Symmetric Graphs Research Articles

Subducted Lithospheric Boundary Tomographically Imaged Beneath Arc‐Continent Collision in Eastern Indonesia

AbstractWe use traveltimes from a temporary seismic deployment of 30 broadband seismometers and a national catalog of arrival times to construct a finite‐frequency teleseismic P‐wave tomographic model of the upper mantle beneath eastern Indonesia, where subduction of the Indo‐Australian plate beneath the Banda Arc transitions to arc‐continent collision. The change in tectonics is due to a change from oceanic to continental lithosphere in the lower plate as inferred from geological mapping and geophysical, geochemical, and geodetic measurements. At this inferred transition, we seismically image the subducted continent‐ocean boundary at upper mantle depths that links volcanism on Flores to amagmatic orogenesis on Timor. Our tomographic images reveal a relatively high‐velocity feature within the upper mantle, which we interpret as the subducted Indo‐Australian slab. The slab appears continuous yet deformed as a result of the change in buoyancy due to the composition of the incoming continental lithosphere. Accordingly, there is a difference in dip angle between the oceanic and continental sections of the slab albeit not a gap or discontinuity. We suggest the slab has deformed without tearing to accommodate structural and kinematic changes across the continent‐ocean boundary as the two sections of the slab diverge. These results suggest that deformation in tectonic collisions can be localized along a continent‐ocean boundary, even at depth. We propose that future slab tearing may develop where we observe slab deformation in our study region and that a similar process may take place in collisions generally.

A new generalization of generalized Petersen graphs

We discuss a new family of cubic graphs, which we call group divisible generalized Petersen graphs (GDGP-graphs), that bears a close resemblance to the family of generalized Petersen graphs; both in definition and properties. The focus of our paper is on determining the algebraic properties of graphs from our new family. We look for highly symmetric graphs, e.g., graphs with large automorphism groups, and vertex- or arc-transitive graphs. In particular, we present arithmetic conditions for the defining parameters that guarantee that graphs with these parameters are vertex-transitive or Cayley, and we find one arc-transitive GDGP-graph which is neither a CQ graph of Feng and Wang, nor a generalized Petersen graph.

Lie similarity analysis of MHD flow past a stretching surface embedded in porous medium along with imposed heat source/sink and variable viscosity

The present examination is centered around the transfer of heat for the flow of a boundary layer free convective incompressible fluid, past a stretching porous surface, assuming viscosity dependent on temperature linearly along with heat source and sink with imposed magnetic field. Lie group similarity transformation is used to obtain the symmetric graphs of the given problem. Solutions for velocity and heat profile are encountered numerically with fourth-order Runga-Kutta shooting technique and graphically presented and explained the impact on velocity profile and temperature profile of several physical parameters as temperature-dependent parameter of viscosity A, k1 as parameter of permeability, Prandtl number, λas parameter of heat generation and absorption and M as parameter of magnetic field. We observed that the thermal boundary layer thickness can be reduced by increasing viscosity parameter A and heat sink parameterλ. As we give increment in k1 we find a decrement in the horizontal velocity profile, which leads to the enhanced deceleration of the flow and, hence, the velocity decreases.

Domination in Rose Window Graphs

A subset D of the vertex set of a graph $$\Gamma $$ is a dominating set for $$\Gamma $$ if each vertex of $$\Gamma $$ is either in D or has a neighbor in D. The size of a minimum cardinality dominating set of a graph is its domination number. In this paper, we initiate the study of domination in a well-known family of rather symmetric tetravalent graphs known as the Rose window graphs. We compare their domination number to the domination number of their spanning generalized Petersen subgraphs, which have been studied quite extensively in the literature.

Symmetric cubic graphs via rigid cells

Properties of symmetric cubic graphs are described via their rigid cells, which are maximal connected subgraphs fixed pointwise by some involutory automorphism of the graph. This paper completes the description of rigid cells and the corresponding involutions for each of the 17 ‘action types’ of symmetric cubic graphs.

