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The main goal of this article is to describe a relation between the asymptotic properties of filtrations on section rings and the geometry at infinity of the space of Kähler potentials. More precisely, for a polarized projective manifold and an ample test configuration, Phong and Sturm associated a geodesic ray of plurisubharmonic metrics on the polarizing line bundle. On the other hand, for the same data, Witt Nyström associated a filtration on the section ring of the polarized manifold. In this article, we establish a folklore conjecture that the pluripotential chordal distance between the geodesic rays associated with two ample test configurations coincides with the spectral distance between the associated filtrations on the section ring. This gives an algebraic description of the boundary at infinity of the space of positive metrics, viewed – as it is usually done for spaces of negative curvature – through geodesic rays. [ABSTRACT FROM AUTHOR]

Matched-field processing (MFP) achieves underwater source localization by measuring the correlation between the array and replica signals, with traditional MFP being equivalent to estimating the Euclidean distance between the data cross-spectral density matrix (CSDM) and replica matrices. However, in practical applications, random inhomogeneities in the marine environment and inaccurate estimation of CSDM reduce MFP performance. The traditional minimum variance matched-field processor with environmental perturbation constraints perturbs a priori environment parameters to obtain linear constraints and yields the optimal weight vectors as the replica vectors. In this paper, within the framework of information geometry, the geometric properties of CSDMs as semi-positive definite and Hermitian enable CSDMs to be described as points in a Riemannian manifold. Source localization can be achieved by quantifying the similarity between the CSDMs as the geodesic distance between the points on the manifold. This paper introduces a constrained replica CSDM composed of perturbed replica vectors and proposes a robust matched-field processor based on two non-Euclidean distances: the Riemannian distance and the modified Jensen–Shannon distance. Simulations and experimental results demonstrate that the proposed processors are more robust against environmental and statistical mismatches than traditional processors and can also reduce sidelobe level and improve the resolution. [ABSTRACT FROM AUTHOR]

Traditional analytical models in groundwater studies often simplify the complexities arising from spatial variations in aquifer geometry and anisotropy, limiting their ability to capture the full theoretical nuances of groundwater flow. In this study, we present a novel methodology that integrates geodesic distances within the intrinsic geometry of confined, constant‐thickness aquifers, while also accounting for directional anisotropy in hydraulic properties. This approach provides a rigorous mathematical framework for accurately capturing the true distances along the aquifer geometry between pumping and observation wells, in contrast to traditional Euclidean distances. Our methodology is compatible with various analytical solutions, including the Theis (1935, https://doi.org/10.1111/jawr.1965.1.3.9) and Papadopulos and Cooper (1967, https://doi.org/10.1029/wr003i001p00241) solutions, extending their theoretical applicability to more complex aquifer geometries and anisotropic conditions. Numerical simulations of synthetic examples illustrate the theoretical consistency of the proposed approach, aligning drawdown patterns within this advanced framework. While primarily focused on enhancing existing analytical models, this methodology sets the stage for future theoretical advances in groundwater modeling, offering a conceptual expansion of analytical solutions to better address geometric and anisotropic complexities. Plain Language Summary: Groundwater models often simplify aquifers as flat, two‐dimensional spaces, but this limits their ability to represent complex aquifer shapes and flow patterns. This study introduces a new method using geodesic distances—the shortest paths on curved surfaces—to provide a more accurate theoretical framework for modeling aquifer geometry and anisotropy. By replacing traditional straight‐line estimates with more precise distance calculations, the method extends established models like the Theis and Papadopulos‐Cooper solutions to more complex aquifers. While primarily theoretical, this approach sets the stage for future advances in understanding groundwater flow in real‐world conditions. Key Points: Geodesic distance was used to capture real‐world aquifer geometry, providing insights into groundwater hydraulicsThe methodology was extended to incorporate directional anisotropy, enhancing the ability to model complex hydraulic conditionsThe method extends existing analytical solutions to complex aquifer geometries, demonstrating applicability [ABSTRACT FROM AUTHOR]

Face recognition models that utilize deep learning techniques can be easily targeted by adversarial attacks. In order to detect these attacks, the majority of detection methods focus on enhancing the resilience of recognition models against adversarial perturbations. Nevertheless, these methods have limited capabilities in terms of generalization. Consequently, they remain susceptible to adversarial attacks that have not been previously encountered. On the other hand, deep learning models exhibit considerable robustness against typical perturbations. In the paper, we have proposed a composite manifold learning approach with traditional techniques(CMLAT) detector to detect gradient-based and patch-based adversarial attack detection. The geometrical representation differs from the original input images, thus, we introduce a feature-based embedding that relies on measuring geodesic distances using the isomap manifold learning. This embedding enables us to encode the dissimilarities between adversarial and genuine inputs efficiently. Our training involves a support vector machine classifier that examines the sequence of deep features represented in a distance-based space to identify and classify adversarial images. We have achieved a significant milestone by developing an adversarial face detection system that exclusively utilizes original faces and their adversarial faces and can effectively handle previously unseen attack techniques. The experiment has been conducted on the Labeled Faces in the Wild (LFW) dataset with four gradient-based and patch-based attacks. This experiment confirms that the CMLAT detector is effective and generalizes against various adversarial attacks that were not previously encountered. [ABSTRACT FROM AUTHOR]

Synchronization plays a pivotal role in understanding various natural events. Understanding this concept with reference to a biologically inspired dynamical model of a neuron is also essential. It is basically a rhythm adjustment phenomenon and a consequence of the coupling between the individual units. In the present work, we aim to derive sufficient conditions for the synchronization of coupled Fitzhugh Nagumo Dynamics using Lyapunov stability analysis. In particular, a non-smooth Lyapunov function based upon the geodesic distance between respective states of coupled systems has been chosen as the Lyapunov function, and the concept of upper Dini-derivative has been utilized to calculate the derivative of the Lyapunov function along the error dynamics. The negative definiteness of the derivative of the Lyapunov function gives sufficient coupling gain for synchronization. The findings are verified on the Matlab simulation platform. The results should help to enhance the knowledge of neural dynamics. [ABSTRACT FROM AUTHOR]

