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• Theoretical mechanism of the non-uniqueness optimal solution for cross-efficiency is revealed. • Weight priority is constructed to reflect the comparative advantage of inputs and outputs. • Weight priority strategy can serve as both an independent strategy and a supplementary strategy. • The uniqueness of optimal result obtained by weight priority strategy is theoretically proved. Due to a large number of studies on cross-evaluation strategies, the theoretical problem of DEA cross-efficiency approach has been transformed from the non-uniqueness of the optimal solution to the relative uniqueness, because the existing cross-evaluation strategies can only reduce the possibility of non-unique solutions, but cannot prove the existence of a unique optimal solution. This paper illustrates the relative uniqueness of optimal solution of the cross-efficiency approach with traditional cross-evaluation strategies, and the graphic method and theoretical analysis are used to explain the reasons of relative uniqueness. Based on the data characteristic of inputs and outputs, the weight priority rule is made for constructing the new cross-evaluation strategy, and its optimal solution is proved to be unique. In addition, the weight priority strategy can also be introduced into traditional strategies as a supplementary strategy, and then the unique optimal solution can be obtained on the premise of preserving the characteristics of traditional strategies. In general, this paper solves the non-uniqueness and relative uniqueness problem of optimal solution in the DEA cross-efficiency approach, and then the reliability and robustness of the approach are thus improved. [ABSTRACT FROM AUTHOR]

In this paper we present a scalable approach based on the latency-based linear multistep compound method to use graphic processing unit (GPU) to accelerate the power system simulations with electromagnetic transients. To balance between the computational load and accuracy, we modeled the power system using shifted frequency analysis. Then, to efficiently exploit the hardware, our computational approach is designed to utilize both data-parallel and task-parallel execution. In addition, a graph-based thread safety design is introduced to achieve high scalability in the paralleled component computations. Furthermore, our implementation introduces a translation layer for different heterogeneous computing frameworks during compile time, so that a wide range of GPU devices can be supported without losing performance. Finally, benchmark results show that our approach achieves faster-than-real-time capability for systems with hundreds to thousands of nodes. [Display omitted] • Exploits data- and task-parallelism together in an automated way. • A graph-based approach to ensure thread safety to increase scalability. • A compile-time translation layer to allow execution on various platforms. • Faster-than-real-time for system with more than 10,000 dynamic components. • 82 × faster compared to an optimized sequential simulation. [ABSTRACT FROM AUTHOR]

Vitrinite reflectance (R o) is a significant geological index that evaluates the thermal maturity of source rock. However, measured R o data and suitable evaluation methods are lacking, making it difficult to predict the thermal maturity of source rock in basin, especially in those with a low exploration degree. In this study, we propose a novel method for estimating R o from well logs and seismic data using seismic velocity inversion and the vitrinite reflectance-mudstone porosity (R o - ϕ) model. First, using a wavelet neural network, acoustic transit time curve was reconstructed from spontaneous potential, gamma rays, resistivity, and density logs, and new curve was used as inputs in a colored inversion to obtain seismic relative velocity. Second, a low-frequency model was established to counteract critical frequency and sequence framework constraints. Third, the seismic absolute velocity was merged by relative and low-frequency velocity components. Finally, R o distributions were calculated using the R o - ϕ model. Our findings indicate that the inversion effect improved with low-frequency supplement; compared with the graphic and geochemical method, the R o - ϕ model predicted R o in poor-data areas more accurately, with a relative error of <9.5205%. We also propose an explanation for the appearance of highly mature source rocks distributed from dispersion to aggregation in depression-rift transitions: the thick stratum in the downthrow wall of boundary faults promote source rock maturity in the rift period; hence, in an open depression, the source rocks in large subsidence areas are highly mature, particularly near the downthrow wall of a boundary fault, which has the highest maturity owing to the superimposed subsidence of the overlying rifted basin. • Set a novel method for predicting thermal maturity of source rock. • Use WNN model for reconstructing AC curve to identify complex lithologies. • Obtain seismic absolute velocity by merging medium-high and low frequency velocity. • Derive a theoretical R o - ϕ model to predict R o from seismic absolute velocity. • Establish a new mode to explain R o distribution in depression-rift transition basin. [ABSTRACT FROM AUTHOR]

Aldehydes are carbonyl compounds that are highly reactive and extensively abundant in nature. Aldehydes are biomarkers for oxidative stress-linked disorders since they are formed as a result of oxidative processes. Aldehydes may occur in food as a result of food processing or degradation, and their level has been utilized as a guide of food quality level. Therefore, aldehydes are identified in biological and food samples as illness indicators and as by-products of food manufacturing, respectively. Among analytical methodologies, chromatographic methods are the most used for the simultaneous determination of various aldehydes. However, chromatographic methods consume a lot of harmful organic solvents and reagents. Hence, herein, a comprehensive greenness evaluation of the reported chromatographic methods for aldehydes has been conducted using AGREE—Analytical GREEnness Metric. This review helps to recommend those methods that are eco-friendly to be further used for the assay of aldehydes in versatile samples. [Display omitted] • AGREE was applied to assess the greenness of the reported methods for aldehydes determination. • A comparison was conducted based on the 12 input variables of AGREE. • Different derivatization agents for aldehydes and their analytical application were discussed. • Weaknesses and strength points were highlighted within the framework of greenness. • Recommendations were emphasized for empowering analytical methods' greenness. [ABSTRACT FROM AUTHOR]

