Cascade Size Research Articles

Number versus structure: towards citing cascades

This paper proposes a novel concept of the citing cascade, defined as a network comprising citing relationships between a paper and its citing paper, as well as those among its citing papers. Compared with citation counts using a single number, citing cascades reveal the structural information of citation networks of a scientific publication and thus help us better understand the citation impact of a scientific publication (called the owner of the citing cascade). We then define and elaborate on several basic and advanced properties of citing cascades. By employing computer science publication records in the Microsoft Academic Graph dataset, we found that cascade size, edge count, in-degree, and out-degree all follow typical power law distributions with various exponential parameters (α). In addition, cascade depth is observed to follow an exponential distribution. We also examine the relation between citation count of the owner and some advanced properties that we defined. Many related future studies are also illustrated at the end of this paper.

Postmortem Analysis of Decayed Online Social Communities: Cascade Pattern Analysis and Prediction

Recently, many online social networks, such as MySpace, Orkut, and Friendster, have faced inactivity decay of their members, which contributed to the collapse of these networks. The reasons, mechanics, and prevention mechanisms of such inactivity decay are not fully understood. In this work, we analyze decayed and alive subwebsites from the Stack Exchange platform. The analysis mainly focuses on the inactivity cascades that occur among the members of these communities. We provide measures to understand the decay process and statistical analysis to extract the patterns that accompany the inactivity decay. Additionally, we predict cascade size and cascade virality using machine learning. The results of this work include a statistically significant difference of the decay patterns between the decayed and the alive subwebsites. These patterns are mainly cascade size, cascade virality, cascade duration, and cascade similarity. Additionally, the contributed prediction framework showed satisfactorily prediction results compared to a baseline predictor. Supported by empirical evidence, the main findings of this work are (1) there are significantly different decay patterns in the alive and the decayed subwebsites of the Stack Exchange; (2) the cascade’s node degrees contribute more to the decay process than the cascade’s virality, which indicates that the expert members of the Stack Exchange subwebsites were mainly responsible for the activity or inactivity of the Stack Exchange subwebsites; (3) the Statistics subwebsite is going through decay dynamics that may lead to it becoming fully-decayed; (4) the decay process is not governed by only one network measure, it is better described using multiple measures; (5) decayed subwebsites were originally less resilient to inactivity decay, unlike the alive subwebsites; and (6) network’s structure in the early stages of its evolution dictates the activity/inactivity characteristics of the network.

Explicit size distributions of failure cascades redefine systemic risk on finite networks

How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain and missing information. In infinitely large networks, the average cascade size can often be estimated by approaches building on local tree and mean field approximations. Yet, as we demonstrate, in finite networks, this average does not need to be a likely outcome. Instead, we find broad and even bimodal cascade size distributions. This phenomenon persists for system sizes up to 107 and different cascade models, i.e. it is relevant for most real systems. To show this, we derive explicit closed-form solutions for the full probability distribution of the final cascade size. We focus on two topological limit cases, the complete network representing a dense network with a very narrow degree distribution, and the star network representing a sparse network with a inhomogeneous degree distribution. Those topologies are of great interest, as they either minimize or maximize the average cascade size and are common motifs in many real world networks.

Framework for cascade size calculations on random networks.

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

The Analysis of Influencing Factors of Information Dissemination on Cascade Size Distribution in Social Networks

The cognitive behavior of online user groups on information promotes the dissemination of information. The trajectories of information dissemination in social networks can be described by treelike cascades, and the distribution of the sizes of these cascades can capture the distribution of popularity of a social network. Numerous studies have shown that the cascade size distribution follows fat-tail distributions, including power-law distribution and bimodal distribution; however, the underlying characteristic of this highly skewed distribution lacks quantitative experimental analysis. Based on the stochastic epidemic-like information dissemination model, namely, the susceptible view forward removed model, this paper explores the impact of the content attractiveness and influence, and information source on the cascade size distribution through computational experiments. On the one hand, we find that when the mean value of the information influence and attractiveness is small, the cascade sizes follow a power-law distribution, and the larger the variance, the heavier the tail. On the other hand, the more random the distribution of information sources in social networks, the smaller the slope of the power-law cascade size distribution. Our findings quantitatively reveal the causality of power-law cascade size distribution from computational experiments, clarify the role of information attractiveness, influence, and sources on the distribution of popularity in social networks.

