Geometric Point Research Articles

On an artificial neural network for inverse scattering problems

In this paper, we consider artificial neural networks for inverse scattering problems. As a working model, we consider the inverse problem of recovering a scattering object from the (possibly) limited-aperture radar cross section (RCS) data collected corresponding to a single incident field. This nonlinear and ill-posed inverse problem is practically important and highly challenging due to the severe lack of information. From a geometrical and physical point of view, the low-frequency data should be able to resolve the unique identifiability issue, but meanwhile lose the resolution. On the other hand, the machine learning can be used to break through the resolution limit. By combining the two perspectives, we develop a fully connected neural network (FCNN) for the inverse problem. Extensive numerical results show that the proposed method can produce stunning reconstructions. The proposed strategy can be extended to tackling other inverse scattering problems with limited measurement information.

6D pose measurement of metal parts based on virtual geometric feature point matching

The 6D pose measurement of metal parts is of significance in intelligent manufacturing. This paper proposes a new method which provides a solution through the utilization of geometric features for pose measurement problem in intelligent manufacturing. The proposed method extracts the geometric features in the image and then calculates and matches the virtual geometric feature points according to the pose relation of the geometric features. We propose an algorithm to implement the method. Specifically, the straight lines and ellipses are extracted from the edges and the holes of parts as the geometric features. The crosspoints of the lines and the centers of the ellipses are calculated and utilized as virtual geometric feature points. In addition, to address the fact that the geometric features cannot be easily detected in a single image, this paper proposes a feature extraction method based on multi-image fusion. The experimental results demonstrate that the proposed method can achieve high robustness and accuracy.

Stability margin of undirected homogeneous relative sensing networks: A geometric perspective

In this paper, we study the stability margin (SM) of undirected homogeneous relative sensing networks (UH-RSNs) from a geometric point of view. SM is an important robustness measure indicating the amount of simultaneous gain and phase perturbations in the feedback channels before the instability occurs. A UH-RSN is characterized by the identical local dynamics (a single-input-single-output (SISO) open-loop transfer function T l o c ( s ) ) of individual agent and the graph Laplacian L G representing how the agents are connected. It is shown in this paper that UH-RSNs having multiple inputs and outputs in general may be represented as a unity feedback system including the SISO T l o c ( s ) and one of the real eigenvalues of L G . This representation then helps to identify a class of cooperative T l o c ( s ) for which (1) SM becomes maximized or equal to 1 when the network’s connectivity (the second smallest eigenvalue of L G ) is greater than or equal to the curvature of the Nyquist plot of T l o c ( s ) at the origin; and (2) two bounds on SM are obtained for the SM estimation based on the geometric shape of Nyquist plot. Also, the representation of unity feedback system implies that UH-RSNs with non-cooperative T l o c ( s ) become unstable when the agents are joined with high connectivity. Numerical examples are provided to demonstrate these findings.

Expanded glass spheres applications for low thermal transfer

This study addresses the possibility of using expanded glass to obtain elements with low thermal transfer and stable from a geometric point of view when exposed to high temperatures, which may later be part of a fire-resistant multi-layer element. For this purpose, three types of recipes were designed and produced, which are composed of expanded foam glass spheres bounded with polymeric resin. Subsequently, 3 sets of each sample were subjected to baking: T1 (heating to 700°C, maintaining for 3 hours, oven cooling); T2 (heating to 600 ° C, maintaining for 3 hours, oven cooling); T3 (heating to 600° C, oven cooling). The 4 sets of samples (1 set in initial state and 3 sets of heat treated samples) were exposed for 1 hour at direct flame. It was found that the samples maintained their structural integrity and all three types of material ensure a temperature difference between the side exposed to temperature and the unexposed side higher than 200°C (considered satisfactory according to SREN 1363-1 / 2001).

Clique-width of point configurations

While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of clique-width to geometric point configurations represented by their order type. We study basic properties of this clique-width notion, and show that it is aligned with the general concept of clique-width of relational structures by Blumensath and Courcelle (2006). We also relate the new notion to monadic second-order logic of point configurations. As an application, we provide several linear FPT time algorithms for geometric point problems which are NP-hard in general, in the special case that the input point set is of bounded clique-width and the clique-width expression is also given.