Multiphysics simulations frequently require transferring solution fields between subproblems with nonmatching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness between points by means of the Euclidean distance, which does not account for curvature, cuts, cavities, or other nontrivial geometrical or topological features of the domain. This may lead to spurious oscillations in the interpolant in proximity to these features. To overcome this issue, we propose a modification to rescaled localized radial basis function (RL-RBF) interpolation to account for the geometry of the interpolation domain, by yielding conformity and fidelity to geometrical and topological features. The proposed method, referred to as RL-RBF-G, relies on measuring the geodesic distance between data points. RL-RBF-G removes spurious oscillations appearing in the RL-RBF interpolant, resulting in increased accuracy in domains with complex geometries. We demonstrate the effectiveness of RL-RBF-G interpolation through a convergence study in an idealized setting. Furthermore, we discuss the algorithmic aspects and the implementation of RL-RBF-G interpolation in a distributed-memory parallel framework, and present the results of a strong scalability test yielding nearly ideal results. Finally, we show the effectiveness of RL-RBF-G interpolation in multiphysics simulations by considering an application to a whole-heart cardiac electromechanics model. [ABSTRACT FROM AUTHOR]

Non-rigid point cloud registration holds significant importance for human body pose analysis in the fields of sports, medicine, gaming, etc. In this paper, we propose a non-rigid point cloud registration algorithm based on geodesic distance measurement, which can improve the accuracy of the registration for matching point pairs during non-rigid deformations. Firstly, a graph is constructed for two sets of point clouds using geodesic distance measurement considering that geodesic distance changes minimally during non-rigid deformation of the human body, which can preserve the point cloud matching information between corresponding points. Furthermore, a maximal clique search is employed to find combinations of matching pairs between point clouds. Finally, by driving the human body model parameters, sparse matching pairs are overlapped as much as possible to achieve non-rigid point cloud registration of the human body. The accuracy of the proposed algorithm is verified with FAUST and CAPE datasets. [ABSTRACT FROM AUTHOR]

The high dimensionality and noise challenges in genomic data make it difficult for traditional clustering methods. Existing multi-kernel clustering methods aim to improve the quality of the affinity matrix by learning a set of base kernels, thereby enhancing clustering performance. However, directly learning from the original base kernels presents challenges in handling errors and redundancies when dealing with high-dimensional data, and there is still a lack of feasible multi-kernel fusion strategies. To address these issues, we propose a Multi-Kernel Clustering method with Tensor fusion on Grassmann manifolds, called MKCTM. Specifically, we maximize the clustering consensus among base kernels by imposing tensor low-rank constraints to eliminate noise and redundancy. Unlike traditional kernel fusion approaches, our method fuses learned base kernels on the Grassmann manifold, resulting in a final consensus matrix for clustering. We integrate tensor learning and fusion processes into a unified optimization model and propose an effective iterative optimization algorithm for solving it. Experimental results on ten datasets, comparing against 12 popular baseline clustering methods, confirm the superiority of our approach. Our code is available at https://github.com/foureverfei/MKCTM.git.   • Base kernels achieve mutual learning and noise reduction through clustering consensus. • The fused kernel is obtained by solving the optimization problem of minimizing the geodesic distance on Grassmannian manifold. • The tensor learning and fusion processes are innovatively integrated into an efficient iterative minimization framework. [ABSTRACT FROM AUTHOR]

Fermat–Wiener index based on topological Wiener index is the total sum of Fermat distance over all the triplets for vertices. In this paper, we construct a class of hierarchical graphs based on hierarchical product generalized from Cartesian product. We study some critical properties of the hierarchical networks by investigating its topological indices. Applying the finite pattern method, we analytically deduce the dominant term of average Fermat distance and obtain its asymptotic formula, which implies small-world property. We finally exhibit a close connection between Fermat–Wiener index and related graph invariants like average geodesic distance, Wiener index and eigenvalues of Laplacian matrix. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the average geodesic distance on Sierpiński torus networks. We construct Sierpiński torus networks based on the classic Sierpiński carpet in an iterative way. By applying finite patterns on integrals, we deduce the exact value of the average geodesic distance of the Sierpiński torus. Furthermore, the asymptotic formula for the average geodesic distance of the corresponding networks can be obtained. [ABSTRACT FROM AUTHOR]

AbstractManifold learning obtains a low-dimensional representation of an underlying Riemannian manifold supporting high-dimensional data. Kernel density estimates of the low-dimensional embedding with a fixed bandwidth fail to account for the way manifold learning algorithms distort the geometry of the Riemannian manifold. We propose a novel distortion-corrected kernel density estimator (DC-KDE) for any manifold learning embedding, with a bandwidth that depends on the estimated Riemannian metric at each data point. Exploiting the geometric information of the manifold leads to more accurate density estimation, which subsequently could be used for anomaly detection. To compare our proposed estimator with a fixed-bandwidth kernel density estimator, we run two simulations including one with data lying in a 100 dimensional ambient space. We demonstrate that the proposed DC-KDE improves the density estimates as long as the manifold learning embedding is of sufficient quality, and has higher rank correlations with the true manifold density. Further simulation results are provided via a supplementary R shiny app. The proposed method is applied to density estimation in statistical manifolds of electricity usage with the Irish smart meter data. [ABSTRACT FROM AUTHOR]

Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in ℝ2 or ℝ3, such as curves or surfaces. Such manifold PDEs often involve boundary conditions (e.g., Dirichlet or Neumann) prescribed at points or curves on the manifold's interior or along the geometric (exterior) boundary of an open manifold. However, input manifolds can take many forms (e.g., triangle meshes, parametrizations, point clouds, implicit functions, etc.). Typically, one must generate a mesh to apply finite element-type techniques or derive specialized discretization procedures for each distinct manifold representation. We propose instead to address such problems in a unified manner through a novel extension of the closest point method (CPM) to handle interior boundary conditions. CPM solves the manifold PDE by solving a volumetric PDE defined over the Cartesian embedding space containing the manifold and requires only a closest point representation of the manifold. Hence, CPM supports objects that are open or closed, orientable or not, and of any codimension. To enable support for interior boundary conditions, we derive a method that implicitly partitions the embedding space across interior boundaries. CPM's finite difference and interpolation stencils are adapted to respect this partition while preserving second-order accuracy. Additionally, we develop an efficient sparse-grid implementation and numerical solver that can scale to tens of millions of degrees of freedom, allowing PDEs to be solved on more complex manifolds. We demonstrate our method's convergence behavior on selected model PDEs and explore several geometry processing problems: diffusion curves on surfaces, geodesic distance, tangent vector field design, harmonic map construction, and reaction-diffusion textures. Our proposed approach thus offers a powerful and flexible new tool for a range of geometry processing tasks on general manifold representations. [ABSTRACT FROM AUTHOR]

