Cascade Size Research Articles

Unveiling the reproduction number scaling in characterizing social contagion coverage

The spreading of diseases depends critically on the reproduction number, which gives the expected number of new cases produced by infectious individuals during their lifetime. Here we reveal a widespread power-law scaling relationship between the variance and the mean of the reproduction number across simple and complex contagion mechanisms on various network structures. This scaling relation is verified on an empirical scientific collaboration network and analytically studied using generating functions. Specifically, we explore the impact of the scaling law of the reproduction number on the expected size of cascades of contagions. We find that the mean cascade size can be inferred from the mean reproduction number, albeit with limitations in capturing spreading variations. Nonetheless, insights derived from the tail of the distribution of the reproduction number contribute to explaining cascade size variation and allow the distinction between simple and complex contagion mechanisms. Our study sheds light on the intricate dynamics of spreading processes and cascade sizes in social networks, offering valuable insights for managing contagion outbreaks and optimizing responses to emerging threats.

A Model for the Temperature Distribution in a Rolled Joint in a CANDU Reactor Exploiting the Decomposition of the β-Zr Phase

A competing-rates model is presented to account for operational changes in the metastable β-Zr phase of the Zr-2.5Nb alloy used to make CANDU reactor pressure tubes and is used to predict temperature gradients at the outlet rolled joints using the decomposition of the β-Zr phase as a proxy for temperature. High temperatures decompose the β phase by enhancing the formation of small particles of ω and α phases. Fast neutron flux causes the ω and α phases to shrink. This process is assumed to depend on the total volume of the particles, because they are comparable to, or smaller than, the size of the neutron displacement cascades. The barrier energy for thermal growth was determined to be 2.43 eV, when an Arrhenius A factor of 1013/s was assumed. The cross section for (ω+α)-phase shrinkage is 24.5 barns for Zr-2.5Nb irradiated in CANDU reactors. Assuming that the shrinkage is dominated by the migration of self-interstitial point defects, a defect production efficiency of 1.4% was found.

The Virality of Hate Speech on Social Media

Online hate speech is responsible for violent attacks such as, e.g., the Pittsburgh synagogue shooting in 2018, thereby posing a significant threat to vulnerable groups and society in general. However, little is known about what makes hate speech on social media go viral. In this paper, we collect N = 25,219 cascades with 65,946 retweets from X (formerly known as Twitter) and classify them as hateful vs. normal. Using a generalized linear regression, we then estimate differences in the spread of hateful vs. normal content based on author and content variables. We thereby identify important determinants that explain differences in the spreading of hateful vs. normal content. For example, hateful content authored by verified users is disproportionally more likely to go viral than hateful content from non-verified ones: hateful content from a verified user (as opposed to normal content) has a 3.5 times larger cascade size, a 3.2 times longer cascade lifetime, and a 1.2 times larger structural virality. Altogether, we offer novel insights into the virality of hate speech on social media.

Monodispersed Renewable Particles by Cascade and Density Gradient Size Fractionation to Advance Lignin Nanotechnologies.

Control over particle size and shape heterogeneity is highly relevant to the design of photonic coatings and supracolloidal assemblies. Most developments in the area have relied on mineral and petroleum-derived polymers that achieve well-defined chemical and dimensional characteristics. Unfortunately, it is challenging to attain such control when considering renewable nanoparticles. Herein, a pathway toward selectable biobased particle size and physicochemical profiles is proposed. Specifically, lignin is fractionated, a widely available heterogeneous polymer that can be dissolved in aqueous solution, to obtain a variety of monodispersed particle fractions. A two-stage cascade and density gradient centrifugation that relieves the need for solvent pre-extraction or other pretreatments but achieves particle bins of uniform size (~60 to 860nm and polydispersity, PDI<0.06, dynamic light scattering) along with characteristic surface chemical features is introduced. It is found that the properties and associated colloidal behavior of the particles are suitably classified in distinctive size populations, namely, i) nanoscale (50-100nm), ii) photonic (100-300nm) and iii) near-micron (300-1000nm). The strong correlation that exists between size and physicochemical characteristics (molar mass, surface charge, bonding and functional groups, among others) is introduced as a powerful pathway to identify nanotechnological uses that benefit from the functionality and cost-effectiveness of biogenic particles.

