arXiv subjects

Michael Small

Publications and source records attributed to Michael Small.

At least 37 records · Page 2Linked to original sources

arXiv2020

Modelling strong control measures for epidemic propagation with networks -- A COVID-19 case study

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform decisions. Contact between individuals in the community is characterised by a contact graph, the structure of that contact graph is selected to mimic community control measures. Our model of city-level transmission of an infectious agent (SEIR model) characterises spread via a (a) scale-free contact network (no control); (b) a random graph (elimination of mass gatherings); and (c) small world lattice (partial to full lockdown -- "social" distancing). This model exhibits good qualitative agreement between simulation and data from the 2020 pandemic spread of coronavirus. Estimates of the relevant rate parameters of the SEIR model are obtained and we demonstrate the robustness of our model predictions under uncertainty of those estimates. The social context and utility of this work is identified, contributing to a highly effective pandemic response in Western Australia.

q-bio.PE↗

arXiv2019

A novel metric for community detection

Research into detection of dense communities has recently attracted increasing attention within network science, various metrics for detection of such communities have been proposed. The most popular metric -- Modularity -- is based on the so-called rule that the links within communities are denser than external links among communities, has become the default. However, this default metric suffers from ambiguity, and worse, all augmentations of modularity and based on a narrow intuition of what it means to form a "community". We argue that in specific, but quite common systems, links within a community are not necessarily more common than links between communities. Instead we propose that the defining characteristic of a community is that links are more predictable within a community rather than between communities. In this paper, based on the effect of communities on link prediction, we propose a novel metric for the community detection based directly on this feature. We find that our metric is more robustness than traditional modularity. Consequently, we can achieve an evaluation of algorithm stability for the same detection algorithm in different networks. Our metric also can directly uncover the false community detection, and infer more statistical characteristics for detection algorithms.

physics.soc-ph↗

arXiv2019

Fast Automatic Detection of Geological Boundaries from Multivariate Log Data Using Recurrence

Manual interpretation of data collected from drill holes for mineral or oil and gas exploration is time-consuming and subjective. Identification of geological boundaries and distinctive rock physical property domains is the first step of interpretation. We introduce a multivariate technique, that can identify geological boundaries from petrophysical or geochemical data. The method is based on time-series techniques that have been adapted to be applicable for detecting transitions in geological spatial data. This method allows for the use of multiple variables in detecting different lithological layers. Additionally, it reconstructs the phase space of a single drill-hole or well to be applicable for further investigations across other holes or wells. The computationally cheap method shows efficiency and accuracy in detecting boundaries between lithological layers, which we demonstrate using examples from mineral exploration boreholes and an offshore gas exploration well.

physics.geo-ph↗

arXiv2019

The key to the weak-ties phenomenon

The study of the weak-ties phenomenon has a long and well documented history, research into the application of this social phenomenon has recently attracted increasing attention. However, further exploration of the reasons behind the weak-ties phenomenon is still challenging. Fortunately, data-driven network science provides a novel way with substantial explanatory power to analyze the causal mechanism behind social phenomenon. Inspired by this perspective, we propose an approach to further explore the driving factors behind the temporal weak-ties phenomenon. We find that the obvious intuition underlying the weak-ties phenomenon is incorrect, and often large numbers of unknown mutual friends associated with these weak ties is one of the key reason for the emergence of the weak-ties phenomenon. In particular, for example scientific collaborators with weak ties prefer to be involved in direct collaboration rather than share ideas with mutual colleagues -- there is a natural tendency to collapse short strong chains of connection.

physics.soc-ph↗

arXiv2019

Consistency in Echo-State Networks

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.

math.DS↗

arXiv2018

Constructing directed networks from multivariate time series using linear modelling technique

