Consensus In Networks Research Articles

Graph matching for knowledge graph alignment using edge-coloring propagation

Knowledge graph (KG) is a kind of structured human knowledge of modeling the relationships between real-world entities. High quality KG is of crucial importance for many knowledge-based applications, e.g., question answering, recommender systems, etc. This paper studies the problem of entity alignment in KGs to promote knowledge fusion. Existing methods model the semantic representation of entities by using graph structural information or attribute information of the KG and then align the entities across different domains by calculating the distances between entities’ embeddings. However, these methods only consider the node-to-node similarity in the alignment procedure while the edge-to-edge similarity is ignored. Our research hypothesis is that the graph edge alignment information is critical in entity alignment. We reformulate the knowledge entity alignment as a quadratic assignment problem (QAP) by adding relation alignment under the one-to-one mapping constraint. To solve the notorious QAP in a large-scale heterogeneous graph like KG, we propose a model, dual neighborhood consensus network (DNCN), which approximately decomposes the QAP into two small-scale linear assignment problems, i.e., entity alignment and relation alignment. After that, an edge-coloring propagation method is proposed to refine the coarse entity alignment result using the relation correspondence. Theoretical proof shows that this method can guarantee the isomorphism between local sub-graphs. The performance of DNCN is evaluated using the DBP15K and DWY100K benchmarks. Experimental results show that DNCN achieves the best performance on the DBP15K benchmark, and is computationally efficient. Ablation studies verify the importance of graph edge alignment information.

Distributed state estimation for uncertain nonlinear time-delay AC islanded micro grids

This article deals with the problem of distributed observer design containing time delays for uncertain nonlinear distributed generators systems in alternating current–islanded micro grids. In contrast with the centralized observer with the ability to accumulate full output of the plant, we design a set of distributed observers, each having access to partial output of the plant through a distributed observer network. Each observer obtains partial plant output and communicates with its neighboring observers through consensus network. The design method is based on the Lipschitz condition of uncertain nonlinear terms while having time-delay system in view. Suitable selection of Lyapunov functions is made, and the Jensen inequality is considered in delayed uncertain nonlinear micro grids in an undirected network. Furthermore, via design algorithm, the necessary and sufficient conditions for the design of parameters are determined so as to stabilize the error dynamics. Finally, numerical simulations are provided to consider the effectiveness of the proposed method.

Computing consensus networks for collections of 1-nested phylogenetic networks

An important and well-studied problem in phylogenetics is to compute a consensus tree so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same set \(X\) of species. More recently, however, it has become of interest to find a consensus for a collection of more general, rooted directed acyclic graphs all of whose sink-sets are bijectively labeled by \(X\), so called rooted phylogenetic networks. These networks are used to analyze the evolution of species that cross with one another, such as plants and viruses. In this paper, we introduce an algorithm for computing a consensus for a collection of so-called 1-nested phylogenetic networks. Our approach builds on a previous result by Roselló et al. that describes an encoding for any 1-nested phylogenetic network in terms of a collection of ordered pairs of subsets of \(X\). More specifically, we characterize those collections of ordered pairs that arise as the encoding of some 1-nested phylogenetic network, and then use this characterization to compute a consensus network for a collection of $t \geq 1$ 1-nested networks in $O(t|X|^2+|X|^3)$ time. Applying our algorithm to a collection of phylogenetic trees yields the well-known majority rule consensus tree. Our approach leads to several new directions for future work, and we expect that it should provide a useful new tool to help understand complex evolutionary scenarios.

Controllability of consensus of multi-agent networks over heterogeneous dynamics

This work investigates controllability issues under the leader–follower framework of consensus problem on multi-agent networks where its agents exhibit the heterogeneous dynamics involving first-, second-, and third-order integrator agents on a continuous time-scale. The communication topology is directed, time-invariant, and the reliability of all interactions are unity. We employ two kinds of consensus protocols that are linear and distributed. The necessary and sufficient criteria for the controllability of followers’ dynamics through the selected leaders are obtained in terms of matrix-rank conditions. We also obtain some necessary conditions of controllability involving eigenvectors of system matrices. It is verified that, if either of the first-, second-, or third-order integrator agents are absent, then the controllability of the network becomes equivalent to the controllability of the communication topology just like those of the networks with homogeneous dynamic agents. Obtained results are verified with illustrative examples.