Information cascade prediction of complex networks based on physics-informed graph convolutional network

Cascade prediction aims to estimate the popularity of information diffusion in complex networks, which is beneficial to many applications from identifying viral marketing to fake news propagation in social media, estimating the scientific impact (citations) of a new publication, and so on. How to effectively predict cascade growth size has become a significant problem. Most previous methods based on deep learning have achieved remarkable results, while concentrating on mining structural and temporal features from diffusion networks and propagation paths. Whereas, the ignorance of spread dynamic information restricts the improvement of prediction performance. In this paper, we propose a novel framework called Physics-informed graph convolutional network (PiGCN) for cascade prediction, which combines explicit features (structural and temporal features) and propagation dynamic status in learning diffusion ability of cascades. Specifically, PiGCN is an end-to-end predictor, firstly splitting a given cascade into sub-cascade graph sequence and learning local structures of each sub-cascade via graph convolutional network , then adopting multi-layer perceptron to predict the cascade growth size. Moreover, our dynamic neural network, combining PDE-like equations and a deep learning method, is designed to extract potential dynamics of cascade diffusion, which captures dynamic evolution rate both on structural and temporal changes. To evaluate the performance of our proposed PiGCN model, we have conducted extensive experiment on two well-known large-scale datasets from Sina Weibo and ArXIv subject listing HEP-PH to verify the effectiveness of our model. The results of our proposed model outperform the mainstream model, and show that dynamic features have great significance for cascade size prediction.

Limit Theorems for Default Contagion and Systemic Risk

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network subjected to an exogenous macroeconomic shock. We show that under certain regularity assumptions, the default cascade model can be transformed into a death process problem represented by a balls-and-bins model. We state various limit theorems regarding the final size of default cascades. Under appropriate assumptions on the degree and threshold distributions, we prove that the final sizes of default cascades have asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions, which enable us to provide systemic risk measures in relation to the structure and heterogeneity of the financial network. Lastly, we demonstrate how these results can be utilized by a social planner to optimally target interventions during a financial crisis given a budget constraint and under partial information of the financial network.

A generating-function approach to modelling complex contagion on clustered networks with multi-type branching processes

Abstract Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this article, we extend the multi-type branching process method developed in Keating et al., (2022), which relies on networks having homogenous node properties, to a more general class of clustered networks. Using a model of socially inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique-cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.

Cascading failure in urban rail transit network considering demand variation and time delay

To study the cascading failure in real-world urban rail transit network, the cascading failure model is proposed by considering two essential characteristics of demand variation and time delay, which has rarely been considered in most existing studies. Specifically, the model utilizes a simulation-based approach where passengers in the rail transit network are abstracted as packets moving through the network. The movement of these packets, including their response to station failures, is planned to model the travel behavior of passengers. The Shanghai rail transit network is chosen as the case study for this research. Comparative experiments suggest that the proposed model may produce very different results for stations with high closeness and enough travel demand. The proposed model can depict the dynamic failure process and yield a longer and more dynamic failure process, which is beneficial for managers to identify the period for prevention. Besides, sensitivity analysis shows that higher travel demand is more likely to cause a cascading failure, while time delay slightly impacts the final cascade size but affects propagation duration. In summary, travel demand plays a vital role in cascading failures, and the presence of time delays complicates the cascading failure propagation process. The research results provide references and support for studying cascading failure in real complex environments.

