Final Adoption Size Research Articles

SAR dynamical mechanism affected by diminishing marginal effect based on personal fashion psychology on multi-layer contacted network

People in complex systems exhibit varying capacities for social interaction because of differences in personal psychology, educational attainment, and social class. It is true that people often use different social networks and show different enthusiasm for obtaining information, but their interest in collecting information will decrease over time. Our study on Personal Fashion Psychology (PFP) has shown that when people get information, they behave in a way known as the Diminishing Marginal Effect (DME-PFP behavior). Next, we created a SAR propagation dynamics model on a multi-layer contact network to represent DME-PFP behavior using a threshold function. Then, to assess and uncover the transmission mechanism of individual behaviour, we use partition theory. A boundary phenomena is displayed by the propagation mode, as demonstrated by both theoretical analysis and simulated tests. The final size can exhibit either discontinuous first-order phase transitions or continuous second-order phase changes in individual DME-PFP behaviour. Meanwhile, through the unit transmission probability changed, the ideal DME-PFP parameters occur at the largest final adoption size. Moreover, the promotion of the propagation pattern and behaviour from continuous second-order to discontinuous first-order is facilitated by interpersonal contact. The numerical analysis and the actual models may eventually agree.

The effects of individual heterogeneity on social contagions

Abstract Despite having significant effects on social contagions, individual heterogeneity has frequently been overlooked in earlier studies. To better understand the complexity of social contagions, a non-Markovian model incorporating heterogeneous social influence and adoption thresholds is introduced. For theoretical analysis, a generalized edge-based compartmental theory which considers the heterogeneities of social influence and adoption thresholds are developed. Focusing on the final adoption size, critical propagation probability and the phase transition type, social contagions for adoption thresholds follow normal distributions with various standard deviations, follow various distributions, and correlate with degrees are investigated. When thresholds follow normal distributions, a larger standard deviation results in a larger the final adoption size when the information propagation probability is relatively low. However, when the information propagation probability is relatively high, a larger standard deviation result in a smaller final adoption size. When thresholds follow various distributions, crossover phenomena in phase transition are observed in investigating the relationship of the final adoption size versus the average adoption threshold for some threshold distributions. When thresholds are correlated with degrees, similar crossover phenomena occur in investigating the relationship of the final adoption size versus the degree correlation index. Additionally, we find that increasing the heterogeneity of social influence suppresses the effects of adoption threshold heterogeneity on social contagions in the three cases. Our theory predictions agree well with the simulation results.

Phase transition phenomena in social propagation with dynamic fashion tendency and individual contact

In complex systems, individuals exhibit various social contact capacities on account of differences in societal strata, educational backgrounds, and individual psychology. It is a fact that people tend to utilize diverse social networks and demonstrate ever-changing fashion trends. From our study on personal psychology, we have noted that individuals display a behaviour known as dynamic fashion tendency (DFT) when receiving information. Next, to represent DFT behaviour through a threshold model, we devised a dynamic SAR propagation model on a multi-layer contact network. For the transmission mechanism of individual behaviour, we utilized partition theory to investigate and uncover. Both theoretical analysis and simulation experiments demonstrate that the propagation mode exhibits a boundary phenomenon. The final adoption size may demonstrate either continuous second-order or discontinuous first-order phase transitions, depending on individual DFT behaviour. When unit propagation probability is constant, the largest final adoption size is attained with the ideal DFT parameters. Additionally, personal contact plays a role in spreading behaviour and shifting the propagation pattern from continuous second-order to discontinuous first-order. Ultimately, numerical analysis can correspond with real models.

Influence of behavioral adoption preference based on heterogeneous population on multiple weighted networks

The study of behavioral propagation is taken more into account intimate heterogeneity on social networks. Meanwhile, with the development of information technology, people present a multiplicity of social ways, i.e., individuals normally receive or spread information on different social networks. More importantly, the behavioral preference of heterogenous population lacks in-depth research on the information propagation. Firstly, a multi-layer network with edge weighted distribution is considered. Then, we build a trapezoid-like and a triangle-like probability functions to represent individual continuous fashion trend (ICFT) and individual fashion passion trend (IFPT) behaviors separately, defining the adoption behavior preference of different population. Furthermore, a generalized edge-based compartmental theory including edge weight, ICFT and IFPT thresholds is proposed to reveal the behavioral preference. Through simulated experiments, decreasing the proportion of sensitive individuals can raise a hybrid phase transition, in which the final adoption size first increases continuously at the first critical value, and then increases discontinuously at the second critical value. Moreover, when the proportion of sensitive individuals is fixed, the strong adoption capacity of individuals can induce a discontinuous phase transition. Contrarily, the weak adoption capacity of individuals can induce a continuous phase transition. Finally, the edge weight and degree heterogeneity can alter the behavioral propagation on social networks.