The t-distributed stochastic neighbor embedding (t-SNE) consists of a powerful algorithm for visualizing high-dimensional data in a lower dimensional space. It is extensively employed in machine learning (ML) and data analysis, including unsupervised metric learning. In this article, we propose improvements concerning two main aspects of the t-SNE. First, the incorporation of class labels is adopted to increase its suitability for supervised classification. Second, stochastic and geodesic distances are used as dissimilarity measures to avoid the dependence of the standard Euclidean distance, which is particularly sensitive to outliers. Computational experiments with several real-world datasets indicate that the proposed methodological approach is capable of improving classification accuracy compared with established methods. The results indicate a superior performance compared with the regular t-SNE and linear discriminant analysis (LDA), and a dependence on fewer parameters in comparison with the state-of-the-art supervised uniform manifold approximation and projection (UMAP) algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the average geodesic distance of the (2 × 3)-type hybrid Sierpinski gasket, using the method of finite pattern. [ABSTRACT FROM AUTHOR]

This paper deals with global compactness and the multiplicity of positive solutions to problems of the type −Δ픹Nu − λu = a(x)|u|2∗−2u + f(x)in 픹N, u ∈ H1(픹N), where 픹N denotes the ball model of the hyperbolic space of dimension N ≥ 4, 2∗ = 2N N−2, N(N−2) 4 < λ < (N−1)2 4 and f ∈ H−1(픹N) (f≢0) is a nonnegative functional in the dual space of H1(픹N). The potential a ∈ L∞(픹N) is assumed to be strictly positive, such that limd(x,0)→∞a(x) = 1, where d(x, 0) denotes the geodesic distance. We establish profile decomposition of the functional associated with the above equation. We show that concentration occurs along two different profiles, namely, hyperbolic bubbles and localized Aubin–Talenti bubbles. For f = 0 and a ≡ 1, profile decomposition was studied in Bhakta and Sandeep [Poincaré–Sobolev equations in the hyperbolic space, Calc. Var. Partial Differential Equations 44 (2012) 247–269]. However, due to the presence of the potential a(.), an extension of profile decomposition to the present set-up is highly nontrivial and requires several delicate estimates and geometric arguments concerning the isometry group (Möbius group) of the hyperbolic space. Further, using the decomposition result, we derive various energy estimates involving the interacting hyperbolic bubbles and hyperbolic bubbles with localized Aubin–Talenti bubbles. Finally, combining these estimates with topological and variational arguments, we establish a multiplicity of positive solutions in the cases: a ≥ 1 and a < 1 separately. The equation studied in this paper can be thought of as a variant of a scalar-field equation with a critical exponent in the hyperbolic space, although such a critical exponent problem in the Euclidean space ℝN has only a trivial solution when f ≡ 0, a(x) ≡ 1 and λ < 0. [ABSTRACT FROM AUTHOR]

In recent years, with the continuous development of technology in the field of artificial intelligence, the field of humancomputer interaction has attracted more scholars' attention. Studies have shown that the characteristic power spectrum density extracted by EEG (electroencephalogram) is sensitive to the change of mental load, but its dimension is too high, which is prone to data disaster. LLE (locally linear embedding) is a commonly used nonlinear dimensionality reduction algorithm, which makes up for the shortcoming of traditional linear dimensionality reduction algorithms that cannot find nonlinear structural relationships in data. Because of the different sparsity and distortion degree of sample distribution in different data sets, the optimal neighborhood parameters are different when using LLE to reduce dimension of different data sets. The relationship between Euclidean distance and geodesy distance between sample points was used to quantify the distortion degree of the data set. VK-LLE (variable k-locally linear embedding) algorithm of adaptive neighborhood parameters dynamically adjusts the optimal neighborhood parameters of each data set. The interference caused by different distortion degree of sample distribution to dimensionality reduction effect was solved. The experimental results show that the classification accuracy of data after VK-LLE dimensionality reduction using SVM (support vector machine) is generally higher than that after traditional LLE dimensionality reduction using SVM, and it has stronger adaptability to complex data sets. [ABSTRACT FROM AUTHOR]

Objective: Autism spectrum disorder (ASD) is a neurodevelopmental condition that is associated with atypical brain network organization, with prior work suggesting differential connectivity alterations with respect to functional connection length. Here, we tested whether functional connectopathy in ASD specifically relates to disruptions in long- relative to short-range functional connections. Our approach combined functional connectomics with geodesic distance mapping, and we studied associations to macroscale networks, microarchitectural patterns, as well as socio-demographic and clinical phenotypes. Methods: We studied 211 males from three sites of the ABIDE-I dataset comprising 103 participants with an ASD diagnosis (mean ± SD age = 20.8 ± 8.1 years) and 108 neurotypical controls (NT, 19.2 ± 7.2 years). For each participant, we computed cortex-wide connectivity distance (CD) measures by combining geodesic distance mapping with resting-state functional connectivity profiling. We compared CD between ASD and NT participants using surface-based linear models, and studied associations with age, symptom severity, and intelligence scores. We contextualized CD alterations relative to canonical networks and explored spatial associations with functional and microstructural cortical gradients as well as cytoarchitectonic cortical types. Results: Compared to NT, ASD participants presented with widespread reductions in CD, generally indicating shorter average connection length and thus suggesting reduced long-range connectivity but increased short-range connections. Peak reductions were localized in transmodal systems (i.e., heteromodal and paralimbic regions in the prefrontal, temporal, and parietal and temporo-parieto-occipital cortex), and effect sizes correlated with the sensory-transmodal gradient of brain function. ASD-related CD reductions appeared consistent across inter-individual differences in age and symptom severity, and we observed a positive correlation of CD to IQ scores. Limitations: Despite rigorous harmonization across the three different acquisition sites, heterogeneity in autism poses a potential limitation to the generalizability of our results. Additionally, we focussed male participants, warranting future studies in more balanced cohorts. Conclusions: Our study showed reductions in CD as a relatively stable imaging phenotype of ASD that preferentially impacted paralimbic and heteromodal association systems. CD reductions in ASD corroborate previous reports of ASD-related imbalance between short-range overconnectivity and long-range underconnectivity. [ABSTRACT FROM AUTHOR]

