Geometric Representation Research Articles

VoxIsle: A new method in InterDosi code for improving internal dosimetry simulation performances in voxelized phantom

In order to assess the internal dose due to exposure to radiation, the ICRP recommends the use of a reference voxelized phantom. Although voxelized geometry is a very promising geometric representation of a complex body, it showed a limitation in dose calculation for large-voxel array phantoms that requires more memory and CPU time. We have developed a new voxel compression method called VoxIsle that merges adjacent voxels that belong to the same organ/tissue. The VoxIsle was based on the LRAH (Largest Rectangular Area Histogram) algorithm. To evaluate the performances of this method, compressed and uncompressed geometries of some voxel-based phantoms were used to calculate dosimetric coefficients of gamma, electron and alpha particles. Results showed that for a given particle, there is a smooth difference between coefficients calculated using the two types of geometry. Additionally, depending on the characteristics of the voxelized phantom, the memory and CPU time required to construct geometry and material of a phantom, and its file size for a compressed geometry appear to be reduced up to 77%, 73% and 97%, respectively. Regarding computational performance, with the exception of alpha particles for which the results showed a steady increase in CPU time, the simulation with compressed geometry was up to 59.3% faster than the uncompressed geometry. The new compression method can considerably improve the simulation performances of InterDosi code that can perform internal dosimetry studies on voxelized phantoms.

Efficacy of a radiographic film holder adapter in generating radiographs of dental implants with improved geometric accuracy and sharpness

Some radiographic film holders produce radiographs with geometric distortion that may interfere with diagnosis. However, whether the distortion can be corrected by adjusting the design of the radiographic film holder is unclear. The purpose of the study was to develop an adapter for a radiographic film holder model aiming to generate radiographs with greater sharpness and a more accurate geometric representation of dental implants. The 2-piece adapter was designed using the SketchUp software program and was 3-dimensionally (3D) printed. Implants with internal conical connections were installed in 19 maxillary prototypes in the central incisor region. Five dentists obtained 285 digital periapical radiographs with 3 different radiographic film holders: standard Cone Indicator, Rinn XCP, and adapted Cone Indicator. They then evaluated the radiographic sharpness of the implants threads and their dimensions using the ImageJ software program. The data were analyzed using the Friedman test with the Durbin-Conover post hoc test and MANOVA with the Tukey post hoc test (α=.05). On the mesial surface of the implants, the threads were sharper for the adapted than for the standard Cone Indicator radiographic film holder (P<.05). The adapted Cone Indicator showed a smaller difference between the radiographic and actual implant diameters compared with the Rinn XCP and standard Cone Indicator radiographic film holders (P<.05). The developed adapter provided radiographs of dental implants with improved sharpness and geometric accuracy.

Psoas force recruitment in full-body musculoskeletal movement simulations is restored with a geometrically informed cost function weighting

Simulations of musculoskeletal models are useful for estimating internal muscle and joint forces. However, predicted forces rely on optimization and modeling formulations. Geometric detail is important to predict muscle forces, and greater geometric complexity is required for muscles that have broad attachments or span many joints, as in the torso. However, the extent to which optimized muscle force recruitment is sensitive to these geometry choices is unclear. We developed level, uphill and downhill sloped walking simulations using a standard (uniformly weighted, “fatigue-like”) cost function with lower limb and full-body musculoskeletal models to evaluate hip muscle recruitment with different geometric representations of the psoas muscle under walking conditions with varying hip moment demands. We also tested a novel cost function formulation where muscle activations were weighted according to the modeled geometric detail in the full-body model. Total psoas force was less and iliacus, rectus femoris, and other hip flexors’ force was greater when psoas was modeled with greater geometric detail compared to other hip muscles for all slopes. The proposed weighting scheme restored hip muscle force recruitment without sacrificing detailed psoas geometry. In addition, we found that lumbar, but not hip, joint contact forces were influenced by psoas force recruitment. Our results demonstrate that static optimization dependent simulations using models comprised of muscles with different amounts of geometric detail bias force recruitment toward muscles with less geometric detail. Muscle activation weighting that accounts for differences in geometric complexity across muscles corrects for this recruitment bias.

