Cascade Size Research Articles

Analyzing the Adoption and Cascading Process of OSN-Based Gifting Applications

To achieve growth in the user base of online social networks--(OSN) based applications, word-of-mouth diffusion mechanisms, such as user-to-user invitations, are widely used. This article characterizes the adoption and cascading process of OSN-based applications that grow via user invitations. We analyze a detailed large-scale dataset of a popular Facebook gifting application, iHeart, that contains more than 2 billion entries of user activities generated by 190 million users during a span of 64 weeks. We investigate (1) how users invite their friends to an OSN-based application, (2) how application adoption of an individual user can be predicted, (3) what factors drive the cascading process of application adoptions, and (4) what are the good predictors of the ultimate cascade sizes. We find that sending or receiving a large number of invitations does not necessarily help to recruit new users to iHeart. We also find that the average success ratio of inviters is the most important feature in predicting an adoption of an individual user, which indicates that the effectiveness of inviters has strong predictive power with respect to application adoption. Based on the lessons learned from our analyses, we build and evaluate learning-based models to predict whether a user will adopt iHeart. Our proposed model that utilizes additional activity information of individual users from other similar types of gifting applications can achieve high precision (83%) in predicting adoptions in the target application (i.e., iHeart). We next identify a set of distinctive features that are good predictors of the growth of the application adoptions in terms of final population size. We finally propose a prediction model to infer whether a cascade of application adoption will continue to grow in the future based on observing the initial adoption process. Results show that our proposed model can achieve high precision (over 80%) in predicting large cascades of application adoptions. We believe our work can give an important implication in resource allocation of OSN-based product stakeholders, for example, via targeted marketing.

Information Cascades in Feed-Based Networks of Users with Limited Attention

We build a model of information cascades on feed-based networks, taking into account the finite attention span of users, message generation rates and message forwarding rates. Using this model, we study through simulations, the effect of the extent of user attention on the probability that the cascade becomes viral. In analogy with a branching process, we estimate the branching factor associated with the cascade process for different attention spans and different forwarding probabilities, and demonstrate that beyond a certain attention span, critical forwarding probabilities exist that constitute a threshold after which cascades can become viral. The critical forwarding probabilities have an inverse relationship with the attention span. Next, we develop a semi-analytical approach for our model, that allows us determine the branching factor for given values of message generation rates, message forwarding rates and attention spans. The branching factors obtained using this analytical approach show good agreement with those obtained through simulations. Finally, we analyze an event specific dataset obtained from Twitter, and show that estimated branching factors correlate well with the cascade size distributions associated with distinct hashtags.

Vulnerability and Cosusceptibility Determine the Size of Network Cascades.

In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Here, we develop a statistical framework that can predict cascade size distributions by incorporating two ingredients only: the vulnerability of individual components and the cosusceptibility of groups of components (i.e., their tendency to fail together). Using cascades in power grids as a representative example, we show that correlations between component failures define structured and often surprisingly large groups of cosusceptible components. Aside from their implications for blackout studies, these results provide insights and a new modeling framework for understanding cascades in financial systems, food webs, and complex networks in general.

Quantifying the evolution of citation cascades

ABSTRACTCitation is an important measurement in science which provides valuable clues to the historical development and trend forecast of science. However, the evolution of citation structure remains poorly understood despite long‐period and frequent use of citation counts for assessment purposes within scientific community. We observe citation structure from a cascade perspective and construct a large and long‐range citation graph based on real data. Two metrics are used to quantify the structural virality and cascade size. Preliminary results show that (1) age plays an important role for the evolution of citation cascades; (2) average depth tends to be influenced by both lifespan and the whole volume of scientific literature and grows much slower than cascade size; (3) there exists a stable positive relationship between average depth and cascade size, and it seems that an ultimate status exists where most papers eventually have large values for both metrics.

Clustering determines the dynamics of complex contagions in multiplex networks.

