Small-world Model Research Articles

Resilient back-propagation approach in small-world feed-forward neural network topology based on Newman–Watts algorithm

The scientific researches are focused on network topologies and training algorithms fields because they reduce overfitting problem in artificial neural networks. In this context, we showed in our previous work that Newman–Watts small-world feed-forward artificial neural networks present better classification and prediction performance than conventional feed-forward artificial neural networks. In this study, we investigate the effects of the Resilient back-propagation algorithm on SW network topology and propose a Resilient Newman–Watts small-world feed-forward artificial neural network model by assuming fixed initial topological conditions. We find that Resilient small-world network further reduces overfitting and further increases the network performance when compared to the conventional feed-forward artificial neural networks. Furthermore, it is shown that the proposed network model does not increase the algorithmic complexity as per other models. The obtained results imply that the proposed model can contribute to the solving of overfitting problem encountered in both deep neural networks and conventional artificial neural networks.

Time Synchronized Node Localization Using Optimal H-Node Allocation in a Small World WSN

Time synchronization and node localization over a wireless sensor network (WSN) is a vital problem in applications such as Internet of Things (IoT) and context-aware pervasive systems. Addressing this problem leads to an efficient data fusion, power scheduling, bandwidth utilization, geographic routing, time-based channel sharing, and clustering among sensor nodes. In a WSN, sensor nodes utilize multi-hop data transmission model towards the data transfer. Utilization of large number of hops for the data transfer leads to poor time synchronization resulting in erroneous node location estimates. In this letter, we make use of a recent development in social networks termed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">small world characteristics</i> and propose a novel method of time synchronized node localization over a small world WSN (SW-WSN). The results are obtained via simulations over a medium scale WSN. The performance of the proposed method is evaluated by conducting detailed analysis of time synchronization and node localization errors over the SW-WSN. The results obtained illustrate that the proposed small world model yields improved localization results when compared to results obtained over a regular WSN.

Impact of Network Topology on the Spread of Infectious Diseases

The complex network theory constitutes a natural support for the study of a disease propagation. In this work, we present a study of an infectious disease spread with the use of this theory in combination with the Individual Based Model. More specifically, we use several complex network models widely known in the literature to verify their topological effects in the propagation of the disease. In general, complex networks with different properties result in curves of infected individuals with different behaviors, and thus, the growth of a given disease is highly sensitive to the network model used. The disease eradication is observed when the vaccination strategy of 10% of the population is used in combination with the random, small world or modular network models, which opens an important space for control actions that focus on changing the topology of a complex network as a form of reduction or even elimination of an infectious disease.

Impact of network topology on the spread of infectious diseases

ABSTRACT The complex network theory constitutes a natural support for the study of a disease propagation. In this work, we present a study of an infectious disease spread with the use of this theory in combination with the Individual Based Model. More specifically, we use several complex network models widely known in the literature to verify their topological effects in the propagation of the disease. In general, complex networks with different properties result in curves of infected individuals with different behaviors, and thus, the growth of a given disease is highly sensitive to the network model used. The disease eradication is observed when the vaccination strategy of 10% of the population is used in combination with the random, small world or modular network models, which opens an important space for control actions that focus on changing the topology of a complex network as a form of reduction or even elimination of an infectious disease.

An Application of Affective Computing on Mental Disorders: A Resting State fNIRS Study

Affective computing is important for making computers smarter. When emotion can be quantified, machines can understand it. This study aims to apply affective computing to mental disorders, and to classify healthy people and mentally illnesses. For this purpose, 85 subjects, including major depressive disorder patients, schizophrenia patients, and health control people were recruited to participate in resting state functional near infrared spectroscopy (fNIRS) experiment. We measured the changes in oxygenated blood concentration in the prefrontal cortex (PFC). We then used three types of correlation analysis methods to construct the functional connectivity matrices: Pearson correlation analysis (CORR), amplitude squared coherence coefficient (COH), and phase locking value (PLV). We performed the small-world model and centrality analysis based on these matrices. The results demonstrated the existence of a small-world model in both patients and healthy people’s brain networks. Furthermore, features such as the characteristic path length and betweenness centrality extracted from the functional connectivity matrix are helpful for classifying patients and healthy people, thus providing a method for detecting and identifying mental disorders.

Religion: costs, signals, and the Neolithic transition

ABSTRACT This paper extends the picture developed in Religion Re-Explained (Sterelny, 2018) to groups in transition from egalitarian to inegalitarian social environments, “big men” societies and their archaeological equivalents. It begins by giving a more nuanced account of the relationship between signals, rituals, and costs, showing that the costly signaling model of religion is best seen as a family of models. These vary in the extent to which they scale from smaller to larger social worlds. Some are scale-independent; others can be scaled up, but only by overcoming increasingly difficult signal broadcast problems; one is an intrinsically small scale intimate social world model. These issues of scalability are then integrated with transformations in the character and function of ritual and belief, as ritual becomes an instrument for competitive interactions within and across groups, and an expression of unequal status and power, while also retaining in important ways earlier roles of mediating social cohesion. Changes in ritual were both a mechanism and an expression of the shift to a less equal social world.

