Shared Edge Research Articles

The cadmium oxidotellurates(IV) Cd5(TeO3)4(NO3)2 and Cd4Te5O14

Monoclinic single crystals of Cd5(TeO3)4(NO3)2 (space group P21/c), pentacadmium tetrakis[oxidotellurate(IV)] dinitrate, and of Cd4Te5O14 (space group C2/c), tetracadmium pentaoxidotellurate(IV), were obtained under the same hydrothermal conditions. Whereas the crystal structure of Cd5(TeO3)4(NO3)2 is distinctively layered, that of Cd4Te5O14 exhibits a tri-periodic framework. In Cd5(TeO3)4(NO3)2, the three CdII atoms have coordination numbers (CN) of 7, 6 and 6. The two types of [CdO6] and the [CdO7] polyhedra [bond lengths range from 2.179 (3) to 2.658 (2) Å] share corners and edges, resulting in layers extending parallel to (100). Both TeIV atoms are coordinated by three oxygen atoms in a trigonal–pyramidal shape. The oxygen atoms of the isolated [TeO3] groups [bond lengths range from 1.847 (3) to 1.886 (3) Å] all are part of the cadmium–oxygen layer. The electron lone pairs ψ of the TeIV atoms are directed away from the layer on both sides. The available interlayer space is co-occupied by the nitrate group, which is directly connected with two of its O atoms to the layer whereas the third O atom is solely bonded to the N atom and points towards the adjacent layer. In Cd4Te5O14, all three unique CdII atoms are coordinated by six oxygen atoms, considering Cd—O distances from 2.235 (2) to 2.539 (2) Å. By edge- and corner-sharing, the distorted [CdO6] polyhedra form an open framework that is partially filled with three different stereochemically active TeIV atoms. All of them exhibit a CN of 4, with Te—O bonds in a range from 1.859 (2) to 2.476 (2) Å. The corresponding [TeO4] units are linked to each other by corner- and edge-sharing, forming infinite helical 1 ∞[Te10O28] chains extending parallel to [203]. The connectivity in the chains can be described as (...–⋄–⋄=⋄–⋄–⋄–⋄–⋄=⋄–⋄–⋄–...) n where ‘⋄’ denotes a [TeO4] unit, ‘–’ a linkage via corners and ‘=’ a linkage via edges. Such a structural motif is unprecedented in the crystal chemistry of oxidotellurate(IV) compounds.

Spatial Distributions and Edge Relationships of Plant Communities in Coastal Barrens in Nova Scotia, Canada

Coastal barrens support varied vegetation that includes wetlands, dwarf shrublands, and small patches of forest. Forest expansion, sea-level rise and recreational trails affect plant communities but spatial vegetation patterns within barrens are unknown. Using high-resolution multispectral aerial imagery, we classified plant communities and other land cover types using 500m x 500m landcover maps at three coastal barrens sites on the Atlantic coast of Nova Scotia, Canada. Community patches were compared using size and shape metrics; shared edge length identified adjacent communities. Community distributions were modelled using environmental variables such as elevation and distance to coast. Forty distinct plant communities were detected, with shrublands (37.5% total area), dwarf shrublands (23.3%) and bog wetlands (13.9%) the most abundant. Average patch size was 9.2 m2; average patch density was 951 patches/ha, indicating fine scale community variability. Recreational vehicle trails occurred primarily in bog wetlands. Dwarf shrublands and some wetland types were closest to the coastline; taller shrublands and tree islands occurred further from the coast. Edge relationships revealed a vegetation height gradient across the forest-barren ecotone: tree islands were mostly adjacent to tall shrub communities, followed by progressively shorter vegetation. Topographic variability and distance to coast were important predictors of community distribution. Edge relationships among communities allowed identification of those most at risk from trail disturbance, forest expansion and coastal squeeze.