Background: Research so far provided few clues on the order in which depressive symptoms typically remit during treatment. This study examined which depressive symptoms improve first, and whether symptoms changed before, simultaneous with, or after the core symptoms of depression (i.e., sad mood, loss of pleasure, and loss of interest).Methods: Participants were 176 patients with Major Depressive Disorder (MDD) receiving outpatient treatment (a combination of pharmacotherapy and psychological interventions) for depression. Participants filled out the Inventory of Depressive Symptomatology - Self Report (IDS-SR) for 16 to 20 consecutive weeks. For each symptom, the timing of onset of a persistent improvement was determined for each single-subject separately.Results: Which symptoms improved first differed markedly across patients. The core depression symptoms improved 1.5 to 2 times more often before (48% - 60%) than after (19% -28%) depressive cognitions ('view of myself' and 'view of the future'), anxiety symptoms ('feeling irritable' and 'feeling anxious / tense') and vegetative symptoms ('loss of energy', 'slowed down', and 'physical energy'). Only improvements in suicidal thoughts were more likely to occur before (46% - 48%) than after (29%) improvements in the depression core symptoms.Limitations: Not all 'core depression-non-core symptom' combinations could be tested because some symptoms did not improve in a sufficient number of patients.Conclusions: Which improvements mark the start of symptom remission differed between patients. Improvements in the core depression symptoms 'sad mood', 'loss of interest', and 'loss of pleasure' were more likely to occur before than after improvements in non-core symptoms. [ABSTRACT FROM AUTHOR]

The network of energy pipelines is extremely important for the proper functioning of a modern society. Even though measurement instruments and sensors are currently widely used to monitor the network's operational status in real time, it is expensive to deploy these extra devices for a large city-scale network. Numerical simulation of fluid networks offers a rather easy and effective technique to track the work performance of pipelines. Because of the computational intensiveness of the pipeline network, it is most suitable to deploy such a massive simulation program on a supercomputer with a parallel technique. The performance of this kind of parallel simulation may undoubtedly be enhanced if the pipeline network is reasonably divided into several subnetworks in which the fluid flows are resolved independently. In this paper, we concentrate on how to achieve a computationally balanced subnetwork partition scheme and propose an acceleration method for energy pipeline network simulations based on a graph partition algorithm. In our approach, each node of the network takes part in the decision of dividing the entire network by learning the weight of its neighbors. Moreover, we utilize graph-tree transformations to merge locally related components as much as possible, and together with subgraph rebalancing, the pipeline network division quality is improved considerably. Numerical simulations show that our approach is much better than others for the degree of balance, and the cut edge ratio is also lower than others when it is compared with the random, k -means, and METIS methods. • Proposal of a novel graph partitioning algorithm based on node self-learning. • A periphery-to-center graph reduction method minimizing the number of cut edges. • A technique of weighted quadratic relaxation to adjust the part balance in k -GP. • Discussion of the impact of k -GP algorithms on EPN simulation performance. [ABSTRACT FROM AUTHOR]

Hydrogen sulfide (H 2 S) is currently considered among the endogenously produced gaseous molecules that exert various signaling effects in mammalian species. It is the third physiological gasotransmitter discovered so far after NO and CO. H 2 S was originally ranked among the toxic gases at elevated levels to humans. Currently, it is well-known that, in the cardiovascular system, H 2 S exerts several cardioprotective effects including vasodilation, antioxidant regulation, inhibition of inflammation, and activation of anti-apoptosis. With an increasing interest in monitoring H 2 S, the development of analysis methods should now follow. This review stages special emphasis on the several analytical technologies used for its determination including spectroscopic, chromatographic, and electrochemical methods. Advantages and limitations with regards to the application of each technique are highlighted with special emphasis on its employment for H 2 S in vivo measurement i.e., biofluids, tissues. Fluorescence methods applied for H 2 S measurement offer an attractive non-invasive and promising approach in addition to its selectivity, however they cannot be considered as H2S-specific probes. On the other hand, colorimetric assays are among the most common methods used for in vitro H 2 S detection, albeit their employment in vivo H 2 S measurement has not yet been possible. Separation techniques such as gas or liquid chromatography offer higher selectivity compared to direct spectrophotometric or fluorescence methods especially for suitable for endpoint H 2 S measurements i.e. plasma or tissue samples. Despite all the developed analytical procedures used for H 2 S determination, the need for highly selective, much work should be devoted to resolve all the pitfalls of the current methods. [ABSTRACT FROM AUTHOR]

• APCP game for addressing collaborative patrolling problem cost-effectively in a large-scale chemical cluster is proposed. • The static partitioning method is applied to realize the collaboration of patrollers. • The greedy deployment algorithm is proposed for determining the initial deployment of patrollers. • Results on three actual scenarios show the feasibility of the APCP game by reducing up to 25.48% of the patrolling costs. Terrorists often take the chemical clusters as the attacking target because of the adverse impacts of a chemical accident on society and the environment. In addition to some fixed countermeasures, previous studies have verified the feasibility of a patrol in addressing adversarial attacks. However, the previous patrolling practices fail to tackle the terrorist attacking problems in a large-scale area cost-effectively. To further tackle the protection issue with cost-beneficial solutions in a large-scale scenario, i.e., in a chemical cluster, we propose an area-partition-involved collaborative patrolling (APCP) game. We first leverage the proposed greedy deployment algorithm to determine the initial deployment of defenders (patrollers), including the quantity and position of patrol vehicles. Then, the large-scale area is partitioned into multiple smaller areas by using the collaborative idea of static partitioning. In the meantime, corresponding patrolling graphs are constructed based on graphic modeling methods. Finally, the APCP game is built between patrol vehicles (namely defender) and potential terrorists (namely attacker), in which patrol vehicles aim at detecting attack behaviors of terrorists by intelligently scheduling the patrolling routes. After formalizing the problem into a sequential game, we compute the Stackelberg equilibrium through the MultiLPs algorithm. Through case studies of three practical chemical cluster scenarios, the results explicitly show the superiority of our proposed APCP game by saving up to 25.48 % patrolling costs in a one-shot game compared to the results before partition. As for the collaborative patrolling problem in a large-scale area, the methods and models proposed in this paper can facilitate the management department of chemical clusters with intelligently scheduled patrolling routes, which can effectively reduce the cost of patrollers, and better protect the chemical cluster. [ABSTRACT FROM AUTHOR]

