Adoption Threshold Research Articles

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.

Propagation characteristic of adoption thresholds heterogeneity in double-layer networks with edge weight distribution

People normally show different relation intensity and adoption behaviors, which can affect information spreading on social networks. To describe the two phenomena, we consider edge weight distribution and adoption thresholds heterogeneity on the networks separately, where the adoption thresholds of nodes obey truncated gaussian distribution. Therefore, we propose a double-layer network model with edge weight distribution to explore the impact of heterogeneous adoption thresholds of nodes on information spreading. And we also develop an edge-based compartmental theory to analyze the information spreading mechanism. Through numerical simulations and theoretical analysis, we find that increasing the values of mean can suppress information spreading, and the impact of the values of standard deviation on information spreading depends on the values of mean. Specifically, for a small value of mean, the size of information spreading will decrease with the increase of the value of standard deviation. Meanwhile, when the values of standard deviation are fixed, the size of information spreading will increase continuously with the increase of transmission probability. For a large value of mean, the size of information spreading will increase first and then decrease with the increase of the value of standard deviation. In addition, this paper shows that the theoretical method agrees with the numerical simulations in the experimental results.

Double transitions and hysteresis in heterogeneous contagion processes.

In many real-world contagion phenomena, the number of contacts to spreading entities for adoption varies for different individuals. Therefore, we study a model of contagion dynamics with heterogeneous adoption thresholds. We derive mean-field equations for the fraction of adopted nodes and obtain phase diagrams in terms of the transmission probability and fraction of nodes requiring multiple contacts for adoption. We find a double phase transition exhibiting a continuous transition and a subsequent discontinuous jump in the fraction of adopted nodes because of the heterogeneity in adoption thresholds. Additionally, we observe hysteresis curves in the fraction of adopted nodes owing to adopted nodes in the densely connected core in a network.

Quantifying high flexion postures in occupational childcare as they relate to the potential for increased risk of knee osteoarthritis

High knee flexion postures, despite their association with increased incidences of osteoarthritis, are frequently adopted in occupational childcare. This study sought to define and quantify high flexion postures typically adopted in childcare to evaluate any increased likelihood of knee osteoarthritis development. Through video analysis of eighteen childcare workers caring for infant, toddler, and preschool-aged children, eight high knee flexion postures were identified and quantified by duration and frequency. An analysis of postural adoption by task was subsequently performed to determine which might pose the greatest risk for cumulative joint trauma. Childcare workers caring for children of all ages were found to adopt kneeling and seated postures for extended durations and at elevated frequencies, exceeding proposed thresholds for incidences of knee osteoarthritis development. Structured activities, playing, and feeding tasks demanded the greatest adoption of high flexion postures and should be evaluated to minimise the potential childcare-related risks of osteoarthritis. Practitioner summary: High knee flexion postures (kneeling, squatting, etc.) have been associated with increased incidences of knee injury yet are commonly adopted in childcare. Childcare workers’ postures were examined through video analysis revealing that proposed adoption thresholds for knee health are commonly exceeded when caring for children of all ages. Abbreviations: OA: osteoarthritis; WSIB: workplace safety insurance board; CAD: Canadian Dollar; DK: dorsiflexed kneeling; PK: plantarflexed kneeling; SAK: single arm supported kneeling; DAK: double arm supported kneeling; FS: flatfoot squatting; HS: heels up squatting; FLRS: floor sitting; SS: side sitting or leaning; STLS: stool sitting; BR: bending and reaching

Investigating the Observability of Complex Contagion in Empirical Social Networks