CasTformer: A novel cascade transformer towards predicting information diffusion

Predicting information diffusion cascade is an essential task in social networks. We mainly focus on predicting the size of the information cascade. The relationships inside a cascade are diverse, including global and relative spatio-temporal relationships, as well as interpersonal influence relationships. These complex relationships between nodes play a crucial role in cascade prediction, but they have not been thoroughly investigated. The Transformer's global receptive field can assist in capturing the relationships between two arbitrary nodes. However, using Transformer directly for a cascade is insufficient without considering its temporal and structural characteristics. In this paper, we propose a novel cascade Transformer for the first time, called CasTformer, specifically designed for cascade size prediction. CasTformer utilizes a global spatio-temporal positional encoding and relative relationship bias matrices on the self-attention mechanism to capture diverse cascade relationships. Moreover, self-knowledge distillation is employed for obtaining a better cascade representation to enhance prediction performance. We use four datasets with nearly millions of cascade samples to validate our model and it achieves training in 3 hours. Experimental results show that it outperforms state-of-the-art methods by an average of 11.9%, 6.1%, and 9.6% on MSLE, MAPE, and R2, respectively.

Effect of cascade size and damage rate on α’ precipitate stability in Fe-15Cr

Samples of a Fe-15Cr model alloy with an established α' precipitate population were irradiated with 1.25 MeV electrons, 1.5 MeV protons, or 4.4 MeV Fe2+/3+ ions over a range of damage rates to doses of 1 or 10 dpa at 400°C to determine the roles of cascade size and damage rate on the stability of α'. Results showed that α' precipitate size and chromium content increased with dpa for electron irradiations. Proton irradiation also resulted in increases in α' precipitate size and Cr content, but at a slower rate than with electrons due to the influence of ballistic dissolution. Self-ion irradiations caused a reduction in the size and Cr content of α' with dose, and above a threshold damage rate of 1–3 × 10−4 dpa/s, the precipitates were completely dissolved. The ballistic dissolution parameter for self-ion irradiations calculated from both the Nelson-Hudson-Mazey model and a mixing model was in the range 2–5 × 1020 atoms/m2‧dpa compared to a value of ∼9 × 1019 atoms/m2‧dpa for proton irradiation, and explains the different behaviors of the precipitates for these two irradiating particles. Overall, it was found that cascade size strongly determines the stability of α' precipitates and damage rate has its major impact on the rate at which α' precipitates grow or dissolve.

Predicting the Popularity of Information on Social Platforms without Underlying Network Structure.

The ability to predict the size of information cascades in online social networks is crucial for various applications, including decision-making and viral marketing. However, traditional methods either rely on complicated time-varying features that are challenging to extract from multilingual and cross-platform content, or on network structures and properties that are often difficult to obtain. To address these issues, we conducted empirical research using data from two well-known social networking platforms, WeChat and Weibo. Our findings suggest that the information-cascading process is best described as an activate-decay dynamic process. Building on these insights, we developed an activate-decay (AD)-based algorithm that can accurately predict the long-term popularity of online content based solely on its early repost amount. We tested our algorithm using data from WeChat and Weibo, demonstrating that we could fit the evolution trend of content propagation and predict the longer-term dynamics of message forwarding from earlier data. We also discovered a close correlation between the peak forwarding amount of information and the total amount of dissemination. Finding the peak of the amount of information dissemination can significantly improve the prediction accuracy of our model. Our method also outperformed existing baseline methods for predicting the popularity of information.

Information cascade final size distributions derived from urn models

Bipolarization is a phenomenon in which either a large or very small information cascade appears randomly when the retweet rate is high. This phenomenon, which has been observed only in simulations, has the potential to significantly advance the prediction of final cascade sizes because forecasters need only focus on the two peaks in the final cascade size distribution rather than considering the effects of various details, such as network structure and user behavioral patterns. The phenomenon also suggests the difficulty of identifying factors that lead to the emergence of large-scale cascades. To verify the existence of bipolarization, this paper theoretically derives mathematical expressions of the cascade final size distribution using urn models, which simplify the diffusion behavior of actual online social networks. Under the assumption of infinite network size, the distribution exhibits power-law behavior, consistent with the results of existing diffusion models and previous Twitter analytical outcomes. Under the assumption of finite network size, bipolarization is observed.

