Statistical Properties Of Network Research Articles

Bifurcation and propagation dynamics of a discrete pair SIS epidemic model on networks with correlation coefficient

The spread of disease in social contact networks is inextricably linked to the topological and statistical properties of networks. In this work, dynamics of discrete epidemic system on networks with correlation and clustering coefficient are studied. In the scenario of ignoring clustering coefficient, critical value and stability of the system are discussed. After reconstructing the pair epidemic with correlations and clustering coefficient, the instability of the Dis-FE, bifurcation and propagation dynamics of the epidemic model are investigated, where some simulations are illustrated to explore the effects of clustering coefficient.

High temperature superradiant phase transition in quantum structures with a complex network interface.

In the present work we propose a novel, to the best of our knowledge, quantum material concept, which enables superstrong and/or ultrastrong interaction of two-level systems with the photonic field in a complex network. Within the mean field approximation we examine phase transition to superradiance that results in two excitation (polariton) branches and is accompanied by the appearance of non-zero macroscopic polarization of two-level systems. We characterize the statistical properties of networks by the first, 〈k〉, and second normalized, ζ ≡ 〈k2〉/〈k〉, moments for node degree distribution. We have shown that the Rabi frequency is essentially enhanced due to the topology of the network within the anomalous domain where 〈k〉 and ζ sufficiently grow. The multichannel (multimode) structure of matter-field interaction leads superstrong coupling that provides primary behavior of the high temperature phase transition. The results obtained pave the way for the design of new photonic and polaritonic circuits, quantum networks for efficient processing quantum information at high (room) temperatures.

Examining the variability in network populations and its role in generative models

AbstractA principled approach to understand networks is to formulate generative models and infer their parameters from given network data. Due to the scarcity of data in the form of multiple networks that have evolved from the same process, generative models are typically formulated to learn parameters from a single network observation, hence ignoring the natural variability of the “true” process. In this paper, we highlight the importance of variability in evaluating generative models and present two ways of quantifying the variability for a finite set of networks. The first evaluation scheme compares the statistical properties of networks in a dissimilarity space, while the other relies on data-driven entropy measures to compute variability in network populations. Using these measures, we evaluate the ability of four generative models to synthesize networks that capture the variability of the “true” process. Our empirical analysis suggests that generative models fitted for a single network observation fail to capture the variability in the network population. Our work highlights the need for rethinking the way we evaluate the goodness-of-fit of new and existing network models and devising models that are capable of matching the variability of network populations when available.

Statistical properties of complex network for seismicity using depth-incorporated influence radius

In recent years, seismic time series has been used to construct complex network models in order to describe the seismic complexity. The effect of the factor focal depth has been elided in some of these models. In this paper, we aim to construct a new complex network model for seismicity by considering depth factor from the earthquake catalog and investigate the statistical properties of the network. Since the networks have been proved to be scale-free and small-world properties, the new network models should be studied whether the properties have changed. The results show that the new network model by considering depth factor is still scale-free and small-world. However, it is found that its average degree is smaller than the original network. The clustering coefficient increases at the year including mainshocks. The assortativity coefficient, which demonstrates preferential attachment of nodes, is positive and shows consistent pattern when main shocks occur.

Dispersion analysis of network traffic for intrusion detection in Smart Grids

We consider the systems of detection and prevention of intrusions in modern telecommunication systems and networks. Methods of monitoring events, consisting of analysis of network activity of individual services and information services, are analyzed. It is proposed to use the mathematical apparatus of analysis of variance for processing results of modeling telecommunication systems and studying the statistical properties of network traffic in determining the significance of discrepancies or coincidence of characteristics. The proposed approach is to use the Fisher statistical criterion based on an estimate of the ratio of sample variances. This allows you to test the hypothesis about the homogeneity of statistical properties of network traffic with respect to the variance index (variance) with a given level of significance. The obtained results of experimental studies are recommended to be used to improve mechanisms for monitoring the network activity of individual services and information services, including for detecting and preventing intrusions in telecommunications systems and networks of promising Smart Grids.