We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models. The models are called reduced auto-regressive (RAR) models. The procedure of the proposed method is composed of three steps: (i) each time series is treated as a basic node of a network, (ii) multivariate RAR models are built and the constituent information in the models is summarized, and (iii) nodes are connected with a directed link based on that summary information. The proposed method is demonstrated for numerical data generated by known systems, and applied to several actual time series of special interest. Although the proposed method can identify connectivity, there are three points to keep in mind: (1) the proposed method cannot always identify nonlinear relationships among components, (2) as constructing RAR models is NP-hard, the network constructed by the proposed method might be near-optimal network when we cannot perform an exhaustive search, and (3) it is difficult to construct appropriate networks when the observational noise is large.

physics.data-an↗

arXiv2018

Global stability of epidemic models with imperfect vaccination and quarantine on scale-free networks

Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic models have a long history of assisting in public health planning and policy making. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infection, which corresponds respectively to the susceptible-vaccinated-infected-quarantined-recovered (SVIQR) model and the susceptible-vaccinated-infected-quarantined (SVIQS) model. We develop different mathematical methods and techniques to study the dynamics of two models, including the basic reproduction number, the global stability of disease-free and endemic equilibria. For the SVIQR model, we show that the system exhibits a forward bifurcation. Meanwhile, the disease-free and unique endemic equilibria are shown to be globally asymptotically stable by constructing suitable Lyapunov functions. For the SVIQS model, conditions ensuring the occurrence of multiple endemic equilibria are derived. Under certain conditions, this system cannot undergo a backward bifurcation. The global asymptotical stability of disease-free equilibrium, and the persistence of the disease are proved. The endemic equilibrium is shown to be globally attractive by using monotone iterative technique. Finally, stochastic network simulations yield quantitative agreement with the deterministic mean-field approach.

q-bio.PE↗

arXiv2017

Multitarget search on complex networks: A logarithmic growth of global mean random cover time

We investigate multitarget search on complex networks and derive an exact expression for the mean random cover time that quantifies the expected time a walker needs to visit multiple targets. Based on this, we recover and extend some interesting results of multitarget search on networks. Specifically, we observe the logarithmic increase of the global mean random cover time with the target number for a broad range of random search processes, including generic random walks, biased random walks, and maximal entropy random walks. We show that the logarithmic growth pattern is a universal feature of multi-target search on networks by using the annealed network approach and the Sherman-Morrison formula. Moreover, we find that for biased random walks, the global mean random cover time can be minimized, and that the corresponding optimal parameter also minimizes the global mean first passage time, pointing towards its robustness. Our findings further confirm that the logarithmic growth pattern is a universal law governing multitarget search in confined media.

physics.soc-ph↗

arXiv2017

Detection of core-periphery structure in networks by 3-tuple motifs

Recently, the core-periphery (CP) structure of networks as one type of meso-scale structure has received attention. The CP structure is composed of a dense core and a sparse connected periphery. In this paper, we propose an algorithm to detect the CP structure based on the 3-tuple motif, which is inspired by the idea of motif. In this algorithm, we first define a 3-tuple motif by considering the property of nodes, and then a motif adjacency matrix is formed based on the defined motif, finally, the detection of the CP structure is converted to find a cluster that minimizes the smallest motif conductance. Our algorithm can detect different CP structures: including single or multiple CP structure; and local or global CP structures. Results in the synthetic and the empirical networks indicate that the method is efficient and can apply to large-scale networks. More importantly, our algorithm is parameter free, where the core and periphery are detected without the need for any predefined parameters.

physics.soc-ph↗

arXiv2016

Navigation by anomalous random walks on complex networks

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Levy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Levy walks and the underlying network structure. Interestingly, applying our framework to the famous PageRank search, we can explain why its damping factor empirically chosen to be around 0.85. The framework for analyzing anomalous random walks on complex networks offers a new useful paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.

physics.soc-ph↗

arXiv2016

Impact of asymptomatic infection on coupled disease-behavior dynamics in complex networks