We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not guaranteed to be positive definite on such domains, while existing non-Euclidean approaches fail to respect the partially Euclidean nature of these domains where the geodesic distance agrees with the Euclidean distances for some pairs of points. Using a visibility graph on the domain, we propose a class of covariance functions that preserve Euclidean-based covariances between points that are connected in the domain while incorporating the non-convex geometry of the domain via conditional independence relationships. We show that the proposed method preserves the partially Euclidean nature of the intrinsic geometry on the domain while maintaining validity (positive definiteness) and marginal stationarity of the covariance function over the entire parameter space, properties which are not always fulfilled by existing approaches to construct covariance functions on non-convex domains. We provide useful approximations to improve computational efficiency, resulting in a scalable algorithm. We compare the performance of our method with those of competing state-of-the-art methods using simulation studies on synthetic non-convex domains. The method is applied to data regarding acidity levels in the Chesapeake Bay, showing its potential for ecological monitoring in real-world spatial applications on irregular domains. [ABSTRACT FROM AUTHOR]

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular, we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Liquid Crystal & Displays is the property of Chinese Journal of Liquid Crystal & Displays and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We call a translation function class a set of zonal translation networks if it is produced by the translations of a convolutional structure, which is a composite function reunited with an even function defined on $ [-1, 1] $ and a geodesic distance. In the present paper, we consider the density of a class of zonal translation networks produced by a convolution structure on the unit ball from the view of Fourier-Laplace series and give a sufficient condition to ensure the zonal translation class is density in $ L^p $ spaces defined on the unit ball. In particular, we construct with De La Vallée Poussin operators a sequence of zonal translation networks and show the approximation order. [ABSTRACT FROM AUTHOR]

Phylogenetic trees represent the evolutionary relationships and ancestry of various species or groups of organisms. Comparing these trees by measuring the distance between them is essential for applications such as tree clustering and the Tree of Life project. Many distance metrics for phylogenetic trees focus on trees defined on the same set of taxa. However, some problems require calculating distances between trees with different but overlapping sets of taxa. This study reviews state‐of‐the‐art distance measures for such trees, covering six major approaches, including the constraint‐based Robinson–Foulds (RF) distance RF(−), the completion‐based RF(+), the generalized RF (GRF), the dissimilarity measure, the vectorial tree distance, and the geodesic distance in the extended Billera‐Holmes‐Vogtmann tree space. Among these, three RF‐based methods, RF(−), RF(+), and GRF, were examined in detail on generated clusters of phylogenetic trees defined on different but mutually overlapping sets of taxa. Additionally, we reviewed nine related techniques, including leaf imputation methods, the tree edit distance, and visual comparison. A comparison of the related distance measures, highlighting their principal advantages and shortcomings, is provided. This review offers valuable insights into their applicability and performance, guiding the appropriate use of these metrics based on tree type (rooted or unrooted) and information type (topological or branch lengths). [ABSTRACT FROM AUTHOR]

ABSTRACTCurved layering has become one of the current research hotspots for its unique advantages. In order to improve the adaptability and accuracy, this paper proposes a new curved layering and path planning algorithm based on voxelization and geodesic distance. High density discrete points are used to approximate the shortest path, voxelization and new optimized search algorithm are adopted to obtain the geodesic distance field within stereolithography (STL) model. Curved layers are formed from points with equal geodesic distance values. The developed algorithm overcomes the limitations of the existing facet offsetting method. Moreover, robot positioner angle planning strategies are exploited to achieve good formation for support-free curved layers of spatial overhang characteristics. The results of comparative analysis and verification experiment indicate that the algorithm accuracy is not affected by the size and intersection angle of the triangles, satisfies the high-precision requirements for parts with curved surface in robotic GMA additive manufacturing.

• Automated tool for neuronal morphology analysis in 2D fluorescence microscopy images. • Reconstructs neurons into binarized images using Hessian-based segmentation to detect thin neurites. • Classifies neurites into axon, dendrites, and branches using geodesic distance transform. • Validated against an established dataset, ensuring reliable quantification. • Facilitates high-throughput analysis for neurodevelopmental research. Brain function emerges from a highly complex network of specialized cells that are interlinked by billions of synapses. The synaptic connectivity between neurons is established between the elongated processes of their axons and dendrites or, together, neurites. To establish these connections, cellular neurites have to grow in highly specialized, cell-type dependent patterns covering extensive distances and connecting with thousands of other neurons. The outgrowth and branching of neurites are tightly controlled during development and are a commonly used functional readout of imaging in the neurosciences. Manual analysis of neuronal morphology from microscopy images, however, is very time intensive and prone to bias. Most automated analyses of neurons rely on reconstruction of the neuron as a whole without a semantic analysis of each neurite. A fully-automated classification of all neurites still remains unavailable in open-source software. Here we present a standalone, GUI-based software for batch-quantification of neuronal morphology in two-dimensional fluorescence micrographs of cultured neurons with minimal requirements for user interaction. Single neurons are first reconstructed into binarized images using a Hessian-based segmentation algorithm to detect thin neurite structures combined with intensity- and shape-based reconstruction of the cell body. Neurites are then classified into axon, dendrites and their branches of increasing order using a geodesic distance transform of the cell skeleton. The software was benchmarked against a published dataset and reproduced the phenotype observed after manual annotation. Our tool promises accelerated and improved morphometric studies of neuronal morphology by allowing for consistent and automated analysis of large datasets. [ABSTRACT FROM AUTHOR]