Mission analysis using aerogravity-assist (AGA) maneuver at Titan is presented in this paper. Considering Saturn arrival, Titan encounter, and different post-AGA orbits, the analysis uses vector diagrams to illustrate the relations among all conditions as well as design constraints. The analysis focuses on Enceladus mission concept and also present a summary result for Cassini-type Saturn system missions. Turn angles using AGA maneuver at Titan are quantified via numerical simulation, showing that 25-deg AGA turn angles are achievable with a Titan inbound excess velocity (V ∞ , IN ) of 10–20 km/s. Results show that for an Enceladus mission, V ∞ , IN of 10 km/s is the minimum velocity required for AGA maneuver to achieve an outbound transfer orbit directly to Enceladus; the corresponding peak g-load is less than 6 g, peak heat rate less than 200 W/cm2, and total heat load of around 25 kJ/cm2. For a Cassini-type Saturn mission, a minimum V ∞ , IN of 5 km/s can be used for Titan AGA. The results showed are for V ∞ , IN of 6 km/s; and the corresponding peak g-load, peak heat rate, and total heat load are 1.5 g, 20 W/cm2, and 5 kJ/cm2 respectively. • Design space for Saturn system missions using Titan aerogravity-assist is fully explored. • A novel method combining graphic approach using vector diagrams and numerical simulation is presented. • Readiness of entry vehicles and TPS technologies for using Titan aerogravity-assist maneuver is evaluated. [ABSTRACT FROM AUTHOR]

Let S be a set of at least two vertices in a graph G. A subtree T of G is an S -Steiner tree if S ⊆ V (T). Two S -Steiner trees T 1 and T 2 are internally disjoint (resp. edge-disjoint) if E (T 1) ∩ E (T 2) = 0̸ and V (T 1) ∩ V (T 2) = S (resp. E (T 1) ∩ E (T 2) = 0̸). Let κ G (S) (resp. λ G (S)) be the maximum number of internally disjoint (resp. edge-disjoint) S -Steiner trees in G , and let κ k (G) (resp. λ k (G)) be the minimum κ G (S) (resp. λ G (S)) for S ranges over all k -subsets of V (G). It is well-known that the connectivity of the line graph of a graph G is closely related to the edge-connectivity of G. Chartrand et al., Li et al., and Li et al. showed that κ k (L (G)) ≥ λ k (G) for k = 2 , 3 , 4 , respectively. In [Discrete Math. 341(2018), 1945–1951.], Li et al. also proposed the following conjecture: κ k (L (G)) ≥ λ k (G) for integer k ≥ 2 and a graph G with at least k vertices. In this paper, we show that κ k (L (G)) ≥ λ k (G) − m a d (G) 2 2 for general k , where m a d (G) is the maximum average degree of a graph G. We also show that κ k (L (G)) ≥ λ k (G) − r 2 2 for any integers k and r such that k ≤ r 2 . Finally, we show that the conjecture holds for k = 5 , and the conjecture holds for the wheel graph and the complete bipartite graph K 3 , n. [ABSTRACT FROM AUTHOR]

In this study, we proposed combined kernel-based methods to leverage patent citation graph performance for patent classification. The concept is to use the combined graph kernels of the citation graph to classify patent documents, as a hybrid approach. A multiple kernel framework was used for integrating multiple datasets of various kernels into a combined kernel. We employed seven graph kernels as the baselines and the combination of random walks and Weisfeiler–Lehman subtree kernels to achieve higher performance. We calculated the kernel values of each patent pairwise and employed an SVM classifier to carry out the classification task. The investigation results demonstrate that the combined graph kernel outperforms single kernels. [ABSTRACT FROM AUTHOR]

Abstract A geometric graph is called self-approaching, if for each (ordered) pair of vertices of the graph, there exists a self-approaching (directed) path between them. A path from a vertex u to a vertex v of the graph is called self-approaching, if for any point (not just vertex) x on the path, the distance between x and any point that starts at u and moves toward x is decreasing. A path is called an increasing-chord, if it is self-approaching from both sides, source to destination and destination to source. A geometric graph is called a self-approaching t -spanner, for t > 1 , if for each pair (u , v) of vertices of the graph, there exists a self-approaching path from u to v of length at most t times the Euclidean distance between u and v. In 2015, Dehkordi et al. (2015) [16] left the problem of the existence of an increasing-chord planar geometric graph for a set of points that lie along the sides of an acute triangle, as an open problem, but they did not mention anything about the case of an obtuse triangle. In this paper, we show that for each set of points on the boundary of an obtuse triangle, there exists an increasing-chord planar geometric graph. Moreover, we show that for each set of points on the boundary of an acute triangle, there exists an increasing-chord planar geometric graph using at most three Steiner points. We also introduce weakly self-approaching geometric graphs (spanners) as a variation of self-approaching geometric graphs (spanners). A weakly self-approaching path is defined similarly to a self-approaching path, except that when a point p on the path moves from the source to the destination, the Euclidean distance between p and the destination vertex (but not all the points on the path) decreases. A weakly self-approaching geometric graph (spanner) is defined by replacing "self-approaching" by "weakly self-approaching" in the above definition. In this paper, we show that for every point set S ⊆ R d , there is a weakly self-approaching planar geometric graph spanning S. Furthermore, this study shows how to test in polynomial time, whether a given geometric graph is weakly self-approaching. Notably, the corresponding decision problem in the context of self-approaching geometric graphs in R d with d ≥ 3 is NP-hard. We also propose some algorithms for constructing a weakly self-approaching geometric t -spanner for a given point set and a real constant t > 1. Also, we show that for every point set S on the boundary of any triangle, there exists an increasing-chord t -spanner spanning S and a weakly self-approaching t -spanner spanning S , both with O (k n) edges, in which k depends only on t. [ABSTRACT FROM AUTHOR]