Discretization of Continuous Spaces using Barycentric Subdivision Method with Metric Space Constraints on the Nearest Neighbour Edges

The Rao-Wilton-Glisson (RWG) is a commonly used basis function in the numerical solution of the electric field integral equation (EFIE) using the Method of Moments (MoM) and Galerkin approach. This method relies on triangular patches to approximate the surface current. Traditionally, barycentric subdivision of a primary triangle into n-sub-triangles has been used with RWG basis function to solve the EFIE using MoM. This paper presents a method of approximating a surface using triangular patches by sub-dividing a primary triangle into (2n-1) subtriangles. which creates a denser mesh than the widely used nine (9) points quadrature method. The structure is approximated by small square patches, which are further sub-divided into two primary triangles. By applying barycentric sub-division, the primary triangles are decomposed into sub-triangles to create a mesh over the surface of the structure. Using graph theory, the triangular meshes are defined by the function, G (V, E), where V and E are the vertices and edges of the triangles in the mesh space, respectively. The connectivity matrix of shared edges is found by imposing a constraint on the edge length using metric spaces. This method approximates a square patch with 32 scalene triangles and shows that it can be used to reconstruct equilateral patches and doubly split double ring into mesh structures.

A Novel Framework for Data Assessment That Uses Edge Technology to Improve the Detection of Communicable Diseases.

Spreading quickly throughout populations, whether animal or human-borne, infectious illnesses provide serious risks and difficulties. Controlling their spread and averting disinformation requires effective risk assessment and epidemic identification. Technology-enabled data analysis on diseases allows for quick solutions to these problems. A Combinational Data Assessment Scheme intended to accelerate disease detection is presented in this paper. The suggested strategy avoids duplicate data replication by sharing data among edge devices. It uses indexed data gathering to improve early detection by using tree classifiers to discern between various kinds of information. Both data similarity and index measurements are considered throughout the data analysis stage to minimize assessment errors. Accurate risk detection and assessment based on information kind and sharing frequency are ensured by comparing non-linear accumulations with accurate shared edge data. The suggested system exhibits high accuracy, low mistakes, and decreased data repetition to improve overall effectiveness in illness detection and risk reduction.

Adaptive Scheduling of Continuous Operators for IoT Edge Analytics

In this paper, we address the problem of adaptive scheduling of data stream processing and analytics (DSPA) applications in a shared edge fog cloud (EFC) continuum with response time constraints. The focus is on handling the dynamic workload of DSPA applications caused by the variability of their input data stream rates generated by mobile IoT devices, and the dynamically available resource capacity in the EFC continuum. To address these challenges, we characterise the different types of resources in the EFC continuum, as well as the operators that make up a DSPA application. Based on this characterisation, we propose models to evaluate the response time and the cost of using the resources in the always dynamic EFC continuum. We then formulate the problem of adaptive scheduling of a DSPA application in the EFC continuum with the objective of minimising the cost of using the shared resources subject to the constraints of the response time and the available capacity of the EFC resources. We propose a heuristic algorithm that dynamically computes a new scheduling of the DSPA application, taking into account its current deployment state and the current state of the shared resources in the EFC continuum. Experimental results, using simulation, show the effectiveness of our proposed algorithm against algorithms of related work.

Open Knowledge Graph Link Prediction with Semantic-Aware Embedding

Link prediction in open knowledge graphs (OpenKGs) is crucial for applications like question answering and recommendation systems. Existing OpenKG models leverage the semantic information of noun phrases (NPs) to enhance the performance in the link prediction task. However, these models only extract superficial semantic information from NPs, ignoring the fact that an NP possesses diverse semantics. Furthermore, these models have not fully exploited the semantic information of the relation phrases (RPs). To address these issues, we propose a model for link prediction called Open Knowledge Graph Link Prediction with Semantic-Aware Embedding (SeAE). First, we develop an adaptive disentanglement embedding (ADE) mechanism to learn the intrinsically abundant semantics of NPs. The ADE mechanism can adaptively calculate the embedding segmentation number according to the dataset and has an ingenious method for updating embeddings. Second, we integrate the attention mechanism into the GRU encoder to obtain the distribution of importance inside RP, facilitating a more comprehensive capture of the RP’s semantic information and enhancing the model’s interpretability. Finally, we design a relation gate, which extracts the RP semantic features of tail NP from the shared edge. This gate realizes the relation constraints on entities while enhancing the interaction between entities and relations. Extensive experiments on four benchmarks demonstrate that SeAE outperforms the state-of-the-art models, resulting in improvements of approximately 5.4% and 7.4% in MRR on ReVerb45K and ReVerb45KF datasets respectively.

