Symmetric Graphs Research Articles

Study of isotropic stellar models via durgapal-lake solutions in rastall system

Abstract This manuscript is dealt with the influences of Rastall factor on the physical aspects of isotropic celestial models. In this scenario, both the ideal fluid distribution and static spherically symmetry are taken into consideration. In specifically, the Durgapal-Lake solutions are taken into consideration to analyze the different characteristics of several specific compact star models like Her X-1, Vela X-1, LMC X-4 and RXJ 1856-37. Due to its innovative combination of two methodologies, this solution is a significant advancement on Durgapal-Fuloria and Lake's previous ansatz in enormous crucial eras. Using observed estimates of radii and masses of certain specific star objects, the undefined parameters in Durgapal-Lake ansatz are derived by matching conditions. The consistency of the adopted solutions is examined through the visual interpretation of matter constituents, equation of state factor, energy conditions, mass function and stability criteria corresponding to distinct choices of Rastall factor. The radially symmetric graphs of matter variables as well as the mass function are also displayed. Moreover, We present the graphical analysis for vanishing Rastall factor. It is concluded that in the context of Rastall theory, the stars under examination exhibit stable compositions with Durgapal-Lake solution, while in the context of general relativity, they exhibit instability.

A clinical case of treatment of temporomandibular joints disease caused by occlusive disorders

A method of treatment,described in this clinicalcase, isaimedateliminatingdisorders of occlusalrelationships of the dentition, (PatentNo.2797641dated06/07/2023) contributing to the normalization of TMJ functioning. At the first stage of treatment, a repositioning occlusal splint was used, applied to all teeth of the lower jaw, which was being corrected for six months. This stage was considered completed on the basis of the following criteria: absence of the patient`s complaints and smooth movements of the mandible without deviations and clicks on objective examination, as well as formation of symmetrical graphs of the TMJ condyles movement on axiographic examination, an optimal location of the TMJ condyles on sagittal projections of MSCT and positive changes in the bioelectric activity of the masticatory muscles, towards higher and more symmetrical values on both sides. Further treatment was carried out by an orthodontist with a non-removable technique,using a brace system. Wearing of the occlusal splint continued until the braces system was put on the teeth of the lowerjaw. It was then replaced by composite liningsin the projection of the firstmolars of the upperjaw. Dynamicmonitoring of thepatientforhalf ayearafter the end of the treatment indicated remission of TMJ disease. Normalization of occlusal relationships of dentitions in intact dentitions and small defects through splint therapy followed by the use of a brace systemis a minimally invasive andeffectivemethod of treatment TMJ diseases.

Glow-to-arc transition in graphite cathode with high-current magnetron discharge

The glow-to-arc transition is a critical phenomenon in plasma discharges, commonly leading to detrimental effects. The physical mechanisms triggering this transition remain poorly understood. The advent of a discharge called Hyper-Power Impulse Magnetron has opened possibilities. Hyper-Power Impulse Magnetron allows the glow mode to be maintained over long periods (1 ms) and at high-current densities (>5 A .cm−2), which has unveiled certain features in the glow-to-arc transition. This work focuses on a graphite target that transits easily in the arc regime. The high-speed video-camera analysis revealed specific properties of graphite in ExB discharges, and the statistical study of the arc transition revealed differences from other refractory target materials. The early stage of cathodic spot formation, observed as bright dots, will be presented and analyzed within the known “ecton” and “vaporization” models for spot formation. This experimental study highlights the role of luminous spot formation prior to arc transition, with possible optimization on the stability of magnetron discharges.

The new insight of tectonic setting in Sunda–Banda transition zone using tomography seismic. Case study: 7.1 M deep earthquake 29 August 2023

