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It is essential to establish a digital twin scene, which helps to depict the dynamically changing geographical environment accurately. Digital twins could improve the refined management level of intelligent tunnel construction; however, research on geographical twin models primarily focuses on modeling and visual description, which has low analysis efficiency. This paper proposes a knowledge-guided intelligent analysis method for the geometric deformation of tunnel excavation profile twins. Firstly, a dynamic data-driven knowledge graph of tunnel excavation twin scenes was constructed to describe tunnel excavation profile twin scenes accurately. Secondly, an intelligent diagnosis algorithm for geometric deformation of tunnel excavation contour twins was designed by knowledge guidance. Thirdly, multiple visual variables were jointly used to support scene fusion visualization of tunnel excavation profile twin scenes. Finally, a case was selected to implement the experimental analysis. The experimental results demonstrate that the method in this article can achieve an accurate description of objects and their relationships in tunnel excavation twin scenes, which supports rapid geometric deformation analysis of the tunnel excavation profile twin. The speed of geometric deformation diagnosis is increased by more than 90% and the cognitive efficiency is improved by 70%. The complexity and difficulty of the deformation analysis operation are reduced, and the diagnostic analysis ability and standardization of the geographic digital twin model are effectively improved. [ABSTRACT FROM AUTHOR]

We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative U(1) gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we interpret as the classical phase space of a point particle on noncommutative spacetime. In this picture gauge fields arise as bisections of the symplectic groupoid while gauge transformations are parameterized by Lagrangian bisections. We provide a geometric construction of a gauge invariant action functional which minimally couples a dynamical charged particle to a background electromagnetic field. Our constructions are elucidated by several explicit examples, demonstrating the appearances of curved and even compact momentum spaces, the interplay between gauge transformations and spacetime diffeomorphisms, as well as emergent gravity phenomena. [ABSTRACT FROM AUTHOR]

Allometry, i.e. morphological variation correlated with size, is a major pattern in organismal evolution. Since size varies both within and among species, allometry occurs at different variational levels. However, the variability of allometric patterns across levels is poorly known since its evaluation requires extensive comparative studies. Here, we implemented a 3D geometric morphometric approach to investigate cranial allometry at three main variational levels—static, ontogenetic, and evolutionary—and two anatomical scales—entire cranium and cranial subunits—based on a dense intra- and interspecific sampling of extant armadillo diversity. While allometric trajectories differ among distantly related species, they hardly do so among sister families. This suggests that phylogenetic distance plays an important role in explaining allometric divergences. Beyond trajectories, our analyses revealed pervasive allometric shape changes shared across variational levels and anatomical scales. At the entire cranial scale, craniofacial allometry (relative snout elongation and braincase reduction) is accompanied notably by variations of nuchal crests and postorbital constriction. Among cranial subunits, the distribution of allometry was highly heterogeneous, with the frontal and petrosal bones showing the most pervasive shape changes, some of which were undetected at a more global scale. Evidence of widespread and superimposed allometric variations raises questions on their determinants and anatomical correlates and demonstrates the critical role of allometry in morphological evolution. [ABSTRACT FROM AUTHOR]

The article explores the topic of projectile motion through an experiment conducted by Alice and Bob. They used a high-speed camera to capture the movement of a projectile and discovered that its trajectory formed a parabola. The article provides equations and tests to determine the aspect ratio of the trajectories and offers hands-on projects of increasing difficulty related to projectile motion. It emphasizes the importance of accurate measurements and uncertainties in conducting such experiments. The article also discusses the use of scaling and geometric approaches, data fitting, and suggests using simulations and video recordings for analysis. Overall, it provides practical methods for understanding and studying projectile motion. [Extracted from the article]

The polytopes U I , J ¯ were introduced by Ceballos, Padrol, and Sarmiento to provide a geometric approach to the study of (I , J ¯) -Tamari lattices. They observed a connection between certain U I , J ¯ and acyclic root polytopes, and wondered if Mészáros' subdivision algebra can be used to subdivide all U I , J ¯ . We answer this in the affirmative from two perspectives, one using flow polytopes and the other using root polytopes. We show that U I , J ¯ is integrally equivalent to a flow polytope that can be subdivided using the subdivision algebra. Alternatively, we find a suitable projection of U I , J ¯ to an acyclic root polytope which allows subdivisions of the root polytope to be lifted back to U I , J ¯ . As a consequence, this implies that subdivisions of U I , J ¯ can be obtained with the algebraic interpretation of using reduced forms of monomials in the subdivision algebra. In addition, we show that the (I , J ¯) -Tamari complex can be obtained as a triangulated flow polytope. [ABSTRACT FROM AUTHOR]

Across the Tree of Life, most studies of phenotypic disparity and diversification have been restricted to adult organisms. However, many lineages have distinct ontogenetic phases that differ from their adult forms in morphology and ecology. Focusing disproportionately on the evolution of adult forms unnecessarily hinders our understanding of the pressures shaping evolution over time. Non-adult disparity patterns are particularly important to consider for coastal ray-finned fishes, which can have juvenile phases with distinct phenotypes. These juvenile forms are often associated with sheltered nursery environments, with phenotypic shifts between adults and juvenile stages that are readily apparent in locomotor morphology. Whether this ontogenetic variation in locomotor morphology reflects a decoupling of diversification dynamics between life stages remains unknown. Here we investigate the evolutionary dynamics of locomotor morphology between adult and juvenile triggerfishes. We integrate a time-calibrated phylogenetic framework with geometric morphometric approaches and measurement data of fin aspect ratio and incidence, and reveal a mismatch between morphospace occupancy, the evolution of morphological disparity, and the tempo of trait evolution between life stages. Collectively, our results illuminate how the heterogeneity of morpho-functional adaptations can decouple the mode and tempo of morphological diversification between ontogenetic stages. [ABSTRACT FROM AUTHOR]