A Fast Consensus for Permissioned Wireless Blockchains

With the wide deployment of Internet-of-Things (IoT), blockchain systems have been playing a crucial role to establish a trusted computing environment among potentially mistrusting agents without depending on a centralized server. Different from previous blockchain consensus protocols adopted in IoT, which rely on efficient and stable transmissions, in this paper, we consider how to reach blockchain consensus in wireless networks without reliable network support. Specifically, a realistic SINR model is adopted to depict the unreliable transmissions in wireless channels. Based on the SINR model, a distributed and randomized consensus algorithm is proposed to reach k-times consensus among n devices within O(k+logn) time steps with high probability. Note that the time complexity of our algorithm is asymptotically optimal since Ω(k+logn) is a lower bound to achieve k-times consensus in a distributed environment. We conduct both rigorous theoretical analysis and extensive simulations to validate our method. It is believed that our work can facilitate the implementation of blockchains in many wireless scenarios in which the reliable and fast transmissions cannot be guaranteed.

RAFT Consensus Reliability in Wireless Networks: Probabilistic Analysis

The centralized system becomes less efficient, secure, and resilient as the network size and heterogeneity increase due to its inherent single point of failure issues. Distributed consensus mechanisms characterized by decentralization, autonomy, parallelism and fault-tolerance can meet the increasing demands of safety and security in critical interconnected systems. This paper establishes a Node and Link probabilistic failure model in the presence of node and communication link failures for a representative crash fault tolerant distributed consensus protocol: RAFT. The analytical results in terms of the probability density function and the mean value of consensus reliability are derived. Two important reliability performance indicators, Reliability Gain and Tolerance Gain are proposed to indicate the linear relationship between the consensus reliability and two basic parameters, i.e. the joint failure rate and the maximum number of tolerant faulty nodes, which provide the theoretical guidance for quickly deploying a RAFT system. The special case of a distributed consensus network with already a certain number of failures and its adverse impact are evaluated. The Markov probabilistic models, definitions of Reliability Gain and Tolerance Gain, and the analysis methods proposed in this paper can be extended to other consensus mechanisms.

Faster Supervised Average Consensus in Adversarial and Stochastic Anonymous Dynamic Networks

How do we reach consensus on an average value in a dynamic crowd without revealing identity? In this work, we study the problem of average network consensus in Anonymous Dynamic Networks (ADN). Network dynamicity is specified by the sequence of topology-graph isoperimetric numbers occurring over time, which we call the isoperimetric dynamicity of the network. The consensus variable is the average of values initially held by nodes, which is customary in the network-consensus literature. Given that having an algorithm to compute the average one can compute the network size (i.e., the counting problem) and vice versa, we focus on the latter. We present a deterministic distributed average network consensus algorithm for ADNs that we call isoperimetric Scalable Coordinated Anonymous Local Aggregation, and we analyze its performance for different scenarios, including worst-case (adversarial) and stochastic dynamic topologies. Our solution utilizes supervisor nodes, which have been shown to be necessary for computations in ADNs. The algorithm uses the isoperimetric dynamicity of the network as an input, meaning that only the isoperimetric number parameters (or their lower bound) must be given, but topologies may occur arbitrarily or stochastically as long as they comply with those parameters. Previous work for adversarial ADNs overestimates the running time to deal with worst-case scenarios. For ADNs with given isoperimetric dynamicity, our analysis shows improved performance for some practical dynamic topologies, with cubic time or better for stochastic ADNs, and our experimental evaluation indicates that our theoretical bounds could not be substantially improved for some models of dynamic networks.

Inferring microbial co-occurrence networks from amplicon data: a systematic evaluation.