Studies on how to model the interplay between diseases and behavioral responses (so-called coupled disease-behavior interaction) have attracted increasing attention. Owing to the lack of obvious clinical evidence of diseases, or the incomplete information related to the disease, the risks of infection cannot be perceived and may lead to inappropriate behavioral responses. Therefore, how to quantitatively analyze the impacts of asymptomatic infection on the interplay between diseases and behavioral responses is of particular importance. In this Letter, under the complex network framework, we study the coupled disease-behavior interaction model by dividing infectious individuals into two states: U-state (without evident clinical symptoms, labelled as U) and I-state (with evident clinical symptoms, labelled as I). A susceptible individual can be infected by U- or I-nodes, however, since the U-nodes cannot be easily observed, susceptible individuals take behavioral responses \emph{only} when they contact I-nodes. The mechanism is considered in the improved Susceptible-Infected-Susceptible (SIS) model and the improved Susceptible-Infected-Recovered (SIR) model, respectively. Then, one of the most concerned problems in spreading dynamics: the epidemic thresholds for the two models are given by two methods. The analytic results \emph{quantitatively} describe the influence of different factors, such as asymptomatic infection, the awareness rate, the network structure, and so forth, on the epidemic thresholds. Moreover, because of the irreversible process of the SIR model, the suppression effect of the improved SIR model is weaker than the improved SIS model.

physics.soc-ph↗

arXiv2016

Prevention of infectious diseases by public vaccination and individual protection

In the face of serious infectious diseases, governments endeavour to implement containment measures such as public vaccination at a macroscopic level. Meanwhile, individuals tend to protect themselves by avoiding contacts with infections at a microscopic level. However, a comprehensive understanding of how such combined strategy influences epidemic dynamics is still lacking. We study a susceptible-infected-susceptible epidemic model with imperfect vaccination on dynamic contact networks, where the macroscopic intervention is represented by random vaccination of the population and the microscopic protection is characterised by susceptible individuals rewiring contacts from infective neighbours. In particular, the model is formulated both in populations without and then with demographic effects. Using the pairwise approximation and the probability generating function approach, we investigate both dynamics of the epidemic and the underlying network. For populations without demography, the emerging degree correlations, bistable states, and oscillations demonstrate the combined effects of the public vaccination program and individual protective behavior. Compared to either strategy in isolation, the combination of public vaccination and individual protection is more effective in preventing and controlling the spread of infectious diseases by increasing both the invasion threshold and the persistence threshold. For populations with additional demographic factors, the integration between vaccination intervention and individual rewiring may promote epidemic spreading due to the birth effect. Moreover, the degree distributions of both networks in the steady state is closely related to the degree distribution of newborns, which leads to uncorrelated connectivity. All the results demonstrate the importance of both local protection and global intervention, as well as the demographic effects.

physics.soc-ph↗

arXiv2016

Transmission dynamics of an SIS model with age structure on heterogeneous networks

Age at infection is often an important factor in epidemic dynamics. In this paper a disease transmission model of SIS type with age dependent infection on a heterogeneous network is discussed. The model allows the infectious rate and the recovery rate to vary and depend on the age of the infected individual at the time of infection. We address the threshold property of the basic reproduction number and present the global dynamical properties of the disease-free and endemic equilibria in the model. Finally, some numerical simulations are carried out to illustrate the main results. The combined effects of the network structure and the age dependent factor on the disease dynamics are displayed.

math.DS↗

arXiv2015

Preferential imitation of vaccinating behavior can invalidate the targeted subsidy on complex network