High-resolution satellite imagery has a limitation in terms of coverage area. This limitation presents challenges for extensive-scale analysis at regional or national levels. To maximize the utility of high-resolution satellite imagery, the implementation of image mosaicking techniques is essential. In this paper, we have developed seamline extraction techniques and relative geometric correction optimized for high-resolution satellite imagery. Ultimately, we proposed a multi-strip image mosaicking method for KOMPSAT-3A (Korea Multi-Purpose Satellite-3A) images. We applied the Dijkstra's shortest path algorithm to efficiently extract seamlines. we also performed image registration based on feature matching and homography transformation to correct the relative geometric errors between input images. We conducted experiments with our methods using 29 scenes from KOMPSAT-3A L1G data. The results indicated high relative geometric accuracy, with an average error of 1.63 pixels. Furthermore, we were able to obtain high-quality seamless mosaic images. Our proposed method is expected to enhance the utility of KOMPSAT-3A imagery for large-scale environmental and urban analysis and to provide more accurate and comprehensive data. [ABSTRACT FROM AUTHOR]

The current challenging problems of learning a robust 6D pose lie in noise in RGB/RGBD images, sparsity of point cloud and severe occlusion. To tackle the problems, object geometric information is critical. In this work, we present a novel pipeline for 6DoF object pose estimation. Unlike previous methods that directly regressing pose parameters and predicting keypoints, we tackle this challenging task with a point-pair based approach and leverage geometric information as much as possible. Specifically, at the representation learning stage, we build a point cloud network locally modeling CNN to encode point cloud, which is able to extract effective geometric features while the point cloud is projected into a high-dimensional space. Moreover, we design a coordinate conversion network to regress point cloud in the object coordinate system in a decoded way. Then, the pose could be calculated through point pairs matching algorithm. Experimental results show that our method achieves state-of-the-art performance on several datasets. [ABSTRACT FROM AUTHOR]

This work investigates the cooperative formation control problem of unmanned surface vehicle-remotely operated vehicles (USV-ROVs) subject to uncertainties under deceptive attacks. In the control design, with the utilization of the desired formation as well as the geometric position between USV and ROVs, a geometric transformation approach is developed and a geometric constraint relationship of governing formation positions is derived. Under the terminal sliding mode control (TSMC) design framework, a novel terminal sliding surface is crafted to circumvent the singularity issue. To further bolster robustness, using the sliding mode damper concept, a variable damping reaching law is devised. To refrain from the effectiveness of attacks and uncertainties, the adaptive technique is integrated into the TSMC framework. To save the communication resources, an event-triggering mechanism is established between the distributed controller and ROVs. Then, an event-triggered adaptive finite-time cooperative formation control scheme is developed for the USV-ROVs. The Lyapunov theory analysis shows that the cooperative formation control issue of USV-ROVs is realized and the deceptive attack can be suppressed efficaciously. The simulation, comparison, and quantitative analysis demonstrate the relative effectiveness and superiority of the developed scheme. [ABSTRACT FROM AUTHOR]

Accurate identification and segmentation of individual tree points are crucial for assessing forest spatial distribution, understanding tree growth and structure, and managing forest resources. Traditional methods based on Canopy Height Models (CHM) are simple yet prone to over- and/or under-segmentation. To deal with this problem, this paper introduces a novel approach that combines marker-controlled watershed segmentation with a spectral clustering algorithm. Initially, we determined the local maxima within a series of variable windows according to the lower bound of the prediction interval of the regression equation between tree crown radius and tree height to preliminarily segment individual trees. Subsequently, using this geometric shape analysis method, the under-segmented trees were identified. For these trees, vertical tree crown profile analysis was performed in multiple directions to detect potential treetops which were then considered as inputs for spectral clustering optimization. Our experiments across six plots showed that our method markedly surpasses traditional approaches, achieving an average Recall of 0.854, a Precision of 0.937, and an F1-score of 0.892. [ABSTRACT FROM AUTHOR]

In the open literature, there are numerous studies on the normal and extreme (flood and drought) behavior of wet and dry periods based on the understanding of the standard precipitation index (SPI), which provides a series of categorizations by considering the standard normal (Gaussian) probability distribution function (PDF). The numerical meaning of each categorization assessment is quite lacking in terms of future predictions of wet and dry period duration based on historical records. This paper presents a new approach for calculating possible formations of future wet and dry period durations based on historical records through an effective fractal geometric forecasting approach. The essence of the proposed methodology is based on the number of dry periods (steps) of non-overlapping monthly duration along consecutive broken line paths in the SPI classification for wet and dry period durations. It has been observed that the plot of periods on double logarithmic paper falls along a straight line against the number of such periods, implying a power function, which is the essence of fractal geometry. Extending the empirically derived straight line provides the number of periods that may occur in the future over a range of SPI levels. This methodology is referred to as SPI fractal (SPIF), and the classic SPI classification is converted into SPIF wet and dry polygons, which provide additional information about the drought period number within a valid polygonal area, compared to the classic SPI results. The wet and dry period features of any hydro-meteorology time series are constrained in SPIF polygons. The application of the methodology was carried out on monthly rainfall records on the European side of the Istanbul Florya meteorological station in Turkey. [ABSTRACT FROM AUTHOR]

We investigate the conformists–contrarians model of identical Kuramoto oscillators evolving on a sphere. Using group-theoretic and geometric approach, we reduce the model to the dynamical system on extended Ott–Antonsen manifold. Further reduction yields the system of three scalar ODE's for global variables. This three-dimensional dynamical system is studied analytically in order to investigate an interplay between conformists and contrarians on spheres. Our study demonstrates that conformists–contrarians models on spheres display the same types of equilibria and dynamical phenomena in all dimensions. However, critical combination of parameters, for which particular equilibrium states arise, does depend on the dimension. In particular, models on spheres exhibit traveling waves consisting of contrarians. We derive an exact formula for the relation between parameter values for which such waves arise in different dimensions. Finally, we take a closer look at trajectories of traveling waves on spheres, demonstrating subtleties of this dynamical phenomenon. [ABSTRACT FROM AUTHOR]

