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We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by the work of Ni-Lin-Luo-Gao in which the discrete time Ricci flow algorithm has been applied successfully as a discrete geometric approach in detecting communities. Our main result is the existence and uniqueness theorem for solutions to a continuous time normalized Ricci flow.We also display possible solutions to the Ricci flow on path graph and prove the Ricci flow on finite star graph with at least three leaves converges to constant-weighted star. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm to geometrically characterize inertial parameter identifiability for an articulated robot. The geometric approach tests identifiability across the infinite space of configurations using only a finite set of conditions and without approximation. It can be applied to general open-chain kinematic trees ranging from industrial manipulators to legged robots, and it is the first solution for this broad set of systems that is provably correct. The high-level operation of the algorithm is based on a key observation: Undetectable changes in inertial parameters can be represented as sequences of inertial transfers across the joints. Drawing on the exponential parameterization of rigid-body kinematics, undetectable inertial transfers are analyzed in terms of observability from linear systems theory. This analysis can be applied recursively, and lends an overall complexity of O (N) to characterize parameter identifiability for a system of N bodies. Matlab source code for the new algorithm is provided. [ABSTRACT FROM AUTHOR]

This paper offers a comprehensive investigation into the forward and inverse kinematics of a wrist rehabilitation robot, utilizing the Denavit-Hartenberg method for forward kinematics (FK) and a geometric approach, as well as artificial neural networks (ANN) and adaptive Neuro-Fuzzy inference systems (ANFIS) for inverse kinematics (IK) analysis. While the geometric method entails precise parameter measurements and faces uncertainties, ANN and ANFIS are explored as potential remedies to enhance accuracy and robustness. Evaluating 11 different training functions sourced from existing literature, our study conducts a thorough assessment of their performance within an ANN network. We aim to pinpoint the most suitable training function for achieving optimal IK solutions in the context of a wrist rehabilitation robotic. Additionally, the ANFIS model, trained using Fuzzy C-Means (FCM), sets itself apart from Grid Partitioning (GP) and Subtractive Clustering (SC). Among the ANN training functions, Bayesian regularization with 5 hidden layers emerges as the most effective, yielding low root mean square error (RMSE) values of 0.003, 0.004, and 0.007 degrees for pronation/supination (P/S), abduction/adduction (AB/AD), and flexion/extension (F/E), respectively. Conversely, ANFIS, trained with FCM, demonstrates satisfactory yet less precise results, with RMSE values of 0.191, 0.082, and 0.165 degrees for P/S, AB/AD, and F/E, respectively. Despite its adequacy, ANFIS trails behind ANN, showcasing RMSE reductions of 98.4%, 95.1%, and 95.7% for P/S, AB/AD, and F/E angles, respectively. This study contributes to leveraging ANN and ANFIS for IK analysis in wrist rehabilitation robotics, highlighting the efficacy of ANN, particularly when employing Bayesian regularization, to enhance accuracy. [ABSTRACT FROM AUTHOR]

Remote sensing in agriculture aims to search new methods to monitor fruit at the tree, thus improving the estimation of yield-related variables. Light detection and range (LiDAR) scanning was introduced to obtain geometric and radiometric information from fruit surfaces by means of 3D point clouds. A geometric model to estimate apple size by means of segmented 3D point cloud of fruit is proposed in the present study. The model consists in the approximation of 3D point clouds to a reference shape given by 2D Fourier series expansion. Each point cloud was approximated to its reference shape using an iterative error minimization routine. The geometric model was applied to laboratory and field data of spheres and apples during fruit growth, ranging from 60 to 151 days after full bloom (DAFB). An overall $RMSE$ RMSE between measured and predicted fruit radius of 20.1, 76.8, and 119.1% was found for the geometric model, mean, and maximum Euclidean distance approaches, respectively, including all studied growth periods in field conditions. Moreover, the linear regression on measured and predicted values showed considerably improved coefficient of determination (${R^2}$ R 2 ) of the geometric model in comparison to Euclidean distance calculations with ${R^2}$ R 2 values of 0.76 and 0.49 for laboratory and field scanned apples, respectively. The data processing method enables fruit monitoring and their application of terrestrial LiDAR sensing in precise orchard management. [ABSTRACT FROM AUTHOR]

This paper proposes a new geometric control method for homography-based visual servo control of Underactuated UAVs. In order to solve the application difficulties of geometric control in HBVS and explore a visual servo control technology that can be applied to aerial detection operations, this paper integrates the geometric control into the visual servoing framework and design a new homography-based geometric visual servoing controller. The outer loop is used as feedback information using the virtual homography matrix between the two images. The inner loop controls the orientation of the UAVs through geometric control. The stability of the proposed controller is proved based on Lyapunov's theory. The proposed method has better transient performance and dynamic performance than the conventional visual servo method. The excellent performance of the controller has been proven by a large number of experiments. In addition, the application of the controller on an unmanned aerial manipulator is demonstrated. [ABSTRACT FROM AUTHOR]

Although evaluating developmental stress is challenging, it is critical to understanding phenotypic adaptation and differentials in morbidity and mortality related to spatiotemporal variation in environmental and cultural factors. This paper presents a new, reproducible, and reliable geometric morphometric (GM) protocol through which stress‐induced deviations to symmetry, known as fluctuating asymmetry (FA), can be robustly quantified. A case study, in which maternally mediated early‐life stress in human skeletal remains is explored through first permanent molar (M1) FA, illustrates the method's effectiveness and wide‐ranging potential to revolutionise the investigation of themes such as stress intensity, developmental processes, and buffering mechanisms in past populations. [ABSTRACT FROM AUTHOR]

