Adoption Threshold Research Articles

Contagion probability in linear threshold model

We study a linear threshold model on a simple undirected connected network G where each non-seed becomes active if and only if the proportion of its active neighbors exceeds its adoption threshold. Each threshold function ϕ:V→[0,1] is viewed as a point (ϕ(v1),…,ϕ(vn)) in the n-cube [0,1]n, where V={v1,…,vn} is the set of nodes in G. We define ϕ as a contagious point of a subset S of nodes if it can induce full contagion from S. Consequently, the volume of the set of contagious points of S in [0,1]n represents the probability of full contagion from S when the adoption threshold of each node is independently and uniformly distributed in [0,1], which we term the contagion probability of S and denote by pc(S). We derive an explicit formula for pc(S), showing that pc(S) is determined by how likely S can produce full contagion exclusively through each spanning tree of the quotient graph GS of G in which S is treated as a single node. Besides, we compare pc(S) with the contagion threshold of S, which is denoted by qc(S) and is the probability of full contagion from S when all nodes share a common adoption threshold q chosen uniformly at random from [0,1]. We show that the presence of a cycle in GS is necessary but not sufficient for pc(S) to exceed qc(S), which indicates that allowing threshold heterogeneity may not always increase the chance of full contagion. Our framework can be extended to study contagion under various threshold settings.

Influence of initiators on the tipping point in the extended Watts model

In this paper, we study how the influence of initiators (seeds) affects the tipping point of information cascades in networks. We consider an extended version of the Watts model, in which each node is either active (i.e., having adopted an innovation) or inactive. In this extended model, the adoption threshold, defined as the fraction of active neighbors required for an inactive node to become active, depends on whether the node is a seed neighbor (i.e., connected to one or more initiators) or an ordinary node (i.e., not connected to any initiators). Using the tree approximation on random graphs, we determine the tipping point, at which the fraction of active nodes in the final state increases discontinuously with an increasing seed fraction. The occurrence of a tipping point and the scale of cascades depend on two factors: whether a giant component of seed neighbors is formed when the seed fraction is large enough to trigger cascades among seed neighbors, and whether the giant component of ordinary nodes is maintained when newly activated nodes trigger further activations among ordinary nodes. The coexistence of two giant components suggests that a tipping point can appear twice. We present an example demonstrating the existence of two tipping points when there is a gap between the adoption thresholds of seed neighbors and ordinary nodes. Monte Carlo simulations clearly show that the first cascade, occurring at a small tipping point, occurs in the giant component of seed neighbors, while the second cascade, occurring at a larger tipping point, extends into the giant component of ordinary nodes.

The coupled dynamics of information-behavior-epidemic propagation considering the heterogeneity of adoption thresholds and network structures in multiplex networks

During epidemics, individual responses to prevention and control information vary significantly, affecting the execution of preventive measures. This paper introduces a novel model to analyze the co-evolution of the information-behavior-epidemic dynamic, accounting for the heterogeneity in individual behavioral adoption thresholds and network structures. The model consists of three layers: the upper layer, utilizing scale-free social networks to represent the diffusion of information; the middle and lower layers, employing community networks, to illustrate individuals’ decision-making and epidemic transmission processes, respectively. We applied the Heaviside step function to depict the effects of information and local environmental factors on individuals’ decisions. Through the microscopic Markov chain approach (MMCA), we determined the epidemic threshold. Our methodology also included extensive Monte Carlo (MC) simulations to validate our theoretical predictions. Our results reveal several key insights: (i) reducing community mobility and the threshold for adopting preventive behaviors can significantly restrain the scale of the epidemic and delay outbreaks; (ii) the level of individual activity in the physical contact network has a significant influence on epidemic transmission; (iii) integrating individuals’ behavior adoption thresholds induces a two-stage phase change, deviating from the continuous phase transition typically observed in epidemic transmission.

Harnessing monocrop breeding strategies for intercrops.

Intercropping is considered advantageous for many reasons, including increased yield stability, nutritional value and the provision of various regulating ecosystem services. However, intercropping also introduces diverse competition effects between the mixing partners, which can negatively impact their agronomic performance. Therefore, selecting complementary intercropping partners is the key to realizing a well-mixed crop production. Several specialized intercrop breeding concepts have been proposed to support the development of complementary varieties, but their practical implementation still needs to be improved. To lower this adoption threshold, we explore the potential of introducing minor adaptations to commonly used monocrop breeding strategies as an initial stepping stone towards implementing dedicated intercrop breeding schemes. While we acknowledge that recurrent selection for reciprocal mixing abilities is likely a more effective breeding paradigm to obtain genetic progress for intercrops, a well-considered adaptation of monoculture breeding strategies is far less intrusive concerning the design of the breeding programme and allows for balancing genetic gain for both monocrop and intercrop performance. The main idea is to develop compatible variety combinations by improving the monocrop performance in the two breeding pools in parallel and testing for intercrop performance in the later stages of selection. We show that the optimal stage for switching from monocrop to intercrop testing should be adapted to the specificity of the crop and the heritability of the traits involved. However, the genetic correlation between the monocrop and intercrop trait performance is the primary driver of the intercrop breeding scheme optimization process.

