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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]

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]

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]

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]

A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma–Trudinger–Wang condition is the Pogorelov second-derivative bound. This translates to an apriori interior C 1 C^{1} estimate for smooth optimal maps. Here we give a new derivation of this estimate which relies in part on Kim, McCann and Warren’s observation that the graph of an optimal map becomes a volume maximizing spacelike submanifold when the product of the source and target domains is endowed with a suitable pseudo-Riemannian geometry that combines both the marginal densities and the cost. [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 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]

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]

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]

To date, the development of unmanned technologies using autonomous underwater vehicles (AUVs) has become an urgent demand for solving the problem of inspecting industrial subsea structures. A key issue here is the precise localization of AUVs relative to underwater objects. However, the impossibility of using GPS and the presence of various interferences associated with the dynamics of the underwater environment do not allow high-precision navigation based solely on a standard suite of AUV navigation tools (sonars, etc.). An alternative technology involves the processing of optical images that, at short distances, can provide higher accuracy of AUV navigation compared to the technology of acoustic measurement processing. Although there have been results in this direction, further development of methods for extracting spatial information about objects from images recorded by a camera is necessary in the task of calculating the exact mutual position of the AUV and the object. In this study, in the context of the problem of subsea production system inspection, we propose a technology to recognize underwater objects and provide coordinate references to the AUV based on stereo-image processing. Its distinctive features are the use of a non-standard technique to generate a geometric model of an object from its views (foreshortening) taken from positions of a pre-made overview trajectory, the use of various characteristic geometric elements when recognizing objects, and the original algorithms for comparing visual data of the inspection trajectory with an a priori model of the object. The results of experiments on virtual scenes and with real data showed the effectiveness of the proposed technology. [ABSTRACT FROM AUTHOR]

This study aims to discuss queueing modeling of machine repair problems under threshold recovery policy (Q), server unreliability and k-type phase repairs. When one or more machines in the system fails/fail, the service facility (or all $R$ R -servers) is activated and repairs the failed machine according to the first come, first served (FCFS) discipline. The service facility may experience a partial or complete breakdown while providing service and needs to be repaired in required phases under the threshold recovery policy (Q). The matrix geometric approach is applied to solve the system governing equations, and a sensitivity analysis is presented to understand the effect of various parameters on system performance metrics. The greedy selection method and the golden section method are used to compute optimal rates of $\left({{R^*}, {\mu ^*}} \right)$ R ∗ , μ ∗ of service facility in order to minimize the cost function of the system. [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]

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]

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,풯) modified gravity, which is characterized by the trace of an energy–momentum tensor as 풯 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]

For this study, a three-species food chain model that considers interactions between small fish, remora fish, and large fish has been developed. It is assumed that large fish consume small fish through the functional response of Holling type II. Remora fish are considered to benefit from eating the remaining parts of small fish hunted by larger fish. Remora fish may benefit from eating the parasites found in the bodies of large fish. The non-negativity and boundedness of the solution of the model are investigated. In addition, each potential stable state for the model has been determined. We also investigated the local stability of the model, which is close to the steady state. The Lyapunov function and geometric technique are used to investigate the global stability of the model. It has been found that the increase in the refuge rate for small fish contributes to the instability of the model. It has been observed that the model may show unstable behaviour due to an increase in the rate of consumption of small fish by big fish. It has been found that the density of remora fish may rise because of their mutualistic relationship with large fishes. [ABSTRACT FROM AUTHOR]