This work presents a monolithic finite element strategy for the accurate solution of strongly‐coupled fluid‐structure‐electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull‐in phenomena and squeeze film damping in high aspect‐ratio micro‐electro‐mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high‐frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation. [ABSTRACT FROM AUTHOR]

We are concerned with the long time existence of smooth solutions to full compressible Navier-Stokes equations in 3D bounded domains with Dirichlet boundary conditions on the velocity and temperature. The smallness restriction on the initial data or time interval is unnecessary. Under the condition that the limiting system admits a reasonably smooth solution on a given time interval, we verify that the compressible system admits the smooth solution on the same interval as well, provided that the Mach number is sufficiently small. Moreover, as the Mach number goes to zero, the solution of the compressible system converges uniformly to that of the incompressible one. We utilize some geometric techniques to overcome difficulties introduced by non-slip boundary conditions. [ABSTRACT FROM AUTHOR]

Uncertainty quantification approaches have been more critical in large language models (LLMs), particularly high-risk applications requiring reliable outputs. However, traditional methods for uncertainty quantification, such as probabilistic models and ensemble techniques, face challenges when applied to the complex and high-dimensional nature of LLM-generated outputs. This study proposes a novel geometric approach to uncertainty quantification using convex hull analysis. The proposed method leverages the spatial properties of response embeddings to measure the dispersion and variability of model outputs. The prompts are categorized into three types, i.e., 'easy', 'moderate', and 'confusing', to generate multiple responses using different LLMs at varying temperature settings. The responses are transformed into high-dimensional embeddings via a BERT model and subsequently projected into a two-dimensional space using Principal Component Analysis (PCA), Isomap, Multidimensional Scaling (MDS). The Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is utilized to cluster the embeddings and compute the convex hull for each selected cluster. The experimental results indicate that the uncertainty of the model for LLMs depends on the prompt complexity, the model, and the temperature setting. [ABSTRACT FROM AUTHOR]

The purpose of this study is to make evaluation regarding significant issues about the customer expectations and technical competencies for successfully integration of batteries in microgrid systems. In this direction, six different customer expectations and technical requirements are identified by considering literature review results. The weights of the criteria are computed with sine trigonometric Pythagorean fuzzy (STPYF) decision making trial and evaluation laboratory (DEMATEL). Moreover, technical requirements are also ranked using a newly developed technique in this study called "ranking technique by geometric mean of similarity ratio to optimal solution" (RATGOS). This new methodology is also integrated with STPYF sets. The main contribution of this study is that it can be much easier to increase the efficiency of battery integration in microgrid systems by making the priority analysis. Moreover, proposing a new ranking-based decision-making technique (RATGOS) has an increasing impact on the methodological originality. On the other side, owing to considering DEMATEL approach in criteria weighting, the causal directions between these factors can be understood. This situation can be accepted as an important superiority of this model by comparing with the previously generated ones. It is determined that efficiency of storing energy is the most critical customer expectation to increase the effectiveness of this process. Furthermore, the ranking results also demonstrate that generating smart battery control systems is the most important technical requirements to have higher performance in microgrid energy systems. It is identified that the proposed model generates similar findings with the previous ones. Based on these results, some strategies should be implemented to increase the efficiency of energy storage processes in microgrid systems. Within this framework, choosing the right battery is of vital importance. Technological infrastructure is necessary to achieve this goal. Similarly, it is important to provide cyber security to increase the efficiency of energy storage processes. In this way, it is possible for the batteries to work more safely against external interventions. [ABSTRACT FROM AUTHOR]

In reliability analysis, the residual life of a component or system plays a key role in explaining a component's present condition as well as how long it will continue to function as intended under specific circumstances, thereby preventing premature failure and saving money. Based on this, Nair and Rajesh [Geometric vitality function and its applications to reliability. IAPQR Trans. 2000;25(1):1–8] proposed a new measure called the geometric vitality function that explains the system's failure pattern. In the present study, we have introduced the geometric vitality function in the context of order statistics by means of the relevation transform and also analysed the monotone and ordering properties of the proposed measure. The application of the proposed measure in the stock markets are explored in the present study. Finally, to estimate the proposed measure using a real life data set, a simple estimator has been introduced as well. [ABSTRACT FROM AUTHOR]

Accurate taxonomic classification of deep-sea taxa is often impeded by the presence of highly morphologically similar but genetically distinct species. This issue is particularly pronounced in the isopods of the deep-sea family Macrostylidae, which exhibit remarkably low morphological variation despite significant genetic diversity. In this study, we present the first application of geometric morphometric techniques to 41 specimens across five species of deep-sea macrostylid isopods collected from Icelandic waters. Our results suggest that geometric morphometric techniques can effectively discriminate between macrostylid species. These techniques, hence, promise to be an important addition to the toolset of macrostylid taxonomists. [ABSTRACT FROM AUTHOR]

