Symmetric Graphs Research Articles

Topological Filtering of Dynamic Functional Brain Networks Unfolds Informative Chronnectomics: A Novel Data-Driven Thresholding Scheme Based on Orthogonal Minimal Spanning Trees (OMSTs).

The human brain is a large-scale system of functionally connected brain regions. This system can be modeled as a network, or graph, by dividing the brain into a set of regions, or “nodes,” and quantifying the strength of the connections between nodes, or “edges,” as the temporal correlation in their patterns of activity. Network analysis, a part of graph theory, provides a set of summary statistics that can be used to describe complex brain networks in a meaningful way. The large-scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory. The adaptation of both bivariate (mutual information) and multivariate (Granger causality) connectivity estimators to quantify the synchronization between multichannel recordings yields a fully connected, weighted, (a)symmetric functional connectivity graph (FCG), representing the associations among all brain areas. The aforementioned procedure leads to an extremely dense network of tens up to a few hundreds of weights. Therefore, this FCG must be filtered out so that the “true” connectivity pattern can emerge. Here, we compared a large number of well-known topological thresholding techniques with the novel proposed data-driven scheme based on orthogonal minimal spanning trees (OMSTs). OMSTs filter brain connectivity networks based on the optimization between the global efficiency of the network and the cost preserving its wiring. We demonstrated the proposed method in a large EEG database (N = 101 subjects) with eyes-open (EO) and eyes-closed (EC) tasks by adopting a time-varying approach with the main goal to extract features that can totally distinguish each subject from the rest of the set. Additionally, the reliability of the proposed scheme was estimated in a second case study of fMRI resting-state activity with multiple scans. Our results demonstrated clearly that the proposed thresholding scheme outperformed a large list of thresholding schemes based on the recognition accuracy of each subject compared to the rest of the cohort (EEG). Additionally, the reliability of the network metrics based on the fMRI static networks was improved based on the proposed topological filtering scheme. Overall, the proposed algorithm could be used across neuroimaging and multimodal studies as a common computationally efficient standardized tool for a great number of neuroscientists and physicists working on numerous of projects.

Neutralization of charged dielectric materials using a dielectric barrier discharge

Safety and efficiency are two characteristics that must be satisfied by an electric charge neutralizer. The dielectric barrier discharge (DBD), which has the advantage of preventing arc transition, is an interesting tool to safely neutralize unwanted charge. This paper is aimed at studying the efficiency of neutralizing charged polyethylene (PE) granules by using a dielectric barrier discharge. During this study, several factors were considered such as the amplitude and the frequency of the AC voltage, the polarity and the charging mode of the samples, as well as the electrode configuration. Two DBD electrode configurations were considered: simple DBD and a DBD with installed metallic grid. The obtained results show that using the DBD can lead to excellent neutralization results when the grid is installed. With the appropriate voltage amplitude and frequency and with grid installed, the elimination of nearly 99% of the initial surface charges can be achieved. The metallic grid placed between the DBD electrode and the target enhances significantly the neutralization efficiency.

Pentavalent symmetric graphs admitting vertex-transitive non-abelian simple groups

A graph Γ is said to be symmetric if its automorphism group Aut(Γ) is transitive on the arc set of Γ. Let G be a finite non-abelian simple group and let Γ be a connected pentavalent symmetric graph with G≤Aut(Γ). In this paper, we show that if G is transitive on the vertex set of Γ, then either G⊴Aut(Γ) or Aut(Γ) contains a non-abelian simple normal subgroup T such that G≤T and (G,T) is one of 58 possible pairs of non-abelian simple groups. In particular, if G is transitive on the arc set of Γ, then (G,T) is one of 17 possible pairs, and if G is regular on the vertex set of Γ, then (G,T) is one of 13 possible pairs, which improves the result on pentavalent symmetric Cayley graph given by Fang, et al. (2011).