Social contagion influenced by active-passive psychology of college students

Educational behavioral psychology refers to the fact that college students within campus networks have various psychological cognition toward novel information and behavior. This is hardly ever taken into account or theoretically examined in weighted network research. According to psychological traits and a student’s willingness to adopt fresh behaviors, we categorize students’ behaviors into the active and passive. On this basis, a threshold models is established for the behavior of active and passive students in weighted networks, and the influence behavioral psychology on information propagation is discussed. In order to qualitatively investigate the information propagation mechanism, a partition theory based on edge-weight and behavioral psychology is developed. Active students encourage the acceptance of new behaviors and the spread of information, according to theoretical study and simulation results. However, the phase transition intersected was more significant. When the percentage of enrolled pupils is high, a continuous phase transition is present in the growth pattern of the final adoption size. In contrast, as the proportion of active students declines, the increasing pattern alterss to discontinuous phase transition. In addition, weight distribution heterogeneity facilitates the dissemination of information and does not alter phase transition pattern. Finally, the theoretical analysis is in good agreement with the simulation results.

Information propagation influenced by individual fashion-passion trend on multi-layer weighted network

In recent years, prior research on information propagation has considered individual relationships on social network as binary but ignored individual intimacy heterogeneity. Furthermore, individuals like to concurrently use multiple social networks and meanwhile show different passions for information acceptance, called individual fashion-passion trend (IFPT) characteristics. Therefore, we first construct a multi-layer weighted social network to catch individual intimacy heterogeneity, and then build an adoption threshold model with tent-like probability function to explore the IFPT characteristics. Next a partition theory based on edge-weight and IFPT threshold is utilized to quantify and analyze individual information propagation mechanism. The simulated results and theoretical analyses exhibit crossover phenomena of phase transition. When individual has a strong IFPT, the increasing style of the final adoption size shows a second-order continuous phase transition. While individual has a weak IFPT, the increasing style of the final adoption size exhibits a first-order discontinuous phase transition. More excitingly, fixing the value of the information propagation unit probability, a maximum final adoption size can be obtained at an optimal IFPT value. Moreover, weight distribution heterogeneity accelerates information propagation and the change of phase transition style from the second-order continuous phase transition to first-order discontinuous phase transition. Finally, our theoretical analyses coincide with the simulated results.

Effects of heterogeneous adoption thresholds on contact-limited social contagions

Limited contact capacity and heterogeneous adoption thresholds have been proven to be two essential characteristics of individuals in natural complex social systems, and their impacts on social contagions exhibit complex nature. With this in mind, a heterogeneous contact-limited threshold model is proposed, which adopts one of four threshold distributions, namely Gaussian distribution, log-normal distribution, exponential distribution and power-law distribution. The heterogeneous edge-based compartmental theory is developed for theoretical analysis, and the calculation methods of the final adoption size and outbreak threshold are given theoretically. Many numerical simulations are performed on the Erdös–Rényi and scale-free networks to study the impact of different forms of the threshold distribution on hierarchical spreading process, the final adoption size, the outbreak threshold and the phase transition in contact-limited propagation networks. We find that the spreading process of social contagions is divided into three distinct stages. Moreover, different threshold distributions cause different spreading processes, especially for some threshold distributions, there is a change from a discontinuous first-order phase transition to a continuous second-order phase transition. Further, we find that changing the standard deviation of different threshold distributions will cause the final adoption size and outbreak threshold to change, and finally tend to be stable with the increase of standard deviation.