Social contagion is the mechanism by which ideas and behaviors spread across human social networks. Simple contagion models approximate the likelihood of adoption as constant with each exposure to an "infected" network neighbor. However, social theory postulates that when adopting an idea or behavior carries personal or social risk, an individual's adoption likelihood also depends on the number of distinct neighbors who have adopted. Such complex contagions are thought to govern the spread of social movements and other important social phenomena. Online sites, such as Twitter, expose social interactions at a large scale and provide an opportunity to observe the spread of social contagions "in the wild." Much of the effort in searching for complex phenomena in real world contagions focuses on measuring user adoption thresholds. In this work, we show an alternative method for fitting probabilistic complex contagion models to empirical data that avoids measuring thresholds directly, and our results indicate bias in observed thresholds under both complex and simple models. We also show 1) that probabilistic models of simple and complex contagion are distinguishable when applied to an empirical social network with random user activity; and 2) the predictive power of these probabilistic adoption models against observed adoptions of actual hashtags used on Twitter. We use a set of tweets collected from Nigeria in 2014, focusing on 20 popular hashtags, using the follow graphs of the users adopting the tags during their initial peaks of activity.

The influence of heterogeneity of adoption thresholds on limited information spreading

The spreading process of information on complex networks has been widely explored. In fact, different individuals in a network usually hold different standards for information adoption. Considering the heterogeneity of adoption thresholds, this study constructs a two-layer network model with limited contacts. The adoption threshold of a node is related to its degree and a parameter obeying truncated normal distribution. This study also proposes a partition theory based on edges to analyze the mechanism of information dissemination quantitatively. Experiments find that increasing the mean of parameters can inhibit information from spreading, and the effect of the standard deviation of parameters on information dissemination depends on the mean of parameters. For instance, when the mean of parameters is a low value, as the standard deviation of parameters increases, the information outbreak size will decrease. On the other hand, the information outbreak size will increase continuously with increased propagation probability. If the mean of parameters is high, the information outbreak size will increase first and then decrease with the increment in the standard deviation of parameters. The theoretical predictions of this study are in good agreement with the numerical simulations.

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.

Robotic strawberry harvest is promising but will need improved technology and higher wages to be economically viable

While the prospect of robotic harvest in strawberry production has received much attention within the strawberry industry and the popular press, there is little available information on the economic feasibility of this technology. It is not clear how close the industry is to being able to profitably adopt robotic harvest systems; also unclear is the relative importance of wage rates, robotic harvest efficiencies and machinery field speeds on the adoption threshold. This study aims to clarify these issues by estimating the net income to strawberry production under robotic harvest scenarios, and comparing the values to standard enterprise budgets for strawberry production in California under different wage rates for harvest labor. Results confirm that robotic harvest remains economically unviable under current wage rates and the field speeds and harvest efficiencies achieved by leading robotic harvest development teams. However, results indicate that with expected increases in wage rates in the coming years, and with modest improvements in the technical parameters, use of robotic systems will likely become profitable in some form.

Network diffusion of competing behaviors.

Research indicates that network structure affects the diffusion of a single behavior. However, in many social settings, two or more behaviors may compete for adoption, as in the case of religious competition, social movements and counter-movements, or conflicting rumors. Lessons from one-behavior diffusion cannot be easily applied because the outcome can take the form of one-behavior domination, two behaviors splitting the network, both behaviors occupying a small fraction of the network, or no diffusion. This article tests how three well-known factors of single-behavior diffusion - network transitivity, adoption threshold, and connectedness of early adopters - apply to scenarios of competitive diffusion. Results show that minor differences in initial adopter size tend to magnify, creating a significant "head-start advantage." Nevertheless, the degree of this advantage depends on the interaction between network transitivity, adoption threshold, and connectedness of initial adopters. The article describes the conditions under which countervailing ties may (or may not) create inequality in behavioral diffusion.

Local Evidence and Diversity in Minipublics

A policymaker selects a group of citizens—a minipublic—to advise her on the desirability of a policy. Each citizen can discover local evidence about the policy but might prefer not to due to political uncertainty in the policymaker’s adoption threshold. Such uncertainty is detrimental to evidence discovery even though evidence is costless, citizens are civic-minded, and the citizens’ and policymaker’s interests are on average aligned. Which minipublic does the policymaker select optimally when constrained by such endogenous evidence discovery? To restore citizens’ incentives, the policymaker chooses a minipublic that is less diverse than the most informative minipublic, both demographically and informationally. She learns too much about citizens around the median citizen and too little about peripheral citizens. Evidence discovery is more challenging to incentivize under moderate, rather than high, political uncertainty. In a sufficiently heterogeneous citizenry, no minipublic discovers any evidence.