Mathematics is considered the language of physics. Starting from idealizations and kinematics, geometric-mathematical physics with paradigms such as flexible spacetime and dark energy has emerged whose physical reality has not been clarified. By analyzing processes regarding their causes and the functional dependencies of energies, this work identifies shortcomings in the basic energy concepts of physics, which cannot be remedied with mathematics. While formal transformations of process equations such as integration are mathematically correct, they do conceal vital physical information, suggesting that mathematics should be used with caution. We propose a physically justified approach that reconciles the mechanical and thermodynamic energy concepts and provides a revised interpretation of E = mc2. Our results suggest that geometric approaches were built too early on a shaky physical foundation, leading to undesirable developments in recent centuries. The language of physics should be physics, not just mathematics. [ABSTRACT FROM AUTHOR]

Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves with respect to the defined metric. We introduce the notion of energy foliation for autonomous ODEs and highlight its connection to the classical energy concept. Additionally, we explore the geometry of the leaves of the foliation. Finally, the results are applied to the analysis of Lagrangian mechanical systems. In particular, we provide an autonomous Lagrangian for a damped harmonic oscillator. [ABSTRACT FROM AUTHOR]

Strong selective pressure on phenotype can arise when habitat transitions fundamentally alter the physical media in which animals live, such as the invasion of land by lobe-finned fishes and insects. When environmental gradients differ drastically among habitats and multiple lineages transition between these habitats, we expect phenotypic convergence to be prevalent. One transition where widespread convergence has been observed is the shift from aboveground to subterranean environments in fossorial animals. Subterranean environments are low-light, confined spaces and tend to be hypoxic or anoxic, not to mention that the act of burrowing itself demands morphological specializations for excavation. Research suggests burrowing promotes morphological convergence in crayfish, with non-burrowing forms having a dorsoventrally compressed carapace and long, slender claws (chelae), while primary burrowing forms have a dorsolaterally compressed carapace and shorter, more powerful claws. However, earlier ecomorphological comparisons relied on qualitative rather than quantitative assessments of phenotypic differences. This study tested for convergence in North American crayfishes using a geometric morphometric approach. We photographed the carapace and claw for representative species across 13 North American genera. We hypothesized that crayfishes that occur in similar habitats and exhibit similar burrowing behaviors, would converge in their carapace and claw shapes. We found evidence for convergence in carapace and claw morphologies in burrowing crayfishes. However, claw phenotypes did not converge as strongly as carapace shape, an example of "imperfect" or "incomplete" convergence we attribute to the multiple competing demands on claw form and function. We argue that nuances in habitat characteristics, like soil type or compaction, make complete convergence unlikely for range- and dispersal-limited fossorial crayfishes. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing some fundamental properties of the Fenchel conjugate for set-valued mappings, we derive its main calculus rules in various settings. Our approach is geometric and draws inspiration from the successful application of this method by B.S. Mordukhovich and coauthors in variational and convex analysis. Subsequently, we demonstrate that our new findings for the Fenchel conjugate of set-valued mappings can be utilized to obtain many old and new calculus rules of convex generalized differentiation in both finite and infinite dimensions. [ABSTRACT FROM AUTHOR]

How many times can a diffusing molecule permeate across a membrane or be adsorbed on a substrate? We employ an encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general confining medium. Various features of these statistics are illustrated for two practically relevant cases: a flat boundary and a spherical confinement. Some applications of these fundamental results are discussed. [ABSTRACT FROM AUTHOR]

The preface to "Geometry and Topology with Applications" highlights the historical significance and evolution of geometry as a research field in mathematics. It discusses the contributions of prominent mathematicians like Euclid, Euler, Gauss, Lobachevsky, Riemann, Hilbert, Poincaré, Thurston, and Gromov to the development of various geometries and topologies. The document also focuses on the work of Thurston and Gromov in geometric topology and geometric group theory, respectively, and their impact on modern mathematics. The Special Issue attracted submissions from researchers worldwide, with 12 papers accepted for publication, including survey papers on discrete groups and topology in the fourth dimension. [Extracted from the article]

Purpose: The purpose of this paper is to reshape a fast-jet electronics pod's external geometry to ensure compliance with aircraft pylon load limits across its carriage envelope while adhering to onboard system constraints and fitment specifications. Design/methodology/approach: Initial geometric layout determination used empirical methods. Performance approximation on the aircraft with added fairings and stabilising fin configurations was conducted using a panel code. Verification of loads was done using a full steady Reynolds-averaged Navier–Stokes solver, validated against published wind tunnel test data. Acceptable load envelope for the aircraft pylon was defined using two already-certified stores with known flight envelopes. Findings: Re-lofting the pod's geometry enabled meeting all geometric and pylon load constraints. However, due to the pod's large size, re-lofting alone was not adequate to respect aircraft/pylon load limitations. A flight restriction was imposed on the aircraft's roll rate to reduce yaw and roll moments within allowable limits. Practical implications: The geometry of an electronics pod was redesigned to maximise the permissible flight envelope on its carriage aircraft while respecting the safe carriage load limits determined for its store pylon. Aircraft carriage load constraints must be determined upfront when considering the design of fast-jet electronic pods. Originality/value: A process for determining the unknown load constraints of a carriage aircraft by analogy is presented, along with the process of tailoring the geometry of an electronics pod to respect aerodynamic load and geometric constraints. [ABSTRACT FROM AUTHOR]