Risk factors associated with depression and anxiety among the Chinese general population after retracting the dynamic zero-COVID policy: A network analysis

BackgroundRecent studies have evidenced the negative psychological consequences of the COVID-19 pandemic and sociodemographic vulnerability among the general population, while limited information was available on which factors make the greatest contribution to psychological distress when these factors were considered concurrently. Herein, we aimed to investigate the pathways that underlie psychological distress in the context of retracting dynamic zero-COVID policy. MethodsWe employed the mixed graphical model to construct the network of depression (PHQ-9), anxiety (GAD-7), and pandemic-related factors in a general population sample (N = 1610). Then, we re-examined the network by adding sociodemographic variables to further explore the influence of sociodemographic factors. Additionally, we repeated the analyses in the second sample (N = 620) collected in the same period to assess the replicability. ResultsThe relationships between the pandemic factors and anxiety and depressive symptoms exhibited a tendency to decrease after adding demographic variables, and income became the most important node and shared edge weights with all anxiety and depressive symptoms. These findings were replicable with the second sample. No significant difference in the network properties was detected between the two samples. LimitationsThe cross-sectional design limits the ability to observe longitudinal changes in these risk factors and their relationship with psychological distress. ConclusionsIncome level, rather than the pandemic-related factors, acted as a vital role in the psychological distress of the general population, implying that livelihood issues may be the critical intervention targets for mental health during the post-pandemic period.

Virgilluethite: A New Mineral and the Natural Analogue of Synthetic β-MoO3·H2O, from Cookes Peak, Luna County, New Mexico, USA

Abstract The new mineral virgilluethite, ideally β-MoO3·H2O, was discovered in an unnamed short adit on the Summit group of claims near Cookes Peak, Luna County, New Mexico, USA. All virgilluethite crystals are pseudomorphs after sidwillite and occur as aggregates of sub-parallel platy crystals. Associated minerals include sidwillite, raydemarkite, tianhuixinite, ilsemannite, jordisite, powellite, fluorite, baryte, pyrite, and quartz. Virgilluethite is pale yellow-green in transmitted light, transparent with white streak and vitreous luster. It is flexible with a Mohs hardness of ∼2; cleavage is perfect on {010}. No twinning was observed visually. The measured and calculated densities are 3.71(5) and 3.69 g/cm3, respectively. Virgilluethite is insoluble in water or hydrochloric acid. An electron probe microanalysis yielded an empirical formula (Mo1.00)O3·H2O based on 4 O apfu. Virgilluethite is the natural analogue of the β-form of MoO3·H2O, which was first synthesized over a century ago (Rosenheim & Davidsohn 1903). It is monoclinic, space group P21/c, with unit-cell parameters a = 7.2834(3), b = 10.6949(6), c = 7.4861(3) Å, β = 112.779(2)°, V = 583.03(5) Å3, and Z = 4. The crystal structure of virgilluethite, which is topologically identical to that of tungstite (WO3·H2O), is characterized by highly distorted and elongated MoO5(H2O) octahedra that share four corners in the equatorial plane with one another to form sheets parallel to (010). These sheets, analogous to those in sidwillite, are held together by H-bonding between the H2O molecule and the O atom in the axial position in the adjacent sheets. Virgilluethite and raydemarkite are dimorphs of MoO3·H2O. Unlike virgilluethite, the MoO6 octahedra in raydemarkite share edges to form isolated double chains, resembling those found in zhenruite, (MoO3)2·H2O.

Emission modulation of Eu3+ via symmetry around dodecahedron in garnet-type Ca2EuZr2-xSnxGa3O12 (x = 0, 0.5, 1, 1.5, and 2) phosphors

White LEDs offer advantages such as high efficiency and a long lifetime. However, their color rendering index is low due to the lack of red components. Herein, we synthesized new garnet-type Ca2EuZr2-xSnxGa3O12 (x = 0, 0.5, 1, 1.5, and 2) phosphors via a solid-state reaction. These phosphors exhibited red emission under ultraviolet excitation at 395 nm and a high internal quantum efficiency (>45 %) in all samples. In addition, the intensity of the emission of the 5D0→7F4 transition (∼710 nm) increased with an increase in the x value. We also explored the relationship between the intensity of the 5D0→7F4 transition and the symmetry around Eu3+. Doping Sn4+ into the garnet-type Ca2EuZr2-xSnxGa3O12 phosphors increased the length of the shared edge between the tetrahedra and dodecahedra in the garnet-type structure. Consequently, the geometry of the dodecahedra approached that of a square antiprism-like polyhedron, which in turn affected the 5D0→7F4 transition of Eu3+.