Improving dynamics of integer-order small-world network models under fractional-order PD control

The optimal control of dynamics is a popular topic for small-world networks. In this paper, we address the problem of improving the behavior of Hopf bifurcations in an integer-order model of small-world networks. In this study, the time delay is used as the bifurcation parameter. We add a fractional-order proportional-derivative (PD) scheme to an integer-order Newman-Watts (N-W) small-world model to better control the Hopf bifurcation of the model. The most important contribution of this paper involves obtaining the stability of the system and the variation of the conditions of the Hopf bifurcation after a fractional PD controller is added to the integer-order small-world model. The results demonstrate that the designed PD controller can be used to restrain or promote the occurrence of Hopf bifurcations by setting appropriate parameters. We also describe several simulations to verify our research results.

SMALL-WORLD EFFECT IN GEOGRAPHICAL ATTACHMENT NETWORKS

AbstractIn this work, we use rigorous probabilistic methods to study the asymptotic degree distribution, clustering coefficient, and diameter of geographical attachment networks. As a type of small-world network model, these networks were first proposed in the physical literature, where they were analyzed only with heuristic arguments and computational simulations.

EXPLORING THE VULNERABILITY OF FRACTAL COMPLEX NETWORKS THROUGH CONNECTION PATTERN AND FRACTAL DIMENSION

The structure of network has a significant impact on the stability of the network. It is useful to reveal the effect of fractal structure on the vulnerability of complex network since it is a ubiquitous feature in many real-world networks. There have been many studies on the stability of the small world and scale-free models, but little has been down on the quantitative research on fractal models. In this paper, the vulnerability was studied from two perspectives: the connection pattern between hubs and the fractal dimensions of the networks. First, statistics expression of inter-connections between any two hubs was defined and used to represent the connection pattern of the whole network. Our experimental results show that statistic values of inter-connections were obvious differences for each kind of complex model, and the more inter-connections, the more stable the network was. Secondly, the fractal dimension was considered to be a key factor related to vulnerability. Here we found the quantitative power function relationship between vulnerability and fractal dimension and gave the explicit mathematical formula. The results are helpful to build stable artificial network models through the analysis and comparison of the real brain network.

Quasi-periodic events on structured earthquake models**Project supported by the National Natural Science Foundation of China (Grant Nos. 11575072 and 11675096), the Fundamental Research Funds for the Central Universities, China (Grant No. GK201702001), and the FPALAB-SNNU, China (Grant No. 16QNGG007).

There has been much interest in studying quasi-periodic events on earthquake models. Here we investigate quasi-periodic events in the avalanche time series on structured earthquake models by the analysis of the autocorrelation function and the fast Fourier transform. For random spatial earthquake models, quasi-periodic events are robust and we obtain a simple rule for a period that is proportional to the choice of unit time and the dissipation of the system. Moreover, computer simulations validate this rule for two-dimensional lattice models and cycle graphs, but our simulation results also show that small-world models, scale-free models, and random rule graphs do not have periodic phenomena. Although the periodicity of avalanche does not depend on the criticality of the system or the average degree of the system or the size of the system, there is evidence that it depends on the time series of the average force of the system.

On the maximum small-world subgraph problem

A clique (or a complete subgraph) is a popular model for an “ideal” cluster in a network. However, in many practical applications this notion turns out to be overly restrictive as it requires the existence of all pairwise links within the cluster. Thus, the researchers and practitioners often rely on various clique relaxation ideas for more flexible models of highly connected clusters. In this paper, we propose a new clique relaxation model referred to as a small-world subgraph, which represents a network cluster with “small-world” properties: low average distance and high clustering coefficient. In particular, we demonstrate that the proposed small-world subgraph model has better “cohesiveness” characteristics than other existing clique relaxation models in some worst-case scenarios. The main focus of the paper is on the problem of finding a small-world subgraph of maximum cardinality in a given graph. We describe a mixed integer programming (MIP) formulation of the problem along with several algorithmic enhancements. For solving large-scale instances of the problem we propose a greedy-type heuristic referred to as the iterative depth-first search (IDF) algorithm. Furthermore, we show that the small-world subgraphs identified by the IDF algorithm have an additional property that may be attractive from the practical perspective, namely, 2-connectivity. Finally, we perform extensive computational experiments on real-world and randomly generated networks to demonstrate the performance of the developed computational approaches that also reveal interesting insights about the proposed clique relaxation model.

