Uniform Distribution Of Points Research Articles

High density mapping accuracy and efficiency in atrial fibrillation: real-world outcomes from the SECURE registry

Abstract Background/Introduction A high-density (HD) mapping catheter is valuable for validating pulmonary vein isolation (PVI) and analysing arrhythmic substrates of the left atrium (LA) during atrial fibrillation (AF) ablation. Multiple HD mapping catheters are available for use in clinical practice. A novel octa-spline mapping catheter with a close internal unipolar reference electrode is now available and may improve mapping efficiencies and image resolutions (Figure). Purpose This study aims to report real-world experiences with different commercially available HD mapping catheters in AF ablation and compare mapping performance. Methods SECURE is an ongoing observational, prospective, post-marketing study collecting real-world data on ablation procedures performed per standard-of-care. At the time of data extraction (Nov. 2023), 16 sites across 8 countries had enrolled 2,366 patients (pts), with 12-month follow-up data available for 828 pts. The current analysis, which included consecutive pts undergoing AF ablation, evaluated mapping efficiency and procedural outcomes with 3 HD mapping catheters: circular catheter (CC), penta-spline catheter (PSC), and octa-spline catheter (OSC). Mapping data were analysed with a cloud-based data management and artificial intelligence-powered algorithm. Results Overall, 859 pts with AF (paroxysmal AF [PAF], n=465; persistent AF [PsAF], n=240; long-standing PsAF [LS PsAF], n=154) were included in this analysis. The CC, PSC, and OSC were used in 428, 210, and 221 pts, respectively. Procedures using the OSC had a significantly higher mean mapping area (31,989.9 mm2) than those performed with the CC (23,152.2 mm2; P<0.0001) and PSC (29,804.6 mm2; P=0.0027), as well as a >3-fold higher mean mapping rate (138.4 vs 20.8 and 43.4 points/min, respectively; both P<0.0001). The higher number of mapping points translated to a higher mean mapping density (OSC, 0.34 vs CC, 0.05 and PSC, 0.07 points/mm2; both P<0.0001), with more uniform point distribution and less interpolation. With the CC, PSC, and OSC, respectively, total mean procedure times (incl PVI + other targets) were 118.0, 118.7, and 165.1 min, (P<0.0001 for OSC vs. both CC and PSC) and mean pre-ablation mapping times were 25.2, 25.0, and 21.5 min (P<0.0004 for OSC vs. both CC and PSC). The improved mapping quality and efficiency with the OSC allowed to include specific ablation targets beyond PVI. Fewer PVI-only procedures were performed with the OSC (29.4%) versus the CC (62.1%) and PSC (54.8%), while ablation of the PVI+ other targets was more common with the OSC versus the CC and PSC, including the cavotricuspid isthmus (37.1% vs 17.3% and 16.7%), LA roof (42.5% vs 13.1% and 21.4%), and LA posterior wall (21.7% vs 10.5% and 16.2%). Results were overall consistent per AF type (Table). Conclusions By providing more accurate mapping, the OSC allows for improved analysis of the arrhythmic substrate, which may improve ablation outcomes for pts with PAF and PsAF.Figure 1

Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems

A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems.

Comparison of Physics Informed Neural Networks and Finite Element Method Solvers for advection-dominated diffusion problems

We present a comparison of Physics Informed Neural Networks (PINN) and Variational Physics Informed Neural Networks (VPINN) with higher-order and continuity Finite Element Method (FEM). We focus on the one-dimensional advection-dominated diffusion problem and the two-dimensional Eriksson–Johnson model problem. We show that the standard Galerkin method for FEM cannot solve this problem on uniform grid. We discuss the stabilization of the advection-dominated diffusion problem with the Petrov–Galerkin (PG) formulation and present the FEM solution obtained with the PG method. The main benefit of using a stabilization method is that it can deliver a good-quality approximation to the solution on a mesh that is not fully refined towards the singularity. We employ PINN and VPINN methods, defining several strong and weak loss functions. We compare the training and solutions of PINN and VPINN methods with higher-order FEM methods. We consider a case with uniform FEM and uniform distribution of points for PINN, as well as uniform distribution of test functions for VPINN. We also consider adaptive FEM, refined towards edge singularity, and non-uniform distribution of points for PINN, as well as non-uniform distribution of test functions for VPINN.

