Cascade Threshold Research Articles

CyNetDiff: A Python Library for Accelerated Implementation of Network Diffusion Models

In recent years, there has been increasing interest in network diffusion models and related problems. The most popular of these are the independent cascade and linear threshold models. Much of the recent experimental work done on these models requires a large number of simulations conducted on large graphs, a computationally expensive task suited for low-level languages. However, many researchers prefer the use of higher-level languages (such as Python) for their flexibility and shorter development times. Moreover, in many research tasks, these simulations are the most computationally intensive task, so it would be desirable to have a library for these with an interface to a high-level language with the performance of a low-level language. To fill this niche, we introduce CyNetDiff, a Python library with components written in Cython to provide improved performance for these computationally intensive diffusion tasks.

Online Behavior Balancing Model for Influence Maximization in Twitter

Background: Social influence estimation is an important aspect of viral marketing. The majority of the influence estimation models for online social networks are either based on Independent Cascade (IC) or Linear Threshold (LT) models. These models are based on some hypothesis: (1) process of influence is irreversible; (2) classification of user’s status is binary, i.e., either influenced or non-influenced; (3) process of influence is either single person’s dominance or collective dominance but not the both at the same time. However, these assumptions are not always valid in the real world, as human behavior is unpredictable. Objective: Develop a generalized model to handle the primary assumptions of the existing influence estimation models. Methods: This paper proposes a Behavior Balancing (BB) Model, which is a hybrid of IC and LT models and counters the underlying assumptions of the contemporary models. Results: The efficacy of the proposed model to deal with various scenarios is evaluated over six different twitter election integrity datasets. Results depict that BB model is able to handle the stochastic behavior of the user with up to 35% improved accuracy in influence estimation as compared to the contemporary counterparts. Conclusion: The BB model employs the activity or interaction information of the user over the social network platform in the estimation of diffusion and allows any user to alter their opinion at any time without compromising the accuracy of the predictions.

On the Robustness of Diffusion in a Network Under Node Attacks

How can we assess a network's ability to maintain its functionality under attacks? <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Network robustness</i> has been studied extensively in the case of deterministic networks. However, applications such as online information diffusion and the behavior of networked public raise a question of robustness in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probabilistic</i> networks. We propose three novel robustness measures for networks hosting a diffusion under the Independent Cascade or Linear Threshold model, susceptible to attacks by an adversarial attacker who disables nodes. The outcome of such a process depends on the selection of its initiators, or seeds, by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">seeder</i> , as well as on two factors outside the seeder's discretion: the attacker's strategy and the probabilistic diffusion outcome. We consider three levels of seeder awareness regarding these two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uncontrolled</i> factors, and evaluate the network's viability aggregated over all possible extents of an attack. We introduce novel algorithms from building blocks found in previous works to evaluate the proposed measures. A thorough experimental study with synthetic and real, scale-free and homogeneous networks establishes that these algorithms are effective and efficient, while the proposed measures highlight differences among networks in terms of robustness and the surprise they furnish when attacked. Last, we devise a new measure of diffusion entropy, and devise ways to enhance the robustness of probabilistic networks.

Influence Maximization on Undirected Graphs

We study the influence maximization problem in undirected networks, specifically focusing on the independent cascade and linear threshold models. We prove APX-hardness (NP-hardness of approximation within factor (1-τ) for some constant τ &gt; 0) for both models, which improves the previous NP-hardness lower bound for the linear threshold model. No previous hardness result was known for the independent cascade model. As part of the hardness proof, we show some natural properties of these cascades on undirected graphs. For example, we show that the expected number of infections of a seed set S is upper bounded by the size of the edge cut of S in the linear threshold model and a special case of the independent cascade model, the weighted independent cascade model. Motivated by our upper bounds, we present a suite of highly scalable local greedy heuristics for the influence maximization problem on both the linear threshold model and the weighted independent cascade model on undirected graphs that, in practice, find seed sets that on average obtain 97.52% of the performance of the much slower greedy algorithm for the linear threshold model and 97.39% of the performance of the greedy algorithm for the weighted independent cascade model. Our heuristics also outperform other popular local heuristics, such as the degree discount heuristic by Chen et al. [7].