Background: Chiari I malformation (CMI) is characterized by inferior descent of the cerebellar tonsils through the foramen magnum and is associated with headache and neck pain. Many morphometric research efforts have aimed to describe CMI anatomy in the midsagittal plane using classical measurement techniques such as linear dimensions and angles. These methods are less frequently applied to parasagittal features and may fall short in quantifying more intricate anatomy with fewer distinct homologous landmarks. Methods: Landmark-based geometric morphometric techniques were used to asses CMI morphology in five anatomical planes of interest. Results: Significant shape differences between CMI and age/sex-matched controls were found in the midsagittal (Pseudo-F=5.4841, p = 0.001) and axial planes through the rostral medulla (Pseudo-F=7.6319, p=0.001). In addition to tonsillar descent, CMI principal component 1 (PC1) scores in the midsagittal protocol were associated with marked anterior concavity of the brainstem and generalized verticality of the cerebellum with anterior rotation of its anterior lobe. In the axial medulla/cerebellum protocol, CMI PC1 scores were associated with greater anterior-posterior (A-P) dimension with loss of medial-lateral (M-L) dimension. Discussion: These results suggest that CMI is associated with greater curvature of the brainstem and spinal cord, which may perturb normal neural activities and disrupt cerebrospinal fluid movements. Previous reports on the A-P diameter of the posterior fossa in CMI have conflicted; our findings of greater A-P cerebellar dimensionality with concomitant loss of width alludes to the possibility that more caudal aspects of the posterior cranial fossa are more bowl-like (homogenous in axial dimensions) and less trough-like or elongated in the M-L direction. [ABSTRACT FROM AUTHOR]

Trajectory-following control is the basis for the practical application of an articulated virtual rail train transportation system. In this paper, a planar nonlinear dynamics model of an articulated vehicle is derived using the Euler–Lagrange method. A trajectory-following control strategy based on the first following point is proposed, and a feedback linearization control algorithm is designed based on the vehicle dynamics model to achieve the trajectory following of the rear vehicle. Based on the target trajectory formed by the first following point and measured by virtual sensors, a vector analysis method grounded in geometric relationships is proposed to solve in real time for the desired position, velocity, and acceleration of the vehicle. Finally, a MATLAB/SIMPACK dynamics virtual prototype is established to test the vehicle's trajectory-following effectiveness and dynamics performance under lane change and circular curve routes. The results indicate that the control algorithm can achieve trajectory following while maintaining good vehicle dynamics performance. It is robust to variations in vehicle mass, vehicle speed, tire cornering stiffness, and road friction coefficient. [ABSTRACT FROM AUTHOR]

This research investigates precision enhancement in regional quasi-geoid refinement through ADS80 tri-linear array scanning stereoscopic imagery for aerial triangulation coupled with GNSS gravity-potential modeling. By acquiring stereoscopic imagery and analyzing triangulation accuracy using an ADS80 camera, we performed this study over the Qinghai–Tibet Plateau's elevated, desolate terrain, collecting 593 GNSS points following high-precision stereoscopic imagery modeling. By utilizing 12 gravity satellite models, we computed geoid heights and China's 1985 Yellow Sea elevations for 28 benchmarks and GNSS points, thereby refining the Qinghai Province Quasi-Geoid Model (QPQM) using geometric techniques. The findings reveal that POS-assisted ADS80 stereoscopic imagery yields high-precision triangulation with maximal horizontal and elevation accuracies of 0.083/0.116 cm and 0.053/0.09 cm, respectively, across five control point arrangements. The RMSE of normal heights for 1985, processed via these GNSS points, achieved decimeter precision. By applying error corrections from benchmarks to the 1985 elevation data from gravity satellites and performing weighted averaging, the precision of EGM2008, SGG-UGM-2, and SGG-UGM-1 models improved to 8.61 cm, 9.09 cm, and 9.38 cm, respectively, surpassing the QPQM by 9.22 cm to 9.99 cm. This research demonstrates that the proposed methods can significantly enhance the precision of regional quasi-geoid surfaces. Additionally, these methods offer a novel approach for rapidly establishing regional quasi-geoid models in the uninhabited areas of the Qinghai–Tibet Plateau. [ABSTRACT FROM AUTHOR]