The role of geography in the complex diffusion of innovations

The urban–rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million friendship ties of 3 million users. We find that the number of adopters as a function of town population follows a scaling law that reveals a strongly concentrated early adoption in large towns and a less concentrated late adoption. We also discover a strengthening distance decay of spread over the life-cycle indicating high fraction of distant diffusion in early stages but the dominance of local diffusion in late stages. The spreading process is modelled within the Bass diffusion framework that enables us to compare the differential equation version with an agent-based version of the model run on the empirical network. Although both model versions can capture the macro trend of adoption, they have limited capacity to describe the observed trends of urban scaling and distance decay. We find, however that incorporating adoption thresholds, defined by the fraction of social connections that adopt a technology before the individual adopts, improves the network model fit to the urban scaling of early adopters. Controlling for the threshold distribution enables us to eliminate the bias induced by local network structure on predicting local adoption peaks. Finally, we show that geographical features such as distance from the innovation origin and town size influence prediction of adoption peak at local scales in all model specifications.

Impact of the heterogeneity of adoption thresholds on behavior spreading in complex networks

Individuals always exhibit distinct personal profiles ranging from education, social experiences to risk tolerance, which induces a vastly different response in the behavior spreading dynamics. To describe this phenomenon, a widely used method is to assign a distinct adoption threshold for each individual, which so far has eluded theoretical analysis. In this paper, we propose a behavior spreading model to describe the heterogeneity of individuals in adopting the behavior, in which the adoption threshold follows the Gaussian distribution. Based on the edge-based compartmental theory, the theoretical solutions of the behavior spreading size and the threshold are given for discontinuous and continuous phase transitions. Through theoretical analysis and extensive numerical simulations, the impact of the heterogeneity of adoption thresholds on behavior spreading is demonstrated, and we find that the phase transition depends on the mean and standard deviation of the adoption thresholds. For small values of the mean adoption threshold, the system exhibits a continuous phase transition. For large values of the mean adoption threshold, the phase transition is discontinuous (continuous) for the small (large) standard deviation of the adoption thresholds. There is a remarkable agreement between theoretical predictions and numerical simulations.

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.

Misunderstanding conservation agriculture: Challenges in promoting, monitoring and evaluating sustainable farming

Commercial agriculture is central to problems of sustainability in food, water, energy and climate change. Appropriate solutions will depend on the effective promotion, monitoring and evaluation of changes in farming practice. Conservation agriculture (CA) is an important example of sustainable intensification and climate-smart agriculture, increasing the productivity and reliability of grain production while reducing agricultural inputs and future climate risks when adopted comprehensively. But to understand its implementation and benefits, researchers often rely on simplified measures of CA adoption (e.g., single proxies, binary measures, broad self-assessments, expert estimates). Here we use a national survey of South Africa’s commercial grain farmers (n = 441), contextualized by previous interviews, to investigate common measures of adoption and their implications for CA’s promotion, monitoring and evaluation. These farmers are unusually informative, because they are unsubsidized but have the capacity, incentive and willingness to adapt to climate change. We find that they are adopting CA autonomously, but that their implementation is highly variable and their interpretation of farming practice differs from that of local experts. Single proxies, binary adoption variables and broad farmer self-assessments suggest that between 40 and 80% of farmers have adopted CA. However, when evaluated across the three CA principles using UN-defined adoption thresholds, the comprehensive adoption rate is only 14%. Farmers’ definition of “conservation” differs substantially from that of the local experts most likely to be asked to contribute adoption estimates to global monitoring efforts, creating the potential for miscommunication. There is therefore substantial cause for concern in how CA is currently promoted, monitored and evaluated. Inaccurate adoption estimates jeopardize CA’s potential as a climate change adaptation strategy, creating illusory progress that may disincentivize further substantive efforts towards agricultural sustainability and climate resilience.