Minimum Memory-Based Sign Adjustment in Signed Social Networks.

In social networks comprised of positive (P) and negative (N) symmetric relations, individuals (nodes) will, under the stress of structural balance, alter their relations (links or edges) with their neighbours, either from positive to negative or vice versa. In the real world, individuals can only observe the influence of their adjustments upon the local balance of the network and take this into account when adjusting their relationships. Sometime, their local adjustments may only respond to their immediate neighbourhoods, or centre upon the most important neighbour. To study whether limited memory affects the convergence of signed social networks, we introduce a signed social network model, propose random and minimum memory-based sign adjustment rules, and analyze and compare the impacts of an initial ratio of positive links, rewire probability, network size, neighbor number, and randomness upon structural balance under these rules. The results show that, with an increase of the rewiring probability of the generated network and neighbour number, it is more likely for the networks to globally balance under the minimum memory-based adjustment. While the Newmann-Watts small world model (NW) network becomes dense, the counter-intuitive phenomena emerges that the network will be driven to a global balance, even under the minimum memory-based local sign adjustment, no matter the network size and initial ratio of positive links. This can help to manage and control huge networks with imited resources.

Generalization of the small-world effect on a model approaching the Erd\u0151s\u2013R\xe9nyi random graph

The famous Watts–Strogatz (WS) small-world network model does not approach the Erdős–Rényi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative which was first introduced by Song and Wang, where instead of rewiring, edges are drawn between pairs of nodes with a distance-based connection probability. We show that this model is simpler to analyze, approaches the true ER random graph model in the completely randomized limit, and demonstrate that the WS model and the alternative model may yield different quantitative results using the example of a random walk temporal observable. An efficient sampling algorithm for the alternative model is proposed. Analytic results regarding the degree distribution, degree variance, number of two-stars per node, number of triangles per node, clustering coefficient, and random walk mixing time are presented. Subsequently, the small-world effect is illustrated by showing that the clustering coefficient decreases much slower than an upper bound on the message delivery time with increasing long-range connection probability which generalizes the small-world effect from informed searches to random search strategies. Due to its accessibility for analytic evaluations, we propose that this modified model should be used as an alternative reference model for studying the influence of small-world topologies on dynamic systems as well as a simple model to introduce numerous topics when teaching network science.

Dynamic optimal control at Hopf bifurcation of a Newman–Watts model of small-world networks via a new [formula omitted] scheme

In this paper, a neoteric fractional-order Proportional–Derivative (PD) feedback controller is proposed to address the problem of bifurcation control for an integer-order small-world network model with discrete delay. The time delay is selected as the bifurcation parameter, and sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed by analyzing the stability of the controlled system. By regulating the controller parameters, the dynamic behavior for the controlled system can be effectively optimized. Finally, by simulating numerical examples, theoretical derivations are verified and the relationships between the onset of the Hopf bifurcation and the controller parameters are obtained.

TOSG: A Topology Optimization Scheme With Global Small World for Industrial Heterogeneous Internet of Things

In Industrial Internet of Things (IIoT), sensor nodes are vulnerable to withstand node failures due to energy exhaustion or external attacks, which leads to the low connectivity of networks. In this situation, how to improve network reliability has became a crucial problem. Adding a small amount of shortcuts to build a small world model in IIoT not only can reduce the delay, but also increases the reliability of networks. In this paper, we propose a Topology Optimization Scheme with Global Small World (TOSG) based on ant colony for IIoT. First, according to the number of appearing on the all shortest paths obtained by the ant colony optimization algorithm, we give the definition of importance for each node. The node with the highest importance in the communication range of a node is defined as an important node. We can find the important nodes in the network topology so that some shortcuts can be created between them to build a global small world model. The experiment results show that the TOSG model has a smaller average shortest path length and higher reliability compared with Greedy Model with Small World properties and Directed Angulation toward the Sink Node Model.

Gompertz’ Hazard Law as a Network Principle of Aging

Background: Life-spanning population survivorship curves (the number of survivors versus age) are conventionally regarded as a demographic issue. Most often, the term hazard, the relative mortality per age-interval, is used as a typical survivorship parameter. Population survivorship curves are construed from cross-sectional data (single event per individual; here, mortality). Objective: We tested (quantitatively) how Gompertz’ law describes the mortality pattern of a wide variety of organisms, some of them fed with lifespan affecting diets. Moreover, we tested (semi-quantitatively) whether Gompertz’ law describes the disintegration of a (biological) small-world network. Methods: The Gompertz tests, explored in demographic data of humans (male/female) and 4 animal species (mice, honeybees, fruit flies, houseflies), were analyzed with conventional software. The Gompertz law was examined in a small-world network model. Results: Gompertz' law applies to all cohorts; thus, with or without exposure to experimental conditions. It describes in all cohorts old-age slowing of mortality. Gompertz’ law is compatible with a gradual and random increase of connections in the network model. Conclusion: Old-age deceleration of mortality is a characteristic of many populations. Aging has to be understood as a lifetime increasing of excitatory or, alternatively, of decreasing inhibitory (biological) connections, thereby facilitating pathogenic mechanisms.

