Geometric Point Research Articles

On the non-flatness nature of noncommutative Minkowski spacetime and the singular behavior of probes

It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.

Parametrical Choice of the Optimized Fusion System for a FFHR

Fusion–fission hybrid reactors are concepts of subcritical reactors based on the coupling of fusion and fission devices. In this case, the fusion reactor would work as an external neutron supplier for the fission core of the machine. Such systems could, in principle, operate as multi-purpose machines, such as energy generators, breeders and waste burners. The large availability of fusion and fission technologies makes the choice of devices to couple quite chaotic. In fact, most of the concepts proposed in the literature are based on attempts without real optimization. The purpose of this paper is to propose a parameter which could provide practical information regarding the choice or the design of the fusion system of an FFHR. An engineering approach based on the estimation of the energy efficiency of FFHRs was used. An evaluation of the parameter and some of its possible practical applications are shown. Obtained results indicate that, from a geometrical point of view, compact machines would need lower Q-values to reach high neutron source performance.

Robust and correspondence-free point cloud registration: an extended approach with multiple hypotheses evaluation

AbstractPoint cloud registration is a fundamental problem in robotics, critical for tasks such as localization and mapping. Most approaches to this problem use feature-based techniques. However, these approaches have issues when dealing with unstructured environments where meaningful features are difficult to extract. Recently, an innovative global point cloud registration algorithm, PHASER, which does not rely on geometric features or point correspondences, has been introduced. It leverages Fourier transforms to identify the optimal rigid transform that maximizes cross-correlation between source and target point clouds. PHASER can also incorporate additional data channels, like LiDAR intensity, to enhance registration results. Because it does not rely on local features and because of its ability to exploit additional data, PHASER is particularly useful when dealing with very noisy point clouds or with many outliers. For this reason, we propose an extension to PHASER that considers multiple plausible rototranslation hypotheses. Our extended approach outperforms the original PHASER algorithm, especially in challenging scenarios where point clouds are widely separated. We validate its effectiveness on the DARPA SubT, and the Newer College datasets, showcasing its potential for improving registration accuracy in complex environments.

Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators

We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functional-analytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we present the associated pair of unbounded adjoint operators. Such a pair is explicitly written for the first time, despite the abundance of the literature on the topic. We use it to find the stress solution as an intersection of the (affinely translated) fundamental subspaces of the adjoint operators. In particular, we treat the equilibrium equation in the operator form, which involves the spaces of traces on a part of the boundary, known as the Lions-Magenes spaces. Our analysis of the pair of adjoint operators for the problem with mixed boundary conditions relies on the properties of the analogous pair of operators for the problem with the displacement boundary conditions, which we also include in the paper.

Geometric approach to define a railway plan model

The construction of new railway lines is based on the railway plan. There are various ways to draw up a railway plan. The basis of all railway plans is a scheme of geometric point locations, the projection of the center of gravity of the carriage is on a horizontal plane and consists of a single flat line. The railway plan consists of linear and curved parts connecting straight sections. However, the curves determining the position of the rails of the railway track in the curved part will be spatial. To extinguish the centrifugal forcearising in the curved part of the road, an external rail rises. In this case, the elevated curve representing the outer rail becomes spatial. Therefore, in the work, it is proposed to draw up a plan of a railway track as two curves, one of which is flat, and the other depicts an external spatial rail. In this case, the distance between the ends of the rectilinear parts and the angle between the rectilinear parts are selected as the main parameters. In the work, for the simplest case, when both linear parts belong to the same horizontal plane, it is proved that the curved part is a spatial curve. The curvature of the required curve was determined and a dynamic system was constructed, the solution of which would be a curve that satisfied the technical conditions presented for the railway route. This dynamic system is proposed as a mathematical model of the railway route. In the rectilinear parts, the railway plan is straight on a horizontal plane. The curve of the road should be spatial.

Numerical methods for shape optimal design of fluid–structure interaction problems

We consider the method of mappings for performing shape optimization for unsteady fluid–structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes several theoretical results into account, such as regularity requirements on the transformations and a differential geometrical point of view on the manifold of shapes. Moreover, we discretize the problem such that we can compute exact discrete gradients. This allows for the use of general purpose optimization solvers. We focus on problems derived from an FSI benchmark to validate our numerical implementation. The method is used to optimize parts of the outer boundary and the interface. The numerical simulations build on FEniCS, dolfin-adjoint and IPOPT. Moreover, as an additional theoretical result, we show that for a linear special case the adjoint attains the same structure as the forward problem but reverses the temporal flow of information.