An information-percolation bound for spin synchronization on general graphs

This paper considers the problem of reconstructing $n$ independent uniform spins $X_1,\dots,X_n$ living on the vertices of an $n$-vertex graph $G$, by observing their interactions on the edges of the graph. This captures instances of models such as (i) broadcasting on trees, (ii) block models, (iii) synchronization on grids, (iv) spiked Wigner models. The paper gives an upper-bound on the mutual information between two vertices in terms of a bond percolation estimate. Namely, the information between two vertices' spins is bounded by the probability that these vertices are connected in a bond percolation model, where edges are opened with a probability that "emulates" the edge-information. Both the information and the open-probability are based on the Chi-squared mutual information. The main results allow us to re-derive known results for information-theoretic non-reconstruction in models (i)-(iv), with more direct or improved bounds in some cases, and to obtain new results, such as for a spiked Wigner model on grids. The main result also implies a new subadditivity property for the Chi-squared mutual information for symmetric channels and general graphs, extending the subadditivity property obtained by Evans-Kenyon-Peres-Schulman [EKPS00] for trees.

A classification of tetravalent arc-transitive graphs of order 5p2

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 5p2 is given.

Combinatorial generation via permutation languages. I. Fundamentals

In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many known results and allows us to prove many new ones. In particular, we obtain four classical Gray codes for permutations, bitstrings, binary trees and set partitions as special cases. We present two distinct applications for our new framework: The first main application is the generation of pattern-avoiding permutations, yielding new Gray codes for different families of permutations that are characterized by the avoidance of certain classical patterns, (bi)vincular patterns, barred patterns, boxed patterns, Bruhat-restricted patterns, mesh patterns, monotone and geometric grid classes, and many others. We also obtain new Gray codes for all the combinatorial objects that are in bijection to these permutations, in particular for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into $n$ rectangles subject to certain restrictions. The second main application of our framework are lattice congruences of the weak order on the symmetric group $S_n$. Recently, Pilaud and Santos realized all those lattice congruences as $(n-1)$-dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc. Our algorithm generates the equivalence classes of each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian. We thus also obtain a provable notion of optimality for the Gray codes obtained from our framework: They translate into walks along the edges of a polytope.

Modeling of working environment and coverage path planning method of combine harvesters

This paper mainly studied the working environment modeling and coverage path planning of combine harvesters. The boundaries of the farmland to be harvested were extracted through the farmland satellite imagery and canny algorithm. The polygon approximation method was used to fit the extracted boundaries as polygons. The edge offset of the farmland and obstacles was realized based on the principle of straight skeleton. According to the structure data of the split points which were obtained through the improved scan line algorithm, the coverage path planning of the combine harvester was realized. Moreover, the circular arc transition algorithm was used to optimize the harvesting paths to achieve the smooth turning of the combine harvester at the edge of farmland and when encountering obstacles. The simulation results show that the proposed the proposed polygon approximation method can accurately depict the boundaries of the farmland to be harvested, and reduce the amount of data to be stored. Additionally, the designed path planning method can realize the coverage path planning of the combine harvester in irregular and internal obstacle farmland. Keywords: combine harvester, environmental modeling, path planning, farmland turning DOI: 10.25165/j.ijabe.20201302.5210 Citation: Lu E, Xu L Z, Li Y M, Tang Z, Ma Z. Modeling of working environment and coverage path planning method of combine harvesters. Int J Agric & Biol Eng, 2020; 13(2): 132–137.

Fate of Forearc Lithosphere at Arc‐Continent Collision Zones: Evidence From Local Earthquake Tomography of the Sunda‐Banda Arc Transition, Indonesia

AbstractA new 3‐D seismic P wave velocity model of the Sunda‐Banda Arc Transition from local earthquake tomography reveals (i) northward subduction of oceanic lithosphere, associated with the convergence of Australia and Sundaland, as a high‐velocity zone extending down to ~200 km depth; (ii) two distinct low‐velocity zones, one immediately above the slab, which is likely a zone of partial melt, and one in the 0–40 km depth range, which is probably a magma chamber associated with active volcanoes above; and (iii) a northerly dipping high‐velocity zone that bisects the two low‐velocity anomalies, which we interpret as an underthrust forearc sliver of continental origin. Based on He3/He4 measurements from volcanic outflows, it is possible that the magma supply is contaminated by interaction with this forearc sliver as it ascends from the melt region below.