This study conducts an in-depth analysis of clustering small molecules using spectral geometry and deep learning techniques. We applied a spectral geometric approach to convert molecular structures into triangulated meshes and used the Laplace–Beltrami operator to derive significant geometric features. By examining the eigenvectors of these operators, we captured the intrinsic geometric properties of the molecules, aiding their classification and clustering. The research utilized four deep learning methods: Deep Belief Network, Convolutional Autoencoder, Variational Autoencoder, and Adversarial Autoencoder, each paired with k-means clustering at different cluster sizes. Clustering quality was evaluated using the Calinski–Harabasz and Davies–Bouldin indices, Silhouette Score, and standard deviation. Nonparametric tests were used to assess the impact of topological descriptors on clustering outcomes. Our results show that the DBN + k-means combination is the most effective, particularly at lower cluster counts, demonstrating significant sensitivity to structural variations. This study highlights the potential of integrating spectral geometry with deep learning for precise and efficient molecular clustering. [ABSTRACT FROM AUTHOR]

While incremental sheet metal forming offers the potential for producing sheet metal parts in small lot sizes, the relatively low forming accuracy prevents widespread industrial use. For improving the forming accuracy, research institutes are using machine learning techniques to predict the geometric accuracy and modify the toolpath based on the prediction. A critical challenge is it to ensure the generalizability of the prediction model as only a small amount of process data is available to train the model due to the lack of industrial collaborations. This publication presents a highly transferable feature engineering approach where surface representations of the part's geometry around each toolpath point are transferred into a standardized coordinate system. Several artificial neural networks were trained and used for predicting the forming accuracy and modifying the toolpath. During the validation experiments, the forming errors of parts which were independent of the training process were reduced by up to 68.5 %. The framework for computing the surface representations alongside with several pre-trained artificial neural networks is publicity available for download. [ABSTRACT FROM AUTHOR]

It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique — there are many very different Hamiltonians that result in the same differential Painlevé equation. Recognizing a Painlevé equation, for example when it appears in some applied problem, is known as the Painlevé equivalence problem. Here we consider its Hamiltonian version. We describe a systematic procedure for finding changes of coordinates that transform different Hamiltonian representations of a Painlevé equation into some canonical form. Our approach is based on Sakai's geometric theory of Painlevé equations. We explain it in detail for Painlevé IV, and give a brief summary for Painlevé V and VI. Such explicit identifications can be helpful for applications, since it gives access to known results about Painlevé equations, such as structure of symmetries and special solutions for certain parameter values. [ABSTRACT FROM AUTHOR]

Considerable morphological and ecological diversity has been found in extinct and extant members of the bear genus, Ursus, and appears to be key in explaining how they have thrived across vast ecological gradients. One example is the cave bear Ursus spelaeus. We applied 2D geometric morphometric techniques to describe morphological changes in the mandibles of extant Ursus species to further interpret the palaeoecology of U. spelaeus. Ursus species were discriminated using their mandibular morphology, which showed intra and interspecific shape variation that was indirectly linked to climatic adaptations through dietary variation. Mandibles of bears that inhabit colder, drier and more seasonal environments were generally slender with large diastema and a dorsoventrally smaller ramus. In contrast, species from warmer environments with higher levels of precipitation were found to have a dorsoventrally taller ramus (relative to the corpus). Discriminant function analyses of the morphology of U. spelaeus suggested adaptations to a series of fluctuating environments through time, helping to assess previously proposed Marine Isotope Stages for sedimentary deposits in Scladina Cave. Our geometric morphometrics analyses of bear mandibular ecomorphology demonstrates how geometric morphometrics provides a valuable tool to enhance paleoenvironmental reconstructions within deposits of the same fossil site. [ABSTRACT FROM AUTHOR]

To improve the accuracy of in situ measurement of the standard volumes of pipe provers and to shorten the traceability chain, a new method of in situ pipe prover volume measurement was developed alongside a supporting measurement device. This method is based on the geometric dimension approach, which measures the inner diameter and length of a pipe prover to calculate its volume. For inner diameter measurement, a three-probe inner-diameter algorithm model was established. This model was calibrated using a standard ring gauge of Φ313 mm, with the parameters calculated through fitting. Another standard ring gauge of Φ320 mm was used to verify the inner diameters determined by the algorithmic model. A laser interferometer was employed for the segmented measurement of the pipe prover length. The comprehensive measurement system was then used for in situ measurement of the standard pipe prover. The newly developed system achieved an expanded uncertainty of 0.012% (k = 2) in volume measurement, with the deviation between the measured and nominal pipe prover volumes being merely 0.007%. These results demonstrate that the proposed in situ measurement method offers ultra-high-precision measurement capabilities. [ABSTRACT FROM AUTHOR]

