of the non-SS. algorithm, the reference optimization algorithms seem to be a better choice.Significance.By combining RM with a spot placement algorithm based on a fixed grid, we can obtain treatment plans with good clinical quality and low irradiation time, thus potentially improving BH treatment efficiency.

ABSTRACTBayesian control charts (BCCs) have gained prominence as effective tools for tracking manufacturing processes and managing variability with precision. Their strength lies in addressing parameter uncertainty, making them especially valuable in industrial applications. This research aims to define a monitoring boundary for the shape parameter of the Inverse Gaussian Distribution (IGD) and to construct several non‐informative Bayesian (NIB) cumulative sum (CUSUM) control charts, each incorporating a distinct loss function (LF). To evaluate their efficacy, both the proposed and existing charts are examined using a range of performance indicators. Through comprehensive simulation studies across various sample sizes, the performance of the new NIB CUSUM charts is thoroughly investigated. Results consistently show that these Bayesian‐based charts surpass traditional classical CUSUM charts in identifying changes in the shape parameter. The NIB charts offer improved fault detection accuracy and heightened responsiveness to process variations. To reinforce the simulation outcomes, the proposed approach is also tested on real manufacturing process data, confirming its practical applicability and effectiveness.

The 3DGS (3D Gaussian Splatting) series of works has achieved significant success in novel view synthesis, but further research is needed for dynamic scene reconstruction tasks. In this paper, we propose a new framework based on 3DGS for handling dynamic scene reconstruction problems involving color changes. Our approach employs a multi-stage training strategy combining motion and color deformation fields to accurately model dynamic geometry and appearance changes. Additionally, we design two modular components: the Dynamic Component for capturing motion variations and the Color Component for managing material and color changes. These components flexibly adapt to different scenes, enhancing our method’s versatility. Experimental results demonstrate that our method achieves real-time rendering at 80 FPS on an RTX 4090 and achieves higher reconstruction accuracy than baseline methods such as HexPlane and Deformable3DGS. Furthermore, it reduces training time by approximately 10%, indicating improved training efficiency. These quantitative results confirm the effectiveness of our approach in delivering high-fidelity 4D reconstruction of complex dynamic environments.

Abstract A two-dimensional mathematical model for wave scattering induced by the interaction of a wave with a non-periodic variable ice sheet with the inclusion of current is presented, primarily focusing on the ice-sheet deflection arising from this interaction. The perturbation approach is initially used to solve the associated boundary value problem (BVP), followed by the Fourier transform technique. The main aim of this study is to derive an explicit analytical expression for the first-order deflection of the ice sheet and to examine its behavior for different physical parameters. Moreover, the surface strain of the ice sheet is also examined. For numerical simulations, an elastic plate having a Gaussian oscillatory shape is explored for its deflection under uniform current in connection to various physical parameters such as the spreading parameter, frequency parameter, and channel depth Froude number (current speed parameter). One significant observation is the emergence of an updrifting pattern in the deflection of ice sheet for very small spreading parameter values. In addition, the subharmonic peaks begin to transition into harmonic peaks as the Froude number increases. The findings of this study could potentially be useful to marine engineers and geologists while building coastal structures based on physical oceanographic conditions.

The system suitability testing of chromatography is an indispensable procedure in pharmaceutical analysis, and it must comply with rules in related pharmacopoeias. An inverse Fourier transform algorithm was developed to accurately evaluate chromatographic features versus a standard Gaussian peak shape. The regular chromatogram is considered a pseudo-frequency spectrum and can be converted to a nominal time signal via inverse Fourier transformation. The system suitability parameters of peak width, theoretical plate number, tailing factor, and noise testing were evaluated using linear regressions directly and compared with the compendial rules. This novel method is simple, accurate, robust, reliable, and efficient for the evaluation of chromatographic peak features.

Abstract We present a microscopic description of cluster emission processes within the Cluster–Hartree–Fock self-consistent field theory. The starting point is a Woods–Saxon mean field with spin–orbit and Coulomb terms. Pairing is treated through standard Bardeen–Cooper–Schrieffer quasiparticles. A two-body interaction is introduced as a density-dependent Wigner force having a Gaussian shape with a center of mass (com) correction located in a region of low nuclear density slightly beyond the geometrical contact radius of a system comprised from a nucleus and a surface cluster. We show that such a description adequately reproduces the ground state shape of a spherical nucleus while the surface correction enhances the radial tail of single particle orbitals, thus allowing for a good description of the decay width for unstable systems.

Radiation pressure dominant (RPD) regime represents a highly efficient mechanism for ion acceleration, where the momentum transfer from an ultra-intense laser pulse to an overdense plasma target is governed primarily by radiation pressure. In this study, we investigate how the shape and polarization of laser pulses influence the dynamics of ion acceleration within the RPD regime. The study focuses on the impact of two key laser pulse characteristics—its profile (comparing Gaussian and Hyperbolic Secant shapes) and its polarization state (whether circular or linear)—on the efficiency of ion acceleration. The paper investigates the comparative effectiveness of energy and momentum transfer into plasma ions. The implications of these findings are significant for the advancement of laser-driven ion acceleration applications such as cancer therapy, nuclear fusion, and materials science etc.