Incomplete Gamma Integrals for Deep Cascade Prediction Using Content, Network, and Exogenous Signals

The behavior of information cascades (such as retweets) has been modeled extensively. While point process-based generative models have long been in use for estimating cascade growths, deep learning has greatly enhanced the integration of diverse features and signals. We observe two significant temporal signals in cascade data that have not been reported or exploited to our knowledge. First, the popularity of the cascade root is known to influence cascade size strongly; but we find that the effect falls off rapidly with time. Second, we find a measurable positive correlation between the novelty of the root content (with respect to a streaming external corpus) and the relative size of the resulting cascade. Responding to these observations, we propose <monospace>GammaCas</monospace>, a new cascade growth model as a parametric function of time, which combines deep influence signals from content (e.g., tweet text), network features (e.g., followers of the root user), and exogenous event sources (e.g., online news). Specifically, our model processes these signals through a customized recurrent network, whose states then provide the parameters of the cascade rate function, which is integrated over time to predict the cascade size. The network parameters are trained end-to-end using observed cascades. <monospace>GammaCas</monospace> outperforms seven recent and diverse baselines significantly on a large-scale dataset of retweet cascades coupled with time-aligned online news &#x2014; it beats the best baseline with 18.98&#x0025; increase in terms of Kendall&#x0027;s <inline-formula><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> correlation and a reduction of 19.2 in Mean Absolute Percentage Error. Extensive ablation and case studies unearth interesting insights regarding retweet cascade dynamics.

Dual-Task Network Embeddings for Influence Prediction in Social Internet of Things

Social Internet of Things (SIoT) is an emerging application area that supports the spread of multimedia information. Detecting critical nodes based on the results of influence prediction is the main solution to maximizing the information propagation in SIoT. However, while the tasks of predicting an influence probability and a cascade size are both critical in influence prediction, there has not yet a study that thoroughly investigates these two influence parameters. This article presents an end-to-end method that learns dual-task network embeddings to jointly predict influence probabilities and cascade sizes, which is called a multidimensional influence-to-vector method (Multi-Influor). First, multidimensional influence contexts are generated based on random walks, incorporating multiple estimating factors for pairwise node interaction, network structure, and global preference similarity. A new method of learning dual-task network embeddings is then devised to simultaneously capture influence probabilities and cascade sizes. The two tasks are both formulated into a unified framework via enforcing an information-sharing embedding matrix. Finally, stochastic gradient descent (SGD) is used to optimize two loss functions for influence prediction in an alternating manner, and the tasks are jointly accomplished that produces an accurate prediction. Extensive simulation results on real-world data sets show that Multi-Influor outperforms six state-of-the-art methods in accuracy and efficiency, and that a joint training method for the two tasks improves the overall prediction performance. Moreover, Multi-Influor is a practical method for SIoT sustainable computing.

CasFlow: Exploring Hierarchical Structures and Propagation Uncertainty for Cascade Prediction

Understanding in-network information diffusion is a fundamental problem in many applications and one of the primary challenges is to predict the information cascade size. Most of the existing models rely either on hypothesized point process (e.g., Poisson and Hawkes processes), or simply predict the information propagation via deep neural networks. However, they fail to simultaneously capture the underlying global and local structures of a cascade and the propagation uncertainty in the diffusion, which may result in unsatisfactory prediction performance. To address these, in this work we propose a novel probabilistic cascade prediction framework <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CasFlow</i> : Hierarchical Cascade Normalizing Flows. CasFlow allows a non-linear information diffusion inference and models the information diffusion process by learning the latent representation of both the structural and temporal information. It is a pattern-agnostic model leveraging normalizing flows to learn the node-level and cascade-level latent factors in an unsupervised manner. In addition, CasFlow is capable of capturing both the cascade representation uncertainty and node infection uncertainty, while enabling hierarchical pattern learning of information diffusion. Extensive experiments conducted on real-world datasets demonstrate that CasFlow reduces the prediction error to 21.0% by only observing half an hour of cascades, compared to state-of-the-art approaches, while also enabling model interpretability.

Predicting the cascading dynamics in complex networks via the bimodal failure size distribution.