Anomaly analysis and visualization for dynamic networks through spatiotemporal graph segmentations

With recent technology advance in Internet of Things (IoT) that involves human, sensors, and mobile devices, networks are not only growing much larger but more complex and dynamic in nature. The spatiotemporal dynamics of networks are represented by both topological changes and temporal shifts of attribute information associated with network components. Understanding the pattern and trend of dynamic networks is increasingly important. While data mining approaches are generally useful in analyzing the statistical properties of networks, there has been recent trend to consider bringing human into the loop, and to examine how feedback from visualizations of large-scale dynamic networks can further improve data mining and machine learning. Traditional visualization methods based on animation and sequences of snapshot graphs are also limited by human cognitive capability. We present a dynamic network analysis and visualization (DNAV) tool which explores the spatiotemporal dimensions of graph components. In particular, nodes and edges are augmented with spatiotemporal segmentation based on both topological and attribute dynamics (e.g., time and locations of connectivity). To further facilitate analysis of large dynamic networks, DNAV includes statistical dynamic overviews alongside graph views, as well as data filtering modules for scalable analysis. Using case studies on public datasets, we demonstrate the effectiveness of DNAV in understanding and analyzing anomalies in dynamic networks such as computer communication networks.

Understanding characteristics in multivariate traffic flow time series from complex network structure

Discovering dynamic characteristics in traffic flow is the significant step to design effective traffic managing and controlling strategy for relieving traffic congestion in urban cities. A new method based on complex network theory is proposed to study multivariate traffic flow time series. The data were collected from loop detectors on freeway during a year. In order to construct complex network from original traffic flow, a weighted Froenius norm is adopt to estimate similarity between multivariate time series, and Principal Component Analysis is implemented to determine the weights. We discuss how to select optimal critical threshold for networks at different hour in term of cumulative probability distribution of degree. Furthermore, two statistical properties of networks: normalized network structure entropy and cumulative probability of degree, are utilized to explore hourly variation in traffic flow. The results demonstrate these two statistical quantities express similar pattern to traffic flow parameters with morning and evening peak hours. Accordingly, we detect three traffic states: trough, peak and transitional hours, according to the correlation between two aforementioned properties. The classifying results of states can actually represent hourly fluctuation in traffic flow by analyzing annual average hourly values of traffic volume, occupancy and speed in corresponding hours.

Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

Abstract. The monitoring of statistical network properties could be useful for the short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalog of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) for the case of the L'Aquila (Italy) mainshock (Mw = 6.3) of 6 April 2009, we provide evidence that network measures, both global (average clustering coefficient, small-world index) and local (betweenness centrality) ones, could potentially be exploited for forecasting purposes both in time and space. Our results reveal statistically significant increases in the topological measures and a nucleation of the betweenness centrality around the location of the epicenter about 2 months before the mainshock. The results of the analysis are robust even when considering either large or off-centered the main event space windows.

Broadband macroscopic cortical oscillations emerge from intrinsic neuronal response failures.

Broadband spontaneous macroscopic neural oscillations are rhythmic cortical firing which were extensively examined during the last century, however, their possible origination is still controversial. In this work we show how macroscopic oscillations emerge in solely excitatory random networks and without topological constraints. We experimentally and theoretically show that these oscillations stem from the counterintuitive underlying mechanism—the intrinsic stochastic neuronal response failures (NRFs). These NRFs, which are characterized by short-term memory, lead to cooperation among neurons, resulting in sub- or several- Hertz macroscopic oscillations which coexist with high frequency gamma oscillations. A quantitative interplay between the statistical network properties and the emerging oscillations is supported by simulations of large networks based on single-neuron in-vitro experiments and a Langevin equation describing the network dynamics. Results call for the examination of these oscillations in the presence of inhibition and external drives.

Spatially embedded growing small-world networks.

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. Motivated by the growth and development of neuronal networks, we propose a class of spatially-based growing network models and investigate the resulting statistical network properties as a function of the dimension and topology of the space in which the networks are embedded. In particular, we consider two models in which nodes are placed one by one in random locations in space, with each such placement followed by configuration relaxation toward uniform node density, and connection of the new node with spatially nearby nodes. We find that such growth processes naturally result in networks with small-world features, including a short characteristic path length and nonzero clustering. We find no qualitative differences in these properties for two different topologies, and we suggest that results for these properties may not depend strongly on the topology of the embedding space. The results do depend strongly on dimension, and higher-dimensional spaces result in shorter path lengths but less clustering.

