Extra Edges Research Articles

Organisational hierarchy constructions with easy Kuramoto synchronisation

We provide a graph theoretic construction enabling tree-based hierarchies to be modified into structures with enhanced connectivity and synchronisability. Specifically, the construct transforms trees into members of a family of graphs known as expanders, which we call ‘expander-augmented-hierarchies’ or trees. We show that this produces graphs with significantly enhanced synchronisation properties in the context of the Kuramoto model of phase oscillators coupled on networks. When considered as organisational structures these networks enjoy both the managability of simple hierarchies with near regular degree distribution, and low critical coupling by the addition of relatively few extra edges. For the expander augmented tree, we examine the synchronisation properties, computed through the time-averaged Kuramoto order parameter over an ensemble of natural frequencies. We compare this with a range of other networks including hierarchies augmented by random matching of the leaf nodes. For these we compute the ratio Q of smallest to largest Laplacian eigenvalues, the smallness of which has been argued to be an indicator of good synchronisability. While not the best of these in Q, the expander-augmented-hierarchy exhibits synchronisability barely distinguishable from others with lower Q within the variance over an ensemble of natural frequencies. However, the expander augmented tree has the advantage that its properties are automatically designed for as opposed to the outcome of a random search for low Q-value graphs that in itself scales very poorly.

Balanced morphological filters for horizontal boundaries enhancement of the potential field sources

The enhancement of horizontal boundaries of potential field sources is of great significance for the study of geological structures. Most of the existing filters for horizontal edges enhancement are presented based on the derivatives of potential field data, but these filters often show some shortcomings, for example, the output edges are divergent, strong and weak anomalies cannot be balanced, or some extra false edges appear in the results. In this paper, the edges enhancement filter MMA based on mathematical morphology is first defined by the combination of the basic operators of mathematical morphology. In order to make the filter have the ability to balance different amplitude anomalies, MMAZ and MMAT are proposed, and both of them can be used to delineate the horizontal edges of the field sources by their maxima. The experimental results of synthetic data show that MMAZ and MMAT have good equalization and anti-noise performances. Compared with several traditional filters, the horizontal edges of geological bodies obtained by these two filters are clearer and more convergent, and there are no extra edges in the output results for the complex situations that positive and negative anomalies exist simultaneously. Finally, the two new equalization filters are applied to gravity anomaly data in a potash mine area in Vientiane basin of Laos and the aeromagnetic anomaly of a metal mine in northwest China, the obtained positions of the structures are more accurate and clearer, which further illustrates the effectiveness of the two filtering techniques.

Decentralized Multi-Subgroup Formation Control With Connectivity Preservation and Collision Avoidance

This paper proposes a formation control algorithm to create separated multiple formations for an undirected networked multi-agent system while preserving the network connectivity and avoiding collision among agents. Through the modified multi-consensus technique, the proposed algorithm can simultaneously divide a group of multiple agents into any arbitrary number of desired formations in a decentralized manner. Furthermore, the agents assigned to each formation group can be easily reallocated to other formation groups without network topological constraints as long as the entire network is initially connected; an operator can freely partition agents even if there is no spanning tree within each subgroup. Besides, the system can avoid collision without loosing the connectivity even during the transient period of formation by applying the existing potential function based on the network connectivity estimation. If the estimation is correct, the potential function not only guarantees the connectivity maintenance but also allows some extra edges to be broken if the network remains connected. Numerical simulations are performed to verify the feasibility and performance of the proposed multi-subgroup formation control.

On Verifying and Maintaining Connectivity of Interval Temporal Networks

An interval temporal network is, informally speaking, a network whose links change with time. The term interval means that a link may exist for one or more time intervals, called availability intervals of the link, after which it does not exist (until, maybe, a further moment in time when it starts being available again). In this model, we consider continuous time and high-speed (instantaneous) information dissemination. An interval temporal network is connected during a period of time [Formula: see text], if it is connected for all time instances [Formula: see text] (instantaneous connectivity). In this work, we study instantaneous connectivity issues of interval temporal networks. We provide a polynomial-time algorithm that answers if a given interval temporal network is connected during a time period. If the network is not connected throughout the given time period, then we also give a polynomial-time algorithm that returns large components of the network that remain connected and remain large during [Formula: see text]; the algorithm also considers the components of the network that start as large at time [Formula: see text] but dis-connect into small components within the time interval [Formula: see text], and answers how long after time [Formula: see text] these components stay connected and large. Finally, we examine a case of interval temporal networks on tree graphs where the lifetimes of links and, thus, the failures in the connectivity of the network are not controlled by us; however, we can “feed” the network with extra edges that may re-connect it into a tree when a failure happens, so that its connectivity is maintained during a time period. We show that we can with high probability maintain the connectivity of the network for a long time period by making these extra edges available for re-connection using a randomized approach. Our approach also saves some cost in the design of availabilities of the edges; here, the cost is the sum, over all extra edges, of the length of their availability-to-reconnect interval.