Modelling of information diffusion on social networks with applications to WeChat

Traces of user activities recorded in online social networks open new possibilities to systematically understand the information diffusion process on social networks. From the online social network WeChat, we collected a large number of information cascade trees, each of which tells the spreading trajectory of a message/information such as which user creates the information and which users view or forward the information shared by which neighbours. In this work, we propose two heterogeneous non-linear models, one for the topologies of the information cascade trees and the other for the stochastic process of information diffusion on a social network. Both models are validated by the WeChat data in reproducing and explaining key features of cascade trees.Specifically, we apply the Random Recursive Tree (RRT) to model the growth of cascade trees. The RRT model could capture key features, i.e. the average path length and degree variance of a cascade tree in relation to the number of nodes (size) of the tree. Its single identified parameter quantifies the relative depth or broadness of the cascade trees and indicates that information propagates via a star-like broadcasting or viral-like hop by hop spreading. The RRT model explains the appearance of hubs, thus a possibly smaller average path length as the cascade size increases, as observed in WeChat. We further propose the stochastic Susceptible View Forward Removed (SVFR) model to depict the dynamic user behaviour including creating, viewing, forwarding and ignoring a message on a given social network. Beside the average path length and degree variance of the cascade trees in relation to their sizes, the SVFR model could further explain the power-law cascade size distribution in WeChat and unravel that a user with a large number of friends may actually have a smaller probability to read a message (s)he receives due to limited attention.

Direct observation of the spatial distribution of primary cascade damage in tungsten

Recently we have presented direct experimental evidence for large defect clusters being formed in primary damage cascades in self-ion irradiated tungsten [Yi et al., EPL 110:36001 (2015)]. This large size is significant, as it implies that strong elastic interaction between the defects will affect their subsequent evolution, especially if defects are formed close together. Here we present a direct experimental observation of the separation between visible defects in self-ion irradiated tungsten, in the form of a 2d pairwise radial distribution function extracted from transmission electron micrographs (TEM). We also present a detailed analysis of the observed radial distribution function, and infer the probable size and shape of individual cascades. We propose and validate a simple exponential form for the spatial distribution of defects within a single cascade. The cascade statistics necessary have been acquired by developing an automated procedure for analysing black-dot damage in TEM micrographs. We confirm that the same model also produces a high-quality fit to the separation between larger defects observed in MD simulations. For the first time we present experimental evidence for the sub-nanometre-scale spatial distribution of defect clusters within individual cascades.

The Brexit Botnet and User-Generated Hyperpartisan News

In this article, we uncover a network of Twitterbots comprising 13,493 accounts that tweeted the United Kingdom European Union membership referendum, only to disappear from Twitter shortly after the ballot. We compare active users to this set of political bots with respect to temporal tweeting behavior, the size and speed of retweet cascades, and the composition of their retweet cascades (user-to-bot vs. bot-to-bot) to evidence strategies for bot deployment. Our results move forward the analysis of political bots by showing that Twitterbots can be effective at rapidly generating small- to medium-sized cascades; that the retweeted content comprises user-generated hyperpartisan news, which is not strictly fake news, but whose shelf life is remarkably short; and, finally, that a botnet may be organized in specialized tiers or clusters dedicated to replicating either active users or content generated by other bots.

Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows

Cascading failures are a critical vulnerability of complex information or infrastructure networks. Here we investigate the properties of load-based cascading failures in real and synthetic spatially-embedded network structures, and propose mitigation strategies to reduce the severity of damages caused by such failures. We introduce a stochastic method for optimal heterogeneous distribution of resources (node capacities) subject to a fixed total cost. Additionally, we design and compare the performance of networks with N-stable and (N-1)-stable network-capacity allocations by triggering cascades using various real-world node-attack and node-failure scenarios. We show that failure mitigation through increased node protection can be effectively achieved against single-node failures. However, mitigating against multiple node failures is much more difficult due to the combinatorial increase in possible sets of initially failing nodes. We analyze the robustness of the system with increasing protection, and find that a critical tolerance exists at which the system undergoes a phase transition, and above which the network almost completely survives an attack. Moreover, we show that cascade-size distributions measured in this region exhibit a power-law decay. Finally, we find a strong correlation between cascade sizes induced by individual nodes and sets of nodes. We also show that network topology alone is a weak predictor in determining the progression of cascading failures.