Learning Contours for Point Cloud Completion

The integrity of a point cloud frequently suffers from discontinuous material surfaces or coarse sensor resolutions. Existing methods focus on reconstructing the overall structure, but salient points or small irregular surfaces are difficult to be predicted. Toward this issue, we propose a new end-to-end neural network for point cloud completion. To avoid non-uniform point density, the regular voxel centers are selected as reference points. The encoder and decoder are designed with Patchify, transformers, and multilayer perceptrons. An implicit classifier is incorporated in the decoder to mark the valid voxels that are allowed for diffusion after removing vacant grids from completion. With newly designed loss function, the classifier is trained to learn the contours, which helps to identify the grids that are difficult to be judged for diffusion. The effectiveness of the proposed model is validated in the experiments on the indoor ShapeNet dataset, the outdoor KITTI dataset, and the airbone laser dataset by competing with state-of-the-art methods, which show that our method can predict more accurate point coordinates with rich details and uniform point distributions.

Random screening-based feature aggregation for point cloud denoising

Raw point clouds captured by sensing devices are often contaminated with noise, which perturbs the fidelity of the original geometric information. Point cloud denoising is therefore an inseparable post-processing step, aiming to remove the noise in the point clouds. Existing point cloud denoising approaches are typically trained on datasets that have uniform point distributions and densities, making them unsuitable for effectively denoising point clouds with severe noise or irregular point distributions. In this paper, we introduce a novel random screening-based feature aggregation method for point cloud denoising. Our key insight is that merging features of dense and sparse points assists with enhancing the quality of point cloud denoising results. In specific, our approach involves randomly screening the features of local point patches and fusing richer geometric information of denser points into sparser point representations. Comprehensive experiments demonstrate that our method achieves state-of-the-art performance in the point cloud denoising task on both synthetic and real-world datasets.

Towards uniform point distribution in feature-preserving point cloud filtering

While a popular representation of 3D data, point clouds may contain noise and need filtering before use. Existing point cloud filtering methods either cannot preserve sharp features or result in uneven point distributions in the filtered output. To address this problem, this paper introduces a point cloud filtering method that considers both point distribution and feature preservation during filtering. The key idea is to incorporate a repulsion term with a data term in energy minimization. The repulsion term is responsible for the point distribution, while the data term aims to approximate the noisy surfaces while preserving geometric features. This method is capable of handling models with fine-scale features and sharp features. Extensive experiments show that our method quickly yields good results with relatively uniform point distribution.

Generalized limit theorems for U-max statistics

Abstract $U{\hbox{-}}\textrm{max}$ statistics were introduced by Lao and Mayer in 2008. Such statistics are natural in stochastic geometry. Examples are the maximal perimeters and areas of polygons and polyhedra formed by random points on a circle, ellipse, etc. The main method to study limit theorems for $U{\hbox{-}}\textrm{max}$ statistics is via a Poisson approximation. In this paper we consider a general class of kernels defined on a circle, and we prove a universal limit theorem with the Weibull distribution as a limit. Its parameters depend on the degree of the kernel, the structure of its points of maximum, and the Hessians of the kernel at these points. Almost all limit theorems known so far may be obtained as simple special cases of our general theorem. We also consider several new examples. Moreover, we consider not only the uniform distribution of points but also almost arbitrary distribution on a circle satisfying mild additional conditions.

A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability and uniform point distribution

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the sampling points. Since the computation of an optimal selection of sampling points may be an infeasible task, one promising option is to use greedy methods.Although these methods may be very effective, depending on the specific greedy criterion the chosen points might quickly lead to instabilities in the computation. To circumvent this problem, we introduce and investigate a new class of stabilized greedy kernel algorithms, which can be used to create a scale of new selection strategies.We analyze these algorithms, and in particular we prove convergence results and quantify in a precise way the distribution of the selected points. These results allow to prove, in the case of certain Sobolev kernels, that the algorithms have optimal stability and optimal convergence rates, including for functions outside the native space of the kernel. The results also apply to the case of the usual P-greedy algorithm, significantly improving state-of-the-art results available in the literature. Illustrative experiments are presented that support the theoretical findings and show improvements of the stabilized algorithms in terms of accuracy due to improved stability.