Biological assays around "lab-on-a-chip (LoC)" are required in multiple concentration (or dilution) factors, satisfying specific sample concentrations. Unfortunately, most of them suffer from non-locality and are non-protectable, requiring a large footprint and high purchase cost. A digital geometric technique can generate arbitrary gradient profiles for digital microfluidic biochips (DMFBs). A next- generation DMFB has been proposed based on the microelectrode-dot-array (MEDA) architectures are shown to produce and disperse droplets by channel dispensing and lamination mixing. Prior work in this area must address the problem of reactant and waste minimization and concurrent sample preparation for multiple target concentrations. This paper proposes the first splitting-droplet sharing algorithm for reactant and waste minimization of multiple target concentrations on MEDAs. The proposed algorithm not only minimizes the consumption of reagents but also reduces the number of waste droplets by preparing the target concentrations concurrently. Experimental results on a sequence of exponential gradients are presented in support of the proposed method and demonstrate its effectiveness and efficiency. Compared to prior work, the proposed algorithm can achieve up to a 24.8% reduction in sample usage and reach an average of 50% reduction in waste droplets. [ABSTRACT FROM AUTHOR]

In industrial applications, rotating machines operate under real-time variable speed and load regimes. In the presence of faults, the degradation of critical components is accelerated significantly. Therefore, robust monitoring algorithms able to identify these faults become crucial. In the literature, it is hard to find comprehensive monitoring systems that include variable speed and load regimes with combined gearbox faults using electrical and vibration signals. For this purpose, a novel signal processing methodology including a geometric classification technique is proposed. This methodology is based on using different types of sensors such as current, voltage and vibration sensors with a regime normalization, which allows the grouping of different regimes belonging to the same health state. It consists of reducing dispersion between the class observations and separating other classes representing different health states including the variation in speed and load. Then, a peripheral threshold is proposed in our classifier to diagnose new health states. To verify the effectiveness of the methodology, current, voltage and vibration data from a gearbox system are collected under variable speed and load levels. [ABSTRACT FROM AUTHOR]

In this paper, we propose the application of a new geometric procedure in order to calculate a set of transmission zeros of a propagation environment. Since the transmission zeros play a crucial role in modern communication systems, there is a need to apply the efficient solutions characterized by a maximum speed operation. It turns out that the classical method based on the Smith–McMillan factorization is time-consuming, so its contribution to the detection of transmission zeros could be unsatisfactory. Therefore, in order to fill the gap, we present a new algorithm strictly dedicated to the multivariable telecommunications systems described by the transfer-function approach. Consequently, a set of new achievements resulted, particularly in terms of computational efforts. Indeed, the proposed procedure allows us to overcome obstacles derived from technological limitations. The representative simulation examples confirm the great potential of this new method. Finally, it has been pointed out that the newly introduced geometric-originated approach has significantly reduced the computational burden. Indeed, for the randomly selected matrix of the 5 × 5 dimension describing the sensor-related propagation environment, two representative scenarios were performed in order to manifest the crucial properties. In the first scenario, the sets of multiple transmission zeros were analyzed, ultimately leading to intriguing results. The Smith–McMillan solution took three times longer to discover the mentioned sets. On the other hand, the second instance brought us the same result. Naturally, the discussed difference has increased as a function of the number of matrix elements. For the square matrices involving 100 components, we have observed the respective differences, both over Q I = 100 and Q I I = 60 . It should be emphasized that the finding derived from the Smith–McMillan factorization corresponds to the geometric-related approach in the context of some mechanisms. This is particularly visible when appointing the greatest common divisors. [ABSTRACT FROM AUTHOR]

Objectives: In Quebec, genetic and genealogical research are used to document migratory events and family structures since colonial times, because bioarchaeological analysis is limited by poor skeletal preservation. This article aims to fill this gap by exploring past population structure in the St‐Lawrence Valley from the French (1683–1760) and British (1760–1867) regimes using morphological variation of well‐preserved temporal bones. Materials and Methods: 3D geometric morphometrics shape data from seven populations (five Catholics of French descent and two Protestants of British descent; n = 214) were collected from temporal bones. Using Procrustes distances and both MANOVA and Discriminant Function Analysis, morphological differences were measured to calculate affinities patterns among populations. Shape variations were explored with between‐group analysis, Mahalanobis distances and quantified by means of Fst estimates using Relethford–Blangero analysis. Results: Despite strong affinities between all Catholic cemeteries, all show divergent morphological regional diversity ‐especially Montreal and the fortified villages dedicated to its defense. Montreal exhibits low increase in morphological variance over three centuries. As our results show no morphological differences between the Catholic and the Protestant cemeteries in Montreal, this fact may highlight the potential presence of Irish or admixed individuals in Montreal cemeteries after the British takeover. Discussion: Patterns of morphological diversity highlighted that French colonists did not equally contribute to the descendant populations as reflected by significant interregional variation. Although historical records show that French and English‐speaking populations did not tend to admix, morphological affinities between Protestants and Catholics in the beginning of the industrial era in Montreal could reflect the genetic contribution of Catholic Irish migrants. Research Highlights: All Catholic cemeteries display distinct morphologies, highlighting differential contributions from French colonists and founder effects, which have increased regional differences.Montreal Catholic (French descent) and Protestant (English colonists) cemeteries show significant morphological affinities at the beginning of the industrial era.The Irish migration following the British conquest may explain morphological similarities observed between Catholic and Protestant cemeteries. [ABSTRACT FROM AUTHOR]