We present the mathematical analysis of generalized complex contagions in a class of clustered multiplex networks. The model is intended to understand spread of influence, or any other spreading process implying a threshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed to be general enough to account for a content-dependent linear threshold model, where each link type has a different weight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is being spread. Using the generating functions formalism, we determine the conditions, probability, and expected size of the emergent global cascades. This analysis provides a generalization of previous approaches and is especially useful in problems related to spreading and percolation. The results present nontrivial dependencies between the clustering coefficient of the networks and its average degree. In particular, several phase transitions are shown to occur depending on these descriptors. Generally speaking, our findings reveal that increasing clustering decreases the probability of having global cascades and their size, however, this tendency changes with the average degree. There exists a certain average degree from which on clustering favors the probability and size of the contagion. By comparing the dynamics of complex contagions over multiplex networks and their monoplex projections, we demonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions about contagion dynamics, particularly when the correlation of degrees between layers is high.

The evolution of risk and bailout strategy in banking systems

In this paper we analyse the long-term costs and benefits of bailout strategies in models of networked banking systems. Unlike much of the current literature on financial contagion that focuses on systemic risk at one point in time, we consider adaptive banks that adjust risk taking in response to internal system dynamics and regulatory intervention, allowing us to analyse the potentially crucial moral hazard aspect associated with frequent bailouts. We demonstrate that whereas bailout generally serves as an effective tool to limit the size of bankruptcy cascades in the short term, inappropriate intervention strategies can encourage risk-taking and thus be inefficient and detrimental to long term system stability. We analyse points of long-term optimal bailout and discuss their dependence on the structure of the banking network. In the second part of the paper, we demonstrate that bailout efficiency can be improved by taking into account information about the topology of and risk allocation on the banking network, and demonstrate that finely tuned intervention strategies aimed at bailing out banks in configurations with some degree of anti-correlated risk have superior performance. These results demonstrate that a suitable intervention policy may be a useful tool for driving the banking system towards a more robust structure.

Toward early and order-of-magnitude cascade prediction in social networks

When a piece of information (microblog, photograph, video, link, etc.) starts to spread in a social network, an important question arises: will it spread to viral proportions - where viral can be defined as an order-of-magnitude increase. However, several previous studies have established that cascade size and frequency are related through a power-law - which leads to a severe imbalance in this classification problem. In this paper, we devise a suite of measurements based on structural diversity - the variety of social contexts (communities) in which individuals partaking in a given cascade engage. We demonstrate these measures are able to distinguish viral from non-viral cascades, despite the severe imbalance of the data for this problem. Further, we leverage these measurements as features in a classification approach, successfully predicting microblogs that grow from 50 to 500 reposts with precision of 0.69 and recall of 0.52 for the viral class - despite this class comprising under 2% of samples. This significantly outperforms our baseline approach as well as the current state-of-the-art. We also show this approach also performs well for identifying if cascades observed for 60 minutes will grow to 500 reposts as well as demonstrate how we can tradeoff between precision and recall.

Cortical Entropy, Mutual Information and Scale-Free Dynamics in Waking Mice.

Some neural circuits operate with simple dynamics characterized by one or a few well-defined spatiotemporal scales (e.g. central pattern generators). In contrast, cortical neuronal networks often exhibit richer activity patterns in which all spatiotemporal scales are represented. Such “scale-free” cortical dynamics manifest as cascades of activity with cascade sizes that are distributed according to a power-law. Theory and in vitro experiments suggest that information transmission among cortical circuits is optimized by scale-free dynamics. In vivo tests of this hypothesis have been limited by experimental techniques with insufficient spatial coverage and resolution, i.e., restricted access to a wide range of scales. We overcame these limitations by using genetically encoded voltage imaging to track neural activity in layer 2/3 pyramidal cells across the cortex in mice. As mice recovered from anesthesia, we observed three changes: (a) cortical information capacity increased, (b) information transmission among cortical regions increased and (c) neural activity became scale-free. Our results demonstrate that both information capacity and information transmission are maximized in the awake state in cortical regions with scale-free network dynamics.