We consider the effect of inducement to vaccinate during the spread of an infectious disease on complex networks. Suppose that public resources are finite and that only a small proportion of individuals can be vaccinated freely (complete subsidy), for the remainder of the population vaccination is a voluntary behavior --- and each vaccinated individual carries a perceived cost. We ask whether the classical targeted subsidy strategy is definitely better than the random strategy: does targeting subsidy at individuals perceived to be with the greatest risk actually help? With these questions, we propose a model to investigate the \emph{interaction effects} of the subsidy policies and individuals responses when facing subsidy policies on the epidemic dynamics on complex networks. In the model, a small proportion of individuals are freely vaccinated according to either the targeted or random subsidy policy, the remainder choose to vaccinate (or not) based on voluntary principle and update their vaccination decision via an imitation rule. Our findings show that the targeted strategy is only advantageous when individuals prefer to imitate the subsidized individuals' strategy. Otherwise, the effect of the targeted policy is worse than the random immunization, since individuals preferentially select non-subsidized individuals as the imitation objects. More importantly, we find that under the targeted subsidy policy, increasing the proportion of subsidized individuals may increase the final epidemic size. We further define social cost as the sum of the costs of vaccination and infection, and study how each of the two policies affect the social cost. Our result shows that there exist some optimal intermediate regions leading to the minimal social cost.

physics.soc-ph↗

arXiv2015

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -- thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set.

nlin.CD↗

arXiv2014

Exactly scale-free scale-free networks

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to model the growth and structure of scale-free networks. With so many different models of scale-free networks it is unclear what properties of scale-free networks are typical, and what properties are peculiarities of a particular growth or construction process. We propose a simple maximum entropy process which provides the best representation of what are typical properties of scale-free networks, and provides a standard against which real and algorithmically generated networks can be compared. As an example we consider preferential attachment and find that this particular growth model does not yield typical realizations of scale-free networks. In particular, the widely discussed "fragility" of scale-free networks is actually found to be due to the peculiar "hub-centric" structure of preferential attachment networks. We provide a method to generate or remove this latent hub-centric bias --- thereby demonstrating exactly which features of preferential attachment networks are atypical of the broader class of scale-free networks. We are also able to statistically demonstrate whether real networks are typical realizations of scale-free networks, or networks with that particular degree distribution; using a new surrogate generation method for complex networks, exactly analogous the the widely used surrogate tests of nonlinear time series analysis.

physics.soc-ph↗

arXiv2014

Super-star networks: Growing optimal scale-free networks via likelihood

Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree $k$ is proportional to $k^{-γ}$. However, the motivation for this model is entirely ad hoc. We use exact likelihood arguments and show that the optimal way to build a scale-free network is to attach most new links to nodes of low degree. Curiously, this leads to a scale-free networks with a single dominant hub: a star-like structure we call a super-star network. Asymptotically, the optimal strategy is to attach each new node to one of the nodes of degree $k$ with probability proportional to $\frac{1}{N+ζ(γ)(k+1)^γ}$ (in a $N$ node network) --- a stronger bias toward high degree nodes than exhibited by standard preferential attachment. Our algorithm generates optimally scale-free networks (the super-star networks) as well as randomly sampling the space of all scale-free networks with a given degree exponent $γ$. We generate viable realisation with finite $N$ for $1\ll γ<2$ as well as $γ>2$. We observe an apparently discontinuous transition at $γ\approx 2$ between so-called super-star networks and more tree-like realisations. Gradually increasing $γ$ further leads to re-emergence of a super-star hub. To quantify these structural features we derive a new analytic expression for the expected degree exponent of a pure preferential attachment process, and introduce alternative measures of network entropy. Our approach is generic and may also be applied to an arbitrary degree distribution.

nlin.AO↗

arXiv2014

Expected degree of finite preferential attachment networks

We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the degree of a node, and $N$ the number of nodes in the network. The degree distribution is assumed to converge to a power-law (for $k\geq m$) of the form $k^{-γ}$ and we obtain an exact implicit relationship for $γ$, $m$ and $N$. We verify this with numerical calculations over several orders of magnitude. Although this expression is exact, it provides only an implicit expression for $γ(m)$. Nonetheless, we provide a reasonable guess as to the form of this curve and perform curve fitting to estimate the parameters of that curve --- demonstrating excellent agreement between numerical fit, theory, and simulation.

cs.SI↗