Measuring the hierarchical influence in social contagions and the emergence of crossover phase transitions

In social networks, a minority of individuals are more likely to influence others and called opinion leaders. Distinguishing the influence of opinion leaders and the masses is critical to the understanding of how information spreads and to the identification of the opinion leaders. Thus we introduce a social contagion model with heterogeneous influence strength, and analyze the spreading process by developing an edge-based compartmental theory and utilize the permutation and combination theory to examine how heterogeneous individuals exert their influence. We find a hierarchy characteristic of behavior influence: the opinion leaders initially affect the susceptible individuals, and then stimulate the masses who influence other susceptible individuals with opinion leaders and finally do it independently. Moreover, crossover phase transitions exist when varying the proportion of opinion leaders: it changes from being first-order to second-order when the influence of the masses is high; interestingly, when the influence of the masses is relatively low, the changes from first-order to hybrid, and then to second-order have been observed. Similar crossover phenomenon is seen by varying the influence ratio between the masses and opinion leaders. Finally, we consider the situation that both the influence strength and adoption thresholds are heterogeneous, and find that it is not always beneficial for spreading if heterogeneity increases. Our theoretical predictions agree well with the simulation results.

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.

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.

Close and ordinary social contacts: How important are they in promoting large-scale contagion?

An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members, etc., and ordinary contacts from encounters with strangers. Typically, social reinforcement occurs for close contacts. Taking into account both types of contacts, we develop a contact-based model for social contagion. We find that, associated with the spreading dynamics, for random networks there is coexistence of continuous and discontinuous phase transitions, but for heterogeneous networks the transition is continuous. We also find that ordinary contacts play a crucial role in promoting large-scale spreading, and the number of close contacts determines not only the nature of the phase transitions but also the value of the outbreak threshold in random networks. For heterogeneous networks from the real world, the abundance of close contacts affects the epidemic threshold, while its role in facilitating the spreading depends on the adoption threshold assigned to it. We uncover two striking phenomena. First, a strong interplay between ordinary and close contacts is necessary for generating prevalent spreading. In fact, only when there are propagation paths of reasonable length which involve both close and ordinary contacts are large-scale outbreaks of social contagions possible. Second, abundant close contacts in heterogeneous networks promote both outbreak and spreading of the contagion through the transmission channels among the hubs, when both values of the threshold and transmission rate among ordinary contacts are small. We develop a theoretical framework to obtain an analytic understanding of the main findings on random networks, with support from extensive numerical computations. Overall, ordinary contacts facilitate spreading over the entire network, while close contacts determine the way by which outbreaks occur, i.e., through a second- or first-order phase transition. These results provide quantitative insights into how certain social behaviors can emerge and become prevalent, which has potential implications not only to social science but also to economics and political science.

Social contagions on interconnected networks of heterogeneous populations.

Recently, the dynamics of social contagions ranging from the adoption of a new product to the diffusion of a rumor have attracted more and more attention from researchers. However, the combined effects of individual's heterogenous adoption behavior and the interconnected structure on the social contagions processes have yet to be understood deeply. In this paper, we study theoretically and numerically the social contagions with heterogeneous adoption threshold in interconnected networks. We first develop a generalized edge-based compartmental approach to predict the evolution of social contagion dynamics on interconnected networks. Both the theoretical predictions and numerical results show that the growth of the final recovered fraction with the intralayer propagation rate displays double transitions. When increasing the initial adopted proportion or the adopted threshold, the first transition remains continuous within different dynamic parameters, but the second transition gradually vanishes. When decreasing the interlayer propagation rate, the change in the double transitions mentioned above is also observed. The heterogeneity of degree distribution does not affect the type of first transition, but increasing the heterogeneity of degree distribution results in the type change of the second transition from discontinuous to continuous. The consistency between the theoretical predictions and numerical results confirms the validity of our proposed analytical approach.