Optical solitons retrieval for an extension of novel dual-mode of a dispersive non-linear Schrödinger equation

In this study, we rearrange the non-linear Schrödinger equation (NLSE) into a dual-mode structure, which expands it, and then we investigate the geometrical evaluation and representation of this novel model. Explicit, exact solutions are obtained by implementing the improved modified extended tanh-function (IMETF) approach. The study’s findings have important ramifications for how solitons propagate in nonlinear optics. The resultant solutions can be found in several forms: singular, bright, rational, exponential, Jacobi elliptic function (JEF), Weierstrass elliptic doubly periodic solution, and singular periodic solutions. By comparing our obtained traveling wave solutions with existing literature, we demonstrate their novelty and substantive contribution to current research. The success of our approach suggests its potential applicability to address various nonlinear challenges in different fields, particularly within soliton theory, since the analyzed model appears in a multitude of applications. Besides, in order to better comprehend some of these found solutions behaviors, we showed their outlines in 3D and 2D graphs.

Deep neural network-based emotion recognition using facial landmark features and particle swarm optimization

Relating specifically to human–computer interaction (HCI), computer vision research has placed a substantial emphasis on intelligent emotion recognition in recent years. The primary emphasis lies in investigating speech aspects and bodily motions, while the knowledge of recognizing emotions from facial expressions remains relatively unexplored. Automated facial emotion detection allows a machine to assess and understand a person's emotional state, allowing the system to predict intent by analyzing facial expressions. Therefore, this research provides a novel parameter selection strategy using swarm intelligence and a fitness function for intelligent recognition of micro emotions. This paper presents a novel method based on geometric visual representation obtained from facial landmark points. We employ the Deep Neural Networks (DNN) model to analyze the input features from the normalized angle and distance values derived from these landmarks. The results of the experiments show that Particle Swarm Optimization (PSO) worked very well by using only a few carefully chosen features. The method achieved a recognition success rate of 98.76% on the MUG dataset and 97.79% on the GEMEP datasets.

Multi-granularity learning of explicit geometric constraint and contrast for label-efficient medical image segmentation and differentiable clinical function assessment

Automated segmentation is a challenging task in medical image analysis that usually requires a large amount of manually labeled data. However, most current supervised learning based algorithms suffer from insufficient manual annotations, posing a significant difficulty for accurate and robust segmentation. In addition, most current semi-supervised methods lack explicit representations of geometric structure and semantic information, restricting segmentation accuracy. In this work, we propose a hybrid framework to learn polygon vertices, region masks, and their boundaries in a weakly/semi-supervised manner that significantly advances geometric and semantic representations. Firstly, we propose multi-granularity learning of explicit geometric structure constraints via polygon vertices (PolyV) and pixel-wise region (PixelR) segmentation masks in a semi-supervised manner. Secondly, we propose eliminating boundary ambiguity by using an explicit contrastive objective to learn a discriminative feature space of boundary contours at the pixel level with limited annotations. Thirdly, we exploit the task-specific clinical domain knowledge to differentiate the clinical function assessment end-to-end. The ground truth of clinical function assessment, on the other hand, can serve as auxiliary weak supervision for PolyV and PixelR learning. We evaluate the proposed framework on two tasks, including optic disc (OD) and cup (OC) segmentation along with vertical cup-to-disc ratio (vCDR) estimation in fundus images; left ventricle (LV) segmentation at end-diastolic and end-systolic frames along with ejection fraction (LVEF) estimation in two-dimensional echocardiography images. Experiments on nine large-scale datasets of the two tasks under different label settings demonstrate our model’s superior performance on segmentation and clinical function assessment.

MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory

This report presents a general panorama of recent progress in the arithmetic-geometry theory of Galois and homotopy groups and its ramifications. While still relying on Grothendieck’s original pillars [1], the present program has now evolved beyond the classical group-theoretic legacy to result in an autonomous project that exploits a new geometrization of the original insight and sketches new frontiers between homotopy geometry, homology geometry, and diophantine geometry . This panorama “closes the loop” by including the last twenty-year progress of the Japanese arithmetic-geometry school via Ihara’s program and Nakamura–Tamagawa–Mochizuki’s anabelian approach, which brings its expertise in terms of algorithmic, combinatoric, and absolute reconstructions. These methods supplement and interact with those from the classical arithmetic of covers and Hurwitz spaces and the motivic and geometric Galois representations .This workshop has brought together the next generation of arithmetic homotopic Galois geometers, who, with the support of senior experts, are developing new techniques and principles for the exploration of the next research frontiers. [1] That are, as presented in “Récoltes et semailles”, the resolution of the discrete and the continuous, the local-to-global thinking by generization-specialization, and the quintessential intersection of arithmetic and geometry – see § 2.10 ibid.

A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound

Motivated by the potential connection between metric-affine gravity and linear generalized uncertainty principle (GUP) in the phase space, we develop a covariant form of linear GUP and an associated modified Poincaré algebra, which exhibits distinctive behavior, nearing nullity at the minimal length scale proposed by linear GUP. We use three-torus geometry to visually represent linear GUP within a covariant framework. The three-torus area provides an exact geometric representation of Bekenstein’s universal bound. We depart from Bousso’s approach, which adapts Bekenstein’s bound by substituting the Schwarzschild radius ( rs ) with the radius (R) of the smallest sphere enclosing the physical system, thereby basing the covariant entropy bound on the sphere’s area. Instead, our revised covariant entropy bound is described by the area of a three-torus, determined by both the inner radius rs and outer radius R where rs⩽R due to gravitational stability. This approach results in a more precise geometric representation of Bekenstein’s bound, notably for larger systems where Bousso’s bound is typically much larger than Bekensetin’s universal bound. Furthermore, we derive an equation that turns the standard uncertainty inequality into an equation when considering the contribution of the three-torus covariant entropy bound, suggesting a new avenue of quantum gravity.

Symplectic Fourier–Deligne Transforms on G/U and the Algebra of Braids and Ties

Abstract We explicitly identify the algebra generated by symplectic Fourier–Deligne transforms (i.e., convolution with Kazhdan–Laumon sheaves) acting on the Grothendieck group of perverse sheaves on the basic affine space $G/U$, answering a question originally raised by A. Polishchuk. We show it is isomorphic to a distinguished subalgebra, studied by I. Marin, of the generalized algebra of braids and ties (defined in Type $A$ by F. Aicardi and J. Juyumaya and generalized to all types by Marin), providing a connection between geometric representation theory and an algebra defined in the context of knot theory. Our geometric interpretation of this algebra entails some algebraic consequences: we obtain a short and type-independent geometric proof of the braid relations for Juyumaya’s generators of the Yokonuma–Hecke algebra (previously proved case-by-case in types $A, D, E$ by Juyumaya and separately for types $B, C, F_{4}, G_{2}$ by Juyumaya and S. S. Kannan), a natural candidate for an analogue of a Kazhdan–Lusztig basis, and finally an explicit formula for the dimension of Marin’s algebra in Type $A_{n}$ (previously only known for $n \leq 4$).

Geometric prescribed‐time control of quadrotors with adaptive extended state observers

AbstractThis article studies an adaptive extended state observer (AESO) based prescribed‐time geometric attitude stabilization problem of quadrotors with endogenous uncertainties, exogenous disturbances, and actuator saturation, which can be estimated and compensated by AESOs. The employment of the geometric representation method for system attitude can effectively avoid ambiguity or singularity problems that may arise with other representations. The temporal and scale transformations are employed to solve the global boundedness problem on infinite time instead of the prescribed‐time convergence problem on finite time. By integrating the proposed controller with the backstepping technique, the system of quadrotors can be prescribed‐time stable. Further, a prescribed‐time geometric attitude control technique is devised such that the control signal is bounded and the state signals converge to a small domain near the equilibrium point in the prescribed time. The prescribed time is determined by the user and is independent of the initial conditions. The comparative simulations with different initial information are performed to demonstrate the effectiveness of the proposed design technique.