The idemetric property: when most distances are (almost) the same.

We introduce the idemetric property, which formalizes the idea that most nodes in a graph have similar distances between them, and which turns out to be quite standard amongst small-world network models. Modulo reasonable sparsity assumptions, we are then able to show that a strong form of idemetricity is actually equivalent to a very weak expander condition (PUMP). This provides a direct way of providing short proofs that small-world network models such as the Watts-Strogatz model are strongly idemetric (for a wide range of parameters), and also provides further evidence that being idemetric is a common property. We then consider how satisfaction of the idemetric property is relevant to algorithm design. For idemetric graphs, we observe, for example, that a single breadth-first search provides a solution to the all-pairs shortest paths problem, so long as one is prepared to accept paths which are of stretch close to 2 with high probability. Since we are able to show that Kleinberg's model is idemetric, these results contrast nicely with the well known negative results of Kleinberg concerning efficient decentralized algorithms for finding short paths: for precisely the same model as Kleinberg's negative results hold, we are able to show that very efficient (and decentralized) algorithms exist if one allows for reasonable preprocessing. For deterministic distributed routing algorithms we are also able to obtain results proving that less routing information is required for idemetric graphs than in the worst case in order to achieve stretch less than 3 with high probability: while Ω(n 2) routing information is required in the worst case for stretch strictly less than 3 on almost all pairs, for idemetric graphs the total routing information required is O(nlog(n)).

Temporal Analysis of the Diffusion of Knowledge in Networks of Software Maintenance and Development Project Team

Different approaches have been established for applications of social and complex networks involving biological systems, passing through collaborative systems in knowledge networks and organizational systems. In this latter application, we highlight the studies focused on the diffusion of information and knowledge in networks. However, most of the time, the propagation of information in these networks and the resulting process of creation and diffusion of knowledge, have been studied from static perspectives. Additionally, the very concept of diffusion inevitably implies the inclusion of the temporal dimension, due to that it is an essentially dynamic process. Although static analysis provides an important perspective in structural terms, the behavioral view that reflects the evolution of the relationships of the members of these networks over time is best described by temporal networks. Thus, it is possible to analyze both the information flow and the structural changes that occur over time, which influences the dynamics of the creation and diffusion of knowledge. This article describes the computational modeling used to elucidate the creation and diffusion of knowledge in temporal networks formed to execute software maintenance and construction projects, for the period between 2007 and 2013, in the SERVIÇO FEDERAL DE PROCESSAMENTO DE DADOS (FEDERAL DATA PROCESSING SERVICE-SERPRO)—a public organization that provides information and communication technology services. The methodological approach adopted for the study was based on techniques for analyzing social and complex networks and on the complementary extensions that address temporal modeling of these networks. We present an exploratory longitudinal study that enabled a dynamic and structural analysis of the knowledge networks formed by members of software maintenance and development project teams between 2007 and 2013. The study enabled identification of knowledge categories throughout this period, in addition to the determination that the networks have a structure with small-world and scale-free models. Finally, we concluded that, in general, the topologies of the networks studies had characteristics for facilitating the flow of knowledge within the organization.

Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges.

The well-known small-world network model was established by randomly rewiring edges, aiming to enhance the synchronizability of an undirected nearest-neighbor regular network. This paper demonstrates via extensive numerical simulations that randomly redirecting edges could enhance the robustness of the network controllability for directed snapback networks against both random and intentional node-removal and edge-removal attacks.

Study on internet of vehicles traffic congestion detection algorithm based on big data

In order to improve the traffic congestion detection capability of the vehicle network, a vehicle network congestion detection algorithm based on big data is proposed. The algorithm uses the Small-World model to construct a traffic distributed internet, and uses RFID tag reading technology to sample and fuse big data in the vehicle network, and to extract the inherent modal feature quantity of the vehicle traffic big data internet, and the road traffic network. The overall state information is reorganised; according to the modal feature extraction results inherent in the vehicle traffic data interconnection network, the vehicle path is optimally scheduled, and according to the big data analysis result, the linear traffic planning algorithm is used to detect the vehicle traffic congestion network. The simulation results show that the proposed method has higher accuracy in vehicle traffic jam detection, and the detection time is below 10 s, and the efficiency is higher. The method can improve the anti-congestion capability of the vehicle and has a strong traffic diversion capability, thereby effectively improving the traffic effect of the vehicle in the network environment.