Abstract The Sunda–Banda arc transition zone features the collision of the Indo-Australian oceanic plate and the Australian continent, resulting in intricate geological and geodynamic conditions. Tectonic activity in this region is shaped by the convergence of multiple major plates, including the Indo-Australian oceanic plate and the Eurasian plate. The crustal structure along the Sunda–Banda arc transition zone is complex and influenced by various factors such as subduction, continental collision, and volcanic activity. The tectonic complexity of the region in eastern Indonesia makes it an interesting area for study. In this research, International Seismological Centre-Engdahl-van der Hilst-Buland catalogue data from 1964 to 2020 were used, which include recorded information on 69.705 earthquake events from 1.185 recording stations and consist of 2.943.974 P phases. Resolution testing was performed using various velocity grids, and optimal results were obtained with a medium resolution of ∼100 km × 100 km × 80 km for the inversion process. The tomographic inversion analysis provided valuable insights into subsurface structures within Earth’s crust and mantle up to a depth of approximately 750 km. The occurrence of deep earthquakes in the study area has provided valuable insights into complex dynamics associated with subduction and plate tectonics. The results of the tomographic inversion analysis reveal that earthquakes are concentrated in areas with high-velocity anomalies, indicating intense tectonic activity near the subduction zone. This study offers the perspective on the structural complexities and earthquake origins in the Sunda–Banda arc transition zone following the 2023 Mw 7.1 Bali Sea earthquake, which occurred on August 29, 2023, at 02:55:32 UTC + 7, approximately 163 km northeast of Lombok, Indonesia. This earthquake was caused by slab pull activity from the Australian Plate and involved a combination of downward and oblique-normal movement. These characteristics indicate the convergence and interaction between tectonic plates in the subduction process occurring in the Bali Sea area. As a result, there have been frequent occurrences of various tectonic and volcanic activities including earthquakes of different magnitudes. These results highlight the significance of the high-velocity anomaly connected to this occurrence, offering valuable insights into seismic behaviour and tectonic phenomena in the region. The findings of this study indicate that the deep earthquakes in the Bali Sea may be induced by faulting due to the transformation of metastable olivine into denser spinel at significant depths, along with shear instability caused by phase transitions within Earth’s mantle layers. This theory proposes that stress-induced changes in phase can initiate shear instabilities and subsequently lead to deep earthquakes.

Bipolar Neutrosophic Transportation Problem in Symmetric Graphs

Bipolar Neutrosophic Transportation Problem in Symmetric Graphs

Fatigue performance of Q420C high-strength steel at room and low temperatures

Steel structures are frequently exposed to the environment with variable temperature, where the fatigue failure of steel is difficult to be predicted. In this paper, the standard Q420C high-strength steel specimens were tested to explore their fatigue performance at room (25°C) and low temperatures (0°C, −15°C and −30°C). Before fatigue tests, the tensile tests have been done, and the results indicate that the yield and ultimate strengths of Q420C steel significantly grew when the temperature decreased. The fatigue behavior of Q420C steel was discussed from different perspectives, including the crack initiation, crack growth, fracture mode and fatigue life. The fatigue failure was observed mainly near the arc transition section of specimen, with the fatigue crack initiated from the surface and internal discontinuity defects. Furthermore, the test fatigue life was compared with the recommended S-N curves provided by specifications from various countries. These comparison results suggest that recommended S-N curves were excessively conservative to evaluate the steel fatigue life at low temperature, leading to a potential economic cost for the steel structures at extremely cold conditions. To avoid needless loss, a calculation method of steel fatigue life considering the effect of low-temperature, stress range and yield strength was proposed.

The λ -fold Spectrum Problem for the Orientations of the 6-Cycle

The λ-fold complete symmetric directed graph of order v, denoted λKv*, is the directed graph on v vertices and λ directed edges in each direction between each pair of vertices. For a given directed graph D, the set of all v for which λKv* admits a D-decomposition is called the λ-fold spectrum of D. In this paper, we settle the λ-fold spectrum of each of the nine non-isomorphic orientations of a 6-cycle.

Structure-inclusive similarity based directed GNN: a method that can control information flow to predict drug-target binding affinity.

Exploring the association between drugs and targets is essential for drug discovery and repurposing. Comparing with the traditional methods that regard the exploration as a binary classification task, predicting the drug-target binding affinity can provide more specific information. Many studies work based on the assumption that similar drugs may interact with the same target. These methods constructed a symmetric graph according to the undirected drug similarity or target similarity. Although these similarities can measure the difference between two molecules, it is unable to analyze the inclusion relationship of their substructure. For example, if drug A contains all the substructures of drug B, then in the message-passing mechanism of the graph neural network, drug A should acquire all the properties of drug B, while drug B should only obtain some of the properties of A. To this end, we proposed a structure-inclusive similarity (SIS) which measures the similarity of two drugs by considering the inclusion relationship of their substructures. Based on SIS, we constructed a drug graph and a target graph, respectively, and predicted the binding affinities between drugs and targets by a graph convolutional network-based model. Experimental results show that considering the inclusion relationship of the substructure of two molecules can effectively improve the accuracy of the prediction model. The performance of our SIS-based prediction method outperforms several state-of-the-art methods for drug-target binding affinity prediction. The case studies demonstrate that our model is a practical tool to predict the binding affinity between drugs and targets. Source codes and data are available at https://github.com/HuangStomach/SISDTA.