Information Propagation Influenced by Population Heterogeneity Behavioral Adoption on Weighted Network

In the realistic world, various individuals have distinct personalities, preferences, and attitudes toward new information and behavior acceptance, called population heterogeneity. It is seldom taken into account and theoretically analyzed in information propagation on a weighted network. Therefore, we divide individuals into fashionable and conservative individuals according to their passion degree and willingness for novel behaviors acceptance. Then, we build two behavior adoption threshold models corresponding to fashionable and conservative individuals on the weighted network to explore the effect of population heterogeneity on information propagation. Next, a partition theory based on edge weight and population heterogeneity is proposed to qualitatively analyze the information propagation mechanism. The theoretical analyses and simulation results show that fashionable individuals promote information propagation and behavior adoption. More importantly, the crossover phenomena of phase transition appear. When the fraction of fashionable individuals is relatively large, the increasing pattern of the final adoption size shows a second‐order continuous phase transition. In comparison, the increasing pattern alters to first‐order discontinuous phase transition with the decrease of the fraction of fashionable individuals. Moreover, reducing weight distribution heterogeneity promotes information propagation and slightly accelerates the change of the phase transition pattern from the first‐order discontinuous to the second‐order continuous. Besides, increasing the degree distribution heterogeneity accelerates the change of the phase transition pattern. Finally, our theoretical analyses coincide well with the simulation results.

Research on information dissemination on social networks based on edge-based compartmental theory

The study of the mechanism of information dissemination on social networks has important practical significance for information dissemination prediction. Aiming at the impact of the reinforcement effect derived from nonredundant information memory on information dissemination, this paper proposes a susceptible–exposed–adopted–recovered (SEAR) information dissemination model. This model considers the reinforcement effect of nonredundant information memory characteristics, and is theoretically analyzed based on an edge-based compartmental theory. This model reveals the law of individual information transmission in real society and better explains the process of information transmission. The simulation results show that the reinforcement effect of nonredundant information memory has a significant impact on information dissemination. The stronger the reinforcement effect, the greater the final behavior adoption size, that is, the wider the scope of information dissemination. The theoretical prediction is basically consistent with the simulation results, which shows that the method of edge-based compartmental theory has a specific validity. In addition, changing the individual’s “on” threshold, the individual’s stability threshold, the proportion of individuals in the initial adopted state, and the heterogeneity of degree distribution can make the final behavior adoption size increase linearly or vertically with the probability of information transmission.

Quantum Contagion: A Quantum-Like Approach for the Analysis of Social Contagion Dynamics with Heterogeneous Adoption Thresholds.

Modeling the information of social contagion processes has recently attracted a substantial amount of interest from researchers due to its wide applicability in network science, multi-agent-systems, information science, and marketing. Unlike in biological spreading, the existence of a reinforcement effect in social contagion necessitates considering the complexity of individuals in the systems. Although many studies acknowledged the heterogeneity of the individuals in their adoption of information, there are no studies that take into account the individuals’ uncertainty during their adoption decision-making. This resulted in less than optimal modeling of social contagion dynamics in the existence of phase transition in the final adoption size versus transmission probability. We employed the Inverse Born Problem (IBP) to represent probabilistic entities as complex probability amplitudes in edge-based compartmental theory, and demonstrated that our novel approach performs better in the prediction of social contagion dynamics through extensive simulations on random regular networks.

Impact of Immunization Strategies on the Dynamics of Social Contagions

Immunization strategies on complex networks are effective methods to control the spreading dynamics on complex networks, which change the topology and connectivity of the underlying network, thereby affecting the dynamics process of propagation. Here, we use a non-Markovian threshold model to study the impact of immunization strategies on social contagions, in which the immune index greater than (or equal to) 0 corresponds to targeted (random) immunization, and when the immune index is less than 0, the probability of an individual being immunized is inversely related to the degree of the individual. A generalized edge-based compartmental theory is developed to analyze the dynamics of social contagions under immunization, and theoretical predictions are very consistent with simulation results. We find that increasing the immune index or increasing the immune ratio will reduce the final adoption size and increase the outbreak threshold, in other words, make the residual network after immunization not conducive to social contagions. Interestingly, enhancing the network heterogeneity is proved to help improve the immune efficiency of targeted immunization. Besides, the dependence of the outbreak threshold on the network heterogeneity is correlated with the immune ratio and immune index.

Impact of contact preference on social contagions on complex networks.

