The relationship between modularity and robustness in signalling networks

Many biological networks tend to have a high modularity structural property and the dynamic characteristic of high robustness against perturbations. However, the relationship between modularity and robustness is not well understood. To investigate this relationship, we examined real signalling networks and conducted simulations using a random Boolean network model. As a result, we first observed that the network robustness is negatively correlated with the network modularity. In particular, this negative correlation becomes more apparent as the network density becomes sparser. Even more interesting is that, the negative relationship between the network robustness and the network modularity occurs mainly because nodes in the same module with the perturbed node tend to be more sensitive to the perturbation than those in other modules. This result implies that dynamically similar nodes tend to be located in the same module of a network. To support this, we show that a pair of genes associated with the same disease or a pair of functionally similar genes is likely to belong to the same module in a human signalling network.     

Periodic dynamics of coupled cell networks II: cyclic symmetry

A coupled cell network is a directed graph whose nodes represent dynamical systems and whose directed edges specify how those systems are coupled to each other. The typical dynamic behaviour of a network is strongly constrained by its topology. Especially important constraints arise from global (group) symmetries and local (groupoid) symmetries. The H/K theorem of Buono and Golubitsky characterises the possible spatio-temporal symmetries of time-periodic states of group-equivariant dynamical systems. A version of this theorem for group-symmetric networks has been proved by Josi? and Török. In networks, spatial symmetries correspond to synchrony of cells, and spatio-temporal symmetries correspond to phase relations between cells. Associated with any coupled cell network is a canonical class of admissible ODEs that respect the network topology. A pattern of synchrony or phase relations in a hyperbolic time-periodic state of such an ODE is rigid if the pattern persists under small admissible perturbations. We characterise rigid patterns of synchrony and rigid phase patterns in coupled cell networks, on the assumption that the periodic state is fully oscillatory (no cell is in equilibrium) and the network has a basic property, the rigid phase property. We conjecture that all networks have the rigid phase property, and that in any path-connected network an admissible ODE with a hyperbolic periodic state can always be perturbed to make the perturbed periodic state fully oscillatory. Our main result states that in any path-connected network with the rigid phase property, every rigid pattern of phase relations can be characterised in two stages. First, sets of cells form synchronous clumps according to a balanced equivalence relation. Second, the corresponding quotient network has a cyclic group of automorphisms, and the phase relations are induced by associating a fixed phase shift with a generator of this group. Thus the clumps of synchronous cells form a discrete rotating wave. As a corollary, we prove an analogue of the H/K theorem for any path-connected network. We also discuss the non-path-connected case.     

Minimum steering node set of complex networks and its applications to biomolecular networks

Many systems of interests in practices can be represented as complex networks. For biological systems, biomolecules do not perform their functions alone but interact with each other to form so‐called biomolecular networks. A system is said to be controllable if it can be steered from any initial state to any other final state in finite time. The network controllability has become essential to study the dynamics of the networks and understand the importance of individual nodes in the networks. Some interesting biological phenomena have been discovered in terms of the structural controllability of biomolecular networks. Most of current studies investigate the structural controllability of networks in notion of the minimum driver node sets (MDSs). In this study, the authors analyse the network structural controllability in notion of the minimum steering node sets (MSSs). They first develop a graph‐theoretic algorithm to identify the MSS for a given network and then apply it to several biomolecular networks. Application results show that biomolecules identified in the MSSs play essential roles in corresponding biological processes. Furthermore, the application results indicate that the MSSs can reflect the network dynamics and node importance in controlling the networks better than the MDSs.Inspec keywords: molecular biophysics, biocontrol, graph theoryOther keywords: graph‐theoretic algorithm, MSS, minimum driver node sets, structural controllability, network dynamics, network controllability, biological systems, biomolecular networks, complex networks, minimum steering node set     