Relocated aftershocks and background seismicity in eastern Indonesia shed light on the 2018 Lombok and Palu earthquake sequences

SUMMARYHigh seismicity rates in eastern Indonesia occur due to the complex interaction of several tectonic plates which resulted in two deadly, destructive earthquake sequences that occurred in Lombok Island and the city of Palu, Sulawesi in 2018. The first sequence began in July with an Mw 6.4 event near Lombok, culminating in an Mw 7.0 event 8 d later. This was then followed by a nearby Mw 6.9 event 12 d later. Approximately 1000 km to the northeast, a separate sequence began several weeks later near Palu where an Mw 7.5 event occurred that triggered a tsunami. In this study, we present hypocentre relocations for both earthquake sequences as well as all other regional earthquakes in eastern Indonesia. The relocations were performed using a teleseismic double-difference relocation method and arrival times for P and S waves from stations at local, regional, and teleseismic distances. The catalogue and phase data were taken from the Agency for Meteorology, Climatology and Geophysics (BMKG) of Indonesia and the International Seismological Centre (ISC) for the period of April 2009 through November 2018. The relocated catalogue provides an improved view of seismicity in eastern Indonesia over the study period, sharpening locations and interpretations of seismogenic features throughout the region. In the Lombok area, the relocated earthquakes clearly show a backarc thrust to the north of the Sunda-Banda Arc transition zone. The relocated aftershocks show that the destructive Mw 7.0 and Mw 6.9 earthquakes of the Lombok sequence ruptured two different regions: The Mw 7.0 earthquake propagated westward, whereas the Mw 6.9 earthquake propagated eastward. The entire sequence of Lombok earthquakes was most likely started by the Mw 6.4 event as the initial event or foreshock, which then triggered backarc thrusts on both sides. Several weeks later and far to the northeast, the Mw 7.5 Palu earthquake occurred along the Palu-Koro Fault, filling a seismic gap that had not ruptured in an Mw 6.0 event or larger since at least 1900. The distribution of aftershocks indicates that the northern part of the Palu-Koro Fault has lower relative seismicity rates than the southern part at shallow depths, and that off fault aftershocks are mostly located to the east of the Palu-Koro Fault.

Devonian bimodal volcanic rocks from the northeastern margin of the North China Block: Implications for post‐collisional extension and orogen‐craton boundary

Devonian is a critical period for reversal of arc polarity and transition of continental margins from passive to active settings in the northern margin of the North China Block (NCB). However, the evolution processes during this period are still poorly constrained due to limited distributions of Devonian magmatism and sedimentary records in the NCB. In this paper, we present new zircon U–Pb geochronological, whole‐rock geochemical and Sr–Nd–Hf isotopic data of some recently identified Devonian volcanic rocks from the Jiefangyingzi area in the northeastern margin of the NCB. The Jiefangyingzi volcanic rocks display a bimodal composition and consist predominantly of amphibolite (meta‐basaltic andesite) and meta‐rhyolite and rhyolitic tuff with minor meta‐andesite. New SHRIMP and LA‐ICP‐MS zircon U–Pb dating results show that the volcanic rocks erupted during the early‐middle Devonian period (397–389 Ma). Geochemical and Sr–Nd–Hf isotopic data indicate that the mafic‐intermediate components were mainly derived from an enriched lithospheric mantle source, and the parental magma experienced fractional crystallization during magma ascent. The felsic rocks were mainly originated by partial melting of ancient lower continental crust, with mixing of some mantle‐derived mafic magmas. The occurrence of Devonian bimodal volcanic rocks, combined with the Devonian alkaline magmatic belt, suggesting that the northern margin of the NCB was a post‐collisional extension environment during the early‐middle Devonian period. In addition, the Sr–Nd–Hf isotopic results of the Devonian felsic volcanic rocks suggest that the Jiefangyingzi area is located in the North China Craton (NCC) rather than the Bainaimiao arc belt, and the orogen‐craton boundary between the northern NCC and Central Asian Orogenic Belt (CAOB) is located in some areas north to the Jiefangyingzi area.

Extended symmetric spaces and θ-twisted involution graphs

For a Weyl group G and an automorphism θ of order 2, the set of involutions and θ-twisted involutions can be generated by considering actions by basis elements, creating a poset structure on the elements. Haas and Helminck showed that there is a relationship between these sets and their Bruhat posets. We extend that result by considering other bases and automorphisms. We show for G = Sn, θ an involution, and any basis consisting of transpositions, the extended symmetric space is generated by a similar algorithm. Moreover, there is an isomorphism of the poset graphs for certain bases and θ.

Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs

In this paper, we study eigenvalues and eigenfunctions of p-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of p-Laplacian, as p→1, we identify the Cheeger constant of a symmetric graph with that of the quotient graph. By this approach, we calculate various Cheeger constants of spherically symmetric graphs.

Non-Negative Symmetric Low-Rank Representation Graph Regularized Method for Cancer Clustering Based on Score Function.