Note on intrinsic metrics on graphs

AbstractWe study the set of intrinsic metrics on a given graph. This is a convex compact set and it carries a natural order. We investigate existence of largest elements with respect to this order. We show that the only locally finite graphs which admit a largest intrinsic metric are certain finite star graphs. In particular, all infinite locally finite graphs do not admit a largest intrinsic metric. For infinite graphs which are not locally finite the set of intrinsic metrics may be trivial as we show by an example. Moreover, we give a characterization for the existence of intrinsic metrics with finite balls for weakly spherically symmetric graphs.

Harnessing graph state resources for robust quantum magnetometry under noise

Precise measurement of magnetic fields is essential for various applications, such as fundamental physics, space exploration, and biophysics. Although recent progress in quantum engineering has assisted in creating advanced quantum magnetometers, there are still ongoing challenges in improving their efficiency and noise resistance. This study focuses on using symmetric graph state resources for quantum magnetometry to enhance measurement precision by analyzing the estimation theory under time-homogeneous and time-inhomogeneous noise models. The results show a significant improvement in estimating both single and multiple Larmor frequencies. In single Larmor frequency estimation, the quantum Fisher information spans a spectrum from the standard quantum limit to the Heisenberg limit within a periodic range of the Larmor frequency, and in the case of multiple Larmor frequencies, it can exceed the standard quantum limit for both noisy cases. This study highlights the potential of graph state-based methods for improving magnetic field measurements under noisy environments.

Multiview Subspace Clustering via Low-Rank Symmetric Affinity Graph.

Multiview subspace clustering (MVSC) has been used to explore the internal structure of multiview datasets by revealing unique information from different views. Most existing methods ignore the consistent information and angular information of different views. In this article, we propose a novel MVSC via low-rank symmetric affinity graph (LSGMC) to tackle these problems. Specifically, considering the consistent information, we pursue a consistent low-rank structure across views by decomposing the coefficient matrix into three factors. Then, the symmetry constraint is utilized to guarantee weight consistency for each pair of data samples. In addition, considering the angular information, we utilize the fusion mechanism to capture the inherent structure of data. Furthermore, to alleviate the effect brought by the noise and the high redundant data, the Schatten p-norm is employed to obtain a low-rank coefficient matrix. Finally, an adaptive information reduction strategy is designed to generate a high-quality similarity matrix for spectral clustering. Experimental results on 11 datasets demonstrate the superiority of LSGMC in clustering performance compared with ten state-of-the-art multiview clustering methods.

Appearance-posture fusion network for distracted driving behavior recognition

In recent years, detection techniques using computer vision and deep learning have shown promise in assessing driver distraction. This paper proposes a fusion network that combines a Spatial-Temporal Graph Convolutional Network (ST-GCN) and a hybrid convolutional network to integrate multimodal input data for recognizing distracted driver behavior. Specifically, to address the limitations of the ST-GCN method in modeling long-distance joint interaction features and inadequate temporal feature extraction, we design the Spatially Symmetric Configuration Partitioning Graph Convolutional Network (SSCP-GCN) to model relative motion information of symmetric relationships between limbs. Specifically, we utilize densely connected blocks for processing multi-scale temporal information between consecutive frames, thereby enhancing the reuse of bottom features. Furthermore, the expression of important temporal information is augmented by the introduction of the channel attention mechanism. To tackle the problem that the Mixed Convolution (MC) combining 3D convolution with 2D convolution cannot extract higher-order timing information and has limitations in modeling global dependency relationships, we compensate for its inability to capture higher-order temporal semantic information using the Time Shift Module (TSM) without consuming additional computational resources. Additionally, the 3D Multi-Head Self-Attention mechanism (3D MHSA) is employed to integrate global spatial–temporal information of high-level features, avoiding the issue of model complexity proliferation caused by the deep stacking design of Convolutional Neural Networks (CNN). Lastly, we introduce a multistream network framework that integrates driver posture and appearance features to harness complementary advantages, enabling us to combine multimodal input features to achieve better model performance. Experimental results indicate that the accuracy of the network designed in this paper reaches 95.6% and 94.3% on ASU dataset and NTU-RGB+D dataset, respectively. The small size of the model offers the possibility for practical application of the algorithm.