Different aspects of foraging strategies in bats have been studied to understand the evolution of flight in mammals. General descriptors of wing morphology associated with flight performance, such as aspect ratio and wing loading, allowed us to describe ecomorphs determined by the dietary preferences of bat species. However, the role of wing shape divergence in the evolution of bat foraging strategies remains little explored. We adopted a two-dimensional geometric morphometric approach to quantify the wing shape and size variation explained by phylogenetic relatedness (families) and to evaluate the covariance between foraging guilds and flight descriptors based on phylogenetic comparative methods in 69 Neotropical bat species. We tested whether wing morphology represents a reliable marker of the foraging guild, and we explored the rate of shape evolution among foraging guilds to describe divergent trends that could explain the morphological and ecological diversification. Our results suggest that the earliest bat ancestor was an aerial forager occupying the edge space, which is congruent with the observed evolution of wing shape from an edge space wing morphology. The relationship between wing shape and foraging space defines wing ecomorphs, which probably evolved early in bat ancestors; a process other than convergence could explain this association. [ABSTRACT FROM AUTHOR]

This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously analyzed by us, in the geometrization of quantum mechanical evolution in a Finsler geometry. We find results with dynamical equations governing the evolution of the trajectories defined by the expectation values of the position. The analysis appears to provide an underlying geometry described by a geodesic equation, with a connection form with a second term which is an essentially quantum effect. These dynamical equations provide a new geometric approach to the quantum evolution where we suggest a definition for "local instability" in the quantum theory. [ABSTRACT FROM AUTHOR]

In this article we show that the conformal nets corresponding to WZW models are rational, resolving a long-standing open problem. Specifically, we show that the Jones-Wassermann subfactors associated with these models have finite index. This result was first conjectured in the early 90s but had previously only been proven in special cases, beginning with Wassermann's landmark results in type A. The proof relies on a new framework for the systematic comparison of tensor products (a.k.a. 'fusion') of conformal net representations with the corresponding tensor product of vertex operator algebra modules. This framework is based on the geometric technique of 'bounded localized vertex operators,' which realizes algebras of observables via insertion operators localized in partially thin Riemann surfaces. We obtain a general method for showing that Jones-Wassermann subfactors have finite index, and apply it to additional families of important examples beyond WZW models. We also consider applications to a class of positivity phenomena for VOAs, and use this to outline a program for identifying unitary tensor product theories of VOAs and conformal nets even for badly-behaved models. [ABSTRACT FROM AUTHOR]

This study aimed to develop and evaluate a deep learning-based model that could automatically measure anterior segment (AS) parameters on preoperative ultrasound biomicroscopy (UBM) images of implantable Collamer lens (ICL) surgery candidates. A total of 1164 panoramic UBM images were preoperatively obtained from 321 patients who received ICL surgery in the Eye Center of Renmin Hospital of Wuhan University (Wuhan, China) to develop an imaging database. First, the UNet++ network was utilized to segment AS tissues automatically, such as corneal lens and iris. In addition, image processing techniques and geometric localization algorithms were developed to automatically identify the anatomical landmarks (ALs) of pupil diameter (PD), anterior chamber depth (ACD), angle-to-angle distance (ATA), and sulcus-to-sulcus distance (STS). Based on the results of the latter two processes, PD, ACD, ATA, and STS can be measured. Meanwhile, an external dataset of 294 images from Huangshi Aier Eye Hospital was employed to further assess the model's performance in other center. Lastly, a subset of 100 random images from the external test set was chosen to compare the performance of the model with senior experts. Whether in the internal test dataset or external test dataset, using manual labeling as the reference standard, the models achieved a mean Dice coefficient exceeding 0.880. Additionally, the intra-class correlation coefficients (ICCs) of ALs' coordinates were all greater than 0.947, and the percentage of Euclidean distance distribution of ALs within 250 μm was over 95.24%.While the ICCs for PD, ACD, ATA, and STS were greater than 0.957, furthermore, the average relative error (ARE) of PD, ACD, ATA, and STS were below 2.41%. In terms of human versus machine performance, the ICCs between the measurements performed by the model and those by senior experts were all greater than 0.931. A deep learning-based model could measure AS parameters using UBM images of ICL candidates, and exhibited a performance similar to that of a senior ophthalmologist. [ABSTRACT FROM AUTHOR]