Anti‐triangle centrality‐based community detection in complex networks

Community detection has been extensively studied in the past decades largely because of the fact that community exists in various networks such as technological, social and biological networks. Most of the available algorithms, however, only focus on the properties of the vertices, ignoring the roles of the edges. To explore the roles of the edges in the networks for community discovery, the authors introduce the novel edge centrality based on its antitriangle property. To investigate how the edge centrality characterises the community structure, they develop an approach based on the edge antitriangle centrality with the isolated vertex handling strategy (EACH) for community detection. EACH first calculates the edge antitriangle centrality scores for all the edges of a given network and removes the edge with the highest score per iteration until the scores of the remaining edges are all zero. Furthermore, EACH is characterised by being free of the parameters and independent of any additional measures to determine the community structure. To demonstrate the effectiveness of EACH, they compare it with the state‐of‐the art algorithms on both the synthetic networks and the real world networks. The experimental results show that EACH is more accurate and has lower complexity in terms of community discovery and especially it can gain quite inherent and consistent communities with a maximal diameter of four jumps.Inspec keywords: biology computing, complex networks, graph theory, social sciences computingOther keywords: antitriangle centrality‐based community detection, complex networks, technological networks, social networks, biological networks, vertex properties, edge roles, community discovery, antitriangle property, community structure, edge antitriangle centrality, isolated vertex handling strategy, EACH, antitriangle centrality scores, synthetic networks, real world networks     

Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information, lists of chemical reactions, available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure—network modularity (the propensity for edges to be clustered into dense groups that are sparsely connected between each other). To achieve this goal, we design a model of reaction systems where network modularity can be controlled and measure how well the reduction to simple graphs captures the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate–product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreates correlations between degree and mass of the molecules.     

Optimal allocation of multi-state retransmitters in acyclic transmission networks

In this paper, an algorithm for optimal allocation of multi-state elements (MEs) in acyclic transmission networks (ATNs) is suggested. The ATNs consist of a number of positions (nodes) in which MEs capable of receiving and sending a signal are allocated. Each network has a root position where the signal source is located, a number of leaf positions that can only receive a signal, and a number of intermediate positions containing MEs capable of transmitting the received signal to some other nodes. Each ME that is located in a nonleaf node can have different states determined by a set of nodes receiving the signal directly from this ME. The probability of each state is assumed to be known for each ME. The ATN reliability is defined as the probability that a signal from the root node is transmitted to each leaf node.The optimal distribution of MEs with different characteristics among ATN positions provides the greatest possible ATN reliability. The suggested algorithm is based on using a universal generating function technique for network reliability evaluation. A genetic algorithm is used as the optimization tool. Illustrative examples are presented.     

Probabilistic patterns of interaction: the effects of link-strength variability on food web structure

Patterns of species interactions affect the dynamics of food webs. An important component of species interactions that is rarely considered with respect to food webs is the strengths of interactions, which may affect both structure and dynamics. In natural systems, these strengths are variable, and can be quantified as probability distributions. We examined how variation in strengths of interactions can be described hierarchically, and how this variation impacts the structure of species interactions in predator–prey networks, both of which are important components of ecological food webs. The stable isotope ratios of predator and prey species may be particularly useful for quantifying this variability, and we show how these data can be used to build probabilistic predator–prey networks. Moreover, the distribution of variation in strengths among interactions can be estimated from a limited number of observations. This distribution informs network structure, especially the key role of dietary specialization, which may be useful for predicting structural properties in systems that are difficult to observe. Finally, using three mammalian predator–prey networks (two African and one Canadian) quantified from stable isotope data, we show that exclusion of link-strength variability results in biased estimates of nestedness and modularity within food webs, whereas the inclusion of body size constraints only marginally increases the predictive accuracy of the isotope-based network. We find that modularity is the consequence of strong link-strengths in both African systems, while nestedness is not significantly present in any of the three predator–prey networks.     

Quantifying the underlying landscape and paths of cancer

Cancer is a disease regulated by the underlying gene networks. The emergence of normal and cancer states as well as the transformation between them can be thought of as a result of the gene network interactions and associated changes. We developed a global potential landscape and path framework to quantify cancer and associated processes. We constructed a cancer gene regulatory network based on the experimental evidences and uncovered the underlying landscape. The resulting tristable landscape characterizes important biological states: normal, cancer and apoptosis. The landscape topography in terms of barrier heights between stable state attractors quantifies the global stability of the cancer network system. We propose two mechanisms of cancerization: one is by the changes of landscape topography through the changes in regulation strengths of the gene networks. The other is by the fluctuations that help the system to go over the critical barrier at fixed landscape topography. The kinetic paths from least action principle quantify the transition processes among normal state, cancer state and apoptosis state. The kinetic rates provide the quantification of transition speeds among normal, cancer and apoptosis attractors. By the global sensitivity analysis of the gene network parameters on the landscape topography, we uncovered some key gene regulations determining the transitions between cancer and normal states. This can be used to guide the design of new anti-cancer tactics, through cocktail strategy of targeting multiple key regulation links simultaneously, for preventing cancer occurrence or transforming the early cancer state back to normal state.     