RF-ULM: Ultrasound Localization Microscopy Learned From Radio-Frequency Wavefronts.

In Ultrasound Localization Microscopy (ULM), achieving high-resolution images relies on the precise localization of contrast agent particles across a series of beamformed frames. However, our study uncovers an enormous potential: The process of delay-and-sum beamforming leads to an irreversible reduction of Radio-Frequency (RF) channel data, while its implications for localization remain largely unexplored. The rich contextual information embedded within RF wavefronts, including their hyperbolic shape and phase, offers great promise for guiding Deep Neural Networks (DNNs) in challenging localization scenarios. To fully exploit this data, we propose to directly localize scatterers in RF channel data. Our approach involves a custom super-resolution DNN using learned feature channel shuffling, non-maximum suppression, and a semi-global convolutional block for reliable and accurate wavefront localization. Additionally, we introduce a geometric point transformation that facilitates seamless mapping to the B-mode coordinate space. To understand the impact of beamforming on ULM, we validate the effectiveness of our method by conducting an extensive comparison with State-Of-The-Art (SOTA) techniques. We present the inaugural in vivo results from a wavefront-localizing DNN, highlighting its real-world practicality. Our findings show that RF-ULM bridges the domain shift between synthetic and real datasets, offering a considerable advantage in terms of precision and complexity. To enable the broader research community to benefit from our findings, our code and the associated SOTA methods are made available at https://github.com/hahnec/rf-ulm.

Robotic MR-guided high dose rate brachytherapy needle implantation in the prostate (ROBiNSon)—a proof-of-concept study

Objective. A robotic needle implant device for MR-guided high-dose-rate (HDR) prostate brachytherapy was developed. This study aimed to assess the feasibility and spatial accuracy of HDR brachytherapy using the robotic device, for a single intraprostatic target point. Approach. Five patients were treated from November 2019–June 2022 with the robot. The robot fits a 1.5 T MR scanner and the needle can be shifted and angulated. An intraprocedural MR scan was fused with the diagnostic MR and one preplanned needle position was selected for robotic insertion. The needle entry point and angles were set for a needle tip target point within the intraprostatic target volume. The needle was tapped stepwise towards the target point pneumatically. Final needle position was verified with MR, followed by plan optimization and dose delivery. Any remaining planned needles were inserted manually. Needle tip to geometrical target error (NTG-error) was defined as the deviation of the actual tip position relative to the predefined geometric target point, using MR-coordinates. Needle tip to treatment target error (NTT-error) was defined as the deviation of the actual tip position relative to the treatment target point, using fused MR-images pre- and post-needle implantation taking into account prostate deformation. Difference between NTT-error and NTG-error and fiducial marker shifts indicated prostate movement. For determining prostate deformation, the Jaccard index and prostate volumes were assessed. Main results. The robotic device was able to tap the needle to the planned depth for all patients. Mean robotic procedure duration was 142 min. NTG-error was 3.2 (range 1.1–6.7) mm and NTT-error 4.5 (range 2.6–9.6) mm. Marker displacements were smaller than 3 mm. No treatment-related acute toxicity was reported. Feasibility of needle placement within the prostate was considered adequate. Significance. MR-guided robotic needle insertion is feasible with a mean geometric accuracy of 3.2 mm and <3 mm prostate movement.

Occurrence of Wetness on the Fruit Surface Modeled Using Spatio-Temporal Temperature Data from Sweet Cherry Tree Canopies

Typically, fruit cracking in sweet cherry is associated with the occurrence of free water at the fruit surface level due to direct (rain and fog) and indirect (cold exposure and dew) mechanisms. Recent advances in close range remote sensing have enabled the monitoring of the temperature distribution with high spatial resolution based on light detection and ranging (LiDAR) and thermal imaging. The fusion of LiDAR-derived geometric 3D point clouds and merged thermal data provides spatially resolved temperature data at the fruit level as LiDAR 4D point clouds. This paper aimed to investigate the thermal behavior of sweet cherry canopies using this new method with emphasis on the surface temperature of fruit around the dew point. Sweet cherry trees were stored in a cold chamber (6 °C) and subsequently scanned at different time intervals at room temperature. A total of 62 sweet cherry LiDAR 4D point clouds were identified. The estimated temperature distribution was validated by means of manual reference readings (n = 40), where average R2 values of 0.70 and 0.94 were found for ideal and real scenarios, respectively. The canopy density was estimated using the ratio of the number of LiDAR points of fruit related to the canopy. The occurrence of wetness on the surface of sweet cherry was visually assessed and compared to an estimated dew point (Ydew) index. At mean Ydew of 1.17, no wetness was observed on the fruit surface. The canopy density ratio had a marginal impact on the thermal kinetics and the occurrence of wetness on the surface of sweet cherry in the slender spindle tree architecture. The modelling of fruit surface wetness based on estimated fruit temperature distribution can support ecophysiological studies on tree architectures considering resilience against climate change and in studies on physiological disorders of fruit.