Abstract A (1 , ≤ ℓ) -identifying code in digraph D is a dominating subset C of vertices of D , such that all distinct subsets of vertices of D with cardinality at most ℓ have distinct closed in-neighborhoods within C. As far as we know, it is the very first time that the spectral graph theory has been applied to the identifying codes. We give a new method to obtain an upper bound on ℓ for digraphs. The results obtained here can also be applied to graphs. [ABSTRACT FROM AUTHOR]

Abstract With the aim of finding useful tools and invariants to classify finite dimensional evolution algebras, we introduce and study the notion of a basic ideal. Every n -dimensional perfect evolution algebra has a maximal basic ideal I which is unique except when the dimension of I is n-1. An application of our results leads to the description of the four dimensional perfect non-simple evolution algebras over a field with mild restrictions. [ABSTRACT FROM AUTHOR]

Abstract Asymptotic stability of linear nabla Riemann–Liouville (q, h)-fractional difference equation is investigated in this paper. A Liapunov functional is constructed for the fractional difference equation. The sufficient condition for the asymptotic stability of considered equations is proposed. The results are illustrated with the corresponding numerical examples. [ABSTRACT FROM AUTHOR]

Abstract So far, research into pubic goods games has been limited to studying the effects of leadership in an experimental works. The results found differ according to the population studied, the number of participants and the country chosen, which makes ideas imprecise when it comes to understanding how cooperation evolves. In this article we try to generalize these works by introducing an agent-based model to simulate interactions in public goods games on a graph, and study the impact of leadership by example on the evolution of cooperation among selfish individuals in a scale-free network. Consistent with recent experimental studies, our results show that leading by example leads to a significant increase in the overall contribution and the group's welfare, as compared to the situation without leadership. We have demonstrated also that strong leaders have an important role in promoting optimal cooperation in public goods games and consequently they bring more welfare to their groups. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the asynchronous H ∞ control problem for a class of continuous-time semi-Markov jump linear systems. Under the assumption that the system mode is not accessible, we introduce a discrete-state and continuous-time process which is related to the system mode by a conditional probability as a switching signal of the controller. By constructing a semi-Markov-based Lyapunov funcational, a sufficient condition to ensure the stability of the system with a prescribed H ∞ performance is established. In addition, an equivalent statement is derived by introducing a slack variable, and the asynchronous controller is designed. Two examples are presented to illustrate the effectiveness of the proposed new design method. [ABSTRACT FROM AUTHOR]

Abstract A function f : V (G) → { 0 , 1 , ... , k } is called a k -rainbow independent dominating function of G if V i = { x ∈ V (G) : f (x) = i } is independent for 1 ≤ i ≤ k , and for every x ∈ V 0 it follows that N (x) ∩ V i ≠ ∅, for every i ∈ [ k ]. The k -rainbow independent domination number, γ ri k (G), of a graph G is the minimum of w (f) = ∑ i = 1 k | V i | over all such functions. In this paper we show that the problem of determining whether a graph has a k -rainbow independent dominating function of a given weight is NP-complete for bipartite graphs and that there exists a linear-time algorithm to compute γ ri k (G) of trees. In addition, sharp bounds for the k -rainbow independent domination number of the lexicographic product are presented, as well as the exact formula in the case k = 2. [ABSTRACT FROM AUTHOR]

Highlights • Graphic synthesis method for multi-technique separation sequences was established. • Dominant feed regions were determined for refinery gas separation techniques. • Near-optimal separation sequences can be readily synthesized by graphic method. • Hybrid process was developed to treat refinery gases with recovery exceeding 90%. • Laborious work to screen numerous sequences was saved by graphic synthesis method. Abstract In petroleum and chemical industries, many valuable species are depleted into various refinery gases. In order to fractionate and reclaim these valuable components efficiently and sufficiently, it is necessary to integrate diverse separation techniques together. The major obstacle to synthesize and optimize such a multi-component and multi-input process is the combinatorial explosion. In this research, graphic synthesis method is established to construct the multi-technique integration processes, in which the optimum or near-optimum sequence would be programmed to couple high efficient separation unit operations together to improve efficiency. As the support, three technical measures are summarized: the pseudo-ternary mixtures of H 2 , light hydrocarbons and fuel gases are proposed to depict refinery gases, after ranking species with their separation characteristics and belongings in products, so that the composition space can be visualized into triangular coordinate system; the dominant feed ranges for the pivotal separation units, i.e., adsorption, condensation, glassy and rubbery polymeric membranes, are determined after efficiency analysis, in which the represented technique is more efficient than the others for the composition matched feedstock; the shortcut calculation and the visualized representation with vectors in triangular coordinate system are created to quickly estimate separation operations, owing to their selectivity unique to a certain component group. Without laborious work to screen numerous sequences, this method programs recovery strategies and synthesizes processes appropriately and quickly. [ABSTRACT FROM AUTHOR]

Abstract A mitochondria-targeted ratiometric fluorescent probe based on hemicyanine and pyrido[1,2-a]benzimidazole was presented. It shows high sensitivity and selectivity toward SO 2 in pure water. The limit of detection (LOD) was as low as 26.7 nM, which is superior to most reported probes. Most importantly, the probe was successfully used for fluorescence imaging of endogenous bisulfite in mitochondria in Glioma cells. Graphical abstract Image 1 Highlights • A novel FRET platform constructed by pyrido[1,2-a]benzimidazole and hemicyanine fluorophores was designed. • The probe exhibits highly sensitivity and selectivity toward SO 2 in pure water. • The probe can be applied to determine the endogenous SO 2 levels in mitochondria. [ABSTRACT FROM AUTHOR]