Influence maximization diffusion models based on engagement and activeness on instagram

An influencer is an impactful content creator on social media. The emergence of influencers led to increased influencer marketing. The task of picking the right influencers is widely studied through influence maximization (IM). Existing IM studies have matured in terms of theoretical performance, but not very realistic in real-world. First, existing IM diffusion models didn't consider the engagement level and activeness of the users. Secondly, there were no studies that compare activated users against actual influenced users on Instagram. To address both problems, three new realistic diffusion models are proposed, based on the Independent Cascade and Linear Threshold models, namely IC-u, LT-u and UAD models. This study was implemented using Instagram data. Meanwhile, UAD model uses two thresholds, namely user's awareness, and user's tendency. These models incorporate user's activeness and engagement factors that represent the susceptibility to influence and the degree of influence, respectively. The proposed models were proven to be up to 2.72x more realistic and produced more engaging and more active users. The seeds set (influencers) identified by the IM algorithms under the proposed models are expected to have more impact on an actual brand marketing campaign if compared to existing models.

Efficient algorithms based on centrality measures for identification of top-K influential users in social networks

The problem of influence maximization has grown in popularity and interest in recent decades due to its valuable application in various fields. This problem mainly focuses on identifying Top-K influential users that, when selected, the influence spread will be maximized. Thus, the identification of such nodes is pivotal in increasing the adoption of promoted information and behavior within the network. In this paper, we propose two new efficient algorithms, namely, “MinCDegKatz d-hops (MaxCDegKatz d-hops)” that relies on a combination of centralization measures due to their known efficiency and performance in terms of influence spread and their low runtime complexity. The proposed algorithms combine between the degree centrality as local measure and the Katz centrality as global centrality metric on a graph with preselected weight edges that should exceed a predefined threshold value. Thus, each selected seed set is separated by a number of hops that differ depending on the graph radius. Then, the influence spread is measured for the two proposed algorithms under the Independent Cascade (IC) and Linear Threshold (LT) models. We conducted extensive experiments on a large-scale graph that demonstrated the performance of our proposed algorithms against existing approaches in term of spreading ability and time complexity.

Deep Reinforcement Learning-Based Approach to Tackle Topic-Aware Influence Maximization

Motivated by the application of viral marketing, the topic-aware influence maximization (TIM) problem has been proposed to identify the most influential users under given topics. In particular, it aims to find k seeds (users) in social network G, such that the seeds can maximize the influence on users under the specific query topics and diffusion model such as independent cascade (IC) or linear threshold (LT).This problem has been proved to be NP-hard, and most of the proposed techniques suffer from the efficiency issue due to the lack of generalization. Even worse, the design of these algorithms requires significant specialized knowledge which is hard to be understood and implemented. To overcome these issues, this paper aims to learn a generalized heuristic framework to solve TIM problems by meta-learning. To this end, we first propose two topic-aware social influence propagation models based on IC and LT model, respectively, which is conducive to better advertising injections. We then encode the feature of each node by a vector and introduce a model, called deep influence evaluation model , to evaluate the user influence under different circumstances. Based on this model, we can construct the solution according to the influence evaluations efficiently, rather than spending a high cost to compute the exact influence by considering the complex graph structure. We conducted experiments on generated graph instances and real-world social networks. The results show the superiority in performance and comparable quality of our framework.

On the effect of cascade transitions after electron-impact excitation of Zn by spin-polarized electrons

SynopsisWe investigate the possible effect of cascade transitions from the (4s5p)3P0,1,2 states to the (4s5s)3S1 state of Zn. Our calculations suggest that the excitation cross sections and the polarization of the cascade radiation cannot explain the serious controversy between two existing experimental datasets below the cascade threshold and raise additional questions regarding the measurements at higher energies.