A matrix norm-based Pythagorean fuzzy metric and its application in MEREC-SWARA-VIKOR framework for solar panel selection

Due to the escalating electricity demand from industrialization and modernization, it is imperative to explore clean and sustainable energy sources. Solar energy has become a feasible solution for this surging demand. Solar panels, vital components of solar power systems, are crucial in converting sunlight into electricity. However, selecting the most suitable solar panel is a complex task involving subjective and measurable parameters involving uncertainties. To address the uncertainties and ambiguities in real-life problems, the theory of Pythagorean fuzzy sets with distance measures has emerged as a flexible and superior tool. Nevertheless, many existing distance functions often fail to meet necessary metric conditions, leading to inaccurate and unreasonable outcomes. These limitations are pointed out by many literature. In addition, we observe a serious drawback of parameter dependency of some existing measures. This paper proposes a novel metric for Pythagorean fuzzy sets using the matrix norm to overcome these drawbacks. Additionally, we discuss various mathematical properties and provide geometrical representations for the proposed distance measure. To demonstrate the superiority of the proposed measure, we conduct a comparative study against existing distance measures. Furthermore, we develop a Pythagorean fuzzy-method based on the removal effects of criteria-stepwise weight assessment ratio analysis-vlse kriterijumska optimizacija kompromisno resenje (PF-MEREC-SWARA-VIKOR) method for selecting solar panel systems. Our approach incorporates the MEREC method for objective criteria, utilizes the SWARA method to calculate subjective weights, and employs the VIKOR method in the Pythagorean fuzzy context to determine the preference order of alternatives. We conduct sensitivity analysis and comparative studies with existing developed methods to validate our method. Highlight the effectiveness and advantages of our novel approach in selecting solar panels. Finally, exploring the future research directions and challenges associated with the proposed methodology.

Unlocking the Potential of 3D Printing in Modern Manufacturing

The process of producing tangible items by layering on materials according to geometric representations is called digital fabrication technology, sometimes referred to as additive manufacturing or 3D printing. This innovative technique has gained popularity. Numerous industries, including healthcare, automotive, locomotive, and aviation, now make extensive use of the quickly expanding area of 3D printing technology. This page discusses the materials utilized in the production process, provides a summary of the many types of 3D printing technology, and illustrates the extensive variety of uses for them With the potential to create intricate structures and personalized patterns straight from computer-aided design (CAD) models, 3D printing technology is a potent instrument that has the potential to completely alter the face of contemporary production.

A hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress: II. An isogeometric discretization method for incompressible materials

This is Part II of a multipart article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We introduce an isogeometric discretization method for incompressible materials and present test computations. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The return is more than what we get from accounting for the out-of-plane deformation mapping. The traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the model is now free from the “midsurface’ location in terms of specifying the traction. In dealing with incompressible materials, we start with an augmented formulation that includes the pressure as a Lagrange multiplier and then eliminate it by using the geometrical representation of the incompressibility constraint. The resulting model is an extended one, in the Kirchhoff–Love category in the degree-of-freedom count, and encompassing all other extensions in the isogeometric subcategory. We include ordered details as a recipe for making the implementation practical. The implementation has two components that will not be obvious but might be critical in boundary integration. The first one is related to the edge-surface moment created by the Kirchhoff–Love assumption. The second one is related to the pressure/traction integrations over all the surfaces of the finite-thickness geometry. The test computations are for dome-shaped inflation of a flat circular shell, rolling of a rectangular plate, pinching of a cylindrical shell, and uniform hydrostatic pressurization of the pinched cylindrical shell. We compute with neo-Hookean and Mooney–Rivlin material models. To understand the effect of the terms added in the extended model, we compare with models that exclude some of those terms.