Highlights • Incremental estimation of commute time in constant time using random walks. • The first method to estimate the commute time in an online fashion. • A design of an online anomaly detection application using the incremental commute time. • The proposed method is effective of in terms of accuracy and performance. Abstract Commute time is a robust measure on graphs based on random walks. It has been successfully applied in many application domains including personalized search, collaborative filtering and network intrusion detection. However, the computation of the commute time is expensive since it involves the eigen decomposition of the graph Laplacian matrix. There has been effort to approximate the commute time but they only work in an offline mode. In this work, an accurate and efficient approximation for computing the commute time is proposed in an incremental fashion in order to facilitate online applications. Using the incremental commutime, we design an online anomaly detection application where the commute time of each new arriving data point to any point in the current graph can be estimated in constant time. The proposed approach shows its high accuracy and efficiency in synthetic and real datasets for online applications. It takes only 8 milliseconds on average to detect anomalies online on the DBLP graph which has more than 600,000 nodes and 2 millions edges. We also discuss the use of incremental commute time for other online applications such as classification, graph ranking and clustering. [ABSTRACT FROM AUTHOR]

Abstract Datasets are often collected from different resources or comprised of multiple representations (i.e., views). Multi-view clustering aims to analyze the multi-view data in an unsupervised way. Owing to the efficiency of uncovering the hidden structures of data, graph-based approaches have been investigated widely for various multi-view learning tasks. However, similarity measurement in these methods is challenging since the construction of similarity graph is impacted by several factors such as the scale of data, neighborhood size, choice of similarity metric, noise and outliers. Moreover, nonlinear relationships usually exist in real-world datasets, which have not been considered by most existing methods. In order to address these challenges, a novel model which simultaneously performs multi-view clustering task and learns similarity relationships in kernel spaces is proposed in this paper. The target optimal graph can be directly partitioned into exact c connected components if there are c clusters. Furthermore, our model can assign ideal weight for each view automatically without additional parameters as previous methods do. Since the performance is often sensitive to the input kernel matrix, the proposed model is further extended with multiple kernel learning ability. With the proposed joint model, three subtasks including construct the most accurate similarity graph, automatically allocate optimal weight for each view and find the cluster indicator matrix can be simultaneously accomplished. By this joint learning, each subtask can be mutually enhanced. Experimental results on benchmark datasets demonstrate that our model outperforms other state-of-the-art multi-view clustering algorithms. [ABSTRACT FROM AUTHOR]

Highlights • We propose a new graph convolutional neural architecture based on a depth-based representation of graph structure which integrates both the global topological and local connectivity structures within a graph. • Depth-based subgraph convolution operation: The depth-based subgraph convolution operation scans a 'tree' of parameters deriving from the quantum walks on graph, which extracts local features analogous to the standard convolution operation on grid data. These local features can potentially be composed to form multi-scale structures. • Depth-based subgraph pooling operation: our depth-based subgraph pooling operation acts on the output of the preceding layer directly without any preprocessing scheme such as clustering. • Experiments on eight graph-structured datasets demonstrate that our model QS-CNNs are able to outperform fourteen state-of-the-art methods at the tasks of node classification and graph classification. Abstract This paper proposes a new graph convolutional neural network architecture based on a depth-based representation of graph structure deriving from quantum walks, which we refer to as the quantum-based subgraph convolutional neural network (QS-CNNs). This new architecture captures both the global topological structure and the local connectivity structure within a graph. Specifically, we commence by establishing a family of K -layer expansion subgraphs for each vertex of a graph by quantum walks, which captures the global topological arrangement information for substructures contained within a graph. We then design a set of fixed-size convolution filters over the subgraphs, which helps to characterise multi-scale patterns residing in the data. The idea is to apply convolution filters sliding over the entire set of subgraphs rooted at a vertex to extract the local features analogous to the standard convolution operation on grid data. Experiments on eight graph-structured datasets demonstrate that QS-CNNs architecture is capable of outperforming fourteen state-of-the-art methods for the tasks of node classification and graph classification. [ABSTRACT FROM AUTHOR]

Abstract Let C ℓ be a cycle of length ℓ and S n , k = K k ∨ K n − k ‾ , the join graph of a complete graph of order k and an empty graph on n − k vertices, and S n , k + be the graph obtained from S n , k by adding an edge in the independent set of S n , k. Nikiforov conjectured that for a given integer k ≥ 2 , any graph G of sufficiently large order n with spectral radius μ (G) ≥ μ (S n , k) (or μ (G) ≥ μ (S n , k +)) contains C 2 k + 1 or C 2 k + 2 (or C 2 k + 2), unless G = S n , k (or G = S n , k +). In this paper, a weaker version of Nikiforov's conjecture is considered, we prove that for a given integer k ≥ 2 , any graph G of sufficiently large order n with spectral radius μ (G) ≥ μ (S n , k) (or μ (G) ≥ μ (S n , k +)) contains a cycle C ℓ with ℓ ≥ 2 k + 1 (or C ℓ with ℓ ≥ 2 k + 2), unless G = S n , k (or G = S n , k +). These results also imply a result given by Nikiforov in (2010) [3, Theorem 2]. [ABSTRACT FROM AUTHOR]

Abstract A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. Let K n ∖ P ℓ be the graph obtained from K n by removing edges of P ℓ , where P ℓ is a path of length ℓ − 1 which is a subgraph of a complete graph K n. Cámara and Haemers (2014) conjectured that K n ∖ P ℓ is determined by its adjacency spectrum for every 2 ≤ ℓ ≤ n. In this paper we show that the conjecture is true for 7 ≤ ℓ ≤ 9. [ABSTRACT FROM AUTHOR]