A Dataset for Kinship Estimation from Image of Hand Using Machine Learning

Kinship (Familial relationships) detection is crucial in many fields and has applications in biometric security, adoption, forensic investigations, and more. It is also essential during wars and natural disasters like earthquakes since it may aid in reunion, missing person searches, establishing emergency contacts, and providing psychological support. The most common method of determining kinship is DNA analysis which is highly accurate. Another approach, which is noninvasive, uses facial photos with computer vision and machine learning algorithms for kinship estimation. Each part of the Human -body has its own embedded information that can be extracted and adopted for identification, verification, or classification of that person. Kinship recognition is based on finding traits that are shared by every family. We investigate the use of hand geometry for kinship detection, which is a new approach. Because of the available hand image Datasets do not contain kinship ground truth; therefore, we created our own dataset. This paper describes the tools, methodology, and details of the collected MKH, which stands for the Mosul Kinship Hand, images dataset. The images of MKH dataset were collected using a mobile phone camera with a suitable setup and consisted of 648 images for 81 individuals from 14 families (8 hand situations per person). This paper also presents the use of this dataset in kinship prediction using machine learning. Google MdiaPipe was used for hand detection, segmentation, and geometrical key points finding. Handcraft feature extraction was used to extract 43 distinctive geometrical features from each image. A neural network classifier was designed and trained to predict kinship, yielding about 93% prediction accuracy. The results of this novel approach demonstrated that the hand possesses biometric characteristics that may be used to establish kinship, and that the suggested method is a promising way as a kinship indicator.

A Fourier transform for Banach–Colmez spaces

We define and study an \ell -adic Fourier transform for a relative version of Banach–Colmez spaces (over a perfectoid space which is not necessarily a geometric point), which can be thought of as some analytic analogue of the \ell -adic Fourier transform for unipotent perfect group schemes. We explicitly describe it on some examples.

Remotely Controlled 3D-Engineered Scaffolds for Biomimetic In Vitro Investigations on Brain Cell Cocultures.

Most in vitro studies regarding new anticancer treatments are performed on 2D cultures, despite this approach imposes several limitations in recapitulating the real tumor behavior and in predicting the effects of therapy on both cancer and healthy tissues. Herein, advanced in vitro models based on scaffolds that support the 3D growth of glioma cells, further allowing the cocultures with healthy brain cells, are presented. These scaffolds, doped with superparamagnetic iron oxide nanoparticles and obtained through 2-photon polymerization, can be remotely manipulated thanks to an external magnet, thus obtaining biomimetic 3D organization recapitulating the brain cancer microenvironment. From a geometric point of view, the structure is functional to both cell culture on individual unit scaffolds and to tailored cocultures fostered by magnetic-driven unit assembly, also allowing for cell migration thanks to passages/fenestrations on adjacent structures. Leveraging magnetic dragging, for which a mathematical model is introduced, multiple cocultures are achieved, highlighting the high versatility and the user-friendly character of the proposed platform that can help overcome the current challenges in 3D cocultures handling, and open the way to the construction of increasingly biomimetic artificial systems.

A new kinematic model for revolute clearance joints with noncircular bushing and pin in planar multibody systems

Due to manufacturing error and wear, the profiles of bushing and pin in revolute clearance joints are usually non-circular, while traditional kinematic models for revolute clearance joints generally assume a circular profile for the pin or bushing, which may not be able to accurately capture the kinematic behavior of real revolute joints in multibody systems. To this end, a curvature center method was proposed for the kinematic modeling of revolute clearance joints with noncircular bushing and pin. In the proposed method, both the noncircular bushing and pin were discretized, and the curvature center and radius corresponding to each discrete point were then obtained to detect the point of contact between the bushing and pin based on their kinematic constraints. The number of discrete points was determined based on both accuracy and efficiency of the proposed curvature center method, which was then applied to model a revolute clearance joint between the slider and the link of a slider-crank mechanism. Via comparison to the traditional geometric center method and discrete point method, it was validated that the proposed method can achieve a comparable accuracy in modeling revolute joints with a circular pin. The unique advantage of the proposed curvature center method is its ability in modeling revolute joints with noncircular bushing and noncircular pin, which was also demonstrated via a series of simulations. Simulation results show a significant influence of noncircular bushing and noncircular pin on the dynamic response of the multibody system. This implies the promising value of the proposed method in studying the effect of manufacturing error or wear of both bushing and pin on the system’s dynamic performance and/or service life.