On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs

On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs

On automorphisms of distance-regular graphs with intersection arrays {2r + 1, 2r − 2, 1; 1, 2, 2r + 1}

Let Γ be an antipodal graph with intersection array {2r+1, 2r−2, 1; 1, 2, 2r+1}, where 2r(r + 1) ≤ 4096. If 2r + 1 is a prime power, then Mathon’s scheme provides the existence of an arc-transitive graph with this intersection array. Note that 2r + 1 is not a prime power only for r ∈ {7, 17, 19, 22, 25, 27, 31, 32, 37, 38, 42, 43}. We study automorphisms of hypothetical distance-regular graphs with the specified values of r. The cases r ∈ {7, 17, 19} were considered earlier. We prove that, if Γ is a vertex-symmetric graph with intersection array {2r + 1, 2r − 2, 1; 1, 2, 2r +1}, 2r + 1 is not a prime power, and r ≤ 43, then r = 25, 27, or 31.

Study on 2-D Crustal Shear Wave Splitting Tomography along The Sunda-Banda Arc Transition Zone

The Sunda-Banda Arc transition zone is an active region characterized by a change in tectonic regime from subduction of Indo-Australia oceanic lithosphere along the eastern part of Sunda Arc to collision of the Australian continental crust with islands arc in the western part of the Banda Arc. This complicated tectonic setting causes this area is an ideal place to study the crustal deformation along the plate boundary. The density contrast between the Australian continental crust and Indo-Australia oceanic crust in the transition zone may cause large stresses around the boundary between them. These plate boundary forces may control the distribution pattern of the deformation in the subduction to collision transition zone. The geometry of this deformation can be investigated using shear wave splitting (seismic anisotropy) study. We conduct shear wave splitting measurements from local earthquakes recorded at 17 broadband seismic stations around the Sunda-Banda arc transition zone. The 2D delay time tomography is then applied to determine the first order approximation of lateral varying anisotropic layers due to the local effect of geological structures. We observe strong anisotropy regions which coincide with the geological features as possible causes of anisotropy in the Sunda-Banda Arc transition zone. For instance, the high anisotropy zone found in Timor Island can be related to the alignment of metamorphic and igneous rocks, whereas the high anisotropy area around Sumba Island might correspond to the interaction of Sumba basement with the Australian margin increasing the frictional strength at the plate boundary.

THE TWO-ARC-TRANSITIVE GRAPHS OF SQUARE-FREE ORDER ADMITTING ALTERNATING OR SYMMETRIC GROUPS

Let $G$ be a finite group with $\mathsf{soc}(G)=\text{A}_{c}$ for $c\geq 5$. A characterization of the subgroups with square-free index in $G$ is given. Also, it is shown that a $(G,2)$-arc-transitive graph of square-free order is isomorphic to a complete graph, a complete bipartite graph with a matching deleted or one of $11$ other graphs.

Distributed methods for synchronization of orthogonal matrices over graphs

This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization problem. The latter is stable for small step sizes when the graph is quasi-strongly connected. The proposed methods are verified in numerical simulations.

Establishing symmetric connectivity in directional wireless sensor networks equipped with $$2\pi /3$$ 2 π / 3 antennas

In this paper, we study the antenna orientation problem concerning symmetric connectivity in directional wireless sensor networks. We are given a set of nodes each of which is equipped with one directional antenna with beam-width $$\theta = 2\pi /3$$ and is initially assigned a transmission range 1 that yields a connected unit disk graph spanning all nodes. The objective of the problem is to compute an orientation of the antennas and to find a minimum transmission power range $$r=O(1)$$ such that the induced symmetric communication graph is connected. We propose two algorithms that orient the antennas to yield symmetric connected communication graphs where the transmission power ranges are bounded by 6 and 5, which are currently the best results for this problem. We also study the performance of our algorithms through simulations.

On tetravalent symmetric dihedrants

Let Γ be a tetravalent X-arc-transitive Cayley graph of dihedral group for X ≤ AutΓ. Let Xv be the stabilizer of X on v ∈ VΓ. Γ has been determined when it is 2-arc-transitive or one-regular. This paper studies the case where Γ is one-transitive but not one-regular, and gives it an exactly characterization. As an application of this result, we give a compete classification of such graphs when |Xv| ≤ 24. By production, a compete classification is given for the stabilizers of tetravalent symmetric Cayley graphs whenever its order is less than 25.