Multi-DORGP for fast uncertainty quantification of multi-scale irregular defects in super large-scale fiber-reinforced composite

The presence of randomly distributed irregular defects in fiber-reinforced composites significantly impacts the structural response, yet traditional machine learning schemes often require an extensive number of samples, resulting in time-consuming processes. Therefore, this paper introduces a novel approach, termed the dual order-reduced Gaussian Process emulators (Multi-DORGP), aimed at efficiently quantifying the uncertainty of multi-scale irregular defects in fiber-reinforced composites. This is achieved by accurately characterizing the multi-scale irregular defects through precise geometric representations, utilizing massive discrete nodes and fine meshes to address the limitations of parameterization methods that may overlook shape and size differences of defects. Moreover, we comprehensively quantify uncertainty across micro, meso, and macro scales, considering spatially randomly distributed locations, sizes, and irregular shapes of defects. Notably, the Multi-DORGP scheme is presented to alleviate the computational burden associated with extremely high-dimensional data (e.g., up to 23.3 million variables). In which, we decouple and build the latent spaces for raw data assisted by principal component analysis, and Gaussian Process regression is built and trained by the coefficients between the latent spaces. Through illustrative examples, including a real-life application involving an airplane wing, we validate the proposed scheme's capability to accurately quantify the uncertainty of multi-scale irregular defects in large-scale fiber-reinforced composites using significantly few samples (e.g., 100).

Geometry-Based Molecular Generation With Deep Constrained Variational Autoencoder.

Finding target molecules with specific chemical properties plays a decisive role in drug development. We proposed GEOM-CVAE, a constrained variational autoencoder based on geometric representation for molecular generation with specific properties, which is protein-context-dependent. In terms of machine learning, it includes continuous feature embedding encoder and molecular generation decoder. Our key contribution is to propose an efficient geometric embedding method, including the spatial structure representations of drug molecule (converting the 3-D coordinates into image) and the geometric graph representations of protein target (modeling the protein surface as a mesh). The 3-D geometric information is vital to successful molecular generation, which is different from previous molecular generative methods based on 1-D or 2-D. Our model framework generates specific molecules in two phases, by first generating special image with molecular 3-D information to learn latent representations and generating molecules with constrained condition based on geometric graph convolution for specific protein and then inputting the generated structural molecules into a parser network for obtaining Simplified Molecular Input Line Entry System (SMILES) strings. Our model achieves competitive performance that implies its potential effectiveness to enable the exploration of the vast chemical space for drug discovery.

Local environment interaction-based machine learning framework for predicting molecular adsorption energy

Machine learning (ML) models in materials science are mainly developed for predicting global properties, such as formation energy, band gap, and elastic modulus. Thus, these models usually fall short in describing local characteristics, such as molecular adsorption on surfaces. Here, we introduce a local environment interaction-based ML framework that contains a modified graph-based Voronoi tessellation geometrical representation, improved fingerprint feature engineering, and traditional ML and advanced deep learning (DL) algorithms. The precise characterization can be extracted using this framework for representing local information of adsorption of molecules on a surface. Using both traditional ML and advanced DL algorithms, we demonstrate remarkable prediction accuracy and robustness on 0D, two-dimensional (2D), and three-dimensional (3D) catalysts. Furthermore, it is found that the employment of this approach reduces data requirements and augments computational speed, specifically for DL algorithms. This work provides an effective and universal ML framework for various applications of molecular adsorption from catalysis, sensors, carbon capture, and energy storage to drug delivery, signifying a novel and promising avenue in the field of materials informatics. The implementation code in this work is available at https://github.com/mpeshel/LEI-framework LERN .