As an important approach to cancer classification, cancer sample clustering is of particular importance for cancer research. For high dimensional gene expression data, examining approaches to selecting characteristic genes with high identification for cancer sample clustering is an important research area in the bioinformatics field. In this paper, we propose a novel integrated framework for cancer clustering known as the non-negative symmetric low-rank representation with graph regularization based on score function (NSLRG-S). First, a lowest rank matrix is obtained after NSLRG decomposition. The lowest rank matrix preserves the local data manifold information and the global data structure information of the gene expression data. Second, we construct the Score function based on the lowest rank matrix to weight all of the features of the gene expression data and calculate the score of each feature. Third, we rank the features according to their scores and select the feature genes for cancer sample clustering. Finally, based on selected feature genes, we use the K-means method to cluster the cancer samples. The experiments are conducted on The Cancer Genome Atlas (TCGA) data. Comparative experiments demonstrate that the NSLRG-S framework can significantly improve the clustering performance.

Local Peaks-Based Clustering Algorithm in Symmetric Neighborhood Graph

Density-based clustering methods have achieved many applications in data mining, whereas most of them still likely suffer poor performances on data sets with extremely uneven distributions, like the manifold or ring data. The paper proposes a novel method for clustering with local peaks in the symmetric neighborhood. Local peaks are points with maximum densities at the local level. During the searching of local peaks, all data, except those outliers, can be easily divided into a number of small clusters in accordance with the local peaks in each point's neighborhood. Especially, a graph-based scheme is adopted here to merge similar clusters based on their similarity in the symmetric neighborhood graph, followed by assigning each outlier to the closest cluster. A variety of artificial, real data sets and a real building data set have been tested for clustering by the proposed method and compared against other popular density-based methods and other algorithms.

阶为8p<sup>2</sup>的5度对称图

阶为8p<sup>2</sup>的5度对称图

On Mixed Metric Dimension of Rotationally Symmetric Graphs

A vertex $u\in V(G)$ resolves (distinguish or recognize) two elements (vertices or edges) $v,w\in E(G) \cup V(G)$ if $d_{G}(u,v)\neq d_{G}(u,w)$ . A subset $L_ {\textrm {m}}$ of vertices in a connected graph $G$ is called a mixed metric generator for $G$ if every two distinct elements (vertices and edges) of $G$ are resolved by some vertex set of $L_ {\textrm {m}}$ . The minimum cardinality of a mixed metric generator for $G$ is called the mixed metric dimension and is denoted by $dim_{m}(G)$ . In this paper, we studied the mixed metric dimension for three families of graphs $\mathcal {D}_{n}$ , $\mathcal {A}_{n}$ , and $\mathcal {R}_{n}$ , known from the literature. We proved that, for $\mathcal {D}_{n}$ the $dim_{m}(\mathcal {D}_{n})=dim_{e}(\mathcal {D}_{n})=dim(\mathcal {D}_{n})$ , when $n$ is even, and for $\mathcal {A}_{n}$ the $dim_{m}(\mathcal {A}_{n})=dim_{e}(\mathcal {A}_{n})$ , when $n$ is even and odd. The graph $\mathcal {R}_{n}$ has mixed metric dimension 5.

阶为8p<sup>2</sup>的7度对称图

阶为8p<sup>2</sup>的7度对称图

Graph Simplification-Aided ADMM for Decentralized Composite Optimization.

In this article, we consider the problem of decentralized composite optimization over a connected and symmetric graph, in which each node holds its own agent-specific private convex functions, and communications are only allowed between nodes with direct links. A variety of algorithms has been proposed to solve such a problem in an alternating direction method of multiplier (ADMM) framework. Many of these algorithms, however, need to include some extra proximal term in the augmented Lagrangian function such that the resulting algorithm can be implemented in a decentralized manner. The use of the extra proximal term slows down the convergence speed because it forces the current solution to stay close to the solution obtained in the previous iteration. To address this issue, in this article, we first introduce the notion of simplest bipartite graph, which is defined as a bipartite graph that has a minimum number of edges to keep the graph connected. A simple two-step message passing-based procedure is proposed to find a simplest bipartite graph associated with the original graph. We show that the simplest bipartite graph has some interesting properties. By utilizing these properties, an ADMM without involving extra proximal terms can be developed to perform decentralized composite optimization over the simplest bipartite graph. The simulation results show that our proposed method achieves a much faster convergence speed than the existing state-of-the-art decentralized algorithms.