Chemical and Structural Factors Affecting the Stability of Wadsley-Roth Block Phases.

Wadsley-Roth phases have emerged as highly promising anode materials for Li-ion batteries and are an important class of phases that can form as part of the oxide scales of refractory multiprinciple element alloys. An algorithmic approach is described to systematically enumerate two classes of Wadsley-Roth crystallographic shear structures. An analysis of algorithmically generated Wadsley-Roth phases reveals that a diverse set of oxide crystal structures belongs to the Wadsley-Roth family of phases. First-principles calculations enable the identification of crystallographic and chemical factors that affect Wadsley-Roth phase stability, pointing in particular to the importance of the number and nature of the edges shared by neighboring metal-oxygen octahedra. A systematic study of Wadsley-Roth phases in the Ti-Nb-O ternary system shows that the cations with the highest oxidation states segregate to octahedral sites that minimize the number of shared edges, while cations with the lowest oxidation state accumulate to edge-sharing octahedra at shear boundaries.

Mössbauer analysis, structural parameter studies and magnetic properties of LiCoxFe5-xO8 (x= 0, 0.025, 0.05, 0.075, 0.1) nanoparticles

We report on detailed structural parameter analysis, Mössbauer spectra and magnetic properties of LiCoxFe5-xO8 (x = 0, 0.025, 0.05, 0.075, 0.1) nanoparticles prepared by sol-gel method. Prepared LiCoxFe5-xO8 nanoparticles crystalizes in inverse spinel structure with the crystallite size ranging from 23.7 to 29.8 nm. Hopping length, radii of tetrahedral and octahedral sites (rA and rB), tetrahedral bond length (dAx), octahedral bond lengths (dBx), tetrahedral and octahedral shared edges (dAxE, dBxE), unshared octahedral edges (dBxEU) values and oxygen positional parameter (u) are seen to increase with increasing Co concentration. Chemical state of all the elements are confirmed by X-ray photoelectron spectroscopy technique. The hyperfine field, isomer shift, quadrupole shift and line width parameters calculated from the Mössbauer spectra confirms the Co2+ substitution in LiFe5O8. The saturation magnetization value decreases from 59.2 to 54.1 emu/g with increasing Co concentration, which is examined by three sublattice model derived by Yafet and Kittel (Y-K model). Y-K angles increases with Co concentration from 16.46 to 19.98°. Curie temperature of LiFe5O8 decreases from 865 K to 858 K with increasing Co concentration to x = 0.1.

Edge aggregation placement for semi-decentralized federated learning in Industrial Internet of Things

Rapid technological advancements have resulted in more smart devices with an increased volume of data in Industrial Internet of Things (IIoT) systems. These data often contain significant levels of heterogeneity and privacy in accordance with the various requirements of industrial applications, therefore controlling for these data in an intelligent and secure way is still an outstanding problem. Federated edge learning (FEEL), a distributed machine learning paradigm, has become a viable option for developing learning models while maintaining data privacy. In this paper, we concentrate on a semi-decentralized FEEL (SD-FEEL) framework, taking into account the limited training data in a single central cluster, where the shared edge models is trained among devices and edge servers. An edge aggregation optimization problem with joint device association, resource block allocation, and edge server placement is then formulated based on the evaluated upper bound of the convergence performance for SD-FEEL, with the goal of minimizing the training loss while taking into account the cost budget of edge servers. Based on the calculation of training loss degradation, the proposed optimization issue can be transformed into a dynamic optimum problem. A Trilateral Matching-based association (TMA) method is then proposed to discover solutions to the sub-problems of device association and resource block allocation. Additionally, a Tabu Search-based Service location (TSP) method is suggested to optimize the placement of the edge servers. To fully address the optimization problem, a combination iterative approach including the TMA and TSP is proposed. According to simulation data, the proposed algorithm can greatly beat the baselines in terms of test accuracy with limited cost budget.