Network theory for data-driven epistasis networks.

One of the challenges of understanding the genetic basis of complex phenotypes is explaining variability not attributable to individual genes. While most existing methods that investigate variant mutations or differential gene expression focus on individual effects, a complex system of gene interactions (epistasis) and pathways is likely needed to explain phenotypic variation. Herein, we examine methods for treating the interactions in these biological data sets as edges in a network model of the phenotype and review relevant network theory methods for analyzing network structure and identifying important genes. In particular, we review methods for detecting community structure, describing the statistical properties of networks, and computing network centrality of genes that may reveal insights missed by individual genetic effects. We also discuss available tools to facilitate the construction and visualization of epistasis networks of GWAS data.

What exactly are the properties of scale-free and other networks?

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools and procedures to analyse the statistical properties of networks defined by arbitrary degree distributions and other constraints. Doing so reveals the highly likely properties, and some unrecognised richness, of scale-free networks, and casts doubt on some previously claimed properties being due to a scale-free characteristic.

Automated Malware Detection Based on Novel Network Behavioral Signatures

In this paper we introduce the second generation of the experimental detection framework of AIPS system which is used for experimentation with detection models and with their combinations. Our research aims mainly on detection of attacks that abuse vulnerabilities of buffer overflow type, but the final goal is to extend detection techniques to cover various types of vulnerabilities. This article describes the concept of detection framework, updated set of network metrics, provides a design of model architecture and shows an experimental results with draft of framework on the set of laboratory simulated attacks. Index Terms—Artificial intelligence, behavioral signatures, metrics, network security, security, security design. 112 metrics divided into five categories according to their nature. These metrics are used to describe properties of detected attack not upon the fingerprint of common signature, but based on its behavior. During the experiments we found several limitations of the original idea and some parts of the architecture were changed. We extended the metric dataset to 169 metrics containing approximately 4000 parameters and changed the categories to reflect the nature of the new dataset. The main goals of this research is (a) to design the architecture of detection framework that will enhance the overall network security level with the ability to learn new behaviors of attacks without intervention of human by using the expert knowledge from Honeypot (or similar) systems; (b) to find the most suitable set of metrics that will successfully describe the behavior of attacks in the network traffic and will significantly higher the detection rate and lower the false positive rate. In this article we introduce the second generation of the experimental detection framework of AIPS system which is used for experimentation with detection models and with their combinations. The fundamental principle of the detection is based on evaluation of metrics set, which describes the behavior of attack. These metrics are formally specified and extraction of them can be generally realized for each data flow. We could interpret the specification of metrics set as formally extended protocol NetFlow (9), which describes more than statistical properties of network

Fractal-Driven Distortion of Resting State Functional Networks in fMRI: A Simulation Study

Fractals are self-similar and scale-invariant patterns found ubiquitously in nature. A lot of evidences implying fractal properties such as 1/f power spectrums have been also observed in resting state fMRI time series. To explain the fractal behavior in rs-fMRI, we have proposed the fractal-based model of resting state hemodynamic response function (rs-HRF) whose properties can be summarized by a fractal exponent. Here we show, through a simulation studies, that the fractal behavior of cerebral hemodynamics may cause significant distortion of network properties between neuronal activities and BOLD signals. We simulated neuronal population activities based on the stochastic neural field model from the Macaque brain network, and then obtained their corresponding BOLD signals by convolving them with the rs-HRF filter. The precision of centrality estimated in each node was deteriorated overall in three networks based on transfer entropy, mutual information, and Pearson correlation; particularly the distortion of transfer entropy was more sensitive to the standard deviation of fractal exponents. A node with high centrality was resilient to desynchronized fractal dynamics over all frequencies while a node with small centrality exhibited huge distortion of both wavelet correlation and centrality over low frequencies. This theoretical expectation indicates that the difference of fractal exponents between brain regions leads to discrepancy of statistical network properties, especially at nodes with small centrality, between neuronal activities and BOLD signals, and that the traditional definitions of resting state functional connectivity may not effectively reflect the dynamics of spontaneous neuronal activities.