Microbes commonly organize into communities consisting of hundreds of species involved in complex interactions with each other. 16S ribosomal RNA (16S rRNA) amplicon profiling provides snapshots that reveal the phylogenies and abundance profiles of these microbial communities. These snapshots, when collected from multiple samples, can reveal the co-occurrence of microbes, providing a glimpse into the network of associations in these communities. However, the inference of networks from 16S data involves numerous steps, each requiring specific tools and parameter choices. Moreover, the extent to which these steps affect the final network is still unclear. In this study, we perform a meticulous analysis of each step of a pipeline that can convert 16S sequencing data into a network of microbial associations. Through this process, we map how different choices of algorithms and parameters affect the co-occurrence network and identify the steps that contribute substantially to the variance. We further determine the tools and parameters that generate robust co-occurrence networks and develop consensus network algorithms based on benchmarks with mock and synthetic data sets. The Microbial Co-occurrence Network Explorer, or MiCoNE (available at https://github.com/segrelab/MiCoNE) follows these default tools and parameters and can help explore the outcome of these combinations of choices on the inferred networks. We envisage that this pipeline could be used for integrating multiple data sets and generating comparative analyses and consensus networks that can guide our understanding of microbial community assembly in different biomes. IMPORTANCE Mapping the interrelationships between different species in a microbial community is important for understanding and controlling their structure and function. The surge in the high-throughput sequencing of microbial communities has led to the creation of thousands of data sets containing information about microbial abundances. These abundances can be transformed into co-occurrence networks, providing a glimpse into the associations within microbiomes. However, processing these data sets to obtain co-occurrence information relies on several complex steps, each of which involves numerous choices of tools and corresponding parameters. These multiple options pose questions about the robustness and uniqueness of the inferred networks. In this study, we address this workflow and provide a systematic analysis of how these choices of tools affect the final network and guidelines on appropriate tool selection for a particular data set. We also develop a consensus network algorithm that helps generate more robust co-occurrence networks based on benchmark synthetic data sets.

A new distributed protocol for consensus of discrete-time systems

In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols.

Robustness of consensus in m-rose networks

The consensus of deterministic networks investigates the relationships between consensus and network topology, which can be measured by network coherence. The m-rose networks are composed of m circles, which share a common node. Recently, scholars have obtained the first-order coherence of 5-rose networks. This paper takes the more general m-rose networks as the research object, firstly, the m-rose networks are introduced. Secondly, the relationships between Laplacian eigenvalues and polynomial coefficients are used to obtain the first-order and second-order coherence of the m-rose networks. Finally, the effects of topology parameters such as the number of petals m and the length of a cycle n on the robustness of network consensus are discussed, and the validity of the conclusion is verified by numerical simulation.

Visualizing incompatibilities in phylogenetic trees using consensus outlines.

Phylogenetic analysis frequently leads to the creation of many phylogenetic trees, either from using multiple genes or methods, or through bootstrapping or Bayesian analysis. A consensus tree is often used to summarize what the trees have in common. Consensus networks were introduced to also allow the visualization of the main incompatibilities among the trees. However, in practice, such networks often contain a large number of nodes and edges, and can be non-planar, making them difficult to interpret. Here, we introduce the new concept of a phylogenetic consensus outline, which provides a planar visualization of incompatibilities in the input trees, without the complexities of a consensus network. Furthermore, we present an effective algorithm for its computation. We demonstrate its usage and explore how it compares to other methods on a Bayesian phylogenetic analysis of languages using data from a published database and on multiple gene trees from a published study on water lilies.

On constructing network Lyapunov function for leaderless consensus over switching digraphs

This paper investigates the exponential Lyapunov analysis for leaderless consensus of networks with directed switching graphs. Both discrete-time and continuous-time linear agent dynamics are considered. A quadratic Lyapunov function is constructed using two positive definite matrices. Two graph matrix inequalities are proposed using the graph Laplacian matrix to calculate the graph positive definite matrix for constructing the Lyapunov function. The continuous-time Riccati inequality and a modified discrete-time Riccati inequality are utilized to calculate the dynamics positive definite matrix for the Lyapunov function design as well as the distributed control design. Average dwell time (ADT) is used to describe the switching signal. Lyapunov analysis is performed to achieve exponential leaderless consensus with convergence rate specified by the parameters in the matrix inequalities and ADT.

