Shadowing and shielding: Effective heuristics for continuous influence maximisation in the voting dynamics

Influence maximisation, or how to affect the intrinsic opinion dynamics of a social group, is relevant for many applications, such as information campaigns, political competition, or marketing. Previous literature on influence maximisation has mostly explored discrete allocations of influence, i.e. optimally choosing a finite fixed number of nodes to target. Here, we study the generalised problem of continuous influence maximisation where nodes can be targeted with flexible intensity. We focus on optimal influence allocations against a passive opponent and compare the structure of the solutions in the continuous and discrete regimes. We find that, whereas hub allocations play a central role in explaining optimal allocations in the discrete regime, their explanatory power is strongly reduced in the continuous regime. Instead, we find that optimal continuous strategies are very well described by two other patterns: (i) targeting the same nodes as the opponent (shadowing) and (ii) targeting direct neighbours of the opponent (shielding). Finally, we investigate the game-theoretic scenario of two active opponents and show that the unique pure Nash equilibrium is to target all nodes equally. These results expose fundamental differences in the solutions to discrete and continuous regimes and provide novel effective heuristics for continuous influence maximisation

Dynamics of new strain emergence on a temporal network

Multi-strain competition on networks is observed in many contexts, including infectious disease ecology, information dissemination or behavioral adaptation to epidemics. Despite a substantial body of research has been developed considering static, time-aggregated networks, it remains a challenge to understand the transmission of concurrent strains when links of the network are created and destroyed over time. Here we analyze how network dynamics shapes the outcome of the competition between an initially endemic strain and an emerging one, when both strains follow a susceptible-infected-susceptible dynamics, and spread at time scales comparable with the network evolution one. Using time-resolved data of close-proximity interactions between patients admitted to a hospital and medical health care workers, we analyze the impact of temporal patterns and initial conditions on the dominance diagram and coexistence time. We find that strong variations in activity volume cause the probability that the emerging strain replaces the endemic one to be highly sensitive to the time of emergence. The temporal structure of the network shapes the dominance diagram, with significant variations in the replacement probability (for a given set of epidemiological parameters) observed from the empirical network and a randomized version of it. Our work contributes towards the description of the complex interplay between competing pathogens on temporal networks.Comment: 9 pages, 4 figure

Competitive influence maximisation in social networks

Network-based interventions have shown immense potential in prompting behaviour changes in populations. Their implementation in the real world however, is often difficult and prone to failure as they are typically delivered on limited budgets and in many instances can be met with resistance in populations. Therefore, utilising available and limited resources optimally through careful and efficient planning is key for the successful implementation of any intervention. An important development in this aspect, is the influence maximisation framework —which lies at the interface of network science and computer science —and is commonly used to study network-based interventions in a theoretical setup with the aim of determining best practices that can optimise intervention outcomes in the real world. In this thesis, we explore the influence maximisation problem in a competitive setting (inspired by real-world conditions) where two contenders compete to maximise the spread of their intervention (or influence) in a social network. In its traditional form, the influence maximisation process identifies the k most influential nodes in a network —where k is given by a fixed budget. In this thesis, we propose the influence maximisation model with continuous distribution of influence where individuals are targeted heterogeneously based on their role in the influence spread process. This approach allows policymakers to obtain a detailed plan of the optimal distribution of budgets which is otherwise abstracted in traditional methods. In the rest of the thesis we use this approach to study multiple real-world settings. We first propose the competitive influence maximisation model with continuous allocation of resources. We then determine optimal intervention strategies against known competitor allocations in a network and show that continuous distribution of resources consistently outperform traditional approaches where influence is concentrated on a few nodes in the network (i.e. k optimal nodes). We further extend the model to a game-theoretic framework which helps us examine settings with no prior information about competitor strategies. We find that the equilibrium solution in this setting is to uniformly target the network —implying that all nodes, irrespective of their topological positions, contribute equally to the influence maximisation process. We extend this model further in two directions. First, we introduce the notion of adoption barriers to the competitive influence maximisation model, where an additional cost is paid every time an individual is approached for intervention. We find that this cost-of-access parameter ties our model to traditional methods, where only k individuals are discretely targeted. We further generalise the model to study other real-world settings where the strength of influence changes nonlinearly with allocations. Here we identify two distinct regimes —one where optimal strategies offer significant gains, and the other where they do not yield any gains. The two regimes also vary in their sensitivity to budget availability, and we find that in some cases, even a tenfold increase in the budget only marginally improves the outcome of the intervention. Second, we extend the continuous allocation model to analyse network-based interventions in the presence of negative ties. Individuals sharing a negative tie typically influence each other to adopt opposing views, and hence they can be detrimental to the influence spread process if not considered in the dynamics. We show that in general it is important to consider negative ties when planning an intervention, and at the same time we identify settings where the knowledge of negative ties yields no gains, or leads to less favourable outcomes

Competitive influence maximisation with nonlinear cost of allocations

We explore the competitive influence maximisation problem in the voter model. We extend past work by modelling real-world settings where the strength of influence changes nonlinearly with external allocations to the network. We use this approach to identify two distinct regimes — one where optimal intervention strategies offer significant gain in outcomes, and the other where they yield no gains. The two regimes also vary in their sensitivity to budget availability, and we find that in some cases, even a tenfold increase in the budget only marginally improves the outcome of an intervention in a population