Increased entropy of signal transduction in the cancer metastasis phenotype

BackgroundThe statistical study of biological networks has led to important novel biological insights, such as the presence of hubs and hierarchical modularity. There is also a growing interest in studying the statistical properties of networks in the context of cancer genomics. However, relatively little is known as to what network features differ between the cancer and normal cell physiologies, or between different cancer cell phenotypes.ResultsBased on the observation that frequent genomic alterations underlie a more aggressive cancer phenotype, we asked if such an effect could be detectable as an increase in the randomness of local gene expression patterns. Using a breast cancer gene expression data set and a model network of protein interactions we derive constrained weighted networks defined by a stochastic information flux matrix reflecting expression correlations between interacting proteins. Based on this stochastic matrix we propose and compute an entropy measure that quantifies the degree of randomness in the local pattern of information flux around single genes. By comparing the local entropies in the non-metastatic versus metastatic breast cancer networks, we here show that breast cancers that metastasize are characterised by a small yet significant increase in the degree of randomness of local expression patterns. We validate this result in three additional breast cancer expression data sets and demonstrate that local entropy better characterises the metastatic phenotype than other non-entropy based measures. We show that increases in entropy can be used to identify genes and signalling pathways implicated in breast cancer metastasis and provide examples of de-novo discoveries of gene modules with known roles in apoptosis, immune-mediated tumour suppression, cell-cycle and tumour invasion. Importantly, we also identify a novel gene module within the insulin growth factor signalling pathway, alteration of which may predispose the tumour to metastasize.ConclusionsThese results demonstrate that a metastatic cancer phenotype is characterised by an increase in the randomness of the local information flux patterns. Measures of local randomness in integrated protein interaction mRNA expression networks may therefore be useful for identifying genes and signalling pathways disrupted in one phenotype relative to another. Further exploration of the statistical properties of such integrated cancer expression and protein interaction networks will be a fruitful endeavour.

Network synchronization: Spectral versus statistical properties

We consider synchronization of weighted networks, possibly with asymmetrical connections. Focusing on causal relations rather than the observed correlations, we show that the synchronizability of networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation and clustering coefficient, can fail to characterize the synchronizability of networks in terms of causal relations, despite the observed correlations.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input–output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis.

Topology of large-scale engineering problem-solving networks.

The last few years have led to a series of discoveries that uncovered statistical properties that are common to a variety of diverse real-world social, information, biological, and technological networks. The goal of the present paper is to investigate the statistical properties of networks of people engaged in distributed problem solving and discuss their significance. We show that problem-solving networks have properties (sparseness, small world, scaling regimes) that are like those displayed by information, biological, and technological networks. More importantly, we demonstrate a previously unreported difference between the distribution of incoming and outgoing links of directed networks. Specifically, the incoming link distributions have sharp cutoffs that are substantially lower than those of the outgoing link distributions (sometimes the outgoing cutoffs are not even present). This asymmetry can be explained by considering the dynamical interactions that take place in distributed problem solving and may be related to differences between each actor's capacity to process information provided by others and the actor's capacity to transmit information over the network. We conjecture that the asymmetric link distribution is likely to hold for other human or nonhuman directed networks when nodes represent information processing and using elements.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Topological Invariants in Microscopic Transport on Rough Landscapes: Morphology, Hierarchical Structure, and Horton Analysis of Riverlike Networks of Vortices

River basins as diverse as the Nile, the Amazon, and the Mississippi satisfy certain topological invariants known as Horton's laws. Do these macroscopic (up to ${10}^{3}$ km) laws extend to the micron scale? Through realistic simulations, we analyze the morphology and statistical properties of networks of vortex flow in flux-gradient-driven superconductors. We derive a phase diagram of the different network morphologies, including one in which Horton's laws of length and stream number are obeyed---even though these networks are about ${10}^{9}$ to ${10}^{15}$ times smaller than geophysical river basins.