This paper proposes a new geometric fault detection and isolation (FDI) strategy for uncertain neutral time-delay systems (UNTDS). Firstly, the concept of unobservability subspace is extended to the considered system. Subsequently, utilizing the geometric properties of factor space and canonical projection, the fault is divided into different unobservability subspaces. Therefore, an algorithm for constructing the subspace is developed for fault isolation. Finally, a set of observers is designed for the subsystems, and generates a set of structured residuals which is sensitive only to a specific fault. Additionally, the H ∞ technique is utilized to suppress the disturbances and error signals due to time-varying delays on the residual. The simulation examples verify the effectiveness of the proposed approach. • A new geometric FDI strategy can decouple all the residuals from the faults. • The H ∞ technique is used to suppress error signals due to time-varying delays. • Geometric approach is used to uncertain neutral time-delay system for the first time. • The occurrence and disappearance of multiple faults can be detected simultaneously. [ABSTRACT FROM AUTHOR]

This paper reports results on the classification of traveling wave solutions, including nonnegative traveling wave solutions in a weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches (in particular, Poincaré compactification). Classification of traveling wave solutions means enumerating those that exist and presenting properties of each solution, such as its profile and asymptotic behavior. The results examine a different range of parameters included in the equation, using the same techniques as discussed in the earlier work [Y. Ichida, Discrete Contin. Dyn. Syst., Ser. B, 28 (2023), no. 2, 1116-1132]. In a clear departure from this previous work, the classification results obtained in this paper and the successful application of the known transformation also yield results for the classification of (weak) nonnegative traveling wave solutions for spatial 1D porous medium equations with special nonlinear terms. Finally, the bifurcations at infinity occur in the two-dimensional ordinary differential equations that characterize these traveling wave solutions are shown. [ABSTRACT FROM AUTHOR]

This article proposes two approaches for a tailored geometrical deviation compensation for Laser-Powder-Bed-Fusion production. The deviation compensation is performed by a non-rigid deformation of the manufacturing geometry in each iteration to reduce the geometrical deviations from the target geometry. It is important for geometric compensation approaches to separate deterministic deviations from random scatter, since compensating scatter can result in unstable behaviour. In order to compensate only deterministic deviations two novel approaches for a local estimation of the scatter are successfully introduced and tested using a hybrid model of a series production cycle. [ABSTRACT FROM AUTHOR]

Background: Changes in epithelial cell shape reflects optimal cell packing and the minimization of surface free energy, but also cell–cell interactions, cell proliferation, and cytoskeletal rearrangements. Results: Here, we studied the structure of the rat pleura in the first 15 days after birth. After pleural isolation and image segmentation, the analysis demonstrated a progression of epithelial order from postnatal day 1 (P1) to P15. The cells with the largest surface area and greatest shape variability were observed at P1. In contrast, the cells with the smallest surface area and most shape consistency were observed at P15. A comparison of polygonal cell geometries demonstrated progressive optimization with an increase in the number of hexagons (six‐sided) as well as five‐sided and seven‐sided polygons. Analysis of the epithelial organization with Voronoi tessellations and graphlet motif frequencies demonstrated a developmental path strikingly distinct from mathematical and natural reference paths. Graph Theory analysis of cell connectivity demonstrated a progressive decrease in network heterogeneity and clustering coefficient from P1 to P15. Conclusions: We conclude that the rat pleura undergoes a striking change in pleural structure from P1 to P15. Further, a geometric and network‐based approach can provide a quantitative characterization of these developmental changes. Key Findings: Evolving topological order of the pleura within the first two weeks after birth:decrease in shape variabilityincrease in 6‐sided polygonsdecrease in network heterogeneity [ABSTRACT FROM AUTHOR]