Experimental Study on Compressive Strength of Magnesium Oxychloride Cement Mortar Using Stone Crushed Powder by Varying Molar Ratio

Abstract: One of the major consumers of natural resources and a significant contributor to CO2 emissions is the construction sector. The manufacture of cement and building materials was found to be the source of the highest greenhouse gas emissions. In order to lessen the damaging effects of the building industry on the environment, this paper seeks to determine whether magnesium oxychloride cement (MOC) may be used as a mortar substitute for regular Portland cement. A thorough review of the literature, an experimental investigation, and an internal structure analysis based on the ideal molar ratio are all part of the research technique. In this study, MOC cement with powdered stone is experimentally investigated utilizing various molar ratios with phases 3 and 5. In the first set of results usage of unheated magnesium oxide powder, SEM image shown some amount of MgO left inactive and compressive strength depicted lower values. Eventually, a modification was implemented in order to boost compressive strength. In order to improve the reaction or gel formation that would boost the compressive strength, the MgO powder was heated and added to the cement. Different molar ratios produced various compressive strength values in the mortar cubes. Two ideal molar ratios are chosen from each phase, SEM and EDXA are used to analyse the micro structure. The MgO6 octahedral crystal structures of Phases 3 and 5 are visible in the SEM pictures as double and tripple ribbons of shared edges with water molecules and chloride anions. The percentage of elemental weight in the specimens is displayed by EDXA.

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator (lambda /4 CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency omega _{textrm{cutoff}} for the coupling between the FQ and the modes in the CPWR, where the coupling grows as sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}ll 1 and decreases as 1/sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}gg 1. Here omega _n is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above omega _{textrm{cutoff}} at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.

An iterative reconstruction algorithm based on total nuclear variation for multi-channel EPRI

Oxygen concentration in tumor is a key information for effective radiation therapy. Electron paramagnetic resonance imaging (EPRI) is an advanced oxygen imaging technique. However, in the case of multi-channel EPRI， traditional imaging methods including filtered back-projection (FBP) and optimization algorithm related to total variation (TV) only consider the features of individual channel images and ignore the similarities among images of each channel. Total nuclear variation encourages shared edge positions and consistent gradient directions across multi-channel images. In this study, we propose a data divergence constrained, total nuclear variation minimization model and its Chambolle-Pock solving algorithm. We validate the accuracy of the algorithm and analyze its convergence through simulation studies using mathematical phantoms that simulate T1-weighted EPRI. Furthermore, we investigate the influence of algorithm parameters on convergence rate and evaluate the algorithm’s capability for sparse reconstruction and noise suppression. The experimental results show that the total nuclear variation minimization algorithm promotes edge structure information and gradient direction within individual channels of images. As a result, this algorithm successfully preserves essential image features while achieving accurate image reconstruction.

Yuchuanite-(Y), Y2(CO3)3·H2O, a new hydrous yttrium carbonate mineral from the Yushui Cu deposit, South China

Abstract A new mineral species, yuchuanite-(Y), ideally Y2(CO3)3·H2O, has been discovered and characterized in the Yushui Cu deposit in South China. The mineral occurs in bedded/massive ore and is associated with bornite, chalcopyrite, galena, sphalerite, bastnäsite-(Y), xenotime-(Y), anhydrite, and quartz. Individual crystals range in size from 30 to 300 μm. No twinning is observed. The mineral is colorless and transparent with a vitreous luster. The calculated density is 3.62 g/cm3. An electron microprobe analysis yields the empirical formula (based on 10 O apfu), (Y1.61Yb0.11Er0.11Dy0.08Ho0.03 Gd0.02Tm0.02)Σ1.99(CO3)3·H2O. Yuchuanite-(Y) is triclinic, with space group P1 (#2), Z = 6, and unit-cell parameters a = 6.2134(3) Å, b = 8.9697(3) Å, c = 19.9045(7) Å, α = 91.062(3)°, β = 90.398(3)°, γ = 91.832(3)°, and V = 1108.54(8) Å3. The structure is constructed from (110) sheets of eight-coordinated Y polyhedra and C trigonal planar groups. All Y polyhedra are linked by shared edges. The Y atoms occupy six independent crystallographic sites of two different coordination types: [YO7(H2O)] and [YO8]. The chemical composition of yuchuanite-(Y) is similar to tengerite-(Y), Y2(CO3)3·2–3H2O, but is distinct in the crystal structure, such as crystal system, space group, and unit cell, from that of tengerite-(Y). The Y polyhedra of tengerite-(Y) are nine-coordinated, while those of yuchuanite-(Y) are eight-coordinated. Moreover, their structures could be both described as sheet structures built up from Y polyhedra and CO3 trigonal planar groups but link together in significantly different ways. Thus, yuchuanite-(Y) is not a polytype of tengerite-(Y) but is an independent mineral species.