Image feature representation with orthogonal symmetric local weber graph structure

Image feature representation is a hot topic in the computer vision field. Inspired by Weber's law and local graph structure (LGS), we propose a novel image feature representation descriptor, called orthogonal symmetric local weber graph structure (OSLWGS). It contains two components: differential excitation pattern (DEP) and orthogonal symmetric LGS (OSLGS). In particular, DEP is extended by bringing difference of Gaussian (DoG), which can make OSLWGS robust to image noise. In addition, OSLGS can overcome some defects of LGS including non-symmetric and single horizontal structure problems. Furthermore, 2D OSLWGS histogram is generated by fusing DEP and OSLGS to improve the discriminative power and obtain more precise image description. And then, it is further encoded into 1D histogram and classified via sparse representation. Extensive experiments on FERET, CMUPIE, LFW, Yale B, simulated YALE partial occlusion, RawFooT and PhoTex databases validate the effectiveness of the proposed OSLWGS. Experimental results demonstrate that the proposed algorithm is an efficient and robust method compared with some state-of-the-art approaches.

Affine primitive symmetric graphs of diameter two

Let n be a positive integer, q be a prime power, and V be a vector space of dimension n over F q . Let G := V rtimes G 0 , where G 0 is an irreducible subgroup of G L ( V ) which is maximal by inclusion with respect to being intransitive on the set of nonzero vectors. We are interested in the class of all diameter two graphs Γ that admit such a group G as an arc-transitive, vertex-quasiprimitive subgroup of automorphisms. In particular, we consider those graphs for which G 0 is a subgroup of either Γ L(n,q) or Γ Sp( n , q ) and is maximal in one of the Aschbacher classes C i , where i ∈ {2, 4, 5, 6, 7, 8} . We are able to determine all graphs Γ which arise from G 0 ≤ Γ L( n , q ) with i ∈ {2, 4, 8} , and from G 0 ≤ Γ Sp( n , q ) with i ∈ {2, 8} . For the remaining classes we give necessary conditions in order for Γ to have diameter two, and in some special subcases determine all G -symmetric diameter two graphs.

Symmetric Graphs with Respect to Graph Entropy

Let $F_G(P)$ be a functional defined on the set of all the probability distributions on the vertex set of a graph $G$. We say that $G$ is symmetric with respect to $F_G(P)$ if the uniform distribution on $V(G)$ maximizes $F_G(P)$. Using the combinatorial definition of the entropy of a graph in terms of its vertex packing polytope and the relationship between the graph entropy and fractional chromatic number, we characterize all graphs which are symmetric with respect to graph entropy. We show that a graph is symmetric with respect to graph entropy if and only if its vertex set can be uniformly covered by its maximum size independent sets. This is also equivalent to saying that the fractional chromatic number of $G$, $\chi_f(G)$, is equal to $\frac{n}{\alpha(G)}$, where $n = |V(G)|$ and $\alpha(G)$ is the independence number of $G$. Furthermore, given any strictly positive probability distribution $P$ on the vertex set of a graph $G$, we show that $P$ is a maximizer of the entropy of graph $G$ if and only if its vertex set can be uniformly covered by its maximum weighted independent sets. We also show that the problem of deciding if a graph is symmetric with respect to graph entropy, where the weight of the vertices is given by probability distribution $P$, is co-NP-hard.

Pentavalent symmetric graphs of order 16p

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.