Wireless Distributed Consensus in Vehicle to Vehicle Networks for Autonomous Driving

Vital societal and industrial autonomous components are increasingly interconnected through communication networks to complete critical tasks cooperatively. However, as the reliability and trust requirements for connected autonomous systems continue to grow, the centralized communication and decision approaches that are in use today are reaching their limits. Focusing on autonomous driving applications, this paper proposes a resilient and trustworthy framework on wireless distributed consensus networks, where the communication links are less reliable or are even in the presence of incorrect local sensor readings/decisions. To accomplish that, a novel three stages consensus mechanism is proposed based on the practical Byzantine fault tolerance (PBFT), where the veto collection and gossip stages are designed to meet the stringent and complex requirements for a vehicle's maneuvers. A plan tree synthesis is also proposed to make consensus on a series of decisions while adopting network members' decision preferences. A detailed protocol including the distributed consensus, plan tree synthesis, dynamic grouping, etc. is proposed. Simulation results show that the proposed consensus mechanism is able to be reached and propagated through the network under poor wireless communication conditions and the presence of faulty vehicles with incorrect sensor readings. The result can be extended to other autonomous systems to significantly enhance safety in critical industrial applications.

Decoding individual differences in self-prioritization from the resting-state functional connectome

Although the self has traditionally been viewed as a higher-order mental function by most theoretical frameworks, recent research advocates a fundamental self hypothesis, viewing the self as a baseline function of the brain embedded within its spontaneous activities, which dynamically regulates cognitive processing and subsequently guides behavior. Understanding this fundamental self hypothesis can reveal where self-biased behaviors emerge and to what extent brain signals at rest can predict such biased behaviors. To test this hypothesis, we investigated the association between spontaneous neural connectivity and robust self-bias in a perceptual matching task using resting-state functional magnetic resonance imaging (fMRI) in 348 young participants. By decoding whole-brain connectivity patterns, the support vector regression model produced the best predictions of the magnitude of self-bias in behavior, which was evaluated via a nested cross-validation procedure. The out-of-sample generalizability was further authenticated using an external dataset of older adults. The functional connectivity results demonstrated that self-biased behavior was associated with distinct connections between the default mode, cognitive control, and salience networks. Consensus network and computational lesion analyses further revealed contributing regions distributed across six networks, extending to additional nodes, such as the thalamus, whose role in self-related processing remained unclear. These results provide evidence that self-biased behavior derives from spontaneous neural connectivity, supporting the fundamental self hypothesis. Thus, we propose an integrated neural network model of this fundamental self that synthesizes previous theoretical models and portrays the brain mechanisms by which the self emerges at rest internally and regulates responses to the external environment.

Managing consensus in balanced networks based on opinion and Trust/Distrust evolutions

Trust and distrust relationships are both common in social interactions of group decision making (GDM). Traditionally, trust/distrust levels are fixed in the opinion evolution process and irrelevant to the divergence of opinions. Breaking the routine, our paper considers a GDM problem with an intertwined evolution of opinions and trust/distrust levels in a balanced network (BN). To solving this problem, we propose a consensus-reaching framework to characterize the interactive and iterative process of opinion dynamics and trust/distrust level evolution in BNs. From the framework, we obtain the stable results of opinion dynamics and determine their convergence range in different BNs. Meanwhile, despite no consensus formed in these results, the key role of opinion leaders is captured in settling divergences. To eliminate the divergence and promote the consensus-reaching, we then devise leader-based strategies of minimum adjustments corresponding to different BNs by building consensus models. Finally, a series of simulation experiments are provided to validate the feasibility and effectiveness of our theoretical results, and a comparative analysis is implemented to further verify the effect of our consensus models.

Robustness of Consensus of Two-Layer Ring Networks

The topology structure of multi-layer networks is highly correlated with the robustness of consensus. This paper investigates the influence of different interlayer edge connection patterns on the consensus of the two-layer ring networks. Two types of two-layer ring network models are first considered: one is a kind of two-layer ring network with two linked edges between layers (Networks-a), and the other is a kind of two-layer ring network with three linked edges between layers (Networks-b). Using the Laplacian spectrum, the consensus of the network model is derived. The simulation experiments are used to demonstrate the influence of different interlayer edge connection patterns on the consensus of networks. To determine the best edge connection pattern for Networks-a and Networks-b, the number of nodes in a single-layer ring network is denoted by n. The best edge connection pattern for Networks-a is 1 & [(n+2)/2]. Furthermore, n is subdivided into 3k,3k+1,3k+2, and the best edge connection patterns of Networks-b are near 1 & k+1 & 2k+1.