Abstract Modeling the aerodynamic interactions between Airborne Wind Energy Systems (AWES) is an open and challenging problem. To this end, a new Gaussian wake model is introduced for fly-gen AWES, also called windplanes here. The engineering wake models of windplanes can be split in induction models, used to find the induced velocities at the wing, and wake models, used to account for the wind deficit downwind. The proposed model combines an improved induction model, starting from one available in the literature, with a novel wake model that assumes that the wake velocity has a Gaussian shape and imposes momentum conservation. The variance of the Gaussian wake is assumed to vary with the downstream distance from the windplane. The model entails just one tuning parameter that is estimated using CFD results from the literature, showing high accuracy. The new model is then used to study the influence of an upwind system on a downwind one. A sensitivity analysis is carried out by moving the downwind system in the direction transverse to the wind speed or by yawing it with respect to the wind direction. A maximum in power production of the downwind system is found when the projections of the two trajectories are partially overlapping. The extremely low computational cost of the model and the physical insights provided by this paper contribute to clear the way for simulation, planning and control of large scale airborne wind farms.

Raman spectroscopy is a powerful characterization technique with increasing applications that would greatly benefit from data harmonization. Several standards deal with calibration in Raman spectroscopy, but no detailed procedure covers the complete calibration of an instrument, including both spectral axes, from reference material spectra generation to data processing. Moreover, the type of reference materials, the quality of the recorded spectra and the choice of the fitting functions are critical for obtaining precise and reliable reference data for calibration. This report describes the challenges and importance of peak fitting for Raman signal calibration based on an interlaboratory study with 10 different instruments. Spectra of neon emission, silicon, calcite, and polystyrene were fitted using common peak shapes, observing that Gaussian, Pearson IV, Voigt, and Voigt shapes are preferred for these materials, respectively. An analysis of the effect on the fitting of the signal-to-noise ratio (S/N) recommends a minimum value of 100 for a Raman peak if it should be used to calibrate a Raman instrument. Some factors that might affect the peak shape of the Raman signal, such as the physical and chemical properties of the sample, the nature of the electronic transitions, the instrument response and the spectral resolution are discussed. The results highlight the role of peak fitting analysis in improving the quality and reliability of Raman spectra calibration and, thus, enhancing data transfer and comparability, especially for handheld and portable Raman analyzers, as well as applications based on quantification, multivariate data analysis, and other complex processing steps.

Context. Observations of molecular emission lines are commonly used to derive the physical properties of cold molecular gas clouds. In external galaxies, these measurements suffer from limited spatial resolution, typically averaging a complex position–position– velocity distribution of emission over several tens of parsecs. Aims. We aim to quantify the variability in the basic parameters (peak brightness and line width) of spatially unresolved (>20 pc) line profiles that can be attributed to beam averaging. We focus on the commonly observed low-J transitions of CO isotopologues, HCN, HNC, HCO+, CS, SO and N2H+. Methods. We generated a sample of 1000 toy molecular cloud observations by resampling high-resolution (<0.05 pc) multiline Galactic observations of the Orion B molecular cloud. In the construction of our toy clouds, we imposed a range of density and velocity fields, characterised by their statistics and power spectra. These high-resolution molecular cloud observations were then averaged to single spatially unresolved spectra. We examined the resulting distribution of line profile parameters, and searched for potential correlations among line profile parameters and the underlying sub-beam density and velocity fields. Results. We find that unresolved line profiles’ parameters can vary significantly because of the sub-beam distribution of the emission. Emission lines that tend to be excited at higher densities show the most variability, up to a factor of two for N2H+ (J = 1 0). This variability in an emission line profile is related to the emission line’s covering fraction. As the spectral index of the velocity field increases, unresolved emission lines’ profiles increasingly diverge from a Gaussian shape. Conclusions. Line profile parameters exhibit non-negligible variability solely due to the sub-beam position-position-velocity distribution of the emission. This variability may exceed calibration and noise-related uncertainties.

Feature extraction and analysis of adjustable surfaces in computer graphics

In ultra-precision optical components polishing, the shape of the Tool Influence Function (TIF) is an important factor that affects the processing efficiency and processing accuracy of optical components. For a self-rotating small tool polishing device commonly used in computer-controlled optical surfacing (CCOS), its TIF deviates from the Gaussian shape, and the processing is prone to cause surface figure divergence. Inspired by the theory of eccentric compression, this paper proposes a method to optimize the shape of the TIF based on pressure distribution control. Based on the finite element method, a contact pressure distribution model is established. The influence of different positions of the pressure contact points on the contact pressure distribution is analyzed, and the position of the pressure application point that makes the TIF close to the Gaussian shape is determined. On this basis, a new type of small tool polishing device that can realize the above optimization method is designed. The optimized actual TIF is obtained, and an aspheric mirror processing experiment is completed. After three rounds of processing, the value of PV of the surface form error converged from 1861.180 nm to 64.875 nm, with a convergence rate of 96.5%. The value of RMS converged from 299.857 nm to 6.043 nm, with a convergence rate of 97.9%. The surface figure accuracy has reached the expected goal with the root mean square value less than 10 nm, which verifies the feasibility and effectiveness of this optimization method.

Abstract Atomic frequency comb (AFC) quantum memories are a promising technology for quantum repeater networks because they enable multi-mode, long-time, and high-fidelity storage of photons with on-demand retrieval. The optimization of the retrieval efficiency of an AFC memory is important because it strongly impacts the entanglement distribution rate in quantum networks. Despite initial theoretical analyses and recent experimental demonstrations, a rigorous proof of the universally optimal configuration for the highest AFC retrieval efficiency has not been presented. In this paper we present a simple analytical proof which shows that the optimized square tooth offers the highest retrieval efficiency among all tooth shapes, under the physical constraint of finite optical depth of an atomic ensemble. The optimality still holds when the non-zero background absorption and the finite optical linewidth of atoms are considered. We further compare square, Lorentzian and Gaussian tooth shapes to reinforce the practical advantage of the square-tooth AFC in retrieval efficiency. Our proof lays rigorous foundation for the recipe of creating optimal AFC under realistic experimental conditions.