The impact of politicians’ behaviors on hate speech spread: hate speech adoption threshold on Twitter in Japan

In this paper, we hypothesized that a leading politician’s behavior signaling support for the ideas of hate groups will increase hate speech by shifting social norms. To examine the hypotheses, in particular, to quantify the social norms shift, the study utilized an adoption threshold measure based on Twitter retweet networks. Our empirical study focused on the hate speech spread effect of an announcement by Yuriko Koike, Governor of Tokyo, declining to participate in a memorial ceremony for Korean massacre victims. The results support the hypothesis: after Koike’s announcement, adoption thresholds of hate speech users were significantly lowered, while the number of hate speech users increased. Further, this study compared the effect of Koike’s announcement to the effect of a North Korean missile launch, a national security threat to Japan. The average hate speech adoption threshold was lower after Koike’s announcement than after the missile launch, suggesting that a leading politician’s behavior could have a greater impact on shifting norms of prejudice than even a nationally threatening event.

Rush to Charge, Dead to Drive: Application of Deadline Rush Model to Electric Vehicle User's Charging Behavior.

This work aims to estimate the portion of electric vehicle (EV) users who exhibit procrastination-like behavior, almost equivalent to an "empty" battery, before they decide to charge their vehicles. There is a human tendency to procrastinate when a deadline approaches. Human behavior in the presence of deadlines has been studied in different fields to evaluate individuals' performance or organizational efficiency and effectiveness. However, this phenomenon has not been investigated among EV users. This study explores users' procrastination-like behavior among 69 Rhode Island public charging stations' data representing 70,611 charging events. The Deadline Rush Model is incorporated to model frequent users' charging profiles. To conduct a robust estimation, the Bayesian Mixture Model is implemented. With the selection of an informative prior, the Bayesian Mixture Model estimated that almost one-third of frequent users procrastinate charging. The majority of procrastination-like users have small battery sizes. Although procrastination-like users need to charge when they arrive at a location, that might not necessarily be true for a plug-in hybrid; thus, systematically, they can clog the system for other users whose needs are more pressing. Understanding unique and unexplored charging behaviors among EV users is beneficial to EV infrastructure stakeholders in reducing the adoption threshold by providing a reliable and ubiquitous charging network. The findings identify a different kind of demand on the EV infrastructure than previously modeled and can directly influence future decision-making criteria in terms of planning to optimize to accommodate EV drivers with different charging behaviors.

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.

Blockchain-driven dual-channel green supply chain game model considering government subsidies

In order to improve the performance of green supply chain and promote the adoption of blockchain, this paper establishes a dual-channel green supply chain consisting of a green manufacturer and a retailer, and builds Stackelberg game model considering different scenarios. We analyze the impact of blockchain operating costs and consumer uncertainty about the product greenness. Furthermore, we study the government subsidy for manufacturers' green costs and its impact on supply chain performance and blockchain adoption. Findings reveal that without blockchain technology, government subsidy can improve manufacturers' and retailers' profits. However, when blockchain is adopted, the subsidy effect depends on the blockchain operating costs. In case of higher blockchain operating cost, the product prices and greenness decrease as the green cost subsidies increase; In case of lower blockchain operating cost, the increase in green cost subsidies will lead to increased product prices and greenness; Green cost subsidies can raise profits and lower the blockchain adoption threshold.

Overcoming Integration Thresholds for Augmented Reality

The advent of augmented reality (AR) is reshaping the way people experience physical and virtual environments, from observation to immersion. Growing interest in adopting AR provides opportunities for immersive learning, upskilling, and renewal. However, uncertainties exist in how to maneuver a transition toward making use of this technology through systematic integration. Due to the turmoil caused by the global pandemic health crisis, implementation of AR now faces urgency in minimizing adoption thresholds and establishing a more systematic escalation approach. This paper investigates the characteristics of such learning approaches and examines the integration of AR with customized progression. Two solution suppliers were investigated to uncover the integration process of AR, which, to the best of our knowledge, is scarcely explored in existing research. This study reveals that a balanced escalation of user-centric learning activities, i.e., an onboarding process, harmonizes anticipated cognition levels for a designated AR application tool.