Scale fragilities in localized consensus dynamics

We consider distributed consensus in networks where the agents have integrator dynamics of order two or higher (n≥2). We assume all feedback to be localized in the sense that each agent has a bounded number of neighbors and consider a scaling of the network through the addition of agents in a modular manner, i.e., without re-tuning controller gains upon addition. We show that standard consensus algorithms, which rely on relative state feedback, are subject to what we term scale fragilities, meaning that stability is lost as the network scales. For high-order agents (n≥3), we prove that no consensus algorithm with fixed gains can achieve consensus in networks of any size. That is, while a given algorithm may allow a small network to converge, it causes instability if the network grows beyond a certain finite size. This holds in families of network graphs whose algebraic connectivity, that is, the smallest non-zero Laplacian eigenvalue, is decreasing towards zero in network size (e.g. all planar graphs). For second-order consensus (n=2) we prove that the same scale fragility applies to directed graphs that have a complex Laplacian eigenvalue approaching the origin (e.g. directed ring graphs). The proofs for both results rely on Routh–Hurwitz criteria for complex-valued polynomials and hold true for general directed network graphs. We survey classes of graphs subject to these scale fragilities, discuss their scaling constants, and finally prove that a sub-linear scaling of nodal neighborhoods can suffice to overcome the issue.

Resilient Structural Sparsity in the Design of Consensus Networks.

The consensus problem is relevant to different areas ranging from biology, social psychology, and physics to power systems and robotics. Two crucial aspects of the design of a consensus system are the implementation issues that arise in densely connected networks and the presence of malicious agents that try to cause a deviation from a synchronization state. In this article, we introduce a formulation to design the topology of a consensus network to improve its resilience to attacks while remaining sparse and consistent with the a priori structural relations between the agents. Through mathematical analysis and simulations on artificial and real-world cases, we show the benefits and usefulness of using this strategy to design resilient and structurally sparse consensus networks.

Is Santaniella a ranunculid? Reassessment of this enigmatic fossil angiosperm from the Lower Cretaceous (Aptian, Crato Konservat-Lagerstätte, Brazil) provides a new interpretation.

The Lower Cretaceous Crato Konservat-Lagerstätte (CKL) preserves a rich flora that includes early angiosperms from northern Gondwana. From this area, the recently described fossil genus Santaniella was interpreted as a ranunculid (presumably Ranunculaceae). However, based on our examination of an additional specimen and a new phylogenetic analysis, we offer an alternative interpretation. The new fossil was collected from an active quarry for paving stones in the state of Ceará, northeastern Brazil. We assessed support for alternative phylogenetic hypotheses using a combined analysis of morphological data and DNA sequence data using Bayesian inference. We used a consensus network to visualize the posterior distribution of trees, and we used RoguePlot to illustrate the support for alternative positions on a scaffold tree. The new material includes a flower-like structure not present in the original material and also includes follicles preserved at early stages of development. The flower-like structure is a compact terminal cluster of elliptical sterile laminar organs surrounding internal filamentous structures that occur on flexuous axes. Phylogenetic analyses did not support the fossil placement among eudicots. Instead, Santaniella appears to belong in the magnoliid clade. The presence of seeds in a marginal-linear placentation and enclosed in a follicle supports the fossil as an angiosperm. However, even though most characters are clearly recognizable, its combination of characters does not provide strong support for a close relationship to any extant order of flowering plants. Its position in the magnoliid clade is intriguing and, based on plicate carpels, it is definitely a mesangiosperm.

Analysis of the consensus of double-layer chain networks

The multi-layer network topology structures directly affect the robustness of network consensus. The different positions of edges between layers will lead to a great difference in the consensus of double-layer chain networks. Finding the optimal positions of edges for consensus can help to design the network topology structures with optimal robustness. In this paper, we first derive the coherence of double-layer chain networks with one and two connected edges between layers by graph theory. Secondly, the optimal and worst connection edges positions of the two types of networks are simulated. When there is one edge between layers, the optimal edge connection position is found at 1/2 of each chain, and the worst edge connection position is found at the end node of the chain. When there are two edges between layers, the optimal edges connection positions are located at 1/5 and 4/5 of each chain respectively, and the worst edges connection positions are located at the end node of the chain and its neighbor node. Furthermore, we find that the optimal edge connection positions are closely related to the number of single-layer network nodes, and obtain their specific rules.