On the interplay between CPE metrics, vacuum static spaces and $$\sigma _2$$-singular spaces

We call CPE metrics the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume. In this short note, we give a necessary and sufficient condition for a CPE metric to be Einstein in terms of $$\sigma _2$$ σ 2 -singular spaces. Such a result improves our understanding about CPE metrics and Besse’s conjecture with a new geometric point of view. Moreover, we prove that the CPE condition can be replaced by the related vacuum static space condition to characterize closed Einstein manifolds in terms of $$\sigma _2$$ σ 2 -singular spaces.

Form and Function of Disorder

The Special Issue “Form and Function of Disorder” has been assembled to honor David A. Drabold on the occasion of his 60th birthday (see the Guest Editorial, article number 2100366). The issue includes an array of topics on disordered materials encompassing applications of classical, quantum-mechanical, and machine-learning approaches to glasses, as well as a generic understanding of disordered systems from geometric and topological points of view. The artwork on the cover page depicts an artist’s impression of a disordered landscape showing the interplay of colors and forms. (Artwork by Katja Biswas.)

Eye Accommodation, Near Vision, and Far Vision from a Geometrical Optics Point of View

The eye should have a particular focal length in order to see an object. As there are many things to see, the focal length of the eye must vary because these things are not all at the same distance from the eye. We explore the eye accommodation from a geometrical optics point of view and present our results in this paper; the study includes a description of the accommodation mechanism and a scientific definition of near vision and far vision.

A geometric representation of fragmentation processes on stable trees

We provide a new geometric representation of a family of fragmentation processes by nested laminations which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation, obtained by cutting a random stable tree at random points, which split the tree into smaller subtrees. When coding each of these cutpoints by a chord in the unit disk, we separate the disk into smaller connected components, corresponding to the smaller subtrees of the initial tree. This geometric point of view allows us in particular to highlight a new relation between the Aldous–Pitman fragmentation of the Brownian continuum random tree and minimal factorizations of the n-cycle, that is, factorizations of the permutation (12⋯n) into a product of (n−1) transpositions, proving this way a conjecture of Féray and Kortchemski. We discuss various properties of these new lamination-valued processes, and we notably show that they can be coded by explicit Lévy processes.

Tool path planning for five-axis U-pass milling of an impeller

U-pass milling is a roughing method that combines the characteristics of flank milling with conventional trochoidal milling. The tool cuts in and out steadily, and the tool–workpiece wrap angle is maintained within a small range. This method can smooth the cutting force and reduce the peak cutting force while avoiding cutting heat accumulation, which can significantly improve the processing efficiency and reduce tool wear. In this study, a tool path model is established for U-pass milling, and the characteristic parameters of the path are defined. Through a comparative test of three-axis groove milling, it is demonstrated that the peak value and average value of the cutting force are reduced by 25% and 60%, respectively. An impeller runner is considered as the processing object, and the milling boundary parameters are pretreated. A tiling micro-arc mapping algorithm is proposed, which maps the three-dimensional boundary to the two-dimensional parameter domain plane with the arc length as the coordinate axis, and the dimensionally reduced tool contact point distribution form is obtained. The geometric domain tool position point and the interference-free tool axis vector are obtained by calculating the bidirectional proportional domain of the runner and the inverse mapping of any vector in the parameter domain. Finally, the calculation results are nested into the automatically programmed tool (APT) encoding form, and the feasibility of the five-axis U-pass milling tool path planning method is verified through a numerical example.

A Phase I, Open-label, Randomized, 2-Way Crossover Study to Evaluate the Relative Bioavailability of Intranasal and Oral Varenicline

PurposeTo estimate the systemic bioavailability of OC-01 (varenicline) nasal spray, an investigational treatment for dry eye disease, relative to oral varenicline approved for smoking cessation. MethodsThe Study to Evaluate the Relative Bioavailability of Varenicline Administered as OC-01 (Varenicline) Nasal Spray as Compared to Varenicline Administered Orally as Chantix (ZEN study) was a Phase I, open-label, randomized, single-center, 2-way crossover study. On day 1, 22 healthy participants were randomized 1:1 to a single intranasal dose of varenicline 0.12 mg in OC-01 nasal spray or a single oral dose of varenicline 1 mg. On day 15, all participants crossed over to receive a single dose of the alternate treatment. Plasma samples were collected for 6 days after each dose, and pharmacokinetic parameters were estimated using noncompartmental analysis. Tolerability was monitored throughout. FindingsAfter a single dose of intranasal varenicline 0.12 mg in OC-01 nasal spray, peak systemic exposure (mean plasma Cmax) was 0.34 ng/mL, which occurred at a median Tmax of 2.0 hours. In comparison, mean plasma Cmax after oral varenicline 1 mg was 4.63 ng/mL at a median Tmax of 3.0 hours. On the basis of geometric mean ratio point estimates, peak exposure (Cmax) and total exposure (AUC0–∞) after intranasal varenicline 0.12 mg were 7.0% and 7.5%, respectively, of the systemic exposure associated with oral varenicline 1 mg. Dose-normalized Cmax and AUC0–∞ for intranasal varenicline remained 39% and 33% lower versus oral varenicline, respectively. No new or unexpected tolerability signals were detected. ImplicationsAt its highest intended single dose in OC-01 nasal spray, intranasal varenicline delivered less drug to the systemic circulation than oral varenicline at its highest approved single dose. ClinicalTrials.gov identifier: NCT04072146.