Different ways of representing the group SU(3)$$ SU(3) $$ within a Geometric Algebra approach are explored. As part of this, we consider characteristic multivectors for SU(3)$$ SU(3) $$ and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra. We then go on to consider whether the fundamental forces of particle physics might arise from symmetry considerations in just the 4d geometric algebra of spacetime—the STA. As part of this, a representation of SU(3)$$ SU(3) $$ is found wholly within the STA, involving preservation of a bivector norm. We also show how Octonions can be fully represented within the Spacetime Algebra, which we believe will be useful in making them understandable and accessible to a new community in Physics and Engineering. The two strands of the paper are drawn together in showing how preserving the octonion norm is the same as preserving the timelike part of the Dirac current of a particle. This suggests a new model for the symmetries preserved in particle physics. Following on from work by Günaydin and Gürsey on the link between quarks, and octonions, and by Furey on chains of octonionic multiplications, we show how both of these fit well within our scheme and give some wholly STA versions of the operations involved, which in the cases considered have easily understandable equivalents in terms of 4d geometry. Links with larger groups containing SU(3)$$ SU(3) $$, such as G2$$ {G}_2 $$ and SU(8)$$ SU(8) $$, are also considered. [ABSTRACT FROM AUTHOR]

We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step 2 invariant with respect to the action of SO(3)$$ SO(3) $$. We understand the geodesics as the curves in suitable geometric algebras which allows us to assess a new algorithm for the local control. [ABSTRACT FROM AUTHOR]

Legged locomotion is essential for navigating challenging terrains where conventional robotic systems encounter difficulties. This study investigates the sensitivity of the reconfigurable Klann legged mechanism (KLM) to variations in the input geometric parameters, such as joint position location, link lengths, and angles between linkages, on the continuous coupler curve, which represents the output trace of the leg movement.The continuous coupler curve's sensitivity is explored using global sensitivity analysis based on Sobol's sensitivity method. Furthermore, a novel reconfigurability strategy is presented for the Klann mechanism, aiming to reduce the number of required actuators and the complexity in control. In simulation, the coupler curves obtained from the reconfigurable KLM are classified as hammering, digging, jam avoidance, and step climbing using machine learning approaches. Experimental validation is presented, discussing an approach to identifying geometric parameters and the resultant coupler curve. Illustrations of the the complete assembly of the reconfigured KLM with the obtained gaits using limited experiments are also highlighted. [ABSTRACT FROM AUTHOR]

Important morphological and ecological modifications occur during the transition between pelagic and demersal phases in marine fish. However, it is still unknown how fast these shape changes may occur. We studied the shape changes of a common cryptobenthic fish, the triplefin Helcogrammoides chilensis (Cancino, 1960) during the shift from pelagic larvae to recently settled individuals, along rocky shores in central Chile during the austral summers of 2020 and 2021. The working hypothesis was that larval stages would show more allometry and faster shape changes in the head and the paired fins insertion than benthic juveniles, in preparation for their new environment. Shape changes were analyzed utilizing landmark-based geometric morphometrics, while age was estimated using sagittal otolith microstructure analysis. There was an important overlap in the size (length and weight) between older larvae and recently settled individuals (between 20 and 25 mm SL, and 0.08–0.17 g), nonetheless, the head shape and paired fins were clearly different between stages. Pelagic larvae (46–88 days post hatch) had a shorter pectoral fin base, a frontal mouth opening, and eyes located at the level of the tip of the upper jaw. Meanwhile, recently settled individuals (80–112 days post hatch) had wider, vertically positioned pectoral fins, mouths displaced to a vertical position, and eyes located upper and forward the head. Larvae experienced faster growth rates than settlers (0.24 vs. 0.02 mm day−1, respectively), and the pattern of ontogenetic shape changes decreased two orders of magnitude after settlement. It is plausible that after the pelagic–demersal shift most of the fish's energy was used in body structure rearrangement and incrementing body pigmentation, as an adaptation of cryptobenthic juvenile to the rocky reef. [ABSTRACT FROM AUTHOR]

Approximating Bézier curve by polygon is a traditional technique in computer-aided geometric design, and there are several methods for constructing such polygons. In this paper, we propose to approximate Bézier curve by the least square polygon (LSP). LSP was derived by least square fitting which minimizes the integral of approximating errors. We provide a closed formula for the vertices of LSP. Because of its optimization method, LSP has lower approximation errors than existing approximating polygons. This observation is verified by many numerical examples we tested and several typical examples are included in this paper. [ABSTRACT FROM AUTHOR]

This work is aimed to study the effect of turbidity on the swordtail’s body shape during its early developmental stages. For this purpose, two treatments were designed as turbid and clear water, each with three replicates for 60 days. The body shape data was extracted by digitizing 16 landmark points on 2D pictures to analysis using the geometric morphometric technique. The results showed a significant difference between the two treatments in terms of body shape. Fish under turbid conditions had shorter eye diameters, lower and shorter heads, more dorsal position snout, and deeper caudal peduncles. The priorities in the new environment i.e. turbid water needs to be changed to decrease the adverse effect of the resulting pressures of this environment and increase the survival rate leading to increasing the ability of the developing fish to occupy a wider range of habitats. [ABSTRACT FROM AUTHOR]

A set of edges Γ ${\rm{\Gamma }}$ of a graph G $G$ is an edge dominating set if every edge of G $G$ intersects at least one edge of Γ ${\rm{\Gamma }}$, and the edge domination number γe(G) ${\gamma }_{e}(G)$ is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study γe(G) ${\gamma }_{e}(G)$ for graphs G $G$ which are the incidence graph of some incidence structure D $D$, with an emphasis on the case when D $D$ is a symmetric design. In particular, we show in this latter case that determining γe(G) ${\gamma }_{e}(G)$ is equivalent to determining the largest size of certain incidence‐free sets of D $D$. Throughout, we employ a variety of combinatorial, probabilistic and geometric techniques, supplemented with tools from spectral graph theory. [ABSTRACT FROM AUTHOR]