Aggressive Spiral Toolpaths for Pocket Machining Based on Medial Axis Transformation

High-speed machine tools typically provide high spindle speeds and feedrates to achieve an effective material removal rate (MRR). However, it is not possible to realize the full extent of their high-speed capabilities due to the sharp corners of toolpaths which are introduced by conventional machining strategies, such as contour- and direction-parallel toolpaths. To address this limitation, spiral toolpaths that can reduce the magnitude of sudden direction changes have been developed in previous researches. Nevertheless, for some pockets, the average radial cutting width is significantly decreased while the total length of the toolpath is significantly increased as compared to contour- and direction-parallel toolpath. In this situation, spiral toolpath may take more machining time. To overcome these drawbacks, an aggressive spiral toolpath generation method based on the medial axis (MA) transformation is proposed in machining pocket without islands inside, which refers to no additional material inside the counter. The salient feature of this work is that it integrates the advantages of both conventional contour-parallel machining strategy and the existing spiral toolpath machining strategy. The cutting width at each MA point is determined based on the diameter of the locally inscribed circle (LIC) of the MA point and the topological structure of MA. A distance-constrained contour determination algorithm is utilized to calculate the toolpath for each pass. Finally, a circular arc transition strategy is used to transform all the isolated passes into a spiral toolpath. Experiments are conducted to show the effectiveness of the proposed method.

Finite 2‐Distance Transitive Graphs

AbstractA noncomplete graph Γ is said to be (G, 2)‐distance transitive if G is a subgroup of the automorphism group of Γ that is transitive on the vertex set of Γ, and for any vertex u of Γ, the stabilizer is transitive on the sets of vertices at distances 1 and 2 from u. This article investigates the family of (G, 2)‐distance transitive graphs that are not (G, 2)‐arc transitive. Our main result is the classification of such graphs of valency not greater than 5. We also prove several results about (G, 2)‐distance transitive, but not (G, 2)‐arc transitive graphs of girth 4.

关于弧传递Cayley图的判定

1938年R. Fruchet证明了对于任意给定的抽象群，都存在一个图以它为自同构群。自此，关于利用群来研究图这一领域，揭开了帷幕。但是，这个领域的广泛研究则是从1960年才真正开始的，尤其是最近30年，在这方面完成了很多重要的工作。本文主要研究了图论的一个分支，即：Cayley图以及它的判定，尤其是弧传递Cayley图的判定。首先，通过研究图的性质以及群的交换性，从而得出本文的主要定理。其次，根据正规弧传递Cayley图的定义以及主要结论的推导过程，得出了一个关于正规弧传递Cayley图的判定条件。 In 1938, R. Fruchet proved that for any given abstract group, there is a graph of it as an automorphism group. Since then, this area, which is about using the groups to study the graphs, opened the curtain. However, extensive research in this area began in 1960, especially in the last 30 years, where a number of important tasks were done. In this paper, we study a branch of graph theory that is, Cayley graph and its decision, especially the arc transitive graph. Firstly, by studying the properties of graph and the exchange of group, we get the main theorem of this paper. Secondly, according to the definition of the normal arc transitive graph and the pushing process of the main conclusion, a judgment condition of the normal arc transitive graph is given.

Large-scale DCMs for resting-state fMRI.

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity. This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.

Arc-transitive cyclic covers of graphs with order twice a prime

Arc-transitive cyclic covers of symmetric graphs with a specific prime valency and order twice a prime have been studied by nearly ten papers in the literature. In this paper, we will give a general characterization of arc-transitive cyclic covers of graphs with any prime valency and order twice a prime.

Crustal Structure Along Sunda-Banda Arc Transition Zone from Teleseismic Receiver Functions

We analyzed receiver function of teleseismic events recorded at twelve Indonesian-GEOFON (IA-GE) broadband stations using nonlinear Neighbourhood Algorithm (NA) inversion and H-k stacking methods to estimate crustal thickness, Vp/Vs ratios and S-wave velocity structure along Sunda-Banda arc transition zone. We observed crustal thickness of 34–37 km in Timor Island, which is consistent with the previous works. The thick crust (> 30 km) is also found beneath Sumba and Flores Islands, which might be related to the arc-continent collision causing the thickened crust. In Timor and Sumba Islands, we observed high Vp/Vs ratio (> 1.84) with low velocity zone that might be associated with the presence of mafic and ultramafic materials and fluid filled fracture zone. The high Vp/Vs ratio observed at Sumbawa and Flores volcanic Islands might be an indication of partial melt related to the upwelling of hot asthenosphere material through the subducted slab.