The Brexit Botnet and User-Generated Hyperpartisan News

In this paper we uncover a network of Twitterbots comprising 13,493 accounts that tweeted the U.K. E.U. membership referendum, only to disappear from Twitter shortly after the ballot. We compare active users to this set of political bots with respect to temporal tweeting behavior, the size and speed of retweet cascades, and the composition of their retweet cascades (user-to-bot vs. bot-to-bot) to evidence strategies for bot deployment. Our results move forward the analysis of political bots by showing that Twitterbots can be effective at rapidly generating small to medium-sized cascades; that the retweeted content comprises user-generated hyperpartisan news, which is not strictly fake news, but whose shelf life is remarkably short; and, finally, that a botnet may be organized in specialized tiers or clusters dedicated to replicating either active users or content generated by other bots.

Modeling cascade formation in Twitter amidst mentions and retweets

This paper presents an analytical framework for cascade formation considering both retweet and mentioning activities into account. We introduce two mention strategies (a) random mention and (b) smart mention to model the mention preferences of the users. The proposed framework \({\mathcal {C}}^M_F\) analytically computes the cascade size, depicting tweet popularity and discovers the presence of a critical retweet rate, under which mentioning in a tweet significantly helps in cascade formation. We validate the proposed framework with the help of Monte Carlo simulation; we demonstrate the generality of the framework taking both empirical and synthetic follower networks into consideration. This framework proves the elegance of smart mention strategy in boosting tweet popularity, specially in the low retweeting environment.

Network analysis of surgical innovation: Measuring value and the virality of diffusion in robotic surgery.

BackgroundExisting surgical innovation frameworks suffer from a unifying limitation, their qualitative nature. A rigorous approach to measuring surgical innovation is needed that extends beyond detecting simply publication, citation, and patent counts and instead uncovers an implementation-based value from the structure of the entire adoption cascades produced over time by diffusion processes. Based on the principles of evidence-based medicine and existing surgical regulatory frameworks, the surgical innovation funnel is described. This illustrates the different stages through which innovation in surgery typically progresses. The aim is to propose a novel and quantitative network-based framework that will permit modeling and visualizing innovation diffusion cascades in surgery and measuring virality and value of innovations.Materials and methodsNetwork analysis of constructed citation networks of all articles concerned with robotic surgery (n = 13,240, Scopus®) was performed (1974–2014). The virality of each cascade was measured as was innovation value (measured by the innovation index) derived from the evidence-based stage occupied by the corresponding seed article in the surgical innovation funnel. The network-based surgical innovation metrics were also validated against real world big data (National Inpatient Sample–NIS®).ResultsRankings of surgical innovation across specialties by cascade size and structural virality (structural depth and width) were found to correlate closely with the ranking by innovation value (Spearman’s rank correlation coefficient = 0.758 (p = 0.01), 0.782 (p = 0.008), 0.624 (p = 0.05), respectively) which in turn matches the ranking based on real world big data from the NIS® (Spearman’s coefficient = 0.673;p = 0.033).ConclusionNetwork analysis offers unique new opportunities for understanding, modeling and measuring surgical innovation, and ultimately for assessing and comparing generative value between different specialties. The novel surgical innovation metrics developed may prove valuable especially in guiding policy makers, funding bodies, surgeons, and healthcare providers in the current climate of competing national priorities for investment.

Spatio-temporal dynamics of web pages diffused in WeChat

PurposeWeChat is the largest acquaintance social networking platform in China, in which users can view and reshare web pages shared by friends. This paper aims to analyze the spatio-temporal dynamics of web pages diffused in WeChat and advice on commercials.Design/methodology/approachA large number of web pages diffused in WeChat are collected and exclusively divided into four categories according to their titles, including advertisements, news bulletins, holiday greetings and emotional essays. For each web page, an information cascade (tree structure) is constructed to describe the diffusion trace. Based on the categories, the spatio-temporal popularity is characterized; the topological, temporal and spatial properties are examined; and the spatio-temporal diffusion velocity is explored.FindingsThrough comparative analysis, different categories of pages show diversity. For spatio-temporal popularity, there is no significant difference in cascade size; holiday greetings usually last for a relatively short time on average; emotional essays are more likely to spread to more provinces. For topological, temporal and spatial characteristics, the diffusion process of advertisements is more likely to be broadcasting than other categories; news bulletins and holiday greetings have an obvious bursty; the number of viewing behavior decreases from east to west in general. For spatio-temporal diffusion velocity, emotional essays diffuse the fastest in topological and spatio-temporal dimensions.Originality/valueThese findings contribute to promoting products and providing support for data driven modeling of information diffusion and human activity in spatio-temporal dimensions.