Uncovering and predicting the dynamic process of information cascades with survival model

Cascades are ubiquitous in various network environments. Predicting these cascades is decidedly nontrivial in various important applications, such as viral marketing, epidemic prevention, and traffic management. Most previous works have focused on predicting the final cascade sizes. As cascades are dynamic processes, it is always interesting and important to predict the cascade size at any given time, or to predict the time when a cascade will reach a certain size (e.g., the threshold for an outbreak). In this paper, we unify all these tasks into a fundamental problem: cascading process prediction. That is, given the early stage of a cascade, can we predict its cumulative cascade size at any later time? For such a challenging problem, an understanding of the micromechanism that drives and generates the macrophenomena (i.e., the cascading process) is essential. Here, we introduce behavioral dynamics as the micromechanism to describe the dynamic process of an infected node's neighbors getting infected by a cascade (i.e., one-hop sub-cascades). Through data-driven analysis, we find out the common principles and patterns lying in the behavioral dynamics and propose the novel NEtworked WEibull Regression model for modeling it. We also propose a novel method for predicting cascading processes by effectively aggregating behavioral dynamics and present a scalable solution to approximate the cascading process with a theoretical guarantee. We evaluate the proposed method extensively on a large-scale social network dataset. The results demonstrate that the proposed method can significantly outperform other state-of-the-art methods in multiple tasks including cascade size prediction, outbreak time prediction, and cascading process prediction.

How damage diversification can reduce systemic risk.

We study the influence of risk diversification on cascading failures in weighted complex networks, where weighted directed links represent exposures between nodes. These weights result from different diversification strategies and their adjustment allows us to reduce systemic risk significantly by topological means. As an example, we contrast a classical exposure diversification (ED) approach with a damage diversification (DD) variant. The latter reduces the loss that the failure of high degree nodes generally inflict to their network neighbors and thus hampers the cascade amplification. To quantify the final cascade size and obtain our results, we develop a branching process approximation taking into account that inflicted losses cannot only depend on properties of the exposed, but also of the failing node. This analytic extension is a natural consequence of the paradigm shift from individual to system safety. To deepen our understanding of the cascade process, we complement this systemic perspective by a mesoscopic one: an analysis of the failure risk of nodes dependent on their degree. Additionally, we ask for the role of these failures in the cascade amplification.

Origin of the dimpled critical-current-versus-magnetic-field-angle relation in YBa2Cu3O7 films studied using sub-MeV ion irradiation

In high-temperature superconductor (HTSC) films, the magnetic-field-angle (θ) dependence of critical current density (Jc) is often observed to have a characteristic local maximum at intermediate θ between H||ab and H||c. This local maximum appears as a ‘shoulder’ when Jc(θ) has a predominant peak at H||c, and when such a peak is absent, it appears as a ‘dimple edge’ in a very broad dome-like Jc(θ) that is centered and dimpled at H||c. Despite such common observation, there is still no consensus on the physical origin of this anomalous Jc(θ). In this work, to determine this physical origin. we measured the temperature and microstructure dependence of Jc(B, θ) in YBa2Cu3O7 films irradiated with 3 MeV Au, 500 keV Si, and 200 keV B ions (where B is magnetic induction). The film microstructure was controlled by varying the mass of irradiation ions (Mi) known to alter the size and spacing of collision cascades. Results revealed two observations: (i) the dimple structure diminishes with decreasing temperature, and (ii) the maximum pinning force density in a θ profile, which is recorded at the dimple edge, systematically becomes more B-dependent with decreasing Mi. Both experimental findings suggest that the sharp-shaped anomaly in Jc(θ) in HTSC films originates from flux-line-lattice shear and electron mass anisotropy.

Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology

In a cascading power transmission outage, component outages propagate non-locally, after one component outages, the next failure may be very distant, both topologically and geographically. As a result, simple models of topological contagion do not accurately represent the propagation of cascades in power systems. However, cascading power outages do follow patterns, some of which are useful in understanding and reducing blackout risk. This paper describes a method by which the data from many cascading failure simulations can be transformed into a graph-based model of influences that provides actionable information about the many ways that cascades propagate in a particular system. The resulting "influence graph" model is Markovian, in that component outage probabilities depend only on the outages that occurred in the prior generation. To validate the model we compare the distribution of cascade sizes resulting from $n-2$ contingencies in a $2896$ branch test case to cascade sizes in the influence graph. The two distributions are remarkably similar. In addition, we derive an equation with which one can quickly identify modifications to the proposed system that will substantially reduce cascade propagation. With this equation one can quickly identify critical components that can be improved to substantially reduce the risk of large cascading blackouts.

Atomic structure of cascades of atomic displacements in metals and alloys after different types of radiation

Using the methods of field ion microscopy, we studied radiation induced defects on an atomically clean surface and within a subsurface volume of platinum initiated by the interaction of neutron (E > 0.1MeV) and Ar+ beams (E = 30 keV). It is shown that the interaction of fast neutrons (E > 0.1 MeV) F = 6.7-1021 m-2, F = 3.5-1022 m-2 with matter leads to the formation in the amount of platinum such as radiation damage which occur after ion irradiation by beams of charged Ar+ ions with E = 30 keV, F = 1020 ion/m2. They are observed at a depth of about 1.5-2 nm irradiated under the surface of Pt by ions Ar+. Thus, we have carried out modeling of neutron impact with matter when replacing the neutron beam by an ion beam that causes the same radiation damage in the bulk of the material. Experimental results on atomic-spatial investigation of radiative defect formation in surface layers of materials, initiated by neutron bombardment (of Pt, E > 0.1 MeV) and ion implantation (in Cu3Au: E = 40 keV, F = 1020 ion/m2, j = 10-3 A/cm2), are considered. Quantitative estimates obtained for the size, shape, and volume fraction of cascades of atomic displacements formed under various types of irradiation in the surface layers of the materials. It is showing that the average size of radiation clusters after irradiation of platinum to a fast neutron fluence of 6.7-1022 m-2 (E > 0.1 MeV) is about 3.2 nm. The experimentally established average size of a radiation cluster (disordered zone) in the alloy after ion bombardment is 4×4×1.5 nm.

Trend-driven information cascades on random networks.

Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a vanishingly small seed fraction can spread to a finite fraction of an infinitely large network through local infections. In social and economic networks, however, individuals' behavior is often influenced not only by what their direct neighbors are doing, but also by what the majority of people are doing as a trend. A trend affects individuals' behavior while individuals' behavior creates a trend. To analyze such a complex interplay between local- and global-scale phenomena, I generalize the standard threshold model by introducing a type of node called global nodes (or trend followers), whose activation probability depends on a global-scale trend, specifically the percentage of activated nodes in the population. The model shows that global nodes play a role as accelerating cascades once a trend emerges while reducing the probability of a trend emerging. Global nodes thus either facilitate or inhibit cascades, suggesting that a moderate share of trend followers may maximize the average size of cascades.