Abstract Let G = (V , E) be a simple graph without isolated vertices. A set S ⊆ V is called a paired-dominating set if every vertex in V ∖ S has at least one neighbor in S and the subgraph induced by S contains a perfect matching. The paired-domination number of G , denoted by γ p r (G) , is the minimum cardinality of a paired-dominating set of G. We show that γ p r (G) ≤ 4 n ∕ 7 if G is a claw-free graph of order n with minimum degree at least three. The statement partly confirms the conjecture proposed by Goddard and Henning in 2009. [ABSTRACT FROM AUTHOR]

Highlights • This research solves for the first time the problem of calculating the exact robustness of a network. • The methodology allows to efficiently identify the set of removed nodes that maximizes the size of the largest connected component of a network. • The exact robustness of a graph was computed and tested on five graphs of different dimensions and with different structures. • The exact robustness was compared with the estimates obtained from commonly used greedy adaptive methods based on alternative node characteristics. Abstract Finding the most critical nodes regarding network connectivity has attracted the attention of many researchers in infrastructure networks, power grids, transportation networks and physics in complex networks. Static robustness of networks under intentional attacks analyses the ability of a system to maintain its connectivity after the disconnection or deletion of a series of targeted nodes. In this context, connectivity is typically measured by the size of the remaining largest connected component. When targeting these nodes, previous literature has mostly used adaptive strategies that sequentially remove central nodes, or created heuristics in order to improve the results of the adaptive strategies. The proposed methodology based on mathematical programming allows to identify, for every fraction of disconnected or removed nodes, the set that minimizes the size of the largest connected component of a network, i.e. it allows to calculate the exact (most critical) robustness of a network. [ABSTRACT FROM AUTHOR]

We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with δ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As the main result, we find a connection between the arrangement of the gaps and the coefficients in a continued fraction associated with the ratio of edge lengths of the lattice. This knowledge enables a straightforward construction of a periodic quantum graph with any required number of spectral gaps and—to some degree—to control their positions; i.e. to partially solve the inverse spectral problem. [ABSTRACT FROM AUTHOR]

Abstract Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first given a partial alignment that we are tasked with completing. In this article, we modify the state-of-the-art approximate graph matching algorithm "FAQ" of Vogelstein et al. (2015) to make it a fast approximate seeded graph matching algorithm, adapt its applicability to include graphs with differently sized vertex sets, and extend the algorithm so as to provide, for each individual vertex, a nomination list of likely matches. We demonstrate the effectiveness of our algorithm via simulation and real data experiments; indeed, knowledge of even a few seeds can be extremely effective when our seeded graph matching algorithm is used to recover a naturally existing alignment that is only partially observed. [ABSTRACT FROM AUTHOR]

Abstract Given compact metric spaces X 1 and X 2 , closed subsets Y 1 and Y 2 of X 1 and X 2 respectively, and an upper semicontinuous function g : Y 1 ⊸ Y 2 , we define a special kind of extension f : X 1 ⊸ X 2 of the function g and prove some of its properties. Using this special extension, we answer a question stated by Banič, Črepnjak, Merhar and Milutinović. We also introduce the notions of the weak L -extension property and the strong L -extension property of an inverse sequence for any property L of graphs of set-valued functions. We show that, in the case where L means the surjectivity of such graphs, not all inverse sequences of compact metric spaces have the strong L -extension property but they do have the weak L -extension property. [ABSTRACT FROM AUTHOR]

Abstract We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those at the remaining ones under a group penalty. We show that the proposed estimator can be computed by a fast convex optimization algorithm. We show that as the sample size increases, the estimated regression coefficients and the correct graphical structure are correctly estimated with probability tending to one. By extensive simulations, we show the superiority of the proposed method over comparable procedures. We apply the technique on two real datasets. The first one is to identify gene and protein networks showing up in cancer cell lines, and the second one is to reveal the connections among different industries in the US. Highlights • This paper studies a method of finding structure in Gaussian network. • Each node of the network is associated with a multivariate measurement. • Large sample convergence, algorithm as well as performance on datasets are provided. [ABSTRACT FROM AUTHOR]

Abstract Fault diagnosis of systems is an important area of study in the design and maintenance of multiprocessor systems. A new measure for fault diagnosis of systems, namely, h -edge tolerable diagnosability, is the maximum number of faulty nodes that a system G can guarantee to locate when the number of faulty links does not exceed h , denoted by t h e (G). Particularly, t 0 e (G) is the traditional diagnosability of G. Chang et al. (2005) [5] determined the traditional diagnosabilities of regular graphs. In this paper, we establish the h -edge tolerable diagnosabilities of regular graphs under the PMC model and the MM⁎ model, which extends their results and provides a more precise characterization for the fault diagnosis capability of regular graphs. As applications, the h -edge tolerable diagnosabilities of many networks are determined under the PMC model and the MM⁎ model. [ABSTRACT FROM AUTHOR]

Abstract Let λ (D) be the A α spectral radius of digraph D , and let G n r be the set of digraphs with order n and dichromatic number r. In this paper, we characterize the digraph which has the maximal A α spectral radius in G n r. Moreover, we also determine the unique digraph which attains the maximum (resp. minimum) A α spectral radius among all strongly connected bicyclic digraphs. [ABSTRACT FROM AUTHOR]

Abstract Let D (G) and D i a g (T r) denote the distance matrix and diagonal matrix of the vertex transmissions of a simple connected graph G , respectively. The distance signless Laplacian matrix of G is defined as D Q (G) = D i a g (T r) + D (G). Heretofore, the spectral properties of D (G) and D Q (G) have attracted much more attention. In the present paper, we propose to study the convex combinations D α (G) of D i a g (T r) and D (G) , defined as D α (G) = α D i a g (T r) + (1 − α) D (G) , 0 ≤ α ≤ 1. This study sheds new light on D (G) and D Q (G). Some spectral properties of D α (G) are given and a few open problems are discussed. Furthermore, we take effort to obtain some upper and lower bounds of spectral radius of D α (G). Finally, the generalized distance spectra of some graphs obtained by operations are also studied. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we generalize the concept of complete coloring and achromatic number to 2-edge-colored graphs and signed graphs. We give some useful relationships between different possible definitions of such achromatic numbers and prove that computing any of them is NP-complete. [ABSTRACT FROM AUTHOR]