High-performance finite element research has always been a major focus of finite element method studies. This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric finite element method. Firstly, the physical field is approximated by uniform B-spline interpolation, while geometry is represented by non-uniform rational B-spline interpolation. By introducing a transformation matrix, elements of types C0 and C1 are constructed in the isogeometric finite element method. Subsequently, the corresponding calculation formats for one-dimensional bars, beams, and two-dimensional linear elasticity in the isogeometric finite element method are derived through variational principles and parameter mapping. The proposed method combines element construction techniques of the finite element method with geometric construction techniques of isogeometric analysis, eliminating the need for mesh generation and maintaining flexibility in element construction. Two elements with interpolation characteristics are constructed in the method so that boundary conditions and connections between elements can be processed like the finite element method. Finally, the test results of several examples show that: (1) Under the same degree and element node numbers, the constructed elements are almost consistent with the results obtained by traditional finite element method; (2) For bar problems with large local field variations and beam problems with variable cross-sections, high-degree and multi-nodes elements constructed can achieve high computational accuracy with fewer degrees of freedom than finite element method; (3) The computational efficiency of isogeometric finite element method is higher than finite element method under similar degrees of freedom, while as degrees of freedom increase, the computational efficiency between the two is similar. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to determine the effect of clothing fabrics, sizes and air ventilation rate on the volume and thickness of the air gap under the air ventilation garments (AVGs). Design/methodology/approach: The geometric models of the human body and clothing were obtained by using a 3D body scanner. Then the distribution of the volume and thickness of the air gap for four clothing fabrics and three air ventilation rates (0L/S, 12L/S and 20L/S) were calculated by Geomagic software. Finally, a more suitable fabric was selected from the analysis to compare the distribution of the air gap entrapped for four clothing sizes (S, M, L and XL) and the three air ventilation rates. Findings: The results show that the influence of air ventilation rate on the air gap volume and thickness is more obvious than that of the clothing fabrics and sizes. The higher is the air ventilation rate, the thicker is the air gap entrapped, and more evenly distributed is the air gap. It can be seen that the thickness of the air gap in the chest does not change significantly with the changes of the air ventilation rates, clothing fabrics and sizes, while the air gap in the waist is affected significantly. Originality/value: This research provides a better understanding of the distribution of the air gap entrapped in ventilated garments, which can help in designing the optimal air gap dimensions and thus provide a basis and a reference for the design of the AVGs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study the problems of consistency and the existence of finite-dimensional realizations for multi-curve interest rate models of Heath–Jarrow–Morton type, generalizing the geometric approach developed by T. Björk and co-authors for the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model can be realized by a finite-dimensional state process. We illustrate the general theory in a number of model classes and examples, providing explicit constructions of finite-dimensional realizations. Based on these theoretical results, we perform the calibration of a three-curve Hull–White model to market data and analyse the stability of the estimated parameters. [ABSTRACT FROM AUTHOR]

A strategy to assist visualization and analysis of large and complex datasets is dimensionality reduction, with which one maps each data point into a low-dimensional manifold. However, various dimensionality reduction techniques are computationally infeasible for large data. Out-of-sample techniques aim to resolve this difficulty; they only apply the dimensionality reduction technique on a small portion of data, referred to as landmarks, and determine the embedding coordinates of the other points using landmarks as references. Out-of-sample techniques have been applied to online settings, or when data arrive as time series. However, existing online out-of-sample techniques use either all the previous data points as landmarks or the fixed set of landmarks and therefore are potentially not good at capturing the geometry of the entire dataset when the time series is non-stationary. To address this problem, we propose an online landmark replacement algorithm for out-of-sample techniques using geometric graphs and the minimal dominating set on them. We mathematically analyse some properties of the proposed algorithm, particularly focusing on the case of landmark multi-dimensional scaling as the out-of-sample technique, and test its performance on synthetic and empirical time-series data. [ABSTRACT FROM AUTHOR]

The goal of this study is to process digital images to facilitate color discrimination in dichromatic vision without changing their appearances in trichromatic vision as much as possible. Therefore, we propose a simple and effective image enhancement method using the geometric properties of the RGB color space. Concretely, a novel image representation that clarifies the relationship between dichromatic and trichromatic visions in the RGB color space, and an image enhancement method based on this representation are presented. The effectiveness of the proposed method is verified by experiments using several digital images. [ABSTRACT FROM AUTHOR]

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a 3-dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions of its Killing vectors. The resulting Riemannian metric inherits the geodesics for asymptotically flat spacetimes including the stationary and axisymmetric ones. The method allows us to find Riemannian metrics in three and two dimensions plus the radial geodesic equation when we project over three different directions. The 3-dimensional Riemannian metric reduces to the Jacobi metric when static, spherically symmetric and asymptotically flat spacetimes are considered. However, it can be calculated for a larger variety of metrics in any number of dimensions. We show that the geodesics of the original spacetime metrics are inherited by the projected Riemannian metric. We calculate the Gaussian and geodesic curvatures of the resulting 2-dimensional metric, we study its near horizon and asymptotic limit. We also show that this technique can be used for studying the violation of the strong cosmic censorship conjecture in the context of general relativity. [ABSTRACT FROM AUTHOR]

General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein's GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR's spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed. [ABSTRACT FROM AUTHOR]

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use f (T ,) modified gravity, which is characterized by the trace of an energy–momentum tensor as and torsion scalar T , Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics. [ABSTRACT FROM AUTHOR]