Planning Regulations and Modelled Constraints in BIM: A Dutch Case Study

Planning regulations determine a substantial part of buildings, but their constraints are usually not included in the setup of a BIM model or used explicitly for design guidance, but only tested in compliance checks once a model has been made. This is symptomatic of wider tendencies and ingrained biases that emphasize tacit knowledge and assume that information in a project starts from scratch—an assumption that runs contrary to predesign information ordering practices, as well as to the findings of creativity studies. In terms of process control, it negates important possibilities for feedforward. The paper proposes that BIM and design computerization, in general, should avoid the generate-and-test view of design, the view of design knowledge as tacit, and the adherence to analogue workflows, but develop, instead, approaches and workflows that keep information explicit and utilize it to frame design problems. To demonstrate this, we describe an exercise in which the expectation that the geometric representation of planning regulations returns permissible building envelopes was tested on the basis of a large number of cases produced by students who each collected planning regulations for a particular plot of land in the Netherlands and modelled their constraints in BIM, using a workflow that can be accommodated within the scope of predesign information gathering in any project. The results confirm that, for a large part of Dutch housing, the representation of planning regulations in BIM returns the permissible building envelope, and, so, forms a clear frame for subsequent design actions. They also suggest that including such information in the setup of a model is constructive and feasible, even for novices, and produces a bandwidth view of project information that integrates pre-existing information in a BIM workflow through feedforward. By extension, they also indicate a potential for a closer relation between analysis and synthesis in BIM, characterized by transparency and simultaneity, as well as the thorough understanding of problem constraints required for both efficiency and creativity.

Statistical inference for multivariate extremes via a geometric approach

Abstract A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non-/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model. A simulation study confirms that our methodology is very competitive with existing approaches and can successfully allow estimation of small probabilities in regions where other methods struggle. We apply the methodology to two environmental datasets, with diagnostics demonstrating a good fit.

Research on Fault Prediction Method of Elevator Door System Based on Transfer Learning.

The elevator door system plays a crucial role in ensuring elevator safety. Fault prediction is an invaluable tool for accident prevention. By analyzing the sound signals generated during operation, such as component wear and tear, the fault of the system can be accurately determined. This study proposes a GNN-LSTM-BDANN deep learning model to account for variations in elevator operating environments and sound signal acquisition methods. The proposed model utilizes the historical sound data from other elevators to predict the remaining useful life (RUL) of the target elevator door system. Firstly, the opening and closing sounds of other elevators is collected, followed by the extraction of relevant sound signal characteristics including A-weighted sound pressure level, loudness, sharpness, and roughness. These features are then transformed into graph data with geometric structure representation. Subsequently, the Graph Neural Networks (GNN) and long short-term memory networks (LSTM) are employed to extract deeper features from the data. Finally, transfer learning based on the improved Bhattacharyya Distance domain adversarial neural network (BDANN) is utilized to transfer knowledge learned from historical sound data of other elevators to predict RUL for the target elevator door system effectively. Experimental results demonstrate that the proposed method can successfully predict potential failure timeframes for different elevator door systems.

Small-scale variation of atmospheric dynamics applying chaos theory, case study

Characterization and knowledge of the variability of atmospheric dynamics on a small scale in the city of Riobamba, Ecuador, are achieved through the chaos theory. Meteorological data is taken every hour during four years, including variables such as wind speed, wind direction, incident radiation, temperature, and humidity, from the ESPOCH, SAN JUAN, and QUIMIAG weather stations in the canton of Riobamba. The van Ulden and Hostlang models are used to calculate the Obukhov length, surface heat fluxes, and latent heat flux. The chaos theory is applied to study the variation of atmospheric microdynamics. The Lyapunov coefficients, Kolmogorov-Sinai entropy, and Kaplan-Yorke fractal dimension are determined. Before analysis, noise reduction is necessary due to the lack of correlation, especially in the Obukhov length. This research follows a longitudinal design and employs quantitative and explanatory methods based on data analysis, statistical-mathematical techniques, and inductive-deductive approaches. The results indicate a highly variable system, reflected in a high number of Lyapunov coefficients, fractional dimensions, and entropy variations. The microdynamic parameters exhibit hyperchaotic behavior, as indicated by the presence of more than one positive Lyapunov coefficient. The variables also demonstrate a fractional fractal dimension, highlighting the irregularity in the geometric representation of the system.