A machine learning based approach for generating point sketch maps from qualitative directional information

People often use qualitative relations to describe locations or directional information, especially in written communication, such as ‘the restaurant is located at the southeast corner of the square’. However, when a large number of spatial entities are involved, qualitative relations alone are not intuitive enough for people to understand a spatial configuration. In fact, many applications, e.g. pertaining to sharing travel experiences, use sketch maps, i.e. maps focusing on the main features of an area whilst abstracting exact scale measurements, to help demonstrate abstract qualitative relations with more intuitive geometric points. Current approaches for generating point sketch maps from qualitative spatial relations require a high level of expertise, face inherent difficulties with efficiently processing large-scale data in bulk, and are vulnerable to inaccurate or conflicting information contained in qualitative data. To address these limitations, by incorporating machine learning techniques, we propose to translate the problem into an optimization problem of data reconstruction, enabling a novel end-to-end approach for generating point sketch maps from qualitative directional relations in bulk. Experiments on real-world datasets show that the proposed approach has very high accuracy and is robust even with a large portion of inaccurate or incomplete information.

Diffeomorphic structure of evolution equations

In this work the problem of the consistent treatment of multidimensional quadratic Hamiltonians is analyzed and developed from the geometric point of view. To this end, two approaches to the treatment for the problem are studied and developed: the pure matrix representation that involves Madelung type transforms (maps), and the evolution type based in a group manifold endowed with the symplectic groups and their coverings. Some of our goals is to introduce important geometric and group theoretical tools in the proposed approaches, such as Fermi normal coordinates in the first and a generalization of the method of nonlinear realizations in the second one. Several interesting results appear and some examples of application of these concepts in different physical scenarios are developed and presented such as the relationship with the Zeldovich approximation for the dynamic of large-scale cosmological structure, the classic case of Gertsner waves or the evolution problem with an inverted Hamiltonian of Caldirola-Kanai type.

The worst approximable rational numbers

We classify and enumerate all rational numbers with approximation constant at least 13 using hyperbolic geometry. Rational numbers correspond to geodesics in the modular torus with both ends in the cusp, and the approximation constant measures how far they stay out of the cusp neighborhood in between. Compared to the original approach, the geometric point of view eliminates the need to discuss the intricate symbolic dynamics of continued fraction representations, and it clarifies the distinction between the two types of worst approximable rationals: (1) There is a plane forest of Markov fractions whose denominators are Markov numbers. They correspond to simple geodesics in the modular torus with both ends in the cusp. (2) For each Markov fraction, there are two infinite sequences of companions, which correspond to non-simple geodesics with both ends in the cusp that do not intersect a pair of disjoint simple geodesics, one with both ends in the cusp and one closed.

Optimizing Osteoporosis Classification through Femur Bone Volumetric Estimation with Deep Belief Network in X-ray Imaging

The accurate classification of osteoporosis is a crucial requirement in the medical field for identifying patients with skeletal disorders associated with aging. Achieving improved accuracy and reduced computational complexity in classification algorithms is essential. To address this, our research proposes a novel classification method utilizing the Hybrid Gradient Particle Swarm (HSG) Optimization-based Deep Belief Network, integrating the Particle Swarm Optimization (PSO) algorithm into the Gradient Descent (GD) algorithm. The osteoporosis classification process comprises five key steps: Preprocessing, Active Shape Model-based Segmentation, Geometric Estimation employing the proposed template search method, Feature Extraction for extracting medical and image-level features, and Osteoporosis Classification using the HSG-based Deep Belief Network. The proposed template search method efficiently and automatically updates the geometric points of the femur segment. Experimental validation using a real-time database demonstrates the effectiveness of the proposed method in terms of accuracy, sensitivity, and specificity. The results indicate an accuracy of 0.9724, affirming the efficacy of the proposed algorithm in making precise decisions regarding osteoporosis classification.