Determination of critical network interactions: an augmented Boolean pseudo-dynamics approach

Network theory has established that highly connected nodes in regulatory networks (hubs) show a strong correlation with criticality in network function. Although topological analysis is fully capable of identifying network hubs, it does not provide an objective method for ranking the importance of a particular node by relating its contribution to the overall network response. Towards this end, the authors have developed an augmented Boolean pseudo-dynamics approach to a priori determine the critical network interactions in biological interaction networks. The approach utilises network topology and dynamic state information to determine the set of active pathways. The active pathways are used in conjunction with the key cellular properties of efficiency and robustness, to rank the network interactions based on their importance in the sustenance of network function. To demonstrate the utility of the approach, the authors consider the well characterised guard cell signalling network in plant cells. An integrated analysis of the network revealed the critical mechanisms resulting in stomata closure in the presence and absence of abscisic acid, in excellent agreement with published results.     

Reliability evaluation for acyclic consecutively connected networks with multistate elements

In this paper, an algorithm for acyclic consecutively connected networks (ACCN) reliability evaluation is suggested. The ACCNs consist of a number of positions in which multistate elements (MEs) capable of receiving and/or sending a signal are allocated. Each network has a root position where the signal source is located, a number of leaf positions that can only receive a signal, and a number of intermediate positions containing MEs capable of transmitting the received signal to some other nodes. Each ME that is located in a nonleaf node can have different states determined by a set of nodes receiving the signal directly from this ME. The probability of each state is assumed to be known for each ME. The ACCN reliability is defined as the probability that a signal from the root node is transmitted to each leaf node. The suggested algorithm is based on a universal generating function technique.     

Identification of Anomaly Scenes in Videos Using Graph Neural Networks

Generally, conventional methods for anomaly detection rely on clustering, proximity, or classification. With the massive growth in surveillance videos, outliers or anomalies find ingenious ways to obscure themselves in the network and make conventional techniques inefficient. This research explores the structure of Graph neural networks (GNNs) that generalize deep learning frameworks to graph-structured data. Every node in the graph structure is labeled and anomalies, represented by unlabeled nodes, are predicted by performing random walks on the node-based graph structures. Due to their strong learning abilities, GNNs gained popularity in various domains such as natural language processing, social network analytics and healthcare. Anomaly detection is a challenging task in computer vision but the proposed algorithm using GNNs efficiently performs the identification of anomalies. The Graph-based deep learning networks are designed to predict unknown objects and outliers. In our case, they detect unusual objects in the form of malicious nodes. The edges between nodes represent a relationship of nodes among each other. In case of anomaly, such as the bike rider in Pedestrians data, the rider node has a negative value for the edge and it is identified as an anomaly. The encoding and decoding layers are crucial for determining how statistical measurements affect anomaly identification and for correcting the graph path to the best possible outcome. Results show that the proposed framework is a step ahead of the traditional approaches in detecting unusual activities, which shows a huge potential in automatically monitoring surveillance videos. Performing autonomous monitoring of CCTV, crime control and damage or destruction by a group of people or crowd can be identified and alarms may be triggered in unusual activities in streets or public places. The suggested GNN model improves accuracy by 4% for the Pedestrian 2 dataset and 12% for the Pedestrian 1 dataset compared to a few state-of-the-art techniques.     

Optimal series–parallel topology of multi-state system with two failure modes

In this paper, an algorithm for optimal allocation of multi-state elements (MEs) in acyclic transmission networks (ATNs) is suggested. The ATNs consist of a number of positions (nodes) in which MEs capable of receiving and sending a signal are allocated. Each network has a root position where the signal source is located, a number of leaf positions that can only receive a signal, and a number of intermediate positions containing MEs capable of transmitting the received signal to some other nodes. Each ME that is located in a nonleaf node can have different states determined by a set of nodes receiving the signal directly from this ME. The probability of each state is assumed to be known for each ME. The ATN reliability is defined as the probability that a signal from the root node is transmitted to each leaf node.The optimal distribution of MEs with different characteristics among ATN positions provides the greatest possible ATN reliability. The suggested algorithm is based on using a universal generating function technique for network reliability evaluation. A genetic algorithm is used as the optimization tool. Illustrative examples are presented.     