This paper investigates dynamics of Taylor bubble in counter-current flows, leveraging large eddy simulations combined with the volume of fluid method. Utilizing the OpenFOAM framework, we have implemented a high-order Runge–Kutta time-integration scheme, along with a piecewise linear interface calculation method for precise geometric reconstruction of the bubble interface. We examine the performance of algebraic vs geometric capturing techniques in the context of Taylor bubble breakup, focusing specifically on the transitional flow regime with a liquid Reynolds number of 1400. Our results reveal that the geometric capturing technique offers superior accuracy, improving our understanding of the breakup process and providing valuable insight for multiphase flow simulations in various engineering fields. Our study also reveals the emergence of a secondary vortex in the turbulent wake region behind the Taylor bubble, a phenomenon most prominent at finer mesh resolutions. This vortex represents a novel discovery in counter-current Taylor bubble flows. [ABSTRACT FROM AUTHOR]

Mosquitoes are of public health interest as many of them are vectors of pathogens that can cause diseases in humans. If they are not perfectly preserved, their identification can be difficult. Therefore, we tested the use of an alternative, advanced method of geometric morphometrics for the analysis of wing morphological variability in five (Anopheles, Aedes, Coquillettidia, Culex, Culiseta) genera and ten Slovenian mosquito species alone, seven autochthonous and three invasive. We analysed the intragenic and intraspecific variability in wing size and shape. The results showed that the analysed mosquito species differ in wing size and have different levels of variability, which also affects the correct identification of each taxon. Different classification approaches reach up to 80% (Culex and Coquillettidia), 98% (Aedes) and 100% (Anopheles and Culiseta) accuracy, respectively. Furthermore, additional information on wing size can help in identification when the data and wing venation are less reliable. The distances between taxa centroids in morphological space reflect genetic distances and taxonomic hierarchy: on average, they are greatest between the two subfamilies (Anophelinae, Culicinae), followed by the distances between genera within the Culicinae family and finally by the distances between species within the genera Aedes and Culex. Nevertheless, the topology of the similarity tree based on morphological data reflects the topology of the genetic phylogeny only at the subfamily level. We assessed that geometric morphometrics on wings can be used as an alternative method when other structures otherwise traditionally used for species identification are broken. [ABSTRACT FROM AUTHOR]

In this paper, we give some geometric approach for magnetic curves according to quasi model in ordinary space. Firstly, we compute conformable derivatives of Θ t q , Θ n q , Θ b q Lorentz forces. Moreover, we present recursion and normalization operators of magnetic fields according to the quasi model. Then, we give conformable derivatives for these operators. Finally, we construct conformable F–W derivatives for these curves according to the quasi model in space. [ABSTRACT FROM AUTHOR]

Drawing inspiration from transportation theory, in this work, we introduce the notions of "well-structured" and "stable" Gibbs states and we investigate their implications for quantum thermodynamics and its resource theory approach via thermal operations. It is found that, in the quasi-classical realm, global cyclic state transfers are impossible if and only if the Gibbs state is stable. Moreover, using a geometric approach by studying the so-called thermomajorization polytope, we prove that any subspace in equilibrium can be brought out of equilibrium via thermal operations. Interestingly, the case of some subsystem being in equilibrium can be witnessed via the degenerate extreme points of the thermomajorization polytope, assuming that the Gibbs state of the system is well structured. These physical considerations are complemented by simple new constructions for the polytope's extreme points, as well as for an important class of extremal Gibbs-stochastic matrices. [ABSTRACT FROM AUTHOR]

Structural deformation is ubiquitous throughout geological history. For a mineral deposit that underwent structural deformation after its formation, its geological architecture may have been severely distorted from its original geometry. Due to lack of concern for this fact, the effectiveness of existing mineral prospectivity methods could be limited in areas that experienced structural deformation. This paper proposes a three-dimensional (3D) mineral prospectivity modeling method with geometric restoration. An energy-based geometric restoration approach is presented to restore the existing geometry of geological architecture to the original one according to a series of prior constraints. To represent the original ore-forming environment, the original mineralization distribution and the predictor variables are estimated from the restored 3D geological models. Then, Random Forest is applied to build the mineral prospectivity model that associates predictor variables with the original mineralization distribution. The proposed method was applied to the world-class Jinchuan Ni–Cu–(PGE) sulfide deposit, which underwent significant off-fault deformation after its formation. It was found that, by restoration of the geometry of geological objects and the mineralization distribution, the predictor variables are more reasonable and significant to indicate spatial associations to the mineralization at Jinchuan. This led to a more accurate prospectivity model with superior evaluation metrics (AUCs, F1 scores, kappa coefficients, and PR curves, etc.) compared with the prospectivity model built without geometric restoration. Therefore, 3D mineral prospectivity modeling with geometric restoration is probably much more effective and reliable in quantifying spatial associations with mineralization and in targeting subsurface orebodies in areas that underwent structural deformation. [ABSTRACT FROM AUTHOR]

A novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex‐degree‐based topological index of remarkable simplicity, which we call elliptic Sombor index(ESO$$ ESO $$). The main mathematical properties of ESO$$ ESO $$ are established, especially its relations to other, earlier known, indices. Then the applicative potential of ESO$$ ESO $$ is analyzed. [ABSTRACT FROM AUTHOR]

We explore the polymorphism of a weakly polar molecule, dibenzoylmethane, in which the intramolecular hydrogen-bonded enol "chelated" form is favoured. A simple geometric method on the basis of interatomic distance to visualize and count favourable connections between non-hydrogen atoms was constructed to judge the strength of intermolecular interactions in polymorphs of this kind of weakly polar molecule. The number of total favourable connections mirrored with resonance-assisted hydrogen bonds (RAHB) and aromatic interactions in DBM polymorphs increases from forms I to III, in agreement with the order of their equivalent interaction energies, proving that it is feasible for this geometric approach to be used in this weakly polar system. [ABSTRACT FROM AUTHOR]