GBVSSL: Contrastive Semi-Supervised Learning Based on Generalized Bias-Variance Decomposition

Mainstream semi-supervised learning (SSL) techniques, such as pseudo-labeling and contrastive learning, exhibit strong generalization abilities but lack theoretical understanding. Furthermore, pseudo-labeling lacks the label enhancement from high-quality neighbors, while contrastive learning ignores the supervisory guidance provided by genuine labels. To this end, we first introduce a generalized bias-variance decomposition framework to investigate them. Then, this research inspires us to propose two new techniques to refine them: neighbor-enhanced pseudo-labeling, which enhances confidence-based pseudo-labels by incorporating aggregated predictions from high-quality neighbors; label-enhanced contrastive learning, which enhances feature representation by combining enhanced pseudo-labels and ground-truth labels to construct a reliable and complete symmetric adjacency graph. Finally, we combine these two new techniques to develop an excellent SSL method called GBVSSL. GBVSSL significantly surpasses previous state-of-the-art SSL approaches in standard benchmarks, such as CIFAR-10/100, SVHN, and STL-10. On CIFAR-100 with 400, 2500, and 10,000 labeled samples, GBVSSL outperforms FlexMatch by 3.46%, 2.72%, and 2.89%, respectively. On the real-world dataset Semi-iNat 2021, GBVSSL improves the Top-1 accuracy over CCSSL by 4.38%. Moreover, GBVSSL exhibits faster convergence and enhances unbalanced SSL. Extensive ablation and qualitative studies demonstrate the effectiveness and impact of each component of GBVSSL.

Characterizations of Minimal Dominating Sets in γ-Endowed and Symmetric γ-Endowed Graphs with Applications to Structure-Property Modeling

Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph H=(V,E). Graphs possessing the property of being 1-extendable are termedas Berge graphs. This introduction gave rise to the notion of well-covered graphs and well-dominated graphs. A graph is categorized as well-covered if each of its maximal independent sets is, in fact, a maximum independent set. Similarly, a graph attains the classification of well-dominated if every minimal dominating set (DS) within it is a minimum dominating set. In alignment with the concept of k-extendable graphs, the framework of (k,γ)-endowed graphs and symmetric (k,γ)-endowed graphs are established. In these graphs, each DS of size k encompasses a minimum DS of the graph. In this article, a study of γ-endowed dominating sets is initiated. Various results providing a deep insight into γ-endowed dominating sets in graphs such as those characterizing the ones possessing a unique minimum DS are proven. We also introduce and study the symmetric γ-endowed graphs and minimality of dominating sets in them. In addition, we give a solution to an open problem in the literature. which seeks to find a domination-based parameter that has a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the upper dominating number Γ(H) studied in this paper delivers a strong prediction potential.

DPC-DNG: Graph-based label propagation of [formula omitted]-nearest higher-density neighbors for density peaks clustering

Density peaks clustering (DPC) algorithm is a novel density-based clustering approach that effectively determines cluster centers from a decision graph and groups objects by assigning non-center objects to the same cluster as their nearest higher-density neighbor. Although DPC can allocate clusters of arbitrary shapes, its single-chain label propagation mechanism has the risk of “chain error”, where an object assigned an incorrect label causes its subordinates to also be assigned the same incorrect label. Hence, DPC is unable to effectively group objects that are located in overlapping areas between clusters, which leads to unsatisfactory clustering results. To address this issue, this study proposes the graph-based label propagation of k-nearest higher-density neighbor for density peaks clustering (DPC-DNG). DPC-DNG extends the single-chain label propagation of DPC to a graph-based multi-chain label propagation that assigns labels to objects from their k-nearest higher-density neighbors. First, based on k-nearest higher-density neighbors and the selected cluster centers, a symmetric density-based neighbor graph (DNG) is constructed. Second, to assign labels to objects, a classic graph-based label propagation mechanism is utilized in conjunction with DNG. To validate our method, we carry out comprehensive experiments on 6 synthetic and 12 real datasets. Statistically speaking, the results show that our method has improved the clustering performance of DPC and exhibits promising performance over other state-of-the-art DPC-related methods.