An Influence Maximization Algorithm Based on Improved K-Shell in Temporal Social Networks

Influence maximization of temporal social networks (IMT) is a problem that aims to find the most influential set of nodes in the temporal network so that their information can be the most widely spread. To solve the IMT problem, we propose an influence maximization algorithm based on an improved K-shell method, namely improved K-shell in temporal social networks (KT). The algorithm takes into account the global and local structures of temporal social networks. First, to obtain the kernel value Ks of each node, in the global scope, it layers the network according to the temporal characteristic of nodes by improving the K-shell method. Then, in the local scope, the calculation method of comprehensive degree is proposed to weigh the influence of nodes. Finally, the node with the highest comprehensive degree in each core layer is selected as the seed. However, the seed selection strategy of KT can easily lose some influential nodes. Thus, by optimizing the seed selection strategy, this paper proposes an efficient heuristic algorithm called improved K-shell in temporal social networks for influence maximization (KTIM). According to the hierarchical distribution of cores, the algorithm adds nodes near the central core to the candidate seed set. It then searches for seeds in the candidate seed set according to the comprehensive degree. Experiments show that KTIM is close to the best performing improved method for influence maximization of temporal graph (IMIT) algorithm in terms of effectiveness, but runs at least an order of magnitude faster than it. Therefore, considering the effectiveness and efficiency simultaneously in temporal social networks, the KTIM algorithm works better than other baseline algorithms.     

Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection towards hierarchical architectures

Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary time scales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of biological networks is studied by considering a network of a few nodes embedded in a larger context. Taking into account this fact that any network under study is actually embedded in a larger context, we define network architecture, not on the basis of physical interactions alone, but rather as a specification of the manner in which constraints are placed upon the states of its nodes. We show that such network architectures possessing cycles in their topology, in contrast to those that do not, may be subjected to unsatisfiable constraints. This may be a significant factor leading to selection biased against those network architectures where such inconsistent constraints are more likely to arise. We proceed to quantify the likelihood of inconsistency arising as a function of network architecture finding that, in the absence of sampling bias over the space of possible constraints and for a given network size, networks with a larger number of cycles are more likely to have unsatisfiable constraints placed upon them. Our results identify a constraint that, at least in isolation, would contribute to a bias in the evolutionary process towards more hierarchical -modular versus completely connected network architectures. Together, these results highlight the context dependence of the functionality of biological networks.     

Wireless Sensor Network Modeling Using Modified Recurrent Neural Networks: Application to Fault Detection

This paper presents a dynamic model of wireless sensor networks (WSNs) and its application to sensor node fault detection. Recurrent neural networks (NNs) are used to model a sensor node, the node's dynamics, and interconnections with other sensor network nodes. An NN modeling approach is used for sensor node identification and fault detection in WSNs. The input to the NN is chosen to include previous output samples of the modeling sensor node and the current and previous output samples of neighboring sensors. The model is based on a new structure of a backpropagation-type NN. The input to the NN and the topology of the network are based on a general nonlinear sensor model. A simulation example, including a comparison to the Kalman filter method, has demonstrated the effectiveness of the proposed scheme.     

改进遗传-狼群对节点序寻优的贝叶斯网络结构算法

贝叶斯网络是数据挖掘领域的一种重要方法。针对贝叶斯网络结构学习算法寻优效率低和易陷入局部最优的问题，提出一种基于改进的混合遗传-狼群对节点序寻优的贝叶斯网络结构学习算法。该算法首先利用深度优先搜索对最大支撑树的节点进行拓扑排序；然后利用动态变异及最优交叉算子构建适用于节点序寻优的改进捕食行为，引入动态参数因子来增强算法局部寻优能力；最后与K2算法结合得到最优的贝叶斯网络结构。用3种不同大小的标准网络数据集中进行实验，结果表明，该算法收敛到较优值，寻优效率高于其它同类优化算法。     