The impact of earthquake forces on structural stability is critical, especially in high seismic zones. This research examines how different geometric configurations of buildings respond to seismic forces across various seismic zones in Pakistan. The primary goal is to identify a safe and economical design by considering building geometry and seismic analysis methods. The study focuses on a 12-storey building, including a basement, ground floor, and ten stories, with three geometric shapes: rectangular, circular, and triangular. Each shape maintains approximately equal total covered areas and spans. Two seismic analysis methods are employed: the Static Equivalent Method for static analysis and the Response Spectrum Analysis per UBC97 Code for dynamic analysis. These methods help assess key parameters such as storey displacement, storey drift, moment, shear, and base shear to determine the safest and most cost-effective designs. The study reveals that different building geometries have varying performance levels under seismic forces. Rectangular structures typically provide more straightforward construction and cost estimation, while circular and triangular shapes might offer enhanced stability and reduced seismic impact due to their symmetrical properties. Cost estimations are integral to the analysis, ensuring that the final designs are not only structurally sound but also economically viable. The research concludes with recommendations for the optimal geometric design and analysis methods for 12-storey buildings in various seismic zones of Pakistan, balancing safety, performance, and cost-effectiveness. This comprehensive approach aids in developing resilient infrastructure capable of withstanding seismic events, thereby enhancing structural safety and sustainability. [ABSTRACT FROM AUTHOR]

We present interpretation of known results in the theory of discrete asymptotic and discrete conjugate nets from the discretization by Bäcklund transformations point of view. We collect both classical formulas of XIXth century differential geometry of surfaces and their transformations, and more recent results from geometric theory of integrable discrete equations. We first present transformations of hyperbolic surfaces within the context of the Moutard equation and Weingarten congruences. The permutability property of the transformations provides a way to construct integrable discrete analogs of the asymptotic nets for such surfaces. Then after presenting the theory of conjugate nets and their transformations we apply the principle that Bäcklund transformations provide integrable discretization to obtain known results on the discrete conjugate nets. The same approach gives, via the Ribaucour transformations, discrete integrable analogs of orthogonal conjugate nets. [ABSTRACT FROM AUTHOR]

To confirm whether Chinese mitten crabs (Eriocheir sinensis), commonly known as hairy crabs or river crabs, in non-Yangcheng Lake areas undergo morphological convergence with the original crabs in the Yangcheng Lake purse seine and high-standard modified aquaculture ponds after being "introduced" or "bathed"-cultured, we employed a geometric morphometrics approach. This approach allowed us to compare and analyze the dynamic changes in the carapace morphology of both the original and "introduced" crabs in Yangcheng Lake and high-standard ponds in Kunshan City at 0, 7, 14, and 30 days after "bathing" culture. The geometric morphological analysis of the carapace was conducted using a system of 35 established landmarks. The stepwise discriminant analysis of the relative distortion score revealed morphological differences between "introduced" and resident original crabs in the Yangcheng Lake area and in high-standard modified ponds after 7, 14, and 30 days of bathing culture. The accuracy of the discriminant analysis was 100%. The results of the geometric morphological visualization demonstrated that the carapaces of the bathed crabs underwent adaptive changes in the water. However, even after one month of bathing culture, the "introduced" crabs in lakes and ponds could not reach the morphological characteristics of the original crabs, i.e., their carapaces did not exhibit the characteristics of the original crabs. [ABSTRACT FROM AUTHOR]

Every subset S of a Cartesian space R d , endowed with differential structure C ∞ (S) generated by restrictions to S of functions in C ∞ (R d) , has a canonical partition M (S) by manifolds, which are orbits of the family X (S) of all derivations of C ∞ (S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney's conditions A and B. If M (S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces. The partition M (S) of a subcartesian space S by smooth manifolds provides a measure for the applicability of differential geometric methods to the study of the geometry of S. If all manifolds in M (S) are single points, we cannot expect differential geometry to be an effective tool in the study of S. On the other extreme, if M (S) contains only one manifold M, then the subcartesian space S is a manifold, S = M , and it is a natural domain for differential geometric techniques. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves two critical physical constraints: a discretely divergence-free (DDF) constraint on the magnetic field and the positivity-preserving (PP) property, which ensures the positivity of density, pressure, and internal energy. To enforce the DDF condition in each cell, we design a new discrete projection approach that projects the reconstructed point values at the cell interface into a DDF space, without using any approximation polynomials. This projection method is highly efficient, easy to implement, and particularly suitable for the high-order finite volume methods that return only the point values (no explicit approximation polynomials) in the reconstruction. Moreover, we also develop a new finite volume framework for constructing provably PP schemes for the ideal MHD system. The framework comprises the discrete projection technique, a suitable approximation to the Godunov--Powell source terms, and a simple PP limiter. We provide rigorous analysis of the PP property of the proposed finite volume method, demonstrating that the DDF condition and the proper approximation to the source terms eliminate the impact of magnetic divergence terms on the PP property. The analysis is challenging due to the internal energy function's nonlinearity and the intricate relationship between the DDF and PP properties. To address these challenges, we adopt the recently developed geometric quasilinearization approach [K. Wu and C.-W. Shu, SIAM Rev., 65 (2023), pp. 1031--1073], which transforms a nonlinear constraint into a family of linear constraints. Finally, we validate the effectiveness of the proposed method through several benchmark and demanding numerical examples. The results demonstrate that the proposed method is robust, accurate, and highly effective, confirming the significance of the proposed DDF projection and PP techniques. [ABSTRACT FROM AUTHOR]

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields. [ABSTRACT FROM AUTHOR]

As an attempt to enhance landfill capacity and extend its lifespan, this research explores the effect of slope inclination on landfill storage capacity and its implementation on the safety factors using numerical simulations. A geometric approach was used to determine the capacity change with inclination, and a new probabilistic calculation method, which accounts for the heterogeneity of waste layers, was employed to analyze the safety factor for different slope angles. Over 100 conducted calculations for each inclination were used to investigate the effect of slope variation on landfill safety. The results show that increasing inclination leads to a significant increase in landfill capacity. The safety factor results indicate that the conventional method, assuming homogenous waste, classifies 1:3 and 1:2 slopes as safe, while the new suggested method showed that a 2:3 inclination could be considered safe, especially since the calculation is not considering the safety-enhancing effect of daily cover layers. This study highlights the importance of considering the heterogeneity of waste layers in safety factor analysis, and the use of multi-layered nonhomogeneous calculation method, which provides more flexibility in design parameters. This research presents a significant step forward in constructing safe and cost-effective landfills. The use of a new probabilistic calculation method in designing landfills leads to more accurate and reliable results while maintaining safety standards. This research has important implications for the design and management of landfills and can be used as a guide for future studies in this field. [ABSTRACT FROM AUTHOR]