The threatened springsnail subgenus Alzoniella (Navarriella) in the Iberian Peninsula has been suggested to be an old and relict lineage of the family Hydrobiidae. The subgenus is represented by two morphological species, both endemic to the Pyrenees and their southern foothills. We conducted phylogenetic analyses based on mitochondrial and nuclear gene fragments of topotypes and other populations, four molecular species delimitation methods, and morphological examinations to clarify the uncertain systematic position of the subgenus within the family, assess its species diversity, and understand the population genetic structure of the two geographically restricted species. Our phylogenetic results revealed that Alzoniella (Navarriella) is distantly related to all other species of Alzoniella , even belonging to an independent subfamily-level clade, for which we introduce the new genus Navarriella and the new subfamily Navarriellinae subfam. nov. Molecular methods and geometric morphometric analysis of shell shape identified a single species in the new genus. The significant phylogenetic distance from other hydrobiid taxa, narrow distribution, and limited gene flow among its populations (estimated from mitochondrial cytochrome c oxidase subunit I sequences) highlight Navarriella as an isolated lineage within the family that requires urgent conservation attention. Furthermore, our results cast a new light on the northern Iberian Mountains as a dispersal barrier for ancient spring lineages. [ABSTRACT FROM AUTHOR]

Assignation of old type specimens is important for nomenclatural stability, but when it comes to ancient specimens, the use of certain techniques is sometimes not appropriate, due to the condition or age of the specimen. In this study, the supposedly polymorphic and monotypic genus Callirhinus Blanchard was analysed with geometric morphometric techniques and photographs of the pronotum, with the purpose of identifying the locality of the old type specimen (19th century) and to test a priori defined hypothetical species by cumulation of evidence within an integrative taxonomic protocol using geometric morphometry, complemented by morphology and geographical discontinuity. Five morphotypes were defined a priori, and principal component, canonical variates analysis, and distances tests for the assignment of the type specimen based on canonical scores and Procrustes distances between means of groups were carried out. Statistical significance was found in four axes validating the species hypotheses, discovering that the type specimen belongs to the morphotype from Jalisco state. Additionally, a taxonomic treatment, the description of four new species, C. choperi Ramírez-Ponce & Zaragoza sp. nov. , C. nandu Ramírez-Ponce & Zaragoza sp. nov. , C. huiinis Ramírez-Ponce & Zaragoza sp. nov. , and C. veeme Ramírez-Ponce & Zaragoza sp. nov. , keys for the species determination, new distributional records, and a map are provided. The present work demonstrates that Geometric Morphometry is an adequate analytical tool that supports taxonomic identification at low cost and without damaging historical specimens. [ABSTRACT FROM AUTHOR]

When a cavitation bubble re-expands near the surface of a liquid, an axisymmetric crown forms around the jet that is initially produced. Controlling this crown is essential if the first jet is to be used in engineering applications such as laser-induced transfer (LIT). Herein, we introduce a second cavitation bubble to control the formation and growth of the crown. Numerical simulations were performed using the compressibleInterIsoFoam solver within the open-source platform OpenFOAM, incorporating a geometric volume-of-fluid approach for tracking interfaces. Detailed analysis showed that a reversal in curvature across the concave interface indicates the moment of crown formation, and this is induced by flow focusing during bubble contraction or momentum transfer from a second expansion. In the presence of the second bubble, the crown type can be classified as either enhanced or inhibited in comparison with a single-bubble scenario. The velocity of crown formation, v cf , is defined to describe the crown type, and a parametric study of crown types was conducted based on the dimensionless stand-off distances, γ 1 and γ 2 . The findings of this study offer new insights into the field of LIT. [ABSTRACT FROM AUTHOR]

The segmentation of teeth in 3D dental scans is difficult due to variations in teeth shapes, misalignments, occlusions, or the present dental appliances. Existing methods consistently adhere to geometric representations, omitting the perceptual aspects of the inputs. In addition, current works often lack evaluation on anatomically complex cases due to the unavailability of such datasets. We present a projection-based approach towards accurate teeth segmentation that operates in a detect-and-segment manner locally on each tooth in a multi-view fashion. Information is spatially correlated via recurrent units. We show that a projection-based framework can precisely segment teeth in cases with anatomical anomalies with negligible information loss. It outperforms point-based, edge-based, and Graph Cut-based geometric approaches, achieving an average weighted IoU score of 0.97122 ± 0.038 and a Hausdorff distance at 95 percentile of 0.49012 ± 0.571 mm. We also release Poseidon's Teeth 3D (Poseidon3D), a novel dataset of real orthodontic cases with various dental anomalies like teeth crowding and missing teeth. [ABSTRACT FROM AUTHOR]

Current work provides an algebraic and geometric technique for building topological quantum codes. From the lattice partition derived of quotient lattices Λ ′ / Λ of index m combined with geometric technique of the projections of vector basis Λ ′ over vector basis Λ , we reproduce surface codes found in the literature with parameter [ [ 2 m , 2 , | a | + | b | ] ] for the case Λ = Z 2 and m = a 2 + b 2 , where a and b are integers that are not null, simultaneously. We also obtain a new class of surface code with parameters [ [ 2 m , 2 , | a | + | b | ] ] from the Λ = A 2 -lattice when m can be expressed as m = a 2 + a b + b 2 , where a and b are integer values. Finally, we will show how this technique can be extended to the construction of color codes with parameters [ [ 18 m , 4 , 6 (| a | + | b |) ] ] by considering honeycomb lattices partition A 2 / Λ ′ of index m = 9 (a 2 + a b + b 2) where a and b are not null integers. [ABSTRACT FROM AUTHOR]