РЕЗУЛЬТАТЫ МНОГОФАКТОРНОЙ ОПТИМИЗАЦИЯ ПАРАМЕТРОВ ИССЛЕДУЕМЫХ ЭНЕРГОСБЕРЕГАЮЩИХ СИСТЕМ, ПРИМЕНЯЕМЫХ В ЛЕСОВОЗНОМ АВТОМОБИЛЬНОМ ТРАНСПОРТЕ

A promising direction has been substantiated that increases the efficiency of timber road transport during timber hauling, based on the development and use of various recuperative mechanisms in its design. The analysis of foreign literature has been carried out and the authors' developments and the obtained research results in this area are described. Parametric optimization of eight types of investigated recuperative energy-saving systems has been carried out on the basis of mathematical modeling. A diagram of options for optimizing the design parameters of energy-saving systems is presented, including one-factor, two-factor and multi-factor optimization. Algorithms for multifactorial optimization of design parameters and uniform distribution of a given number of points of a computer experiment in a multifactor space are presented. A mathematical apparatus for the uniform distribution of points in a multifactor space has been developed. The choice of neural network approximation for solving the problem of multifactor optimization is substantiated. An artificial neural network topology diagram is presented. An algorithm for studying the factor space using an approximating radial neural network has been developed. A method of multifactor optimization is proposed, which makes it possible to ensure a minimum of computer experiments that uniformly cover the multifactor space with highly detailed representation of response surfaces and ensuring the search for optimal regions of the factor space. Optimization of parameters of eight investigated recuperative energy-saving systems for timber road transport has been made.

Virtual Forestry Generation: Evaluating Models for Tree Placement in Games

A handful of approaches have been previously proposed to generate procedurally virtual forestry for virtual worlds and computer games, including plant growth models and point distribution methods. However, there has been no evaluation to date which assesses how effective these algorithms are at modelling real-world phenomena. In this paper, we tackle this issue by evaluating three algorithms used in the generation of virtual forests—a randomly uniform point distribution method (control), a plant competition model, and an iterative random point distribution technique. Our results show that a plant competition model generated more believable content when viewed from an aerial perspective. Interestingly, however, we also found that a randomly uniform point distribution method produced forestry which was rated higher in playability and photorealism, when viewed from a first-person perspective. We conclude that the objective of the game designer is important to consider when selecting an algorithm to generate forestry, as the algorithms produce forestry that is perceived differently.

Generalized regular k-point grid generation on the fly

In the DFT community, it is common practice to use regular k -point grids (Monkhorst-Pack, MP) for Brillioun zone integration. Recently Wisesa et al. (2016) and Morgan et al. (2018) demonstrated that generalized regular (GR) grids offer an advantage over traditional MP grids. The difference is simple but effective. At the same k -point density, GR grids have greater symmetry and 60% fewer irreducible k -points. GR grids have not been widely adopted because one must search through a large number of candidate grids; in many cases, a brute force search could take hours. This work describes an algorithm that can quickly search over GR grids for those that have the most uniform distribution of points and the best symmetry reduction. The grids are ∼ 60% more efficient, on average, than MP grids and can now be generated on the fly in seconds.

Modification of the Maximin and ϕp (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points

This article proposes a sampling technique that delivers robust designs, that is, point sets selected from a design domain in the shape of a unit hypercube. The designs are guaranteed to provide a statistically uniform point distribution, meaning that every location has the same probability of being selected. Moreover, the designs are sample uniform, meaning that each individual design has its points spread evenly throughout the domain. The sample uniformity (often measured via a discrepancy criterion) is achieved using distance-based criteria ( or Maximin), that is, criteria normally used in space-filling designs. We show that the standard intersite metrics employed in distance-based criteria (Maximin and (phi)) do not deliver statistically uniform designs. Similarly, designs optimized via centered L2 discrepancy or support points are also not statistically uniform. When these designs (after optimization based on intersite distances) are used for Monte Carlo type of integration, their statistical nonuniformity is a serious problem as it may lead to a systematic bias. This article proposes using a periodic metric to guarantee the statistical uniformity of the family of distance-based designs. The presented designs used as benchmarks in the article are only taken from the class of Latin hypercube designs, which forces univariate projections to be uniform and improves accuracy in Monte Carlo integration of some functions. Supplementary materials for this article are available online.

Hyperuniformity on spherical surfaces.

We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.

Path length distribution in two-dimensional causal sets

We study the distribution of maximal-chain lengths between two elements of a causal set and its relationship with the embeddability of the causal set in a region of flat spacetime. We start with causal sets obtained from uniformly distributed points in Minkowski space. After some general considerations we focus on the 2-dimensional case and derive a recursion relation for the expected number of maximal chains n_k as a function of their length k and the total number of points N between the maximal and minimal elements. By studying these theoretical distributions as well as ones generated from simulated sprinklings in Minkowski space we identify two features, the most probable path length or peak of the distribution k_0 and its width varDelta , which can be used both to provide a measure of the embeddability of the causal set as a uniform distribution of points in Minkowski space and to determine its dimensionality, if the causal set is manifoldlike in that sense. We end with a few simple examples of n_k distributions for non-manifoldlike causal sets.