CPB: a classification-based approach for burst time prediction in cascades

Studying the bursty nature of cascades in social media is practically important in many real applications such as product sales prediction, disaster relief, and stock market prediction. Although both the cascade size prediction and the burst patterns of the cascades have been extensively studied, how to predict when a burst will come remains an open problem. It is challenging for traditional time-series-based models such as regression models to address this task directly. Firstly, times-series-based prediction models focus on predicting the future values based on previously observed ones. It is hard to apply them to predict the time of a bursts with the "quick rise-and-fall" pattern. Secondly, besides the cascade popularity, a lot of other side information like user profile and social relation are available in social media. Although the potential utility of such information can be high, it is also hard for time-series-based models to capture and integrate these rich information with diverse formats seamlessly. This paper proposes a classification-based approach for burst time prediction by exploiting rich knowledge in information diffusion. Particularly, we first propose a time-window-based transformation to predict in which time window the burst will appear. By dividing the time spans of all the cascades into the same number of time windows K, the cascades with diverse time spans can thus be handled uniformly. To exploit the rich and heterogenous information in social media, we next propose a scale-independent feature extraction framework to model the heterogenous knowledge in a scale-independent manner. Systematical evaluations are conducted on the Sina Weibo reposting dataset and MemeTracker dataset. Besides the superior performance of the proposed approach, we also observe that: (1) surprisingly, social/structure knowledge is more indicative of the bursts than the cascade popularity information, especially for the bursts occurring in a farther future. (2) Larger cascades are harder to predict as the spreading process of the cascades with higher popularity is usually more diverse and fluctuant. (3) The proposed approach is robust in the sense that the result is not much sensitive to the popularity of the training cascades.

The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators.

The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes’ thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. We demonstrate that for a given size of the initiator set, there is a specific variance of the threshold distribution for which an opinion spreads optimally. Furthermore, in the case of synthetic graphs we show that the spread asymptotically becomes independent of the system size, and that global cascades can arise just by the addition of a single node to the initiator set.

In-situ observation of radiation damage in nano-structured amorphous SiOC/crystalline Fe composite

The radiation tolerance property of amorphous silicon oxycarbide (SiOC) and crystalline Fe nanocomposites were examined by in-situ transmission electron microscope at 50Kelvin (K), room temperature and 573K. Results showed that intermixing between Fe and SiOC was most severe for irradiation at 50K. However, for irradiations at 573K, a demixing process was observed. The results indicated thermodynamic stability and radiation tolerance of Fe/SiOC nanocomposite at elevated temperature. Compared with thin Fe/SiOC multilayers, thick Fe/SiOC multilayer exhibited better irradiation stability. Discussion cover two possible reasons for these observations including the composite interface energy and collision cascade size.

Systemic risk in multiplex networks with asymmetric coupling and threshold feedback

We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with the case of a single layer network that is an aggregated representation of the two layers. We find that systemic risk in the two-layer network is smaller than in the aggregated one only if the coupling strength between the two layers is small. Above a critical coupling strength, systemic risk is increased because of the mutual amplification of cascades in the two layers. We even observe sharp phase transitions in the cascade size that are less pronounced on the aggregated layer. Our insights can be applied to a scenario where firms decide whether they want to split their business into a less risky core business and a more risky subsidiary business. In most cases, this may lead to a drastic increase of systemic risk, which is underestimated in an aggregated approach.

Analysis of information diffusion for threshold models on arbitrary networks

Diffusion of information via networks has been extensively studied for decades. We study the general threshold model that embraces most of the existing models for information diffusion. In this paper, we first analyze diffusion processes under the linear threshold model, then generalize it into the general threshold model. We give a closed formula for estimating the final cascade size for those models and prove that the actual final cascade size is concentrated around the estimated value, for any network structure with node degrees ω(log n), where n is the number of nodes. Our analysis analytically explains the tipping point phenomenon that is commonly observed in information diffusion processes. Based on the formula, we devise an efficient algorithm for estimating the cascade size for general threshold models on any network with any given initial adopter set. Our algorithm can be employed as a subroutine for numerous algorithms for diffusion analysis such as influence maximization problem. Through experiments on real-world and synthetic networks, we confirm that the actual cascade size is very close to the value computed by our formula and by our algorithm, even when the degrees of the nodes are not so large.

Universal Accretion Growth Using Sandpile Models

AbstractThe Bak Tang Weisenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around the system till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power- law distribution in cascade sizes having slope -5/3. This self-similarity of structure is synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions in fluid turbulence. In this paper, we show that this is a naturally occuring universal process giving rise to scale - free structures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a wide range of objects including molecular clouds, accretion disks and perhaps galaxies.