Covers and pseudocovers of symmetric graphs

Covers and pseudocovers of symmetric graphs

Research on the unsteady flow field and aerodynamic noise characteristics in the circular space of ultra-high-speed elevators

Due to the non-streamlined blunt body shape of the elevator car, intense aerodynamic loads and noise are generated in the annular space when the elevator operates at high speed in a narrow hoistway. This article uses large-eddy simulation and Curle acoustic theory to establish a numerical model of the wellbore flow field under different guiding shapes of the elevator car. First, the mechanism of action between the flow guide shape, vortex characteristics, and aerodynamic load was studied, and the influence of operating speed on aerodynamic load under different flow guide shapes was analyzed. Second, the distribution and spectral characteristics of noise in the annular space under different flow guide shapes were studied from the near field and far field scales. Finally, it can be concluded that increasing the guide surface can significantly reduce the pressure difference between the upper and lower parts of the car, weakening the separation of the tail airflow. The number of guide surfaces, installation position, and vertex offset significantly impact drag and lateral force, with the optimal reduction of 34.65% and 57.6%, respectively. The maximum sound source intensity of near-field noise is mainly concentrated at the arc transition in the upper part of the annular space, and the frequency is mainly concentrated in the range of 500–1000 Hz. The sound pressure level is linearly related to the logarithm of the longitudinal distance, and the noise attenuation speed becomes faster with the increase in the number of guiding surfaces.

Exploiting Symmetric Temporally Sparse BPTT for Efficient RNN Training

Recurrent Neural Networks (RNNs) are useful in temporal sequence tasks. However, training RNNs involves dense matrix multiplications which require hardware that can support a large number of arithmetic operations and memory accesses. Implementing online training of RNNs on the edge calls for optimized algorithms for an efficient deployment on hardware. Inspired by the spiking neuron model, the Delta RNN exploits temporal sparsity during inference by skipping over the update of hidden states from those inactivated neurons whose change of activation across two timesteps is below a defined threshold. This work describes a training algorithm for Delta RNNs that exploits temporal sparsity in the backward propagation phase to reduce computational requirements for training on the edge. Due to the symmetric computation graphs of forward and backward propagation during training, the gradient computation of inactivated neurons can be skipped. Results show a reduction of ∼80% in matrix operations for training a 56k parameter Delta LSTM on the Fluent Speech Commands dataset with negligible accuracy loss. Logic simulations of a hardware accelerator designed for the training algorithm show 2-10X speedup in matrix computations for an activation sparsity range of 50%-90%. Additionally, we show that the proposed Delta RNN training will be useful for online incremental learning on edge devices with limited computing resources.

On Symmetric bi-Cayley Graphs of Prime Valency on Nonabelian Simple Groups

Let $\Gamma$ be a bipartite graph, and let $\mathrm{Aut}\Gamma$ be the full automorphism group of the graph $\Gamma$. A subgroup $G\leqslant \mathrm{Aut}\Gamma$ is said to be bi-regular on $\Gamma$ if $G$ preserves the bipartition and acts regularly on both parts of $\Gamma$, while the graph $\Gamma$ is called a bi-Cayley graph of $G$ in this case. A subgroup $X\leqslant \mathrm{Aut} \Gamma$ is said to be bi-quasiprimitive on $\Gamma$ if the bipartition-preserving subgroup of $X$ is a quasiprimitive group on each part of $\Gamma$.
 In this paper, a characterization is given for the connected bi-Cayley graphs on nonabelian simple groups which have prime valency and admit bi-quasiprimitive groups.

Classifying Seven-Valent Symmetric Graphs of Order 8pq

A graph is symmetric if its automorphism group is transitive on the arcs of the graph. Guo et al. determined all of the connected seven-valent symmetric graphs of order 8p for each prime p. We shall generalize this result by determining all of the connected seven-valent symmetric graphs of order 8pq with p and q to be distinct primes. As a result, we show that for each such graph of Γ, it is isomorphic to one of seven graphs.