The Auger spectra in argon induced by electron impact – new measurements with high resolution

The Auger spectrum of argon in the kinetic energy region (135–235 eV) has been measured using a non-monochromatic electron beam (incident energy from 313 to 2019 eV) at two ejection angles of 60° and 90° with a high resolution electrostatic analyzer. The electron impact energies of 313 and 323 eV have been used in order to disentangle the contribution of the ionization and decay of the 2s state. The systematic analysis of the measured spectra shows the dominance of the Coster-Kronig transitions from the 2s ionization in the energy region 135–159 eV and 208–235 eV, while the Auger transitions from the 2p ionization are dominant in the energy region 160–208 eV. The high resolution of the present work led to the observation of a certain number of new features in two energy regions 135–159 and 208–235 eV, respectively. Recent literature data on the cascade Auger processes and threshold formation of Ar2+ satellite states allow the assignment of some of them, while other have been left without assignments. The influence of the PCI effect on the line-shape, width and energy position of the features in the kinetic energy region 200–208 eV has been also investigated and the PCI shift versus excess energy above threshold compared with previous data and theoretical predictions.

Effect of cascade transitions on the polarization of light emitted after electron-impact excitation of Zn by spin-polarized electrons

We investigate the possible effect of cascade transitions from the $(4s5p)\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0,1,2}$ states to the $(4s5s)\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ state of Zn. The polarization of the light emitted in the subsequent decay to the $(4s4p)\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0,1,2}$ states has been the subject of recent controversy, with significant disagreement between the experimental data reported by Pravica et al. [Phys. Rev. A 83, 040701 (2011)] and by Clayburn and Gay [Phys. Rev. Lett. 119, 093401 (2017)] in the cascade-free region below $\ensuremath{\approx}7.6$ eV incident energy and relatively good agreement above. The cross sections for excitation of the $(4s5p)\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0,1,2}$ states, as well as higher-lying triplet states, and the linear polarization of the cascade radiation seem too small to produce a significant alignment of the $(4s5s)\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ state, thereby raising additional questions regarding the origin of the relatively large linear polarizations measured above the cascade threshold.

Identifying influential spreaders in large-scale networks based on evidence theory

Identifying the most influential spreaders is an important issue in epidemic spreading, viral marketing, and controlling the spreading process of information. Thus, methods for identifying influential spreaders in complex networks have received increasing attention from researchers. During recent decades, researchers have proposed many methods. However, each of these methods has advantages and disadvantages. In this paper, we propose a new efficient algorithm for identifying influential spreaders based on the Dempster–Shafer (D–S) evidence theory, which is a complete theory that deal with uncertainty or imprecision. We call our proposed algorithm D-2SN, which trades off between the degree (D) and the 2-step neighbor information (2SN) of every node in a network. Specifically, the influence of both the degree and the 2SN of each node are represented by a basic probability assignment (BPA). D-2SN is determined by the fusion of these BPAs. Since the algorithm considers not only the topological structure of each node, but also its neighbors’ structure, it is a good choice to balance cost and performance. In addition, it also exhibits very low time complexity O(⟨k⟩n), which makes it applicable to large-scale networks. To evaluate the performance of D-2SN, we employ the Independent Cascade (IC) and Liner Threshold (LT) models to examine the spreading efficiency of each node and compare D-2SN with several classic methods in eight real-world networks. Extensive experiments demonstrate the superiority of D-2SN to other baseline methods.

Threshold Estimation Models for Linear Threshold-Based Influential User Mining in Social Networks

Influence Maximization (IM) is a popular social network mining mechanism that mines influential users for viral marketing in social networks. Most of the Influence Maximization techniques employ either the independent cascade (IC) or linear threshold (LT) model in the node activation process. In the IC model, all the active in-neighbors are given a single chance to activate a node with a particular probability whereas, in the LT model, a node is activated if the aggregated influence of all the activated in-neighbors is no less than a threshold value. Thus, the threshold plays a significant role in the LT-based influence maximization. In this paper, we comprehensively survey the different threshold values used in various IM models. Based on the survey, we observe that the current studies lack threshold estimation models. Therefore, we develop a system model and propose four threshold estimation models based on influence-weight and degree distribution. The empirical results show that our algorithms generate threshold values that resemble the thresholds used by most IM algorithms along with faster running time. Besides, the proposed models are scalable and applicable to any influence-weight estimation technique and offer narrower threshold ranges rather than the broad ranges used in many existing works.