Geometric modeling techniques presented in this study target the important problem of improving the quality of milling processes through simulation-assisted research and development. Geometric modeling capabilities include generating the tool swept volumes for each tool motion, subtracting these from a dynamically changing in-process workpiece model, and calculating the instantaneous cutter engagements. In this study, the workpiece has been represented with a series of evenly distributed vectors oriented in three directions of the Cartesian coordinate system. Thus, sampling in multiple directions, called the triple-ray rap-based method, overcomes the problems associated with z -Map-based techniques, in which sampling only along one direction misses surface portions such as sharp edges and vertical walls. In addition, since the tool-swept volumes are regarded as envelope surfaces in the vector model-based techniques, the intersection calculations have been reduced to line/surface intersections. In the tool engagement extractions, the tool removal volumes represented by the vectors have been utilized instead of the in-process workpiece to reduce memory usage and the program runtime. Later, these removal volumes were voxelized at the predetermined resolutions for performing the arc and voxel intersections. In this research, the milling tools have been modeled as the surface of revolutions. Thereby, the method has been broadened to use more than just the APT type cutters, and it can be generalized for other types of cutting tools. [ABSTRACT FROM AUTHOR]

Stabbing Planes (also known as Branch and Cut) is a proof system introduced very recently which, informally speaking, extends the DPLL method by branching on integer linear inequalities instead of single variables. The techniques known so far to prove size and depth lower bounds for Stabbing Planes are generalizations of those used for the Cutting Planes proof system. For size lower bounds these are established by monotone circuit arguments, while for depth these are found via communication complexity and protection. As such these bounds apply for lifted versions of combinatorial statements. Rank lower bounds for Cutting Planes are also obtained by geometric arguments called protection lemmas. In this work we introduce two new geometric approaches to prove size/depth lower bounds in Stabbing Planes working for any formula: (1) the antichain method, relying on Sperner's Theorem and (2) the covering method which uses results on essential coverings of the boolean cube by linear polynomials, which in turn relies on Alon's combinatorial Nullenstellensatz. We demonstrate their use on classes of combinatorial principles such as the Pigeonhole principle, the Tseitin contradictions and the Linear Ordering Principle. By the first method we prove almost linear size lower bounds and optimal logarithmic depth lower bounds for the Pigeonhole principle and analogous lower bounds for the Tseitin contradictions over the complete graph and for the Linear Ordering Principle. By the covering method we obtain a superlinear size lower bound and a logarithmic depth lower bound for Stabbing Planes proof of Tseitin contradictions over a grid graph. [ABSTRACT FROM AUTHOR]

This paper presents a geometric approach to solve the inverse kinematics for an anthropomorphic robotic arm with seven degrees of freedom (DoF). The proposal is based on conformal geometric algebra (CGA), by which many geometric primitives can be operated naturally and directly. CGA allows for the intersection of geometric entities such as two or more spheres or a plane's projection over a sphere. Rigid transformations of such geometric entities are performed using only one operation through another geometric entity called a motor. CGA imposes geometric restrictions on the inverse kinematics solution, which avoids computation of the forward kinematics or other numerical solutions, unlike traditional approaches. Comparisons with state-of-the-art algorithms are included to prove our algorithm's superior performance: such as decreased execution time and errors of the end-effector for a series of desired poses. [ABSTRACT FROM AUTHOR]

We present a geometric approach to the finite Rational Inattention (RI) model, recasting it as a convex optimization problem with reduced dimensionality that is well suited to numerical methods. We provide an algorithm that outperforms existing RI computation techniques in terms of both speed and accuracy in both static and dynamic RI problems. We further introduce methods to quantify the impact of numerical inaccuracy on the model's outcomes and to produce robust predictions regarding the most frequently implemented actions. [ABSTRACT FROM AUTHOR]

Wireless Sensor Networks (WSNs) contain coverage holes caused by both random node sensor deployment and malfunctioning nodes. Because fixing the battery is challenging, collaborative discovery and assessment of coverage shortfalls, as well as getting rid of these holes, has been recognized as critical in WSNs. While placing nodes for sensors in a large-scale WSN is challenging. This research provides a cost-effective coverage hole detection approach based on collaborative distributed point placement. Create a polygon first by employing an angle estimate approach and neighbor data. Following that, a based on points hole identification technique is used to assess if a coverage issue appears in a large-scale WSN's supplied ROI. Furthermore, the region of the coverage hole is estimated using computational geometry-based polygonal triangulation methods. The accuracy of the method is tested here using statistical data. The results show that it outperforms earlier coverage hole-detecting algorithms. In particular, the method improves coverage rate by 75% when compared to conventional methodologies. It also lowers energy usage by 90%, adding to increased network lifetime. The quantitative favourable results demonstrate the effectiveness of the collaborative distributed point placement technique in detecting and successfully resolving coverage gaps in WSNs. In regards to coverage rate, energy consumption, and network longevity, the system being proposed beats previous coverage hole-detecting techniques. [ABSTRACT FROM AUTHOR]

Geometric approaches have been well developed for both linear and nonlinear systems, which are useful in the analysis and design of control systems. However, geometric approaches have been less considered for discrete‐time bilinear systems. In this paper, controllability and near‐controllability of driftless discrete‐time bilinear systems are dealt with from a geometric point of view. More specifically, geometric characterizations are presented for controllability and near‐controllability as well as for controllable subspaces and nearly controllable subspaces of the systems. Differently from the classical geometric approach for linear systems, it is shown that, for the bilinear systems, a controllable subspace has to be determined by two linear subspaces, while a nearly controllable subspace is determined by one linear subspace. As a result, geometric criteria for controllability, near‐controllability, controllable subspaces, and nearly controllable subspaces of the systems are respectively derived, which are also applied to multi‐input discrete‐time bilinear systems and to linear time‐invariant systems with a multiplicative perturbation. Examples are given to illustrate the derived geometric criteria. [ABSTRACT FROM AUTHOR]