In this paper, we construct a family of self-similar networks, named Coral networks, whose Iterated Function System (IFS) contains a rotation transformation. Using self-similarity, we obtain the weighted average geodesic distance of Coral fractal and networks. [ABSTRACT FROM AUTHOR]

This paper aims to understand how a group of academics cite each others' work through time, considering the simultaneous co-evolution of three networks representing their scientific collaboration, the journals in which they publish and institutional membership. It argues that both social and cognitive processes contribute to these dynamics. Two types of network mechanisms are considered specifically: closures by affiliation and closures by association. To assess whether these mechanisms generate the macro features of the network under study, we propose new features for three-mode multilevel networks such as the mixed geodesic distances, mixed degree distributions, and the mixed quadrilateral census. We investigate whether a micro-level model that considers the above-mentioned network mechanisms is able to correctly reproduce these features. We apply stochastic actor-oriented models (SAOMs) for one-mode and two-mode networks to link the micro-macro processes using a dataset of a scientific community of astronomers from 2013 to 2015. The results suggest that social relationships grounded on scientific collaboration and proximity based on institutional affiliation are more accurately suited to understanding the co-evolution of the network of citations than an alternative approach that merely considers cognitive-based networks measured as the similarity in publishing in the same journals. • We investigate how a group of academics cite each others' work through time considering the co-evolution of a multilevel network. • The co-evolution of a three-mode multilevel network is analysed considering cross-level effects. • New and already available measures for diagnostics are used for statistical models for social networks to identify how micro-mechanisms trigger different structures at the macro level. • Social relationships grounded on scientific collaboration and space proximity based on institutional affiliation are more accurately suited to understand the co-evolution of the networks in a scientific network. [ABSTRACT FROM AUTHOR]

We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional-order q ∈ [ 0 , ∞) . We establish the critical Sobolev index on the metric for several key geometric properties. Our first main result shows that the Riemannian metric induces a metric space structure if and only if q > 1 / 2 . Our second main result shows that the metric is geodesically complete (i.e., the geodesic equation is globally well posed) if q > 3 / 2 , whereas if q < 3 / 2 then finite-time blowup may occur. The geodesic completeness for q > 3 / 2 is obtained by proving metric completeness of the space of H q -immersed curves with the distance induced by the Riemannian metric. [ABSTRACT FROM AUTHOR]

A cohesive organizational structure is essential for coordinated efforts, effective resource planning, and enhanced governance outcomes. Additionally, dynamic power that enables efficient governance responses can enhance the resilience of socioal-ecological systems. This study aims to explore the organizational cohesion among stakeholders in the Development and Advancement Plan of Rural Constellations in Gachsaran County County, which serves as a pilot area for assessing effective local gov-ernance. The information exchange and cooperation among these stakeholders were analyzed using social network analysis methods, contrasting the results before and after the project's implementation. To achieve this, the betweenness centrality index at the micro level, along with the density, centralization, and average geodesic distance indices at the macro level of the network, were measured. The findings showed that before the implementation of the project, the Governorate, the Omid Entrepreneurship Fund, and Technical and Vocational Training had the highest betweenness centrality, playing significant roles in controlling the flow of information and resources. After the project's implementation, the Governorate, Cultural Heritage and Tourism, and the Omid Entrepreneurship Fund were identified as the key actors with the highest betweenness centrality. The average betweenness centrality index indicated improved information flow and a more balanced distribution of key roles within the network, leading to increased efficiency and coordination among organizations. The macro-level network indices showed increased cohesion, reduced centralization, and faster information circu-lation compared to before the project's implementation. This study's approach can be applied to other regions to enhance local governance. [ABSTRACT FROM AUTHOR]

Copyright of Mexican Journal of Economics & Finance / Revista Mexicana de Economia y Finanzas is the property of Instituto Mexicano de Ejecutivos de Finanzas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Background: Lentil (Lens culinaris Medik.) is a globally-significant agricultural crop used to feed millions of people. Lentils have been cultivated in the Australian states of Victoria and South Australia for several decades, but efforts are now being made to expand their cultivation into Western Australia and New South Wales. Plant architecture plays a pivotal role in adaptation, leading to improved and stable yields especially in new expansion regions. Image-based high-throughput phenomics technologies provide opportunities for an improved understanding of plant development, architecture, and trait genetics. This paper describes a novel method for mapping and quantifying individual branch structures on immature glasshouse-grown lentil plants grown using a LemnaTec Scanalyser 3D high-throughput phenomics platform, which collected side-view RGB images at regular intervals under controlled photographic conditions throughout the experiment. A queue and distance-based algorithm that analysed morphological skeletons generated from images of lentil plants was developed in Python. This code was incorporated into an image analysis pipeline using open-source software (PlantCV) to measure the number, angle, and length of individual branches on lentil plants. Results: Branching structures could be accurately identified and quantified in immature plants, which is sufficient for calculating early vigour traits, however the accuracy declined as the plants matured. Absolute accuracy for branch counts was 77.9% for plants at 22 days after sowing (DAS), 57.9% at 29 DAS and 51.9% at 36 DAS. Allowing for an error of ± 1 branch, the associated accuracies for the same time periods were 97.6%, 90.8% and 79.2% respectively. Occlusion in more mature plants made the mapping of branches less accurate, but the information collected could still be useful for trait estimation. For branch length calculations, the amount of variance explained by linear mixed-effects models was 82% for geodesic length and 87% for Euclidean branch lengths. Within these models, both the mean geodesic and Euclidean distance measurements of branches were found to be significantly affected by genotype, DAS and their interaction. Two informative metrices were derived from the calculations of branch angle; 'splay' is a measure of how far a branch angle deviates from being fully upright whilst 'angle-difference' is the difference between the smallest and largest recorded branch angle on each plant. The amount of variance explained by linear mixed-effects models was 38% for splay and 50% for angle difference. These lower R2 values are likely due to the inherent difficulties in measuring these parameters, nevertheless both splay and angle difference were found to be significantly affected by cultivar, DAS and their interaction. When 276 diverse lentil genotypes with varying degrees of salt tolerance were grown in a glasshouse-based experiment where a portion were subjected to a salt treatment, the branching algorithm was able to distinguish between salt-treated and untreated lentil lines based on differences in branch counts. Likewise, the mean geodesic and Euclidean distance measurements of branches were both found to be significantly affected by cultivar, DAS and salt treatment. The amount of variance explained by the linear mixed-effects models was 57.8% for geodesic branch length and 46.5% for Euclidean branch length. Conclusion: The methodology enabled the accurate quantification of the number, angle, and length of individual branches on glasshouse-grown lentil plants. This methodology could be applied to other dicotyledonous species. [ABSTRACT FROM AUTHOR]