Hierarchical parameter estimation of GRN based on topological analysis

Reverse engineering of gene regulatory network (GRN) is an important and challenging task in systems biology. Existing parameter estimation approaches that compute model parameters with the same importance are usually computationally expensive or infeasible, especially in dealing with complex biological networks.In order to improve the efficiency of computational modeling, the paper applies a hierarchical estimation methodology in computational modeling of GRN based on topological analysis. This paper divides nodes in a network into various priority levels using the graph‐based measure and genetic algorithm. The nodes in the first level, that correspond to root strongly connected components(SCC) in the digraph of GRN, are given top priority in parameter estimation. The estimated parameters of vertices in the previous priority level ARE used to infer the parameters for nodes in the next priority level. The proposed hierarchical estimation methodology obtains lower error indexes while consuming less computational resources compared with single estimation methodology. Experimental outcomes with insilico networks and a realistic network show that gene networks are decomposed into no more than four levels, which is consistent with the properties of inherent modularity for GRN. In addition, the proposed hierarchical parameter estimation achieves a balance between computational efficiency and accuracy.Inspec keywords: biology computing, network theory (graphs), reverse engineering, graph theory, genetics, genetic algorithms, directed graphs, parameter estimationOther keywords: hierarchical parameter estimation, GRN, topological analysis, gene regulatory network, important task, computational systems biology, compute model parameters, complex biological networks, efficient information, model quality, parameter reliability, computational modelling, study divides nodes, priority levels, graph‐based measure, previous priority level, hierarchical estimation methodology obtains, computational resources, single time estimation, insilico network, realistic network show, computational efficiency     

On computing the reliability of opportunistic multihop networks with Mobile relays

Opportunistic multihop networks with mobile relays recently have drawn much attention from researchers across the globe due to their wide applications in various challenging environments. However, because of their peculiar intrinsic features like lack of continuous connectivity, network partitioning, highly dynamic behavior, and long delays, it is very arduous to model and effectively capture the temporal variations of such networks with the help of classical graph models. In this work, we utilize an evolving graph to model the dynamic network and propose a matrix‐based algorithm to generate all minimal path sets between every node pair of such network. We show that these time‐stamped‐minimal‐path sets (TS‐MPS) between each given source‐destination node pair can be used, by utilizing the well‐known Sum‐of‐Disjoint Products technique, to generate various reliability metrics of dynamic networks, ie, two‐terminal reliability of dynamic network and its related metrics, ie, two‐terminal reliabilities of the foremost, shortest, and fastest TS‐MPS, and Expected Hop Count. We also introduce and compute a new network performance metric?Expected Slot Count. We use two illustrative examples of dynamic networks, one of four nodes, and the other of five nodes, to show the salient features of our technique to generate TS‐MPS and reliability metrics.     

MINE: A Method of Multi-Interaction Heterogeneous Information Network Embedding

Interactivity is the most significant feature of network data, especially in social networks. Existing network embedding methods have achieved remarkable results in learning network structure and node attributes, but do not pay attention to the multiinteraction between nodes, which limits the extraction and mining of potential deep interactions between nodes. To tackle the problem, we propose a method called MultiInteraction heterogeneous information Network Embedding (MINE). Firstly, we introduced the multi-interactions heterogeneous information network and extracted complex heterogeneous relation sequences by the multi-interaction extraction algorithm. Secondly, we use a well-designed multi-relationship network fusion model based on the attention mechanism to fuse multiple interactional relationships. Finally, applying a multitasking model makes the learned vector contain richer semantic relationships. A large number of practical experiments prove that our proposed method outperforms existing methods on multiple data sets.     

Prophet_TD Routing Algorithm Based on Historical Throughput and Encounter Duration

Opportunistic networks are self-organizing networks that do not require a complete path between the source node and the destination node as it uses encounter opportunities brought by nodes movement to achieve network communication. Opportunistic networks routing algorithms are numerous and can be roughly divided into four categories based on different forwarding strategies. The Prophet routing algorithm is an important routing algorithm in opportunistic networks. It forwards messages based on the encounter probability between nodes, and has good innovation significance and optimization potential. However, the Prophet routing algorithm does not consider the impact of the historical throughput of the node on message transmission, nor does it consider the impact of the encounter duration between nodes on message transmission. Therefore, to improve the transmission efficiency of opportunistic networks, this paper based on the Prophet routing algorithm, fuses the impact of the historical throughput of the node and the encounter duration between nodes on message transmission at the same time, and proposes the Prophet_TD routing algorithm based on the historical throughput and the encounter duration. This paper uses the Opportunistic Networks Environment v1.6.0 (the ONE v1.6.0) as the simulation platform, controls the change of running time and the number of nodes respectively, conducts simulation experiments on the Prophet_TD routing algorithm. The simulation results show that compared to the traditional Prophet routing algorithm, on the whole, the Prophet_TD routing algorithm has a higher message delivery rate and a lower network overhead rate, and its average latency is also lower when node density is large.