An efficient and effective hop-based approach for influence maximization in social networks

Influence maximization in social networks is a classic and extensively studied problem that targets at selecting a set of initial seed nodes to spread the influence as widely as possible. However, it remains an open challenge to design fast and accurate algorithms to find solutions in large-scale social networks. Prior Monte Carlo simulation-based methods are slow and not scalable, while other heuristic algorithms do not have any theoretical guarantee and they have been shown to produce poor solutions for quite some cases. In this paper, we propose hop-based algorithms that can be easily applied to billion-scale networks under the commonly used Independent Cascade and Linear Threshold influence diffusion models. Moreover, we provide provable data-dependent approximation guarantees for our proposed hop-based approaches. Experimental evaluations with real social network datasets demonstrate the efficiency and effectiveness of our algorithms.

A two-stage stochastic programming approach for influence maximization in social networks

We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem optimally. To this end, we introduce a new class of problems that we refer to as two-stage stochastic submodular optimization models. We propose a delayed constraint generation algorithm to find the optimal solution to this class of problems with a finite number of samples. The influence maximization problems of interest are special cases of this general problem class. We show that the submodularity of the influence function can be exploited to develop strong optimality cuts that are more effective than the standard optimality cuts available in the literature. Finally, we report our computational experiments with large-scale real-world datasets for two fundamental influence maximization problems, independent cascade and linear threshold, and show that our proposed algorithm outperforms the greedy algorithm.

Maximizing the Influence and Profit in Social Networks

Influence maximization problem is to find a set of seeds in social networks such that the cascade influence is maximized. Traditional models assume that all nodes are willing to spread the influence once they are influenced, and they ignore the disparity between influence and profit of a product. In this paper, by considering the role that price plays in viral marketing, we propose price related (PR) frame that contains PR-I and PR-L models for classic independent cascade and linear threshold models, respectively, which is a pioneer work. Two pricing strategies are designed, one is binary pricing (BYC), in which the seeds are offered free samples. The other is panoramic pricing (PAP), in which the seeds are offered different discounts. Furthermore, we find that influence and profit are like two sides of the coin, high price hinders the influence propagation and to enlarge the influence some sacrifice on profit is inevitable. Based on this observation under PR frame, by adopting a parameter to denote the decision maker’s preference toward influence and profit, we propose balanced influence and profit (BIP) maximization problem. We prove the NP-hardness of BIP maximization under PR-I and PR-L model. Unlike influence maximization, the BIP objective function is not monotone. Despite the nonmonotony, we show BIP objective function is submodular under certain conditions. Two unbudgeted greedy algorithms separately, named algorithm of BYC and algorithm of PAP are devised. We conduct extensive simulations on real world data sets, test the effectiveness of our proposed parameters, compare the algorithms’ performances, and evaluate the superiority of our algorithms over existing ones.

Seeded QED cascades in counterpropagating laser pulses.

The growth rates of seeded QED cascades in counterpropagating lasers are calculated with first-principles two- and three-dimensional QED-PIC (particle-in-cell) simulations. The dependence of the growth rate on the laser polarization and intensity is compared with analytical models that support the findings of the simulations. The models provide insight regarding the qualitative trend of the cascade growth when the intensity of the laser field is varied. A discussion about the cascade's threshold is included, based on the analytical and numerical results. These results show that relativistic pair plasmas and efficient conversion from laser photons to γ rays can be observed with the typical intensities planned to operate on future ultraintense laser facilities such as ELI or Vulcan.