Abstract Graph energy can be extended to digraphs via the trace norm. The trace norm of a digraph is the trace norm of its adjacency matrix, i.e. the sum of its singular values. In this work we find the oriented graphs that attain minimal and maximal trace norm over the set of oriented bicyclic graphs. [ABSTRACT FROM AUTHOR]

Abstract In this work we compare solutions of two distinct algorithms that try to increase the value of the algebraic connectivity of a given graph by choosing, with different strategies, edges to be included. Eccentricity and Perturbation Heuristics were considered, as well as random graphs and special families of trees being inputs of those algorithms. As conclusions of the reported experiments, the Eccentricity Heuristic obtains good results when compared with Perturbation Heuristic and a conjecture about broom trees is presented. [ABSTRACT FROM AUTHOR]

Abstract The units forms are algebraic expressions that have important role in representation theory of algebras. We identified that existing algorithms have exponential time complexity for weakly nonnegative and weakly positive types. In this paper we introduce a polynomial algorithm for the recognition of weakly nonnegative unit forms. The related algorithm identifies hypercritical restrictions in a given unit form, testing every subgraph of 9 vertices of the unit form associated graph. By adding Depth First Search approach, a similar strategy could be used in the recognition of weakly positive unit forms. We also present the most popular methods to decide whether or not a unit form is weakly nonnegative or weakly positive, we analyze their time complexity and we compare the results with our algorithms. [ABSTRACT FROM AUTHOR]

Abstract Let G be a finite, simple, and undirected graph and let S be a set of vertices of G. If every vertex having two neighbors inside S is also in S , then S is P 3 -convex. The P 3 -convex hull H (S) of S is the smallest P 3 -convex set containing S. If H (S) = V (G) we say that S is a P 3 -hull set of G. The cardinality h (G) of a minimum P 3 -hull set in G is called the P 3 -hull number of G. In this paper, we determine the P 3 -hull number of the strong and lexicographic product of two general graphs. We present lower and upper bounds for the P 3 -hull number of the Cartesian product, G □ H , of general graphs G and H , and we determine the P 3 -hull number of the Cartesian product G □ K n. We also improve the result of Centeno et al., 2011 showing that, given a graph G and an integer k , deciding whether h (G) ≤ k remains NP-complete for the Cartesian product of graphs. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the chromatic number of 2 K 2 -free graphs. We show linear χ -binding functions for several subclasses of 2 K 2 -free graphs, namely (2 K 2 , H) -free graphs where H ∈ { h o u s e , g e m , 2 K 1 + K p , (K 1 ∪ K 2) + K p }. We will also discuss χ -binding functions for (2 K 2 , claw) -free graphs. Finally, we will present extensions of our results to subclasses of P 5 -free graphs. [ABSTRACT FROM AUTHOR]

Abstract A set D ⊆ V of a graph G = (V , E) is called a dominating set of G if every vertex in V ∖ D has at least one neighbor in D. A dominating set D of G is a paired-dominating set of G if G [ D ] , the subgraph of G induced by D , has a perfect matching. Given a graph G , Min-Paired-Dom-Set is the problem to find a paired-dominating set of G of minimum cardinality. Min-Paired-Dom-Set is known to be NP -hard for general graphs and many other restricted classes of graphs. However, Min-Paired-Dom-Set is solvable in polynomial time in some graph classes including strongly chordal graphs and chordal bipartite graphs. In this paper, we strengthen this result by proposing a polynomial time algorithm to compute a minimum paired-dominating set in the class of strongly orderable graphs, which includes strongly chordal graphs and chordal bipartite graphs. The algorithm runs in linear time if a quasi-simple elimination ordering of the strongly orderable graph is provided. [ABSTRACT FROM AUTHOR]

Abstract In order to enable experimentations and simulations of bigraphs, we need an implementation of their dynamics. In this paper, we tackle the matching issue of this task. We present a solution based on an investigation on graph matching. We propose to simulate a bigraphical reactive system (i.e., bigraphs with a set of reaction rules that allow their rewriting) with a graph transformation system. First, we translate a bigraph to a ranked graph. This translation is ensured by defining a faithful functor that allows to move from the bigraph category to the ranked graph category. Then, we show that reaction rules can be simulated with graph rules. Hence, we provide a formal basis allowing to execute bigraph transformations by simulating their translation aiming to use well-established and efficient graph transformation tools. [ABSTRACT FROM AUTHOR]

Abstract This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we empirically profile three algorithms for the Shortest Negative Cost Cycle (SNCC) problem. In this problem, we are given a directed, weighted graph G = 〈 V , E , c 〉 , and the goal is to identify a negative cost cycle with the fewest number of edges. The SNCC problem finds applications in a number of domains ranging from program verification to certifying algorithm design. The first polynomial time algorithm for this problem was proposed in Subramani (2009). Since then, several additional techniques, including a randomized approach, have been proposed for the SNCC problem. Our goal in this paper is to analyze three algorithmic paradigms for this problem from the empirical perspective. Towards this end, we profile these algorithmic approaches over a wide range of inputs. Our results indicated that the randomized algorithm is the algorithm of choice over a number of graph classes. [ABSTRACT FROM AUTHOR]