Coin-Flipping, Ball-Dropping, and Grass-Hopping for Generating Random Graphs from Matrices of Edge Probabilities

Common models for random graphs, such as Erdös--Rényi and Kronecker graphs, correspond to generating random adjacency matrices where each entry is nonzero based on a large matrix of probabilities. Generating an instance of a random graph based on these models is easy, although inefficient, by flipping biased coins (i.e., sampling binomial random variables) for each possible edge. This process is inefficient because most large graph models correspond to sparse graphs where the vast majority of coin flips will result in no edges. We describe some not entirely well-known, but not entirely unknown, techniques that will enable us to sample a graph by finding only the coin flips that will produce edges. Our analogies for these procedures are ball-dropping, which is easier to implement, but may need extra work due to duplicate edges, and grass-hopping, which results in no duplicated work or extra edges. Grass-hopping does this using geometric random variables. In order to use this idea for complex probability matrices such as those in Kronecker graphs, we decompose the problem into three steps, each of which is an independently useful computational primitive: (i) enumerating nondecreasing sequences; (ii) unranking multiset permutations; and (iii) decoding and encoding z-curve and Morton codes and permutations. The third step is the result of a new connection between repeated Kronecker product operations and Morton codes. Throughout, we draw connections to ideas underlying applied math and computer science, including coupon collector problems.

The bunkbed conjecture on the complete graph

The bunkbed conjecture was first posed by Kasteleyn. If G=(V,E) is a finite graph and H some subset of V, then the bunkbed of the pair (G,H) is the graph G×{1,2} plus |H| extra edges to connect for every v∈H the vertices (v,1) and (v,2). The conjecture asserts that (v,1) is more likely to connect with (w,1) than with (w,2) in the independent bond percolation model for any v,w∈V. This is intuitive because (v,1) is in some sense closer to (w,1) than it is to (w,2). The conjecture has however resisted several attempts of proof. This paper settles the conjecture in the case of a constant percolation parameter and G the complete graph.

Speeding up non-Markovian first-passage percolation with a few extra edges

Abstract One model of real-life spreading processes is that of first-passage percolation (also called the SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with independent and identically distributed heavy-tailed passage times on edges. On the other hand, random graphs are often locally tree-like, and spreading on trees with leaves might be very slow due to bottleneck edges with huge passage times. Here we consider the SI model with passage times following a power-law distribution ℙ(ξ>t)∼t-α with infinite mean. For any finite connected graph G with a root s, we find the largest number of vertices κ(G,s) that are infected in finite expected time, and prove that for every k≤κ(G,s), the expected time to infect k vertices is at most O(k1/α). Then we show that adding a single edge from s to a random vertex in a random tree 𝒯 typically increases κ(𝒯,s) from a bounded variable to a fraction of the size of 𝒯, thus severely accelerating the process. We examine this acceleration effect on some natural models of random graphs: critical Galton--Watson trees conditioned to be large, uniform spanning trees of the complete graph, and on the largest cluster of near-critical Erdős‒Rényi graphs. In particular, at the upper end of the critical window, the process is already much faster than exactly at criticality.

A New Score Generation Algorithm for Student Concept Map Evaluation

This article presents a new score generation algorithm to compute the accuracy of student concept maps in comparison to teacher maps. The algorithm follows a compare and remove method to remove the extra vertices and wrong edges of student concept map with respect to teacher map. A group of 230 students were taken to generate student maps on a pretaught chapter for finding multivariate regression coefficients for different independent factors incorporated in the study. It was found that there exists a positive correlation between the score obtained by the students and the degree of knowledge acquired by him while constructing concept maps.