The generalization of the virial theorem, introduced by Clausius in statistical mechanics, has recently been carried out in the framework of geometric approaches to Hamiltonian and Lagrangian theories and it has been formulated in an intrinsic way. It is here revisited not only in its more general situation of a generic vector field but mainly from the perspective of contact and cosymplectic geometry. The previous generalizations allowing virial like relations from one-parameter groups of non-strictly canonical transformations and the rôle of Killing and conformal Killing vector fields for Lagrangians of a mechanical type are here completed with the theory for contact Hamiltonian, as well as gradient and evolution, vector fields. The corresponding theories in the framework of cosymplectic geometry and the particular case of time-dependent vector fields are also developed. [ABSTRACT FROM AUTHOR]

The beveling process is an important process in the manufacturing of resonators, which has a significant impact on the frequency stability of resonators. Without understanding the frequency characteristics of the resonator after beveling, it is impossible to accurately design the beveled resonators. Thus, in order to investigate the vibration characteristics of AT-cut beveled resonators, we investigated the high-frequency vibration in this work by using the subregional geometric fitting method (SGFM) based on Mindlin's plate theory. Quartz crystal plates with nonuniform thicknesses are partitioned into three regions and each region is fitted by using the polynomial functions based on the measured geometric morphology data. The governing equations are obtained based on Mindlin's two-dimensional theory and the coupled vibrations are further solved using the partial differential equation module of COMSOL. In the numerical calculation, we compare the results obtained by the SGFM with those obtained by the global fitting method and the measured data. The accuracy and effectiveness of the SGFM are also verified. It is found that the frequencies obtained by the SGFM are slightly higher than the frequencies obtained by the global fitting method, and the results of SGFM are closer to the measured results. Meanwhile, as the beveling time increases, the frequency increases and the energy trapping effect becomes more significant. The proposed method can significantly improve the computational efficiency of thickness-shear vibration while ensuring accuracy. It is expected to provide a new geometric fitting method for the analysis of beveled crystal resonators. [ABSTRACT FROM AUTHOR]

Traditional denoising methods often lose details or edges, such as Gaussian filtering. Shearlet transform isa multi-scale geometric analysis tool which has the advantages of multi-resolution and multi-directivity. Compared with wavelet, curvelet, and contourlet transforms, it can retain more edge details while denoising, and the subjective vision and objective evaluation indexes are better than other multi-scale geometric analysis methods. Deep learning has made great progress in the field of denoising, such as U_Net, DnCNN, FFDNet, and generative adversarial network, and the denoising effect is better than BM3D, the traditional optimal method. Therefore, we propose a random noise suppression network ST-hFFDNet based on non-subsampled shearlet transform (NSST) and improved FFDNet. It combines the advantages of non-subsampled shearlet transform, Huber norm, and FFDNet, and has three characteristics. 1) Shearlet transform is an effective feature extraction tool, which can obtain the high and low frequency features of a signal at different scales and in different directions, so that the network can learn signal and noise features of different scales and directions. 2) The noise level map can improve the noise reduction performance of different noise levels. 3) Huber norm can reduce the sensitivity of the network to abnormal data and improve the robustness of network. The network training process is as follows. 1) BSD500 datasets are enhanced by flipping, rotating, scaling, and cutting. 2) AWGN with noise level ae[0,75] is added to the enhanced datasets to obtain the training datasets. 3) NSST multi-scale and multi-direction decomposition is performed on each pair of samples of the training datasets to obtain highand low-frequency images of different scales and directions. 4) Based on the decomposed high and low frequency images, the ST-hFFDNet network is trained by Adam algorithm. 5) All samples of the training data set are carried out in steps (3) and (4), and the trained model is thus obtained. Simulation experiments and real seismic data denoising show that for low noise, the proposed method is slightly better than NSST, DnCNN, and FFDNet and that it is superior to NSST, DnCNN, and FFDNet for high noise. [ABSTRACT FROM AUTHOR]