Many design problems involve reasoning about points in high-dimensional space. A common strategy is to first embed these high-dimensional points into a low-dimensional latent space. We propose that a good embedding should be isometric--i.e., preserving the geodesic distance between points on the data manifold in the latent space. However, enforcing isometry is non-trivial for common neural embedding models such as autoencoders. Moreover, while theoretically appealing, it is unclear to what extent is enforcing isometry necessary for a given design analysis. This paper answers these questions by constructing an isometric embedding via an isometric autoencoder, which we employ to analyze an inverse airfoil design problem. Specifically, the paper describes how to train an isometric autoencoder and demonstrates its usefulness compared to non-isometric autoencoders on the UIUC airfoil dataset. Our ablation study illustrates that enforcing isometry is necessary for accurately discovering clusters through the latent space. We also show how isometric autoencoders can uncover pathologies in typical gradient-based shape optimization solvers through an analysis on the SU2-optimized airfoil dataset, wherein we find an over-reliance of the gradient solver on the angle of attack. Overall, this paper motivates the use of isometry constraints in neural embedding models, particularly in cases where researchers or designers intend to use distance-based analysis measures to analyze designs within the latent space. While this work focuses on airfoil design as an illustrative example, it applies to any domain where analyzing isometric design or data embeddings would be useful. [ABSTRACT FROM AUTHOR]

Motion blur of an image is a common phenomenon that occurs while taking a photograph due to the relative movement of the object and an image acquiring device. It is essential to detect this phenomenon of blurring of images in many applications such as information retrieval. This paper proposes a novel local blur detection technique, and it performs better than the existing works. This technique mainly uses Radon transform and Laplacian of Gaussian on the local neighborhood around each pixel to estimate blur information. Additionally, two new weight functions are introduced based on local geodesic distance and local variance. It is shown that these functions play a significant role in segregating blur and non-blurred parts. Simulation results validate the correctness and accuracy by testing the proposed algorithm on some challenging images with similar color information in the foreground and background. Various quantitative performance measures have determined the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Multivariate time series (MTS) clustering has been an essential research topic in various domains over the past decades. However, inherent properties of MTS data—namely, temporal dynamics and inter-variable correlations—make MTS clustering challenging. These challenges can be addressed in Grassmann manifold learning combined with state-space dynamical modeling, which allows existing clustering techniques to be applicable using similarity measures defined on MTS data. In this paper, we present a systematic overview of Grassmann MTS clustering from a geometrical perspective, categorizing the methods into three approaches: (i) extrinsic, (ii) intrinsic, and (iii) semi-intrinsic. Consequently, we outline 11 methods for Grassmann clustering and demonstrate their effectiveness through a comparative experimental study using human motion gesture-derived MTS data.

In this paper, a new method is developed for tool path planning on triangular mesh surfaces with consideration of the scallop height restriction and the path smoothness. This method first maps the triangular mesh surface into a unit disk region by using a harmonic map algorithm, and then the shortest boundary path graph (SBPG) is constructed on the unit disk region to describe the shortest geodesic distance from each mesh vertex to the surface boundary. The tool path is then obtained by inversely mapping the contours of SBPG from the harmonic mapped region to the physical space of mesh surface. During this process, a subdivision method is used to boost the computing efficiency and a smoothing treatment is conducted on the SBPG to improve the path smoothness. The tool path planning is performed starting from the surface boundary in an iteration process. Taking the level difference of SBPG contours as the initial path interval and being supplemented by a correction process, the maximal step distance between any two paths, which meets the requirement of scallop height restriction, can be determined efficiently. Typical simulation cases and experiments are carried out to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis methods, which allows for their comparison. Here, we challenge the widespread idea that graph theory is a universal analysis tool, uniformly applicable to any kind of network data. Instead, we show that many classical graph metrics—including degree, clustering coefficient, and geodesic distance—arise from a common hidden propagation model: the discrete cascade. From this perspective, graph metrics are no longer regarded as combinatorial measures of the graph but as spatiotemporal properties of the network dynamics unfolded at different temporal scales. Once graph theory is seen as a model-based (and not a purely data-driven) analysis tool, we can freely or intentionally replace the discrete cascade by other canonical propagation models and define new network metrics. This opens the opportunity to design—explicitly and transparently—dedicated analyses for different types of real networks by choosing a propagation model that matches their individual constraints. In this way, we take stand that network topology cannot always be abstracted independently from network dynamics but shall be jointly studied, which is key for the interpretability of the analyses. The model-based perspective here proposed serves to integrate into a common context both the classical graph analysis and the more recent network metrics defined in the literature which were, directly or indirectly, inspired by propagation phenomena on networks. [ABSTRACT FROM AUTHOR]

Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise estimated gradients is not larger than 1 is preferable compared to the widely used eikonal condition. Inspired by this, we formulate the geodesic distance field problem as a Quadratically Constrained Linear Programming (QCLP) problem. This formulation can be further adapted into a Quadratically Constrained Quadratic Programming (QCQP) problem by incorporating considerations for smoothness requirements. Specifically, when enforcing a Hessian-energy-based smoothing term, our formulation, named QCQP-Hessian, effectively mitigates the cusps in the geodesic isolines within the near-ridge area while maintaining accuracy in the off-ridge area. We conducted extensive experiments to demonstrate the accuracy and smoothness advantages of QCQP-Hessian. [ABSTRACT FROM AUTHOR]