Criticality predicts maximum irregularity in recurrent networks of excitatory nodes.

A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of cerebral cortex operate at a critical regime, which is defined as a transition point between two phases of short lasting and chaotic activity. However, despite the fact that criticality brings about certain functional advantages for information processing, its supporting evidence is still far from conclusive, as it has been mostly based on power law scaling of size and durations of cascades of activity. Moreover, to what degree such hypothesis could explain some fundamental features of neural activity is still largely unknown. One of the most prevalent features of cortical activity in vivo is known to be spike irregularity of spike trains, which is measured in terms of the coefficient of variation (CV) larger than one. Here, using a minimal computational model of excitatory nodes, we show that irregular spiking (CV > 1) naturally emerges in a recurrent network operating at criticality. More importantly, we show that even at the presence of other sources of spike irregularity, being at criticality maximizes the mean coefficient of variation of neurons, thereby maximizing their spike irregularity. Furthermore, we also show that such a maximized irregularity results in maximum correlation between neuronal firing rates and their corresponding spike irregularity (measured in terms of CV). On the one hand, using a model in the universality class of directed percolation, we propose new hallmarks of criticality at single-unit level, which could be applicable to any network of excitable nodes. On the other hand, given the controversy of the neural criticality hypothesis, we discuss the limitation of this approach to neural systems and to what degree they support the criticality hypothesis in real neural networks. Finally, we discuss the limitations of applying our results to real networks and to what degree they support the criticality hypothesis.

Outward Influence and Cascade Size Estimation in Billion-scale Networks

Estimating cascade size and nodes' influence is a fundamental task in social, technological, and biological networks. Yet this task is extremely challenging due to the sheer size and the structural heterogeneity of networks. We investigate a new influence measure, termed outward influence (OI), defined as the (expected) number of nodes that a subset of nodes S will activate, excluding the nodes in S . Thus, OI equals, the de facto standard measure, influence spread of S minus | S |. OI is not only more informative for nodes with small influence, but also, critical in designing new effective sampling and statistical estimation methods. Based on OI, we propose SIEA/SOIEA, novel methods to estimate influence spread/outward influence at scale and with rigorous theoretical guarantees . The proposed methods are built on two novel components 1) IICP an important sampling method for outward influence; and 2) RSA, a robust mean estimation method that minimize the number of samples through analyzing variance and range of random variables. Compared to the state-of-the art for influence estimation, SIEA is Ω(log 4 n ) times faster in theory and up to several orders of magnitude faster in practice. For the first time, influence of nodes in the networks of billions of edges can be estimated with high accuracy within a few minutes. Our comprehensive experiments on real-world networks also give evidence against the popular practice of using a fixed number, e.g. 10K or 20K, of samples to compute the "ground truth" for influence spread.

Effects of source influence and peer referrals on information diffusion in Twitter

PurposeSocial media have attracted attention as an information channel for content generated in heterogeneous internet services. Focusing on social media platforms, the purpose of this paper is to examine the factors behind social transmission with content crossover from other services through hypertext link (URL). The authors investigate the effects of source influence and peer referrals on diffusion outcome and address their variations in the case of content crossover.Design/methodology/approachThe authors use a Poisson regression model due to the discrete nature of the dependent variable. The authors conduct an empirical study using 233 million real transaction data generated by 1,203,196 Korean users of Twitter.FindingsSource influence and peer referral have a positive impact on cascade size in the content dissemination process. In the case of content crossover, the impact of source influence decreases. However, the impact of peer referrals increases in the process of external content dissemination.Research limitations/implicationsThe authors demonstrate source and peer effects on content diffusion and that these effects vary when shared content is linked from an external service by a URL.Practical implicationsThe findings indicate that firms that wish to diffuse information through social media or enter the social media with new services to provide new ways of creating and sharing content should understand the nature of the social transmission process.Originality/valueGiven the growing popularity of social media, particularly SNSs with online social networks as information channels, the authors first consider online social transmission as a user-driven diffusion process. Based on social factors in the diffusion process, the authors derive source and peer effects on the social transmission process.