Patterns, no patterns, that is the question: Quantifying users’ electric vehicle charging

Policymakers have structured legislation and set targets to increase the adoption of electric vehicles and the deployment of charging stations. As questions arise on how to expand the electric vehicle infrastructure, advanced computational models are attempting to quantify the future placement of charging stations. These models, however, do not necessarily incorporate the variability of user behavior as a subgroup of consumer behavior, as this information is not well-understood. This paper explores a state-wide network of 68 public charging stations' data representing 58,273 charging events to determine users' charging patterns. The methodological approach applied k-means clustering with Minkowski embedded distances to distinguish unique charging subgroups from 608 frequent users. The results indicate four user types: convenient (n = 319, 53%), gradual (n = 147, 24%), anxious (n = 104, 17%), and urgent (n = 38, 6%). Quantifying these users’ unique patterns supports the human variability knowledge required for more comprehensive and holistic models of electric vehicle charging station placement. More broadly, these results support the user-centric design of public charging infrastructure, which assists in reducing the electric vehicle adoption threshold in the long run and facilitating the transition to a low-carbon, sustainable transportation system.

Contagion in social networks: On contagion thresholds

Consider a story initiated by a set S of nodes belonging to a network. We assume that all the remaining nodes in the network have the same adoption threshold q such that each of them will accept the story if and only if the story has been accepted by at least a fraction q of its neighbors. Consequently, there is a maximum threshold q at and below which a full contagion (i.e. acceptance of the story by all nodes in the network) can occur from S, called the contagion threshold of S. We study how it is influenced by the neighborhood of S or by the global topology of the network. Firstly, we establish two algorithms to compute the contagion threshold of any given set of nodes in a network. Secondly, we show that the contagion threshold of a connected set in a tree is completely determined by the maximum degree of the nodes not in the set. Next, we derive bounds for the contagion threshold, while indicating when it preserves the neighborhood-inclusion pre-order and when the preservation may fail. Finally, we look at the structural characterization of the sets of nodes with high contagion thresholds.

Nudging and subsidising farmers to foster smart water meter adoption

Abstract We use a discrete choice experiment with treatments to test if voluntary adoption of smart water meters by French farmers can be fostered by (i) a collective conditional subsidy offered to farmers who adopt a smart meter only if the rate of adoption in their geographic area is sufficiently high and (ii) informational nudges. Using a sample of 1,272 farmers, we find contrasted results regarding our nudges, but we show that a conditional subsidy is an effective tool to foster adoption of smart meters. Interestingly, the willingness to pay for the conditional subsidy is equal to the subsidy amount and independent of the collective adoption threshold.

Analysis of Influence of Behavioral Adoption Threshold Diversity on Multi-Layer Network.

The same people exhibit various adoption behaviors for the same information on various networks. Previous studies, however, did not examine the variety of adoption behaviors on multi-layer networks or take into consideration this phenomenon. Therefore, we refer to this phenomenon, which lacks systematic analysis and investigation, as behavioral adoption diversity on multi-layered networks. Meanwhile, individual adoption behaviors have LTI (local trend imitation) characteristics that help spread information. In order to study the diverse LTI behaviors on information propagation, a two-layer network model is presented. Following that, we provide two adoption threshold functions to describe diverse LTI behaviors. The crossover phenomena in the phase transition is shown to exist through theoretical derivation and experimental simulation. Specifically, the final spreading scale displays a second-order continuous phase transition when individuals exhibit active LTI behaviors, and, when individuals behave negatively, a first-order discontinuous phase transition can be noticed in the final spreading scale. Additionally, the propagation phenomena might be impacted by the degree distribution heterogeneity. Finally, there is a good agreement between the outcomes of our theoretical analysis and simulation.

Web 2.5: The vision of the future needs a plan for the now

For the internet of value (Web 3) to occur, systemic adoption thresholds must be met through reintermediation. In this paper reintermediation and the proceeding network of trust established by it are defined as Web 2.5. This definition is evaluated considering the current fiat access standard and on a conceptual basis within a Web 3 framework. Although there are other Web 2.5 use cases, it is argued here that fiat access is the most urgent. The reason is that users cannot plausibly adopt Web 3 through unreliable (or non-existent) mediums. Enter the banking sector. Banks have an apparent reason to be involved in the process. Secondly, in terms of market opportunity, banks can engage a ±US$1.19tn emerging market. Ultimately, the paper argues that viable Web 2.5 solutions are any solution that amplifies the adoption of blockchain technology towards the progression of a zero-knowledge economy (Web 3). Further, since zero-knowledge solutions will always be incomplete in a socio-economic society, it is demonstrated here that there will always be a need for a Web 2.5 network of trusted intermediaries to facilitate and maintain Web 3 long after its arrival. The paper concludes by recommending different areas of research and exploration.