In this paper, a novel data-centric approach is proposed for solving the 3D mesh segmentation problem. The method uses node2vec, a semi-supervised learning algorithm, to create vector embedding representations for each node in a 3D mesh graph. This makes the mesh data more compact and easier to process which is important for reducing computation costs. K-Means clustering is then used to cluster each node according to their node embedding information. This data-centric approach is more computationally efficient than other complex models such as CNN and RNN. The main contribution of this study is the development of a data-centric AI framework that combines node2vec embedding, machine learning, and deep learning techniques. The use of cosine similarity is also adapted to compare and evaluate the trained node embedding vectors with different hyperparameters. Additionally, a new algorithm is developed to determine the optimal cluster number using geodesic distance on the 3D mesh. Overall, this approach provides competitive results compared to existing mesh segmentation methods. [ABSTRACT FROM AUTHOR]

Differences in travel behaviors and user attributes exist between bikeshare users and regular cyclists. However, little is known about the preference difference in cycling facilities and other built environment elements for regular cyclists and share-bike users, and how the cycling infrastructure and street pattern factors affect the choice between shared bikes and regular bikes. To address this gap, we applied t -test and mode choice generalized additive mixed model (GAMM) to explore the nonlinear effects of cycling facilities and street patterns on the selection of bikeshare and regular bikes. Additionally, we examined the heterogeneous effects across education levels, distinguishing between high and low education. By analyzing bike travel data from Xi'an, China, the GAMM model results reveal the diverse impacts of built environment elements on bike choices at different education levels. Notably, the average geodesic distance (a street pattern indicator) negatively correlated with the likelihood of choosing a shared bike over a regular one. While high intersection density encourages more bikeshare trips compared to regular trips, it has a more pronounced effect on encouraging highly educated cyclists to opt for regular bikes over bikeshare. Bikeshare riders exhibit a preference for riding in areas with a single type of bike lane. Especially, highly educated bikeshare users are more inclined to cycle in areas with a high proportion of bike lanes separated by lines, while less educated cyclists tend to favor areas with a specific type of bike lane without specifying the exact type. Our study has the potential to provide valuable recommendations for planning of cycling facilities to accommodate a substantial number of bikeshare trips. • Differences in the road infrastructures preferences of bikeshare and regular cyclists. • GAMM investigates the nonlinear impacts of road infrastructures on bike choice. • Heterogenous impacts of road infrastructures across education levels. [ABSTRACT FROM AUTHOR]

Among different recent technologies proposed for human face classification and recognition, solutions based on analyzing the 3D geometric facial features emerged as a promising academic and practical direction. Researchers have examined both holistic and local approaches to analyzing the 3D face regions to study the impact of facial features in real-life applications such as medical and security implementations. However, a few works have investigated the relevant impact of the extracted geometric features from the descriptive local regions of the human face on identifying human ethnicity. This work proposes a classifier to categorize individuals into their distinctive ethnic groups and deeply analyzes the facial feature variations to highlight the most descriptive parts and features of the human face in race classification. The proposed ML-based classifier is preceded by extracting the 3D facial features from 3D meshes using the recent SIFT and Geodesic distance calculations. In addition, it implements and discusses the initial important preprocessing steps including, cropping the frontal parts, correcting the head pose, selecting the suitable initial key points, aligning the 3D meshes, and implementing the suitable template-based 3D registration. The proposed NN race classifiers are built and evaluated using Headspace, a well-known multi-ethnic dataset, and achieved high accuracy (90% globally, and 100% for the mouth area) especially while using the SIFT features. [ABSTRACT FROM AUTHOR]

Cover times measure the speed of exhaustive searches which require the exploration of an entire spatial region(s). Applications include the immune system hunting pathogens, animals collecting food, robotic demining or cleaning, and computer search algorithms. Mathematically, a cover time is the first time a random searcher(s) comes within a specified "detection radius" of every point in the target region (often the entire spatial domain). Due to their many applications and their fundamental probabilistic importance, cover times have been extensively studied in the physics and probability literatures. This prior work has generally studied cover times of a single searcher with a vanishing detection radius or a large target region. This prior work has further claimed that cover times for multiple searchers can be estimated by a simple rescaling of the cover time of a single searcher. In this paper, we study cover times of many diffusive or subdiffusive searchers and show that prior estimates break down as the number of searchers grows. We prove a rather universal formula for all the moments of such cover times in the many searcher limit that depends only on (i) the searcher's characteristic (sub)diffusivity and (ii) a certain geodesic distance between the searcher starting location(s) and the farthest point in the target. This formula is otherwise independent of the detection radius, space dimension, target size, and domain size. We illustrate our results in several examples and compare them to detailed stochastic simulations. [ABSTRACT FROM AUTHOR]

In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non-parameterized 2D manifolds at the discrete scale, the problem of computing geodesic distances between two non-adjacent points arise. Here, a routing procedure is implemented for computing geodesic distances by reinterpreting the triangular computational mesh as a non-oriented graph, thus returning a suitable and general method. Moreover, the time integration of the peridynamics equation is demanded to a P-(EC)k formulation of the implicit\beta-Newmark scheme. The convergence of the overall proposed procedure is questioned and rigorously proved. Its abilities and limitations are analyzed by simulating the evolution of a 2D sphere. The performed numerical investigations are mainly motivated by the issues related to the insurgence of singularities in the evolution problem. The obtained results return an interesting picture of the role played by the nonlocal character of the integrodifferential equation in the intricate processes leading to the spontaneous formation of singularities in real materials. [ABSTRACT FROM AUTHOR]