Preferential contact process limited by contact capacity remarkably affects the spreading dynamics on complex networks, but the influence of this preferential contact in social contagions has not been fully explored. To this end, we propose a behavior spreading model based on the mechanism of preferential contact. The probability in the model that an adopted individual contacts and tries to transmit the behavioral information to one of his/her neighbors depends on the neighbor's degree. Besides, a preferential exponent determines the tendency to contact with either small-degree or large-degree nodes. We use a dynamic messaging method to describe this complex contagion process and verify that the method is accurate to predict the spreading dynamics by numerical simulations on strongly heterogeneous networks. We find that the preferential contact mechanism leads to a crossover phenomenon in the growth of final adoption size. By reducing the preferential exponent, we observe a change from a continuous growth to an explosive growth and then to a continuous growth with the transmission rate of behavioral information. Moreover, we find that there is an optimal preferential exponent which maximizes the final adoption size at a fixed information transmission rate, and this optimal preferential exponent decreases with the information transmission rate. The used theory can be extended to other types of dynamics, and our findings provide useful and general insights into social contagion processes in the real world.

Complex Social Contagions on Weighted Networks Considering Adoption Threshold Heterogeneity

Many real-world phenomena can be described as complex contagions, which has attracted much attention in the field of network science. However, the effects of the heterogeneous adoption thresholds on complex contagions in weighted networks have not been systematically investigated. In this paper, we propose a heterogeneous complex contagion model on the weighted network, in which individuals have different adoption thresholds. For individuals with a relatively small adoption threshold, they are more likely to adopt the contagion and act as activists. An edge-weight based compartmental theory is developed to unveil spreading dynamics. Through extensive numerical simulations and theoretical analysis, we find that, for any weight distribution heterogeneity, with the increase of the activist fraction, the growth pattern of the final adoption size versus the information spreading probability changes from hybrid phase transition to a second-order continuous phase transition. Meanwhile, increasing the activist fraction can promote behavior spreading. Through bifurcation analysis, we discover that changing the heterogeneity of the weight distribution will not change the type of phase transition. Besides, reducing weight distribution heterogeneity can facilitate behavior spreading. Extensive numerical simulations verify that the theoretical solutions coincide with the numerical results very well.

Social reinforcement inducing discontinuous spreading in complex networks

Social reinforcement originating from memory is the key characteristic of behavioral adoption in social contagion. Here, we introduce a non-Markovian susceptible-adopted-recovered (SAR) model to incorporate the memory mechanism. The higher the number of accumulated pieces of exposures an individual is exposed to, the larger is the probability that he/she will adopt the behavior. We observed that when the adopting probability per piece of behavioral information was smaller than a critical value, the final adoption size increased with the behavioral information probability discontinuously. Otherwise, the final adoption size increased with the behavioral information probability continuously. A physical understanding of the mechanism inducing discontinuous spreading was obtained through an edge-based compartment method, which also matched well with the simulation results.

Dynamics on Hybrid Complex Network: Botnet Modeling and Analysis of Medical IoT

With the rapid development of Internet of things technology, the application of intelligent devices in the medical industry has become ubiquitous. Connected devices have revolutionized clinicians and patient care but also made modern hospitals vulnerable to cyber attacks. Among the security risks, botnets are of particular concern, which can be used to control thousands of devices for remote data theft and equipment destruction. In this paper, we propose a non-Markovian spread dynamics model to understand the effects of botnet propagation, which can characterize the hybrid contagion situation in reality. Based on the Susceptible-Adopted-Recovered model, we introduce nonredundant memory spread mechanism for global propagation, as a tuner to adjust spreading rate difference. For describing the proposed model, we extend a heterogeneous edge-based compartmental theory. Through extensive numerical simulations, we reveal that the growth pattern of the final adoption size versus the information transmission probability is discontinuous and how the final adoption size is affected by hybrid ratio α, global scope control factor ϵ, accumulated received information threshold T, and other parameters on ER network. Furthermore, we give the theory and simulation result on BA network and also compare the two hybrid methods—single infection in one time slice and double infections in one time slice—to evaluate the influence on final adoption size. We found in SIOT hybrid contagion scenario the final adoption size shows the phenomenon of a decline followed by an increase versus different hybrid ratio, and it is both verified in theory and numerical simulation. Through validation by thousands of experiments, our developed theory agrees well with the numerical simulations.