Combined with Local Neighborhood Characteristics and Remote Sensing Image Fusion Method of C-BEMD

For the sake of ameliorate the high resolution recognition capacity building remote sensing images, a remote sensing image fusion method based on local neighborhood characteristics and C-BEMD is advanced. The building remote sensing image acquisition model and the building remote sensing image picture element edge feature detection model are designed. The wavelet multi-scale denoising method is used to suppress the fuzzy spread of picture element feature points between image residual units, extract the geometric feature points of image sequence, and process the building remote sensing image block by block. The global residual learning and message fusion of building remote sensing image are implemented. The local neighborhood feature matching method is used to reconstruct the building remote sensing image region. Combined with the C-BEMD empirical mode decomposition method, the building remote sensing image fusion and feature point matching in affine region are implemented, and the block image template matching method is used to realize the automatic fusion and recognition of building remote sensing image. Simulation results show that this method has high precision in constructing remote sensing image fusion and good positioning performance in constructing remote sensing image feature points.

A fast and global search method for grasping pose optimization in manufacturing

To use the electromagnetic chuck to precisely absorb industrial parts in manufacturing, this paper presents a hybrid algorithm for grasping pose optimization, especially for the part with a large surface area and irregular shape. The hybrid algorithm is based on the Gaussian distribution sampling and the hybrid particle swarm optimization (PSO). The Gaussian distribution sampling based on the geometric center point is used to initialize the population, and the dynamic Alpha-stable mutation enhances the global optimization capability of the hybrid algorithm. Compared with other algorithms, the experimental results show that ours achieves the best results on the dataset presented in this work. Moreover, the time cost of the hybrid algorithm is near a fifth of the conventional PSO in the discovery of optimal grasping pose. In summary, the proposed algorithm satisfies the real-time requirements in industrial production and still has the highest success rate, which has been deployed on the actual production line of SANY Group.

A Graphic Method for Detecting Multiple Roots Based on Self-Maps of the Hopf Fibration and Nullity Tolerances

The aim of this paper is to study, from a topological and geometrical point of view, the iteration map obtained by the application of iterative methods (Newton or relaxed Newton’s method) to a polynomial equation. In fact, we present a collection of algorithms that avoid the problem of overflows caused by denominators close to zero and the problem of indetermination which appears when simultaneously the numerator and denominator are equal to zero. This is solved by working with homogeneous coordinates and the iteration of self-maps of the Hopf fibration. As an application, our algorithms can be used to check the existence of multiple roots for polynomial equations as well as to give a graphical representation of the union of the basins of attraction of simple roots and the union of the basins of multiple roots. Finally, we would like to highlight that all the algorithms developed in this work have been implemented in Julia, a programming language with increasing use in the mathematical community.

MACHINE LEARNING FOR MOBILE LIDAR DATA CLASSIFICATION OF 3D ROAD ENVIRONMENT

Abstract. 3D road mapping is essential for intelligent transportation system in smart cities. Road features can be utilized for road maintenance, autonomous driving vehicles, and providing regulations to drivers. Currently, 3D road environment receives its data from Mobile Laser Scanning (MLS) systems. MLS systems are capable of rapidly acquiring dense and accurate 3D point clouds, which allow for effective surveying of long road corridors. They produce huge amount of point clouds, which requires automatic features classification algorithms with acceptable processing time. Road features have variant geometric regular or irregular shapes. Therefore, most researches focus on classification of one road feature such as road surface, curbs, building facades, etc. Machine learning (ML) algorithms are widely used for predicting the future or classifying information to help policymakers in making necessary decisions. This prediction comes from a pre-trained model on a given data consisting of inputs and their corresponding outputs of the same characteristics. This research uses ML algorithms for mobile LiDAR data classification. First, cylindrical neighbourhood selection method was used to define point’s surroundings. Second, geometric point features including geometric, moment and height features were derived. Finally, three ML algorithms, Random Forest (RF), Gaussian Naïve Bayes (GNB), and Quadratic Discriminant Analysis (QDA) were applied. The ML algorithms were used to classify a part of Paris-Lille-3D benchmark of about 1.5 km long road in Lille with more than 98 million points into nine classes. The results demonstrated an overall accuracy of 92.39%, 78.5%, and 78.1% for RF, GNB, and QDA, respectively.