Ranging-based localization is a fundamental problem in the Internet of Things and unmanned aerial vehicle networks. However, the nodes' limited-ranging scope and users' broad coverage purpose inevitably cause network sparsity or subnetwork sparsity. The performances of existing localization algorithms are extremely unsatisfactory in sparse networks. A crucial way to deal with the sparsity is to exploit the hidden knowledge provided by the unmeasured edges, which inspires this work to propose a hypothesis-based Joint Edge Inference and Localization algorithm called InferLoc. InferLoc mines the Unmeasured but Inferable Edges (UIEs). Each UIE is an unmeasured edge, but it is restricted through other edges in the network to be inside a rigid component, so it has only a limited number of possible lengths. We propose an efficient method to detect UIEs and geometric approaches to infer possible lengths for UIEs in 2D and 3D networks. The inferred possible lengths of UIEs are then treated as multiple hypotheses to determine the node locations and the lengths of UIEs simultaneously through a joint graph optimization process. In the joint graph optimization model, to make the 0/1 decision variables for hypotheses selection differentiable, differentiable functions are proposed to relax the 0/1 selections, and rounding is applied to select the final length after the optimization converges. We also prove the condition when a UIE can contribute to sparse localization. Extensive experiments show remarkably better accuracy and efficiency performances of InferLoc than the state-of-the-art network localization algorithms. In particular, it reduces the localization errors by more than 90% and speeds up the convergence time more than 100 times than that of the widely used G2O-based methods in sparse networks. [ABSTRACT FROM AUTHOR]

Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often contain both issues, making muscle segmentation especially difficult. In this paper we propose a novel intensity correction and a semi-automatic active contour-based segmentation approach. The approach uses a geometric flow that incorporates a Reproducing Kernel Hilbert Space (RKHS) edge detector and a geodesic distance penalty term from a set of markers and antimarkers. We test the proposed scheme on MR muscle segmentation and compare with some state-of-the-art methods. To help deal with the intensity inhomogeneity in this kind of image, a new approach to estimate the bias field using a fat fraction image, called Prior Bias-Corrected Fuzzy C-means (PBCFCM), is introduced. Numerical experiments show that the proposed scheme leads to significantly better results than compared ones. The average dice values of the proposed method are 92.5%, 85.3%, 85.3% for quadriceps, hamstrings and other muscle groups while other approaches are at least 10% worse. [ABSTRACT FROM AUTHOR]

Fragmentary but scientifically important pterosaur fossils have been reported in Lower Cretaceous strata such as the Jinju and Hasandong formations of South Korea. Recently, several large teeth and a second wing phalanx found in these strata have been suggested to have affinities with Boreopteridae, a clade in which has so far been reported only in the Yixian Formation of China. Here, the phylogenetic affinities of these proposed boreopterid specimens are reassessed, using two-dimensional geometric morphometric shape analyses. The morphometric analyses found the South Korean pterosaur teeth in different morphospaces from the Yixian Fm. boreopterids, and plot them closer to anhanguerians. An isolated second wing phalanx does plot close to a boreopterid Zhenyuanopterus longirostris in a morphospace defined by first two principal component axes, but taxa from different lineages are also plotted as closely, or even closer. Thus, there seems to be no clear evidence that these specimens belong to Boreopteridae, and the tooth fossils appear to be very different from those of established members of this clade. Therefore, the hypothesis that some South Korean pterosaur fossils can be referred to boreopterids, is here tentatively rejected [ABSTRACT FROM AUTHOR]

A Convex Programming Framework for Information Design Under Realistic Human Behavior Platform markets and services typically have additional relevant information in comparison with their users. Information design studies how the sharing of this information can be leveraged by the platform to influence user behavior and obtain desirable outcomes. Previous research has studied information design assuming that the users act to maximize their expected utility, but this assumption does not always hold in reality. Instead, people often exhibit biases and deviations from expected utility maximization. In "Persuading Risk-Conscious Agents: A Geometric Approach," Anunrojwong, Iyer, and Lingenbrink study information design with "risk-conscious" agents whose utility functions may depend nonlinearly on their beliefs. They provide a convex programming approach for solving for the optimal persuasion mechanism and establish their structural properties in different settings. They illustrate their approach in an application involving the sharing of waiting-time information in a queueing system. Overall, this work contributes to the study of information design under realistic models of human behavior. We consider a persuasion problem between a sender and a receiver where utility may be nonlinear in the latter's belief; we call such receivers risk conscious. Such utility models arise when the receiver exhibits systematic biases away from expected utility maximization, such as uncertainty aversion (e.g., from sensitivity to the variance of the waiting time for a service). Because of this nonlinearity, the standard approach to finding the optimal persuasion mechanism using revelation principle fails. To overcome this difficulty, we use the underlying geometry of the problem to develop a convex optimization framework to find the optimal persuasion mechanism. We define the notion of full persuasion and use our framework to characterize conditions under which full persuasion can be achieved. We use our approach to study binary persuasion, where the receiver has two actions and the sender strictly prefers one of them at every state. Under a convexity assumption, we show that the binary persuasion problem reduces to a linear program and establish a canonical set of signals where each signal either reveals the state or induces in the receiver uncertainty between two states. Finally, we discuss the broader applicability of our methods to more general contexts, and we illustrate our methodology by studying information sharing of waiting times in service systems. Funding: The second and the third authors gratefully acknowledge support from the Division of Civil, Mechanical and Manufacturing Innovation of the National Science Foundation [Grants CMMI-1633920 and CMMI-2002156]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2438. [ABSTRACT FROM AUTHOR]