The Ethiopian highlands represent a wide spectrum of ecological gradients that provide suitable conditions for gradient speciation. Previous studies support the gradient model of speciation for two Ethiopian shrew species: Crocidura thalia and C. glassi. Here, we aimed to elucidate for the first time the phylogenetic position of C. afeworkbekelei and to test the gradient model of speciation for these three species. On the basis of a dataset collected from the whole south slope of the Bale Mountains, we reconstructed phylogenetic relationships among these species using mitochondrial and nuclear markers. Additionally, we examined shape and size differentiation of the skull and mandible. The molecular data revealed a similarity of the three species with lack of reciprocal monophyly among them. We demonstrated differences both in size and shape of the skull and mandible between low- and high-elevation forms albeit without a significant morphological hiatus. We identified the most changeable parts of the skull and mandible, which imply adaptive shifts in diet. We revealed the distribution, phylogenetic and morphological patterns that match predictions of the gradient model of speciation for three mammalian forms. Our data suggest intense processes of adaptation to the markedly different habitats along the considerable altitudinal gradient that fit the first stage of the gradient model of speciation. We believe that C. afeworkbekelei and C. thalia should be regarded as different ecotypes, and these species names must be reduced to junior synonyms of C. glassi. [ABSTRACT FROM AUTHOR]

Introduction: Our knowledge of the populations of sub‐Saharan Africa in the periods before European colonization is limited. Few archeological sites containing human remains have been identified, and written sources for these periods are rare. The discovery in 2018 of the Iroungou sepulchral cave (Gabon), whose use predates the arrival of the Portuguese (14th–15th centuries CE), is an exceptional source of information: at least 28 individuals associated with numerous metal artifacts were found there. The anthropobiological remains were left in situ, but the eight best preserved crania were digitized. Objectives: This study focuses on the population affinities of these crania, whose morphology was described using 237 landmarks. Materials and Methods: Geometric morphometric analyses were used to compare the eight Iroungou specimens with 154 individuals representing 12 well‐defined African populations. After alignment (Generalized Procrustes Analysis), morphological affinity was assessed using Euclidean and Mahalanobis distances, and posterior probabilities of population membership (discriminant analysis). Results: Results indicate that the eight Iroungou crania have, on average, more affinity with Bayaka Pygmy, followed by Central African Bantu. Nevertheless, individually, the Iroungou specimens show an important morphological variation and the eight crania can be separated into different affinity groups: Bayaka and Central African Bantu, KhoeSan, and East‐African Bantu. Finally, one individual presents strong affinity with Somalis. Conclusion: This phenetic mapping of the Iroungou sample raises questions about the profile of the individuals deposited in the cave in a geographical area known for the Loango pre‐colonial kingdom, which ruling class seemed to have had privileged relationships with the Pygmy populations. [ABSTRACT FROM AUTHOR]

By using the theory of analytic vectors and manifolds modeled on normed spaces, we provide a rigorous symplectic differential geometric approach to t -dependent Schrödinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by families of unbounded self-adjoint Hamiltonians admitting a common domain of analytic vectors. This allows one to cope with the lack of smoothness of structures appearing in quantum mechanical problems while using differential geometric techniques. Our techniques also allow for the analysis of problems related to unbounded operators that are not self-adjoint. As an application, the Marsden-Weinstein reduction procedure was employed to map the above-mentioned t -dependent Schrödinger equations onto their projective spaces. We also analyzed other physically and mathematically relevant applications, demonstrating the usefulness of our techniques. [ABSTRACT FROM AUTHOR]

We apply a well known technique of theoretical physics, known as geometric algebra or Clifford algebra, to linear electrical circuits with nonsinusoidal voltages and currents. We rederive from the first principles the geometric algebra approach to the apparent power decomposition. The important new point consists of endowing the space of Fourier harmonics with a structure of a geometric algebra (it is enough to define the Clifford product of two periodic functions). We construct a set of commuting invariant imaginary units which are used to define impedance and admittance for any frequency. [ABSTRACT FROM AUTHOR]

Complex and even non-monotonic responses to external control can be found in many thermodynamic systems. In such systems, nonequilibrium shortcuts can rapidly drive the system from an initial state to a desired final state. One example is the Mpemba effect, where preheating a system allows it to cool faster. We present nonequilibrium hasty shortcuts—externally controlled temporal protocols that rapidly steer a system from an initial steady state to a desired final steady state. The term "hasty" indicates that the shortcut only involves fast dynamics without relying on slow relaxations. We provide a geometric analysis of such shortcuts in the space of probability distributions by using timescale separation and eigenmode decomposition. We further identify the necessary and sufficient condition for the existence of nonequilibrium hasty shortcuts in an arbitrary system. The geometric analysis within the probability space sheds light on the possible features of a system that can lead to hasty shortcuts, which can be classified into different categories based on their temporal pattern. We also find that the Mpemba-effect-like shortcuts only constitute a small fraction of the diverse categories of hasty shortcuts. This theory is validated and illustrated numerically in the self-assembly model inspired by viral capsid assembly processes. [ABSTRACT FROM AUTHOR]