Abstract The paper is devoted to a Gram classification of an important class of signed graphs with loops playing an important role in many branches of mathematics, physics and computer science including game theory, crystallography, Diophantine geometry, Lie theory, spectral graph theory, a graph coloring technique, algebraic methods in graph theory. They have many deep applications in spectral machine learning methods, electrical networks, to link sign prediction in signed unipartite and bipartite networks, and community partition in social networks. We continue the study of finite connected edge-bipartite graphs Δ (bigraphs, for short), with m ≥ 2 vertices (a class of signed graphs), started in Simson (2013) and developed in Simson (2016) by means of the non-symmetric Gram matrix G ˇ Δ ∈ M m (Z) defining Δ , its symmetric Gram matrix G Δ : = 1 2 [ G ˇ Δ + G ˇ Δ t r ] ∈ M m (1 2 Z) , and the Gram quadratic form q Δ : Z m → Z. In the present paper, given n ≥ 1 , we mainly study connected principal Cox-regular edge-bipartite graphs Δ with loops and n + 1 ≥ 2 vertices, in the sense that the symmetric Gram matrix G Δ ∈ M n + 1 (Z) of Δ is positive semi-definite of rank n ≥ 1. Our aim is to classify such edge-bipartite graphs by means of an inflation algorithm, up to the weak Gram Z -congruence Δ ∼ Z Δ ′ , where Δ ∼ Z Δ ′ means that G Δ ′ = B t r ⋅ G Δ ⋅ B , for some B ∈ M n + 1 (Z) with det B = ± 1. Our main result of the paper asserts that, given a principal Cox-regular connected edge-bipartite graph Δ with n + 1 ≥ 2 vertices, there exists an edge-bipartite Euclidean graph D n + 1 of Tables A and B, and a suitably chosen sequence t • − of the inflation operators, each of one of the forms Δ ′ ↦ t a − Δ ′ or Δ ′ ↦ t a b − Δ ′ , such that the composite operator Δ ↦ t • − Δ reduces Δ to the bigraph D n + 1 such that: (i) Δ ∼ Z D n + 1 and (ii) the bigraphs Δ , and D n + 1 have the same number of loops. The algorithm does not change loops and computes a matrix B ∈ M n + 1 (Z) , with det B = ± 1 , defining the weak Gram Z -congruence Δ ∼ Z D n + 1 , that is, satisfying the equation G D n + 1 = B t r ⋅ G Δ ⋅ B. [ABSTRACT FROM AUTHOR]

Abstract Community detection is an important problem of complex networks analysis and various methods have been proposed to solve it. However, most of the existing methods only use the link information. As a result, the quality of their detected communities is often poor due to the sparse and noisy data existing in link information. Actually, content information of complex networks can also help to improve the quality of community detection. In this paper, we propose a method based on Multi-View Clustering via Robust Nonnegative Matrix Factorization (MVCRNMF). This method can provide a unified framework to combine link and content information for community detection. Its key idea is to build a multi-view robust NMF model with the co-regularized constraint on community indicator matrices of link view and content view. This can make link and content information complement each other during the factorization process of NMF. We devise iterative update rules as the optimization solution to the community detection model and also give the rigorous convergence proof. It is worth noting that MVCRNMF can learn the contribution weights from link and content information adaptively and this helps to save a lot of time on tuning the weight parameters. We conduct comparative experiments on four real-world complex networks. The results demonstrate that MVCRNMF performs better than state-of-the-art methods. Additionally, results of the case study on a co-authorship network also show that MVCRNMF can obtain higher quality communities. Highlights • A community detection model based on multi-view clustering is proposed. • We devise and prove iterative update rules for the community detection model. • The weight parameters of the community detection model can be learned adaptively. [ABSTRACT FROM AUTHOR]

Abstract Navigation on graphs is the problem how an agent walking on the graph can get from a source to a target with limited information about the graph. The information and the way to exploit it can vary. In this paper, we study navigation on temporal networks—networks where we have explicit information about the time of the interaction, not only who interacts with whom. We contrast a type of greedy navigation – where agents follow paths that would have worked well in the past – with two strategies that do not exploit the additional information. We test these on empirical temporal network data sets. The greedy navigation finds the targets faster and more reliably than the reference strategies, meaning that there are correlations in the real temporal networks that can be exploited. We find that both topological and temporal structures affect the navigation. Highlights • Introducing the problem of navigation on temporal networks. • Exploring different ways to operationalize the incomplete information. • Proposing different navigation strategies that are only using ex ante information. • Found that both static and temporal network structure determine the navigability. • Shows that in real networks there are structures that could be exploited in navigation. [ABSTRACT FROM AUTHOR]

Abstract Purpose The aim of this study is to better understand the neural substrate of intelligence in children, through the characterization of the brain's structural connectivity (graph measures), as well as the major white matter (WM) fibers microstructure. Materials and methods Fourty-three children (8 to 12 years) were include in this study. MRI acquisition included conventional and diffusion tensor imaging sequences. Children also underwent neuropsychological tests, providing the ten WISC-subtests. A factor analysis was performed to explore the inter-correlations of WISC-IV subtests and to extract intelligence domains as well as the general intelligence factor (g-score). Correlations between the intelligence domains and both graphs and diffusivity metrics were also explored. Results Global graph metrics revealed a strong relationship between high intelligence scores and brain network homogeneity (high density and low modularity), mainly in the temporal and parietal lobes. Furthermore, quantitative WM fiber-bundle analysis showed an increased axonal density in the major WM fiber-bundles that was associated to increased intelligence performances. Conclusion These findings demonstrated that intelligence neural substrate is based on a strong WM microstructure of the major intra- and inter- hemispheric fiber-bundles and a well-balanced network organization between local and global scales. Highlights • White Matter integrity is enhanced in children with high intelligence. • High intelligence neural substrate is related to a high fiber density. • High intelligence is related to optimally distributed brain networks in children. [ABSTRACT FROM AUTHOR]