Exchanged folded crossed cube: A new interconnection network for parallel computation

We propose and analyze a new variant hypercube type topology, the Exchanged Folded Crossed Cube (EFCQ) which is basically a standard exchanged crossed cube with some extra edges constructed between the nodes. For the proposed architecture, properties like nodes, edges, degree, isomorphism, diameter and cost are derived and compared to those of standard cubes. For this new design, optimal routing algorithm and broadcasting communication are developed and proven that EFCQ is more efficient than those of conventional n-cube and its variants. We will show that the proposed architecture offers substantial improvement over existing hypercube, type interconnection network in terms of cost and diameter.

Finding a set of candidate parents using dependency criterion for the K2 algorithm

One of the most effective structure-learning methods in a Bayesian network is the K2 algorithm. Because the performance of the K2 algorithm depends on the node ordering, more effective node ordering inference methods are needed. In this paper, we introduce a novel method for finding a set of candidate parents for each node as input for the K2 algorithm. Based on the fact that the candidate parents are identified by estimated Markov Blanket, we first estimate the Markov Blanket of a variable by using the L1-regularized Markov Blanket. We then determine the candidate parents of a variable through its Markov blanket by introducing a new scoring function based on the dependency criterion. Then the candidate parents are used as input for the K2 algorithm for learning Bayesian network structure. Experimental results over most of the datasets indicate that the proposed method avoids creating extra edges and significantly outperforms the previous methods.

When Subgraph Isomorphism is Really Hard, and Why This Matters for Graph Databases

The subgraph isomorphism problem involves deciding whether a copy of a pattern graph occurs inside a larger target graph. The non-induced version allows extra edges in the target, whilst the induced version does not. Although both variants are NP-complete, algorithms inspired by constraint programming can operate comfortably on many real-world problem instances with thousands of vertices. However, they cannot handle arbitrary instances of this size. We show how to generate "really hard" random instances for subgraph isomorphism problems, which are computationally challenging with a couple of hundred vertices in the target, and only twenty pattern vertices. For the non-induced version of the problem, these instances lie on a satisfiable / unsatisfiable phase transition, whose location we can predict; for the induced variant, much richer behaviour is observed, and constrainedness gives a better measure of difficulty than does proximity to a phase transition. These results have practical consequences: we explain why the widely researched "filter / verify" indexing technique used in graph databases is founded upon a misunderstanding of the empirical hardness of NP-complete problems, and cannot be beneficial when paired with any reasonable subgraph isomorphism algorithm.

Optimal Cell-to-Cell Balancing Topology Design for Serially Connected Lithium-Ion Battery Packs

A battery pack can see energy imbalance among its cells resulting from cell-to-cell variation in capacity, internal resistance, and other parameters. Its successful and safe operation thus necessitates dynamic energy equalizing to adjust each cell's state-of-charge to the same level. The cell equalizing system for a serially connected battery pack is modeled as a multiagent system here. A consensus-based state-of-charge equalizing algorithm is proposed with its convergence proved through theoretical analysis. Following this development, an interesting and important problem is investigated: how to add extra individual cell equalizers or edges to the original cell equalizing system's topology to maximally accelerate the equalizing process. It is found that the balancing time depends on the algebraic connectivity of the topology graph, which is measured by the second smallest eigenvalue of the graph's Laplacian matrix. Then, a combinatorial 0-1 optimization problem is formulated and addressed to optimally choose added edges that lead to the maximum increase in the algebraic connectivity. The proposed results are validated through simulation and experiments, which demonstrate that the balancing time can be significantly reduced by just adding one optimal individual cell equalizer to the original cell equalizing system.

On Edge Addition Problem with some graphs

The two questions that: how many edges at least have to be added to the network to ensure the message within the effective bounds, and how large message delay will be increased when faults occur, can re-write this problem as: What the minimum diameter of a connected graph obtained from a graph of diameter after adding extra edges, this problem called “Edge Addition Problem”. In this paper we find some exact values to above problem by using some special graphs (Line Graph, Bipartite graph, and complete Bipartite graph).