Geometric Co-Ordinate Feature Point Estimation (Gfpe): A Novel Approach to Analyse Of Kinematic Characteristics of Yoga Asanas Based on Anybody Simulation Software

The kinematic characteristics of yoga asanas is crucial for comprehending the biomechanical demands and benefits associated with these postures. Utilizing AnyBody simulation software, researchers delve into the intricate movements and alignments involved in various yoga poses. Through advanced biomechanical modeling, AnyBody allows for the analysis of joint angles, muscle activations, and forces exerted on the body during asana practice. This paper presented an analysis of the kinematic characteristics of yoga asanas using AnyBody Simulation in conjunction with Geometric Co-ordinate Feature Point Estimation (GFPE). By integrating advanced biomechanical modelling capabilities of AnyBody with GFPE’s precision in identifying geometric features, this study aims to elucidate the intricate movements and alignments inherent in various yoga poses. Through comprehensive simulations, joint angles, muscle activations, and forces exerted on the body during asana practice are meticulously analyzed. The examination of body posture with GFPE in the downward-facing dog pose, the average joint angles of the shoulder, elbow, and wrist were found to be 130°, 150°, and 160°, respectively. Additionally, muscle activation levels were measured, with the triceps brachii exhibiting an average activation of 70% of maximum voluntary contraction during the pose.

3D geometrical modelling of the non-cylindrical Vélodrome Miocene fold in the southwestern Alps

Fold geometries and kinematics within foreland basins is a major issue for understanding the late evolution of thrust fronts. In the foreland of the southwestern Alps, the Vélodrome complex fold involves the whole Tertiary series which have recorded the evolution of the alpine front. From a geometrical and kinematic point of view, the Vélodrome is classically described as a recumbent Mio-Pliocene syncline with a strongly curved axis; interpreted either as a classic growth-fold, a post-deposit fold, or a result of coeval salt activity. The debate reveals a lack of consensus on the internal structure of the Vélodrome and the potential role of salt motion. By a detailed field analysis coupled with an implicit 3D geometrical modelling approach, we test the different hypotheses and provide a new 3D illustrated interpretation of the Vélodrome series. The Vélodrome consists in a complex non-cylindrical structure composed by several folds with different orientations together with inter- and intra-formations unconformities. Folding is partly syn-depositional and began earlier in the south, near Esclangon village, than in the north. In the north, deformation started with the marly and sandy molasse (m2, middle Burdigalian), attested by the transition from the conformable conglomeratic marine molasse (m1–2, Aquitanian and early Burdigalian) to the unconformable m2 to the Valensole formation. Deformation began earlier in the south, during the deposition of the m1–2, as shown by internal unconformities. We discuss the ingredients controlling the deformation in the Vélodrome, regional tectonics (mainly since middle Burdigalian) versus salt tectonics. This study further brings new constraints on the timing and pattern of deformation of the southwestern orogenic front of the Alps. It also highlights the power of the 3D geometrical modelling approach for testing different hypotheses and better understanding 3D complex structures.

A target containing phantom for accuracy assessment of cone-beam CT-guided histotripsy.

Histotripsy is a nonionizing, noninvasive, and nonthermal focal tumor therapy. Cone-beam computed tomography (CBCT) guidance was developed for targeting tumors not visible on ultrasound. This approach assumes cavitation is formed at the geometrical focal point of the therapy transducer. In practice, the exact location might vary slightly between transducers. In this study, we present a phantom with an embedded target to evaluate CBCT-guided histotripsy accuracy and assess the completeness of treatments. Spherical (2.8cm) targets with alternating layers of agar and radiopaque barium were embedded in larger phantoms with similar layers. The layer geometry was designed so that targets were visible on pre-treatment CBCT scans. The actual histotripsy treatment zone was visualized via the mixing of adjacent barium and agar layers in post-treatment CBCT images. CBCT-guided histotripsy treatments of the targets were performed in six phantoms. Offsets between planned and actual treatment zones were measured and used for calibration refinement. To measure targeting accuracy after calibration refinement, six additional phantoms were treated. In a separate investigation, two groups (N=3) of phantoms were treated to assess visualization of incomplete treatments ("undertreatment" group: 2cm treatment within 2.8cm tumor, "mistarget" group: 2.8cm treatment intentionally shifted laterally). Treatment zones were segmented (3D Slicer 5.0.3), and the centroid distance between the prescribed target and actual treatment zones was quantified. In the calibration refinement group, a 2mm offset in the direction of ultrasound propagation (Z) was measured. After calibration refinement, the centroid-to-centroid distance between prescribed and actual treatment volumes was 0.5±0.2mm. Average difference between the prescribed and measured treatment sizes in the incomplete treatment groups was 0.5±0.7mm. In the mistarget group, the distance between prescribed and measured shifts was 0.2±0.1mm. The proposed prototype phantom allowed for accurate measurement of treatment size and location, and the CBCT visible target provided a simple way to detect misalignments for preliminary quality assurance of CBCT-guided histotripsy.