Contagion of Information on Two-Layered Weighted Complex Network

In recent years, information spreading mechanism on the social networks has received extensive attention. Previous studies usually simplify the social relationships as binary, though in real social networks, the different intimacy between nodes in different layers will affect the information spreading. The enhancement of non-redundant information memory also plays an important role in information spreading. In this paper, we propose a weighted two-layered social network information spreading model based on threshold model. In order to qualitatively understand the impact of weight distribution heterogeneity on information spreading, an edge-weight based compartmental theory is proposed. We find that under an arbitrary adoption threshold, reducing weight distribution heterogeneity can facilitate information spreading and promote the global adoption, yet unable to change the dependence pattern of the final adoption size on the unit transmission probability. We also find that when the initial seed fraction is less than a critical value, information cannot be transmitted explosively in the network. Increasing the fraction of initial seeds or the heterogeneity of degree distribution will alter the dependence pattern of the final adoption size on the unit transmission probability from being discontinuous to being continuous.

Information Spreading on Weighted Multiplex Social Network

Information spreading on multiplex networks has been investigated widely. For multiplex networks, the relations of each layer possess different extents of intimacy, which can be described as weighted multiplex networks. Nevertheless, the effect of weighted multiplex network structures on information spreading has not been analyzed comprehensively. We herein propose an information spreading model on a weighted multiplex network. Then, we develop an edge‐weight‐based compartmental theory to describe the spreading dynamics. We discover that under any adoption threshold of two subnetworks, reducing weight distribution heterogeneity does not alter the growth pattern of the final adoption size versus information transmission probability while accelerating information spreading. For fixed weight distribution, the growth pattern changes with the heterogeneous of degree distribution. There is a critical initial seed size, below which no global information outbreak can occur. Extensive numerical simulations affirm that the theoretical predictions agree well with the numerical results.

Social contagions with communication channel alternation on multiplex networks

Internet communication channels, e.g., Facebook, Twitter, and email, are multiplex networks that facilitate interaction and information-sharing among individuals. During brief time periods users often use a single communication channel, but then communication channel alteration (CCA) occurs. This means that we must refine our understanding of the dynamics of social contagions. We propose a non-Markovian behavior spreading model in multiplex networks that takes into account the CCA mechanism, and we develop a generalized edge-based compartmental method to describe the spreading dynamics. Through extensive numerical simulations and theoretical analyses we find that the time delays induced by CCA slow the behavior spreading but do not affect the final adoption size. We also find that the CCA suppresses behavior spreading. On two coupled random regular networks, the adoption size exhibits hybrid growth, i.e., it grows first continuously and then discontinuously with the information transmission probability. CCA in ER-SF multiplex networks in which two subnetworks are Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) introduces a crossover from continuous to hybrid growth in adoption size versus information transmission probability. Our results extend our understanding of the role of CCA in spreading dynamics, and may elicit further research.

Heterogeneous behavioral adoption in multiplex networks

Heterogeneity is found widely in populations, e.g. different individuals have diverse personalities and a different willingness to accept novel ideas or behaviors. Whereas population heterogeneity is rarely considered in studying the social contagions on complex networks, especially on multiplex networks. To explore the effect of population heterogeneity on the dynamics of social contagions, a novel model based on double-layer multiplex networks is proposed, in which information diffuses synchronously on the two layers, and each layer is assigned with different adoption thresholds. Meanwhile, populations are classified into the activists and conservatives according to their willingness to adopt new behaviors. To qualitatively understand the effect of population heterogeneity on social contagions, a generalized edge-based compartmental theory is proposed. Through rigorous theoretical analysis and extensive simulations, we find the activists in the two layers promote the adoption of behavior. More interestingly, the crossover phenomena in phase transition are found in the growth of the final adopted size when increasing the information transmission rate. When the proportion of activists is relatively large, the phase transition exhibits continuous pattern. Reducing the proportion of activists induces a hybrid transition, in which the final adoption size first grows continuously at the first threshold, and then increases discontinuously at the second threshold. In addition, we find that the network heterogeneity will change the crossover phenomena in phase transition.

A dynamic message-passing approach for social contagion in time-varying multiplex networks

The information about social behavior diffusion on a communication network and the social behavior contagion through a physical-contact network are two related dynamical processes. We investigate here an asymmetrically interacting, double-layer network to elucidate the interplay between information diffusion on a time-varying network and the social contagion on the counterpart layer. We uncover that the time-varying character affects the final adoption size. We also find that the behavior spreading in the physical-contact network introduces the adoption size from first to second order. A maximizing area of the difference between the final infected size and the adoption size appears in a suitable range of the behavioral information transmission rate and the initial seed size. We develop a dynamic message-passing theory to understand the interplay between both types of spreading dynamics.