The evaluation of regional tourism ecological efficiency (RTEE) under high-quality development aims to measure how the tourism industry promotes economic growth while minimizing resource consumption and environmental impact. By analyzing economic output per unit of carbon emissions, it assesses the sustainability and environmental performance of the tourism sector. This evaluation method considers resource utilization, energy efficiency, and ecological protection, helping decision-makers optimize tourism development models, achieve a balance between economic and ecological benefits, and promote the transition of tourism towards a low-carbon, green, and high-quality direction. The RTEE evaluation under high-quality development is MADM. The single-valued neutrosophic number generalized power geometric BM (SVNNGPGBM) technique is put forward and MADM decision techniques are put forward in line with SVNNGPGBM technique and power geometric (PG) technique. Finally, numerical example about RTEE evaluation under high-quality development and comparative analysis was put forward the SVNNGPGBM technique. [ABSTRACT FROM AUTHOR]

Rapid on-site cytopathology evaluation (ROSE) has been considered an effective method to increase the diagnostic ability of endoscopic ultrasound-guided fine needle aspiration (EUS-FNA); however, ROSE is unavailable in most institutes worldwide due to the shortage of cytopathologists. To overcome this situation, we created an artificial intelligence (AI)-based system (the ROSE-AI system), which was trained with the augmented data to evaluate the slide images acquired by EUS-FNA. This study aimed to clarify the effects of such data-augmentation on establishing an effective ROSE-AI system by comparing the efficacy of various data-augmentation techniques. The ROSE-AI system was trained with increased data obtained by the various data-augmentation techniques, including geometric transformation, color space transformation, and kernel filtering. By performing five-fold cross-validation, we compared the efficacy of each data-augmentation technique on the increasing diagnostic abilities of the ROSE-AI system. We collected 4059 divided EUS-FNA slide images from 36 patients with pancreatic cancer and nine patients with non-pancreatic cancer. The diagnostic ability of the ROSE-AI system without data augmentation had a sensitivity, specificity, and accuracy of 87.5%, 79.7%, and 83.7%, respectively. While, some data-augmentation techniques decreased diagnostic ability, the ROSE-AI system trained only with the augmented data using the geometric transformation technique had the highest diagnostic accuracy (88.2%). We successfully developed a prototype ROSE-AI system with high diagnostic ability. Each data-augmentation technique may have various compatibilities with AI-mediated diagnostics, and the geometric transformation was the most effective for the ROSE-AI system. [ABSTRACT FROM AUTHOR]

Contemporary synthetic aperture radar (SAR) image processing techniques face various challenges, particularly in ship detection, background noise reduction, and information preservation. To address these issues, this paper introduces a novel model we called SAR-ShipSwin, which combines the swin transformer and feature pyramid network as the backbone network structure, specifically designed for ship detection in SAR images. The backbone network optimizes computational efficiency and handles occlusion and overlap issues in SAR images successfully by introducing the improved window multi-head self-attention module. To further enhance recognition accuracy, we design the background modeling network, which efficiently identifies and eliminates complex background features. Additionally, we introduce the spatial intensity geometric pooling technique, a novel pooling strategy that preserves geometric and structural information of the original region of interest, significantly reducing information loss and distortion. Considering the diverse ship shapes in SAR images, we specially design the dynamic ship shape adaptive convolution module, which dynamically adjusts the shape of convolution kernels to better match the targets. The proposed model is validated on the SSDD and HRSID datasets, achieving state-of-the-art performance. [ABSTRACT FROM AUTHOR]

Embedded computer systems refer to specialized computer systems that integrate operating systems and functional software into computer hardware systems, are application centric, based on computer technology, and have tailorable software and hardware. They have strict requirements for real-time performance, reliability, cost, volume, and power consumption. The performance and security evaluation of embedded systems is an important aspect of the development, development, and integration process of embedded systems, which can provide various quantitative analysis basis for the development and technical transformation of embedded products. The performance and security evaluation of embedded systems is a very complex issue, and evaluators may have different understandings of the problem due to their different starting points and observation perspectives. The embedded computers' performance evaluation is a classical multiple-attribute decision-making (MADM) issue. In such paper, the generalized weighted geometric Bonferroni mean (GWGBM) operator is built for MADM with single-valued neutrosophic sets (SVNSs). Then, the single-valued neutrosophic number generalized power geometric BM (SVNNGPGBM) operator is built and then the MADM decision methods are proposed based on the SVNNGPGBM operator and power geometric (PG) operator. Finally, an example about embedded computers' performance evaluation and some comparative analysis were given to demonstrate the SVNNGPGBM method. [ABSTRACT FROM AUTHOR]

This work explores the construction of spherically symmetric models of stellar interiors by incorporating the null complexity factor (CF) as an additional constraint. This supplementary condition helps us to close an array of stellar structure equations resulting from the process of gravitational decoupling. By making use of MGD-type gravitational decoupling we analyze the role of gravitational decoupling and its impact on the complexity of static, self-gravitational systems. We begin by considering an anisotropic seed solution described by the Kohler–Chao–Tikekar metric ansatz. We then apply the minimal geometric deformation technique to this seed solution, imposing the constraint that the effective anisotropic factor vanishes. This constraint leads to the generation of an isotropic stellar solution. Furthermore, we construct a second family of solutions in which the CF, remains the same for both the seed solution and its minimally deformed counterpart. Our analysis further investigated the influence of both the deformation parameter and the CF on the structural properties of the static and spherically symmetric stellar objects. [ABSTRACT FROM AUTHOR]

Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates quantum electrodynamics. Here we formalize and generalize the notion of a geometric gauge theory, then apply this framework to classical physical models, including an improved Lagrangian for matter field electromagnetism. We find a remarkably consistent series of actions, with straightforward limits under which each previous one may be obtained. Ancillary benefits include a gauge-independent Galilean Lagrangian, a geometric interpretation for the unusual metric dependence of four-momentum, a modern treatment of the effects of worldline variation on the four-current, a gauge theory of gravity which includes a matter field, and consistent units for matter field electromagnetism. [ABSTRACT FROM AUTHOR]

Tank goby Glossogobius giuris is widely distributed across Vietnamese rivers, estuaries, and lagoons, particularly in the central region where this species plays a pivotal role as a high commercial source for local communities. In this study, we employed landmark-based geometric morphometrics to compare the morphometric variations among three distinct populations of G. giuris inhabiting the Tam Giang Lagoon (Thua Thien Hue Province), Nhat Le Estuary (Quang Binh Province), and Truong Giang River (Quang Nam Province), Vietnam. The analysis, utilizing Permutational Multivariate Analysis of Variance (PERMANOVA) with Mahalanobis distances, revealed significant differences in the body shape among the three populations (P < 0.001). Specifically, with respect to the lateral side, the highest Mahalanobis distance was observed between specimens from the Tam Giang and Nhat Le, followed by the Tam Giang and Truong Giang River, with the lowest value found between the Nhat Le and Truong Giang. A similar pattern was observed for the dorsal side. Canonical variate analysis (CVA) illustrated three distinct groups with statistical significance in all cases (P < 0.001) and the confusion matrix showed a high corrected grouping rate of 88.5% for the lateral side and 82.8% for the dorsal side. These findings indicated notable variations in the body shape of G. giuris among the three studied areas. Fish sampled from the Tam Giang Lagoon exhibited a streamlined body shape, while those from the Truong Giang River and Nhat Le Estuary displayed a deeper body profile. The observed morphological differences among these fish populations are likely attributed to phenotypic adaptations driven by environmental factors and habitat distinctions. Importantly, this study marks the first attempt to compare the body shape variations of G. giuris in both freshwater and estuarine environments within central Vietnam, utilizing a landmark-based geometric approach. These findings provide crucial insights for further investigations into the ecological adaptations and evolutionary processes of this fish species. [ABSTRACT FROM AUTHOR]

Objectives: This study aims to conduct a thorough characterization of hand morphology. Employing a 2D geometric morphometric approach, we scrutinize individual fingers and the palm, delineating the ontogenetic trajectories for each biological sex and investigating the alterations that take place at various stages of human development. Materials and methods: A set of thirty‐two 2D anatomical landmarks were assessed in a sex‐balanced sample of human hands (F = 275, M = 250 males), spanning all stages of human development. Following Procrustes registration, the data on size and shape for individual fingers and the palm were examined for each biological sex and age group. Regression analysis was utilized to quantify ontogenetic trajectories for each biological sex. Results: The findings suggest a gradual escalation in sexual dimorphism throughout human development, with statistically noteworthy distinctions becoming apparent in size starting at the age of 3, and in shape from the age of 7 onwards. Additionally, our analyses uncover a distinctive sigmoid pattern between sexes, indicating that biological male hands exhibit a sturdier build compared to biological female hands from early childhood onward. Conclusions: In conclusion, this study enriches our insights into sexual dimorphism in human hands, stressing the importance of considering both size and shape across different ontogenetic stages. These findings not only expand our understanding of human biological variation but also lay the foundation for future interdisciplinary research in diverse scientific domains. [ABSTRACT FROM AUTHOR]

This paper presents a morphological study of Islamic geometric patterns (IGP) and their role in application of formal grammar in computational modeling of IGPs. Through a comprehensive literature review and data collection, we analyze the morphological properties of these patterns using techniques such as geometric transformations, pattern classification, and symmetry analysis. Based on our findings, we explore how these properties can be used in constructing a formal grammar through string rewriting system for a CAD application. Building on a study on the potential of a string rewriting system for modeling IGPs, the current research suggests an update to the previous system and introduces a new morphological structure for IGPs. The new method has an expanded sample set and is tested on a class of 5-fold star patterns with 12 members and demonstrates successful development. The results are implemented in a Grasshopper add-on, providing a flexible platform to generate the patterns through strings and to control their parameters. This tool opens up new possibilities to bridge traditional patterns with contemporary technologies and make them more accessible. Furthermore, it contributes to the preservation of IGPs as a significant cultural and architectural heritage, while also advancing the evolution of these patterns to a new and contemporary generation. [ABSTRACT FROM AUTHOR]

This research focuses on a novel convertible unmanned aerial vehicle (CUAV) featuring four rotors with tilting capabilities combined with a tapered form. This paper studies the transition motion between multirotor and fixed-wing modes based on the mechanical and aerodynamics design as well as the control strategy. The proposed CUAV involves information about design, manufacturing, operation, modeling, control strategy, and real-time experiments. The CUAV design considers a fixed-wing with tiltrotors and provides the maneuverability to perform take-off, hover flight, cruise flight, and landing, having the characteristics of a helicopter in hover flight and an aircraft in horizontal flight. The manufacturing is based on additive manufacturing, which facilitates the creation of a lattice structure within the wing. The modeling is obtained using the Newton–Euler equations, and the control strategy is a PID controller based on a geometric approach on SE(3). Finally, the real-time experiments validate the proposed design for the complete regime of flight, and the research meticulously evaluates the feasibility of the prototype and its potential to significantly enhance the mission versatility. [ABSTRACT FROM AUTHOR]