Social network pruning for building optimal social network: A user perspective

Social networks with millions of nodes and edges are difficult to visualize and understand. Therefore, approaches to simplify social networks are needed. This paper addresses the problem of pruning social network while not only retaining but also improving its information propagation properties. The paper presents an approach which examines the nodal attribute of a node and develops a criterion to retain a subset of nodes to form a pruned graph of the original social network. To authenticate feasibility of the proposed approach to information propagation process, it is evaluated on small world properties such as average clustering coefficient, diameter, path length, connected components and modularity. The pruned graph, when compared to original social network, shows improvement in small world properties which are essential for information propagation. Results also give a significantly more refined picture of social network, than has been previously highlighted. The efficacy of the pruned graph is demonstrated in the information diffusion process under Independent Cascade (IC) and Linear Threshold (LT) models on various seeding strategies. In all size ranges and across various seeding strategies, the proposed approach performs consistently well in IC model and outperforms other approaches in LT model. Although, the paper discusses the problem with the context of information propagation for viral marketing, the pruned graph generated from the proposed approach is also suitable for any application, where information propagation has to take place reasonably fast and effectively.

Influence maximization by probing partial communities in dynamic online social networks

AbstractWith the rapid development of online social networks, exploring influence maximization for product publicity and advertisement marketing has attracted strong interests from both academia and industry. However, because of the continuous change of network topology, updating the variation of an entire network moment by moment is resource intensive and often insurmountable. On the other hand, the classical influence maximization models Independent Cascade and Linear Threshold together with their derived varieties are all computationally intensive. Thus, developing a solution for dynamic networks with lower cost and higher accuracy is in an urgent necessity. In this paper, a practical framework is proposed by only probing partial communities to explore the real changes of a network. Our framework minimizes the possible difference between the observed topology and the real network through several representative communities. Based on the framework, an algorithm that takes full advantage of our divide‐and‐conquer strategy, which reduces the computational overhead, is proposed. The systemically theoretical analysis shows that the proposed effective algorithm could achieve provable approximation guarantees. Empirical studies on synthetic and real large‐scale social networks demonstrate that our framework has better practicality compared with most existing works and provides a regulatory mechanism for enhancing influence maximization. Copyright © 2016 John Wiley &amp; Sons, Ltd.

On the Upper Bounds of Spread for Greedy Algorithms in Social Network Influence Maximization

Influence maximization, defined as finding a small subset of nodes that maximizes spread of influence in social networks, is NP-hard under both Independent Cascade (IC) and Linear Threshold (LT) models, where many greedy-based algorithms have been proposed with the best approximation guarantee. However, existing greedy-based algorithms are inefficient on large networks, as it demands heavy Monte-Carlo simulations of the spread functions for each node at the initial step [7] . In this paper, we establish new upper bounds to significantly reduce the number of Monte-Carlo simulations in greedy-based algorithms, especially at the initial step. We theoretically prove that the bound is tight and convergent when the summation of weights towards (or from) each node is less than 1. Based on the bound, we propose a new Upper Bound based Lazy Forward algorithm ( UBLF in short) for discovering the top-k influential nodes in social networks. We test and compare UBLF with prior greedy algorithms, especially CELF [30] . Experimental results show that UBLF reduces more than 95 percent Monte-Carlo simulations of CELF and achieves about $2\hbox{-}10$ times speedup when the seed set is small.

Topic-aware social influence propagation models

The study of influence-driven propagations in social networks and its exploitation for viral marketing purposes has recently received a large deal of attention. However, regardless of the fact that users authoritativeness, expertise, trust and influence are evidently topic-dependent, the research on social influence has surprisingly largely overlooked this aspect. In this article, we study social influence from a topic modeling perspective. We introduce novel topic-aware influence-driven propagation models that, as we show in our experiments, are more accurate in describing real-world cascades than the standard (i.e., topic-blind) propagation models studied in the literature. In particular, we first propose simple topic-aware extensions of the well-known Independent Cascade and Linear Threshold models. However, these propagation models have a very large number of parameters which could lead to overfitting. Therefore, we propose a different approach explicitly modeling authoritativeness, influence and relevance under a topic-aware perspective. Instead of considering user-to-user influence, the proposed model focuses on user authoritativeness and interests in a topic, leading to a drastic reduction in the number of parameters of the model. We devise methods to learn the parameters of the models from a data set of past propagations. Our experimentation confirms the high accuracy of the proposed models and learning schemes.