Outward Influence and Cascade Size Estimation in Billion-scale Networks

Estimating cascade size and nodes' influence is a fundamental task in social, technological, and biological networks. Yet this task is extremely challenging due to the sheer size and the structural heterogeneity of networks. We investigate a new influence measure, termed outward influence (OI), defined as the (expected) number of nodes that a subset of nodes S will activate, excluding the nodes in S. Thus, OI equals, the de facto standard measure, influence spread of S minus |S|. OI is not only more informative for nodes with small influence, but also, critical in designing new effective sampling and statistical estimation methods. Based on OI, we propose SIEA/SOIEA, novel methods to estimate influence spread/outward influence at scale and with rigorous theoretical guarantees. The proposed methods are built on two novel components 1) IICP an important sampling method for outward influence; and 2) RSA, a robust mean estimation method that minimize the number of samples through analyzing variance and range of random variables. Compared to the state-of-the art for influence estimation, SIEA is Ω(log 4 n) times faster in theory and up to several orders of magnitude faster in practice. For the first time, influence of nodes in the networks of billions of edges can be estimated with high accuracy within a few minutes. Our comprehensive experiments on real-world networks also give evidence against the popular practice of using a fixed number, e.g. 10K or 20K, of samples to compute the ``ground truth'' for influence spread.

Measuring the value of accurate link prediction for network seeding

Merging two classic questionsThe influence-maximization literature seeks small sets of individuals whose structural placement in the social network can drive large cascades of behavior. Optimization efforts to find the best seed set often assume perfect knowledge of the network topology. Unfortunately, social network links are rarely known in an exact way. When do seeding strategies based on less-than-accurate link prediction provide valuable insight?Our contributionWe introduce optimized-against-a-sample (text{OAS}) performance to measure the value of optimizing seeding based on a noisy observation of a network. Our computational study investigates text{OAS} under several threshold-spread models in synthetic and real-world networks. Our focus is on measuring the value of imprecise link information. The level of investment in link prediction that is strategic appears to depend closely on spread model: in some parameter ranges investments in improving link prediction can pay substantial premiums in cascade size. For other ranges, such investments would be wasted. Several trends were remarkably consistent across topologies.

Areas and sizes of cascades in dissipative one-dimensional sandpile model

A prototypical self-organized sandpile mode is studied on a one-dimensional (1D) chain with periodic boundary conditions. A dissipation mechanism in which every grain being transferred between nodes has a probability ϵ to be taken out is needed, as the system has no boundary nodes for grains to fall off – a feature reminiscent of complex networks. Detailed numerical analysis revealed distributions of cascade areas D(a) and cascade sizes D(s) that are intrinsically different from other 1D sandpile models with an open end. Analyzing cascading processes on a chain, independent-site approximations to D(a) and D(s) are developed. The approximated distributions are given in terms of a single parameter ϕ0, which is the fraction of empty nodes when the system is stable. The approximations are shown to capture the key features of the distributions. The distribution of cascade sizes D(s) is shown to exhibit large fluctuations that cannot be suppressed by averaging over different realizations. Our approximation provides a physically transparent explanation of the intrinsic large fluctuations in terms of the number of ways that a cascade can proceed for achieving a certain size. To close the approximations, a semi-empirical formula for the parameter ϕ0 as a function of the dissipation probability ϵ is found. Our work thus reports non-trivial results on a seemingly simple model and sheds light on analyzing cascading processes in other complex networks with no boundary nodes.

Neocortical activity is stimulus- and scale-invariant.

Mounting evidence supports the hypothesis that the cortex operates near a critical state, defined as the transition point between order (large-scale activity) and disorder (small-scale activity). This criticality is manifested by power law distribution of the size and duration of spontaneous cascades of activity, which are referred as neuronal avalanches. The existence of such neuronal avalanches has been confirmed by several studies both in vitro and in vivo, among different species and across multiple spatial scales. However, despite the prevalence of scale free activity, still very little is known concerning whether and how the scale-free nature of cortical activity is altered during external stimulation. To address this question, we performed in vivo two-photon population calcium imaging of layer 2/3 neurons in primary visual cortex of behaving mice during visual stimulation and conducted statistical analyses on the inferred spike trains. Our investigation for each mouse and condition revealed power law distributed neuronal avalanches, and irregular spiking individual neurons. Importantly, both the avalanche and the spike train properties remained largely unchanged for different stimuli, while the cross-correlation structure varied with stimuli. Our results establish that microcircuits in the visual cortex operate near the critical regime, while rearranging functional connectivity in response to varying sensory inputs.