Ellipses and ovals: two curves so close and so far

In this work we will deal with ellipses and ovals, comparing them both from the geometric point of view and from the one of applications. There is a notable similarity between these curves so often it’s not possible to recognize which of the two figures is, unless we consider other elements to distinguish them. We will show the presence of both curves in architectural works and in treatises, motivating their use, when it’s possible, with geometric and technological considerations.

On a geometrically nonlinear incremental formulation for the modeling of 3D concrete printing

Of interest in this paper is a modeling framework when constitutive relations are given in incremental form. This is particularly true for aging concretes due to hydration. Furthermore, having in mind applications to 3D concrete printing, geometrical nonlinearities must be accounted for due to the soft nature of the fresh material. The kinematics must then be adapted adequately for a theoretically sound formulation. For this, the multiplicative split is chosen here for the deformation gradient into its known part at an earlier time and the relative deformation gradient. From the geometric point of view, this gives rise to an intermediate configuration on which incremental constitutive relations can be ideally defined prior to be transported back to the reference configuration for a Lagrangian formulation. Model examples are given for the purpose of demonstration and a set of simulations illustrate the effectiveness of the proposed framework.

Experimental study on bow flow field of scientific research ship based on flow visualisation

To investigate the bubble sweep-down phenomenon of a scientific research ship from the perspective of its flow mechanism, the flow-field characteristics of the bow were measured in a towing-tank environment. First, the silk-thread method was used to visualise the streamline characteristics of the bow. Next, the flow field of the bow was measured using multiple two-section 2-dimensional computed tomography scans with stereoscopic particle image velocimetry. The flow-field information of different sections at different speeds (e.g., velocity distribution, vector characteristics, and streamline distribution) were then obtained. A 3-dimensional (3D) three-component (3C) space reconstruction of the time-averaged flow field in the bow was thus realised. From the visualisation results, the flow field in the bow generally exhibits a downward movement trend. The flow structure of the bow flow field was found to be closely related to the wave-making change of the bow. On the other hand, the cross-sectional flow characteristics and 3D reconstruction results showed that with the bubble sweep-down, some bubbles flowed along the bilge and amassed with other bubbles, breaking through the geometric inflection point of the bilge. Compressed by the bilge vortex, they slid backward and affected the operation of acoustic equipment.

Uniformity in Mordell–Lang for curves

Consider a smooth, geometrically irreducible, projective curve of genus $g\ge 2$ defined over a number field of degree $d \ge 1$. It has at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of $g$, $d$ and the Mordell–Weil rank of the curve's Jacobian, thereby answering in the affirmative a question of Mazur. In addition we obtain uniform bounds, in $g$ and $d$, for the number of geometric torsion points of the Jacobian which lie in the image of an Abel–Jacobi map. Both estimates generalize our previous work for one-parameter families. Our proof uses Vojta's approach to the Mordell Conjecture, and the key new ingredient is the generalization of a height inequality due to the second- and third-named authors.

On the Convergence of Stochastic Process Convergence Proofs

Convergence of a stochastic process is an intrinsic property quite relevant for its successful practical for example for the function optimization problem. Lyapunov functions are widely used as tools to prove convergence of optimization procedures. However, identifying a Lyapunov function for a specific stochastic process is a difficult and creative task. This work aims to provide a geometric explanation to convergence results and to state and identify conditions for the convergence of not exclusively optimization methods but any stochastic process. Basically, we relate the expected directions set of a stochastic process with the half-space of a conservative vector field, concepts defined along the text. After some reasonable conditions, it is possible to assure convergence when the expected direction resembles enough to some vector field. We translate two existent and useful convergence results into convergence of processes that resemble to particular conservative vector fields. This geometric point of view could make it easier to identify Lyapunov functions for new stochastic processes which we would like to prove its convergence.