Cascading failure as a systematic risk occurs in a wide range of real-world networks. Cascade size distribution is a basic and crucial characteristic of systemic cascade behaviors. Recent research works have revealed that the distribution of cascade sizes is a bimodal form indicating the existence of either very small cascades or large ones. In this paper, we aim to understand the properties and formation characteristics of such bimodal distribution in complex networks and further predict the final cascade size. We first find that the bimodal distribution is ubiquitous under certain conditions in both synthetic and real networks. Moreover, the large cascades distributed in the right peak of bimodal distribution are resulted from either the failure of nodes with high load at the first step of the cascade or multiple rounds of cascades triggered by the initial failure. Accordingly, we propose a hybrid load metric (HLM), which combines the load of the initial broken node and the load of failed nodes triggered by the initial failure, to predict the final size of cascading failures. We validate the effectiveness of HLM by computing the accuracy of identifying the cascades belonging to the right and left peaks of the bimodal distribution. The results show that HLM is a better predictor than commonly used network centrality metrics in both synthetic and real-world networks. Finally, the influence of network structure on the optimal HLM is discussed.

A master equation for power laws.

We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson's Law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value. In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log-log plots in the frequency and rank distributions.

Empirical evaluation of link deletion methods for limiting information diffusion on social media.

Although beneficial information abounds on social media, the dissemination of harmful information such as the so-called fake news has become a serious issue. Therefore, many researchers have devoted considerable effort to limiting the diffusion of harmful information. A promising approach to limiting diffusion of such information is link deletion methods in social networks. Link deletion methods have been shown to be effective in reducing the size of information diffusion cascades generated by synthetic models on a given social network. In this study, we evaluate the effectiveness of link deletion methods by using actual logs of retweet cascades, rather than by using synthetic diffusion models. Our results show that even after deleting 10-50% of links from a social network, the size of cascades after link deletion is estimated to be only 50% the original size under the optimistic estimation, which suggests that the effectiveness of the link deletion strategy for suppressing information diffusion is limited. Moreover, our results also show that there is a considerable number of cascades with many seed users, which renders link deletion methods inefficient.

Structure and fracture behavior of ion-beam-modified SiC-Al2O3-ZrO2 ceramic composites

SiC-Al2O3-ZrO2 ceramic composite with heterointerfaces was prepared by hot pressing and irradiated with 1.2 MeV Si ions at room temperatures. The microstructural evolution and mechanical properties were investigated. The results showed that the phase transformation of zirconia revealed by GIXRD and TEM are associated with the accumulation of oxygen vacancies clusters originated by damage and the size of displacement cascades. Complete amorphization of SiC particles were observed at 5.5 dpa, and developed into collection band at 55 dpa due to the mixture of point defect clusters and extend defects at high damage level. The nanohardness and elastic modulus irradiation decreased with increasing of damage level. The fracture behavior of materials and relative mechanism under ion irradiation were discussed.

Exploring the robustness of public transportation system on augmented network: A case from Nanjing China

A highly robust urban public transportation network is the foundation for the stable and sustainable development of a city. Managers may benefit from a reasonable investigation into the robustness of the public transportation system to recognize and deliver improved public transportation services. This paper developed a robustness analysis framework for public transportation systems on augmented network (AN). Specifically, an AN was first built to treat the public transit network from a multi-layer perspective. The AN carefully considers the boarding, alighting, riding and transfer behaviors, and develops cost functions under the congestion effect, thus sufficiently simulating the real passengers’ behaviors. Then, the user equilibrium (UE) assignment model, a model widely used for passenger flow forecasting, is applied to guide the robustness analysis under cascading failures. Finally, a real large-scale bus–rail hybrid network in Nanjing is used as a case study. The results show that the initial station capacities are significant to the impact of the cascading failure, from which we conclude that a larger initial capacity of stations can prevent the cascading failures. By investigating the relationship between passenger flow and cascade size, the comparative results further explain the mechanisms of cascading failures. Thanks to the AN and UE, three types of travel times can be compared to reflect the quality of public passenger trips, which should provide traffic managers with pertinent advice for improving service.