Jump from parallel to sequential proofs: exponentials

In previous works, by importing ideas from game semantics (notably Faggian–Maurel–Curien'sludics nets), we defined a new class of multiplicative/additive polarized proof nets, calledJ-proof nets. The distinctive feature of J-proof nets with respect to other proof net syntaxes, is the possibility of representing proof nets which are partially sequentialized, by usingjumps(that is, untyped extra edges) as sequentiality constraints. Starting from this result, in the present work, we extend J-proof nets to the multiplicative/exponential fragment, in order to take into account structural rules: More precisely, we replace the familiar linear logic notion of exponential box with a less restricting one (calledcone) defined by means of jumps. As a consequence, we get a syntax for polarized nets where, instead of a structure of boxes nested one into the other, we have one of cones which can bepartially overlapping. Moreover, we define cut-elimination for exponential J-proof nets, proving, by a variant of Gandy's method, that even in case of ‘superposed’ cones, reduction enjoys confluence and strong normalization.

Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers.

The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to network’s architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units.

Median ellipse parameterization for robust measurement of fuel droplet size

The combustion properties of blended fuel combinations can be characterized by performing single droplet fuel combustion experiments. These combustion experiments are visualized using high speed image acquisition. Once the high speed images are obtained, the burn rate and other characteristics of combustion, such as the occurrence of microexplosions, can be characterized. Currently these quantities are either measured manually or are measured using automated software. However, the current software packages used for this task are limited in that they can only measure droplets that are elliptical in shape and manual corrections often have to be made to avoid significant errors in the measurement. An automated droplet tracking algorithm is presented that can automatically track droplet size without manual intervention due to its robustness to the presence of missing or extra edges in the images. In addition, the proposed method can track shapes more general than ellipses, which is required in order to track the droplet during microexplosions. The proposed algorithm starts by fitting ellipses to numerous five point subsets from the droplet edge data. The closed contour is parameterized by determining the median perimeter of the set of ellipses. The resulting curve is not an ellipse, allowing arbitrary closed contours to be parameterized. The performance of the proposed algorithm and the performance of existing algorithms are compared to a ground truth segmentation of the fuel droplet images. This comparison demonstrates that the median ellipse parameterization algorithm has improved performance for both area quantification and edge deviation.

Egg yolk-derived phosphorus and nitrogen dual doped nano carbon capsules for high-performance lithium ion batteries

Egg yolk-derived P and N dual doped nano carbon capsules (PNCCs) have been synthesized and used as lithium ion battery anodes. The application of egg yolk as the carbon source is a new and environmental-friendly approach for biomass recycling. The reversible capacity of half cells made of PNCCs is as high as ~770mAhg−1 at a current density of 0.5Ag−1 with considerable rate capacity and cycling stability. PNCCs show a capsule-like structure, which provide extra edges and active sites for lithium intercalation. The heteroatom doping also introduce defects and disorder, which increases the electrochemical activity and creates more active sites for lithium insertion.

Trees with 2-Reinforcement Number Three

A vertex subset S of a graph G is a 2-dominating set of G if every vertex not in S is adjacent to two vertices of S. The 2-domination number γ2(G) is the minimum cardinality of a 2-dominating set of G. The 2-reinforcement number r2(G) is the smallest number of extra edges whose addition to G results in a graph Gwith γ2(G � )<γ 2(G) .L etT be a tree. It is showed by Lu, Hu, and Xu that r2(T ) ≤ 3. In this paper, we will show that r2(T ) = 3 if and only if there is a 2-dominating set S of T such that T contains neither S-vulnerable vertices nor S-vulnerable paths. Keywords 2-Domination · 2-Reinforcement number · S-vulnerable · Trees

Reconstruction of curves from point clouds using fuzzy logic and ant colony optimization

A new approach based on fuzzy logic and ant colony optimization is presented for the reconstruction of curves from a set of unorganized points. Fuzzy clustering is used to reduce the number of points to cluster centres. Ant colony optimization is used to construct a travelling salesman path which is a closed curve. Extra edges are deleted and new edges are added using the fuzzy membership function. The algorithm presented in this paper has been used for reconstructing open as well as closed curves. The results obtained for multiple and self-intersecting curves are also good. Various examples for open, closed, multiple and intersecting curves with complicated shapes are shown to illustrate the significance of the presented algorithm.

Steiner Tree: approach applying for shortest path in selected network

This paper focus on approach for shortest path from source to destination in which an autonomous system for virtual private network, whose communicate with each other in a private area. For selecting a shortest path we focus on Steiner tree. The general concept of finding minimum path describes an undirected graph, in which vertices (node) and edges (links) are playing main role. we focus on Steiner tree problem, extra intermediate vertices and edges may be added to the graph in order to reduce the length of the spanning tree. Keywords: Steiner tree, Autonomous system (AS).