Normal Direction Measurement and Optimization With a Dense Three-Dimensional Point Cloud in Robotic Drilling

In large-scale structure assembly, the normal direction of a drilled surface is required to be measured online instead of extracted directly from the computer-aided design model because of tool error, cutting force, and other factors. To this end, first, a high-resolution structured-light-based three-dimensional (3-D) measurement is adopted to improve measurement reliability; second, tensor voting is proposed to remove noise and fill in blanks in the measured 3-D point cloud to obtain a uniform point distribution for surface fitting; and third, the surface smoothness after rivet installation is defined and optimized. The proposed methods are verified by simulations and experiments. The results show that the proposed methods are effective.

Refinement of LiDAR point clouds using a super voxel based approach

We propose a new approach for automatic refinement of unorganized point clouds captured by LiDAR scanning systems. Given a point cloud, our method first abstracts the input data into super voxels via over segmentations, and then builds a K-nearest neighbor graph on these voxel nodes. Abstracting into voxel representation provides a means to generate an elastic wireframe over the original data. An iterative resampling method is then introduced to project resampling points to all potential surfaces considering repulsion constraints from both interior and exterior of voxels. Our point consolidation process contributes to accurate normal estimation, uniform point distribution, and sufficient sampling density. Experiments and comparisons have demonstrated that the proposed method is effective on point clouds from a variety of datasets.

The model of UAV formation based on the uniform allocation of points on the sphere

We consider an approach to constructing the desired virtual structure, which should be formed by unmanned aerial vehicles (UAVs). The proposed model is based on the principle of quasi-uniform allocation of points, previously used by the author in clustering problems. The mathematical apparatus for solving the problem of forming the desired structure is given: necessary theorems are proved; the hypothesis on the uniform distribution of points on the boundary of the circle and the sphere is put forward and partially proved. The method for optimal assignment of UAVs to goal positions in the desired formation is considered.

Modeling distances between humans using Taylor’s law and geometric probability

ABSTRACTTaylor’s law states that the variance of the distribution of distance between two randomly chosen individuals is a power function of the mean distance. It applies to the distances between two randomly chosen points in various geometric shapes, subject to a few conditions. In Réunion Island and metropolitan France, at some spatial scales, the empirical frequency distributions of inter-individual distances are predicted accurately by the theoretical frequency distributions of inter-point distances in models of geometric probability under a uniform distribution of points. When these models fail to predict the empirical frequency distributions of inter-individual distances, they provide baselines against which to highlight the spatial distribution of population concentrations.

Data acquisition considerations for Terrestrial Laser Scanning of forest plots

The poor constraint of forest Above Ground Biomass (AGB) is responsible, in part, for large uncertainties in modelling future climate scenarios. Terrestrial Laser Scanning (TLS) can be used to derive unbiased and non-destructive estimates of tree structure and volume and can, therefore, be used to address key uncertainties in forest AGB estimates. Here we review our experience of TLS sampling strategies from 27 campaigns conducted over the past 5years, across tropical and temperate forest plots, where data was captured with a RIEGL VZ-400 laser scanner. The focus is on strategies to derive Geometrical Modelling metrics (e.g. tree volume) over forest plots (≥1ha) which require the accurate co-registration of 10s to 100s of individual point clouds. We recommend a 10m × 10m sampling grid as an approach to produce a point cloud with a uniform point distribution, that can resolve higher order branches (down to a few cm in diameter) towards the top of 30+ m canopies and can be captured in a timely fashion i.e. ∼3–6days per ha. A data acquisition protocol, such as presented here, would facilitate data interoperability and inter-comparison of metrics between instruments/groups, from plot to plot and over time.

Quasi-equal area subdivision algorithm for uniform points on a sphere with application to any geographical data distribution

This paper describes a quasi-equal area subdivision algorithm based on equal area spherical subdivision to obtain approximated solutions to the problem of uniform distribution of points on a 2-dimensional sphere, better known as Smale's seventh problem. The algorithm provides quasi-equal area triangles, starting by splitting the Platonic solids into subsequent spherical triangles of identical areas. The main feature of the proposed algorithm is that the final adjacent triangles share common vertices that can be merged. It applies reshaping to the final triangles in order to remove obtuse triangles. The proposed algorithm is fast and efficient to generate a large number of points. Consequently, they are suitable for various applications requiring a large number of distributed points. The proposed algorithm is then applied to two geographical data distributions that are modeled by quasi-uniform distribution of weighted points.