Typical non-local edge-aware filtering methods build long-range connections by deriving a minimum spanning tree (MST) from the input image. Each pixel on the MST only connects to a sub-set of pixels in the 8-connected neighborhood, resulting in piece-wise constant output with fake edges among sub-trees for the unbalanced information propagation along eight directions. In this paper, we propose two complementary spatial trees to incorporate information from the entire image. The structure of each tree depends on the spatial relationships of neighboring pixels. The distances between any two pixels in both spatial space and intensity space are the shortest distances on each tree. We introduce an efficient algorithm to recursively compute the output and the normalization constant on each tree with linear time complexity. For each pixel, we first calculate the outputs from eight subtrees and then fuse them to obtain the result on each tree structure. The final filtering output of our method is the weighted average of the results from two complementary spatial trees. Moreover, we present a distance mapping scheme to adjust the intensity distance between neighboring pixels, enabling our method to filter out a manageable degree of low-amplitude structures while sharpening major edges. Extensive experiments in graphic applications, such as image denoising, JPEG artifact removal, tone mapping, detail enhancement, and colorization, demonstrate the effectiveness and versatility of our method. [Display omitted] • Novel complementary trees to estimate the geodesic distance between any two pixels. • Efficient algorithms with linear time complexity to compute the weighted average of all pixels in the input image. • A distance mapping scheme in intensity space to manageably filter out low-amplitude structures. • Quantitative evaluation and qualitative comparison on various graphic applications to show the effectiveness and the versatility of our approach. [ABSTRACT FROM AUTHOR]

Aim: Continental comparisons of migration strategies within and between populations of single species are rare but can be insightful to understand key environmental factors shaping differences in migration systems. We investigated differences in stopover networks and migration strategies between three separate Eurasia Greater White‐fronted Geese (GWFG) Anser albifrons populations to better understand how each overcomes the different topographic challenges faced along their migration routes during spring and autumn. Location: Eurasia. Taxon: Birds. Methods: Using 106 (autumn) and 65 (spring) tracks from tagged GWFG from three Eurasian populations (Baltic‐North Sea [BNS] in the west; East Asia Continental [EAC] and West Pacific [WP] in the east), we generated stopover networks, calculated network metrics, quantified migration parameters and compared variation between populations and seasons. Results: BNS showed largest network size, shortest average geodesic distance in both seasons, shortest migration distances, most stopover sites, longest stopover duration and shortest step length. EAC showed longest migration distance and second maximal flight length (>1600 km). WP showed shortest migration durations and longest maximal flight length (>2500 km). Summering ground arrival dates did not differ between populations. Autumn migration duration was shorter and migration speed faster than in spring in all populations. Main Conclusions: We infer lack of obvious ecological barriers to BNS geese shapes their frequent stopovers of short duration. In contrast, EAC geese face two major ecological barriers (3100 km boreal forest, high mountains, dense human settlement and ocean) and WP geese must pass c. 2400 km of forest, mountains and ocean along their migration corridors, necessitating longer staging and migration segments of greater duration. We conclude that, despite almost identical body plan, all populations respond to radically different topographic challenges, adapting to meet these using different movement strategies, balancing migration schedule and fat accumulation patterns with availability and quality of stopovers. [ABSTRACT FROM AUTHOR]

Research on retail food environment (RFE) relies on data availability and accuracy. However, the discrepancies in RFE datasets may lead to imprecision when measuring association with health outcomes. In this research, we present a two-tier hierarchical point of interest (POI) matching framework to compare and triangulate food outlets across multiple geospatial data sources. Two matching parameters were used including the geodesic distance between businesses and the similarity of business names according to Levenshtein distance (LD) and Double Metaphone (DM). Sensitivity analysis was conducted to determine thresholds of matching parameters. Our Tier 1 matching used more restricted parameters to generate high confidence-matched POIs, whereas in Tier 2 we opted for relaxed matching parameters and applied a weighted multi-attribute model on the previously unmatched records. Our case study in San Diego County, California used government, commercial, and crowdsourced data and returned 20.2% matched records from Tier 1 and 18.6% matched from Tier 2. Our manual validation shows a 100% matching rate for Tier 1 and up to 30.6% for Tier 2. Matched and unmatched records from Tier 1 were further analyzed for spatial patterns and categorical differences. Our hierarchical POI matching framework generated highly confident food POIs by conflating datasets and identified some food POIs that are unique to specific data sources. Triangulating RFE data can reduce uncertain and invalid POI listings when representing food environment using multiple data sources. Studies investigating associations between food environment and health outcomes may benefit from improved quality of RFE. [ABSTRACT FROM AUTHOR]

The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov's idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044] to figure out the exact formula of edge-Wiener index of the Sierpinski fractal networks. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the equivalence of connectedness for the Sierpinski-like sponge and skeleton networks, and find out the relation between the geodesic distance on the sponge and renormalized shortest path distance on the skeleton networks. Furthermore, under some assumption on the IFS, we obtain the comparability of the Manhattan distance and the geodesic distance on the sponge. [ABSTRACT FROM AUTHOR]

The geodesic model based on the eikonal partial differential equation (PDE) has served as a fundamental tool for the applications of image segmentation and boundary detection in the past two decades. However, the existing approaches commonly only exploit the image edge-based features for computing minimal geodesic paths, potentially limiting their performance in complicated segmentation situations. In this paper, we introduce a new variational image segmentation model based on the minimal geodesic path framework and the eikonal PDE, where the region-based appearance term that defines then regional homogeneity features can be taken into account for estimating the associated minimal geodesic paths. This is done by constructing a Randers geodesic metric interpretation of the region-based active contour energy functional. As a result, the minimization of the active contour energy functional is transformed into finding the solution to the Randers eikonal PDE. We also suggest a practical interactive image segmentation strategy, where the target boundary can be delineated by the concatenation of several piecewise geodesic paths. We invoke the Finsler variant of the fast marching method to estimate the geodesic distance map, yielding an efficient implementation of the proposed region-based Randers geodesic model for image segmentation. Experimental results on both synthetic and real images exhibit that our model indeed achieves encouraging segmentation performance. [ABSTRACT FROM AUTHOR]

Assume-guarantee reasoning is indeed an effective compositional verification technique that can help mitigate the state explosion problem in model checking. However, the biggest challenge of applying assume-guarantee reasoning is how to best decompose a system. This paper presents a novel compositional verification frame based on geodesic distance. The proposed algorithm introduces novel techniques to decompose system components into groups. The algorithm’s effectiveness and efficiency are evaluated through a comparative analysis with four state-of-the-art methods commonly used in the field. The results of the comparison consistently demonstrate that the proposed algorithm outperforms the state-of-the-art methods. This implies that the new algorithm exhibits superior performance in terms of decomposition quality and verification efficiency.