Model-driven Cluster Resource Management for AI Workloads in Edge Clouds

Since emerging edge applications such as Internet of Things (IoT) analytics and augmented reality have tight latency constraints, hardware AI accelerators have been recently proposed to speed up deep neural network (DNN) inference run by these applications. Resource-constrained edge servers and accelerators tend to be multiplexed across multiple IoT applications, introducing the potential for performance interference between latency-sensitive workloads. In this article, we design analytic models to capture the performance of DNN inference workloads on shared edge accelerators, such as GPU and edgeTPU, under different multiplexing and concurrency behaviors. After validating our models using extensive experiments, we use them to design various cluster resource management algorithms to intelligently manage multiple applications on edge accelerators while respecting their latency constraints. We implement a prototype of our system in Kubernetes and show that our system can host 2.3× more DNN applications in heterogeneous multi-tenant edge clusters with no latency violations when compared to traditional knapsack hosting algorithms.

Clomazone impact on fungal network complexity and stability.

Soil fungal network composition and stability are important for soil functions, but there is less understanding of the impact of clomazone on network complexity and stability. In this work, two agricultural soils were used to investigate the impact of clomazone on fungal network complexity, composition, and stability. The two soils were treated with clomazone solution (0, 0.8, 8, and 80 mg kg-1) and kept in an incubator. Under the influence of clomazone, the fungal network nodes were decreased by 12-42; however, the average degree was increased by 0.169-1.468 and fungal network density was increased by 0.003-0.054. The keystone nodes were significantly changed after clomazone treatment. Network composition was also impacted. Specifically, compared with control and clomazone treatments in both soils, the shared edges were fewer than 54 in all comparisons, and network dissimilarity was 0.97-0.98. These results suggested that fungal network composition was significantly impacted. The network robustness was increased by 0.0018-0.0209, and vulnerability was decreased by 0.00018-0.00059 in both soils, which indicated that fungal network stability was increased by clomazone. In addition, the functions of network communities were also changed in both soils. These results indicated that clomazone could significantly impact soil fungal networks.

Optimal flow and capacity allocation in multiple joint quickest paths of directed networks

Shared vertices or edges in joint paths bring difficulties to flow routing and scheduling with delay requirements in networks with consideration of both edge lengths and capacities since flow along the different paths will encounter each other in capacitated edges with time dislocation. For an amount of flow, the quickest path problem (QPP) presents a good link for path lengths and capacities with the transmission time of the flow. Extended from the QPP, we propose an edge-path form traffic model for an amount of flow through multiple joint paths with different lengths in one-source one-sink directed capacitated networks. Then, an optimization model for minimum transmission time within feasible traffic constrained by edge capacities is constructed. We then derived the vertex–edge form of the optimization model from the edge-path form. The proposed optimization models in both forms are proved to be linear fractional programming problems, which can be solved in polynomial time. A routing algorithm based on the solution of the vertex–edge form optimization is developed combined with the DFS-based route-searching method. The proposed model and algorithm could be applicable in the real-time operation and management of practical network systems.

An Extensive Study on Graph Colourings and Dominator Chromatic Number of Sugeno-Type Fuzzy Graphs

The concept of graph colouring has become a very active field of research that enhances many practical applications and theoretical challenges. An accurate (vertex) colouring through the condition that each vertex is whichever unaccompanied in its colour class or adjoining to all vertices of at least one colour class is known as dominator colouring. A graph is dominator colouring is a suitable colouring in which at least one vertex dominates each colour class. Many difficult and global issues are solved using fuzzy graph colouring approaches. In this paper, we introduce a new Sugeno-Type Fuzzy graph of groups, which is found using several fuzzy graph operations such as dominant path-colouring number, cycle, union, join, and products. A number that is representative based on those vertices in the formations of all paths with those vertices as their starts and ends to compare with other paths is the minimum number of shared edges based on those vertices in the formations of all paths with those vertices as their starts and ends to compare with other paths. The sugeno dominant path-colouring number is the minimum Sugeno number of shared edges among the Sugeno cardinality of all sets of shared edges, which allows for various techniques. These results are used in studying various and recently introduced chromatic numbers of graphs.