Cascading Behavior of an Extended Watts Model on Networks

In this study, we propose an extended Watts model to examine the effect of initiators on information cascades. The extended Watts model assumes that nodes with connections to initiators have low adoption thresholds than other nodes, due to the significant influence of initiators. We develop a tree approximation to describe the active node fraction for the extended Watts model in random networks and derive the cascade condition for a global cascade to occur with a small fraction of initiators. By analyzing the active node fraction and the cascade window of the extended Watts model on the Erdos-Renyi random graph, we find that increasing the influence of initiators facilitates the possibility of global cascades, i.e., how many nodes eventually become active is significantly affected by the fraction of initiators and the threshold of nodes directly connected to initiators, which determine cascade dynamics at early stages.

Opportunities for variable rate application of nitrogen under spatial water variations in rainfed wheat systems—an economic analysis

In fields of undulating topography, where rainfed crops experience different degrees of water stress caused by spatial water variations, yields vary spatially within the same field, thus offering opportunities for variable rate application (VRA) of nitrogen fertilizer. This study assessed the spatial variations of yield gaps caused by lateral flows from high to low points, for rainfed wheat grown in Córdoba, Spain, over six consecutive seasons (2016–2021). The economic implications associated with multiple scenarios of VRA adoption were explored through a case study and recommendations were proposed. Both farm size (i.e., annual sown area) and topographic structure impacted the dynamics of investment returns. Under current policy-price conditions, VRA adoption would have an economic advantage in farms similar to that of the case study with an annual sown area greater than 567 ha year−1. Nevertheless, current trends in energy prices, transportation costs and impacts on both cereal prices and fertilizers costs enhance the viability of VRA adoption for a wider population of farm types. The profitability of adopting VRA improves under such scenarios and, in the absence of additional policy support, the minimum area for adoption of VRA decreases to a range of 68–177 ha year−1. The combination of price increases with the introduction of an additional subsidy on crop area could substantially lower the adoption threshold down to 46 ha year−1, making VRA technology economically viable for a much wider population of farmers.

Crossing the valley of death: Network structure, government subsidies and innovation diffusion of industrial clusters

To successfully cross the “valley of death” between source innovation and industrialization requires two-way efforts of technological innovation and innovative achievement transformation, which is a socialization process of innovation adoption and diffusion. Industrial clusters are the effective organizational carriers for the diffusion of innovation achievements, therefore, the research aims to explore the transformation mechanism of scientific and technological achievements in industrial clusters, especially considering the influence of network structure and government subsidies in helping industrial clusters to cross the valley of death and improve the efficiency of scientific and technological achievements transformation, so as to put forward targeted transformation countermeasures. Accordingly, a “two-stage and double-driving” innovation diffusion dynamics model was built and applied to the empirical research on China's blockchain industrial cluster by network analysis and system dynamics. It is found that government subsidies play a crucial role in the innovation adoption stage, especially for high innovative industrial clusters. In addition, there is an adoption threshold for the utility of government subsidies, and a reasonable exit mechanism should be established when adoption rates reach a certain proportion. However, for the low innovative industrial clusters, government subsidies continue to be effective. On the contrary, internal factors play a vital role in the stage of innovation diffusion, especially for industrial clusters that have developed close cooperation between upstream and downstream. This study provides the following policy implications for industrial clusters to overcome the valley of death, including carrying out classified guidance and precise implementation, appropriate subsidies and reasonable withdrawal, and improving the cultivation mechanism of “opinion leaders” enterprises.

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.

Does crop insurance inhibit climate change technology adoption?

Changing temperatures and precipitation patterns from climate change are a major risk to crop yields. Producers have technology options for mitigating this risk with one such technology termed drainage water recycling (DWR). DWR involves diverting subsurface drainage water to ponds where it is stored for later irrigation. Crop insurance may interfere with DWR adoption by providing producers with another avenue to manage climate change risk. It is hypothesized that government-subsidized crop insurance reduces climate change technology adoption. Based on real options, this analysis considers two policy regimes: when crop insurance is in effect and not. In a Poisson jump process, it further considers the insurance effect of producers’ returns jumping when facing a crop disaster. Results indicate crop insurance has a minimal effect on DWR adoption, and in most scenarios, the DWR adoption thresholds are too large for a producer to invest for climate change adaptation without additional financial incentives. The baseline DWR adoption scenario, with no crop insurance impact, requires revenue of $1,114/acre, or 1.57 times current conventional revenue.

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.