The intrusion detection system is responsible for revealing different intrusion activities, including the denial of service, man-in-middle, Mirai, Scan, and other types of intrusion activities. It is used in many applications, including the smart home Internet of Things networks, where security risks threaten the privacy of individuals. In this context, many works were proposed for detecting and classifying the different types of attacks. However, many challenges are identified for this type of problem, such as the large amount of data available, the imbalanced nature of the data, and the quality of detection and classification outcomes. This paper aims to address these challenges by proposing an approach that considers a metaheuristic-based random weight neural network to detect intrusion activities and classify the different types and subtypes of activities. The following points summarize the contribution of this paper. First, the automatic tuning of the neural network parameters where the weights, biases, regularization value, the number of neurons, and the type of activation function are optimized by different metaheuristic algorithms to produce high-quality results. Second, the proposed approach adopts a clustering with reduction technique to tackle the challenge of processing large volumes of data. Third, oversampling the dataset is also embedded in the proposed approach to avoid a biased classification of the majority class. The experiments are conducted based on a large dataset with more than half a million instances. The results show that the proposed approach outperforms the other classification approaches in geometric mean (G-Mean) and has promising results. [ABSTRACT FROM AUTHOR]

We introduce a novel computational paradigm for reconstructing solid computer-aided design (CAD) features from the surface of a segmented manifold triangular mesh. This paradigm addresses the challenge of capturing high-level design semantics for manifold triangular meshes and facilitates parametric and variational design capabilities. We categorize four prevalent features, namely extrusion, rotation, sweep, and loft, as generalized swept bodies driven by cross-sectional sketches and feature paths, providing a unified mathematical representation for various feature types. The numerical optimization-based approach conducts geometric processing on the segmented manifold triangular mesh patch, extracting cross-sectional sketch curves and feature paths from its surface, and then reconstructing appropriate features using the Open CASCADE kernel. We employ the personalized three-dimensional (3D) printed model as a case study. Parametric and variant designs of the 3D-printed models are achieved through feature reconstruction of the manifold triangular mesh obtained via 3D scanning. [ABSTRACT FROM AUTHOR]

This article is about finding the limit set for banded Toeplitz matrices. Our main result is a new approach to approximate the limit set Λ(b) where b is the symbol of the banded Toeplitz matrix. The new approach is geometrical and based on the formula Λ(b)=∩∈(0,∞)sp T(bρ), where ρ is a scaling factor, i.e. bρ(t):=b(ρt), and sp (⋅) denotes the spectrum. We show that the full intersection can be approximated by the intersection for a finite number of ρ's, and that the intersection of polygon approximations for sp T(bρ) yields an approximating polygon for Λ(b) that converges to Λ(b) in the Hausdorff metric. Further, we show that one can slightly expand the polygon approximations for sp T(bρ) to ensure that they contain sp T(bρ). Then, taking the intersection yields an approximating superset of Λ(b) which converges to Λ(b) in the Hausdorff metric, and is guaranteed to contain Λ(b). Combining the established algebraic (root-finding) method with our approximating superset, we are able to give an explicit bound on the Hausdorff distance to the true limit set. We implement the algorithm in Python and test it. It performs on par to and better in some cases than existing algorithms. We argue, but do not prove, that the average time complexity of the algorithm is O(n²+mnlogm), where n is the number of ρ's and m is the number of vertices for the polygons approximating sp T(bρ). Further, we argue that the distance from Λ(b) to both the approximating polygon and the approximating superset decreases as O(1/√k) for most of Λ(b), where k is the number of elementary operations required by the algorithm. [ABSTRACT FROM AUTHOR]

This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high‐dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the unique stationary solution, they lack positivity, radial symmetry, and exponential decay. By employing variational and geometric approaches, along with perturbation theory, we establish the orbital (in)stability and strong instability of these traveling waves. [ABSTRACT FROM AUTHOR]