Memory and communication efficient algorithm for decentralized counting of nodes in networks

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation

Collective decision making in distributed systems inspired by honeybees behaviour

We propose a design methodology to provide cognitive capabilities to large-scale artificial distributed systems. The behaviour of such systems is the result of non-linear interactions of the individuals with each other and with the environment, and the resulting system behaviour is in general difficult to predict. The proposed methodology is based on the concept of cognitive design patterns, that is, reusable solutions to tackle problems requiring cognitive abilities (e.g., decision-making, attention, categorisation). Cognitive design patterns aim to support the engineering of distributed systems through guidelines and theoretical models that link the individual control rules of the agents to the desired global behaviour. In this paper, we propose a cognitive design pattern for collective decision-making inspired by the nest-site selection behaviour of honeybee swarms. We describe and analyse the theoretical models, and distill a set of guidelines for the implementation of collective decisions in distributed multi-agent systems. We demonstrate the validity of the cognitive design pattern in a case study involving spatial factors: the collective selection of the shortest path between two target areas. We analyse the dynamics of the multi-agent system and we show a very good adherence with the predictions of the macroscopic model. Future refinements of the cognitive design pattern will allow its usage in different application domains

Input-dependent noise can explain magnitude-sensitivity in optimal value-based decision-making

Recent work has derived the optimal policy for two-alternative value-based decisions, in which decision-makers compare the subjective expected reward of two alternatives. Under specific task assumptions — such as linear utility, linear cost of time and constant processing noise — the optimal policy is implemented by a diffusion process in which parallel decision thresholds collapse over time as a function of prior knowledge about average reward across trials. This policy predicts that the decision dynamics of each trial are dominated by the difference in value between alternatives and are insensitive to the magnitude of the alternatives (i.e., their summed values). This prediction clashes with empirical evidence showing magnitude-sensitivity even in the case of equal alternatives, and with ecologically plausible accounts of decision making. Previous work has shown that relaxing assumptions about linear utility or linear time cost can give rise to optimal magnitude-sensitive policies. Here we question the assumption of constant processing noise, in favour of input-dependent noise. The neurally plausible assumption of input-dependent noise during evidence accumulation has received strong support from previous experimental and modelling work. We show that including input-dependent noise in the evidence accumulation process results in a magnitude-sensitive optimal policy for value-based decision-making, even in the case of a linear utility function and a linear cost of time, for both single (i.e., isolated) choices and sequences of choices in which decision-makers maximise reward rate. Compared to explanations that rely on non-linear utility functions and/or non-linear cost of time, our proposed account of magnitude-sensitive optimal decision-making provides a parsimonious explanation that bridges the gap between various task assumptions and between various types of decision making

On the role of zealots in a best-of-n problem on a heterogeneous network

Both humans and social animals live in groups and are frequently faced to choose between options with different qualities. When no leader agents are controlling the group decision, consensus can be achieved through repeated interactions among group members. Various studies on CDM illustrate how the dynamics of opinions are determined by the structure of the social network and the methods that individuals use to share and update their opinion upon a social interaction. In this paper, we are interested in further exploring how cognitive, social, and environmental factors interactively contribute to determining the outcome of a collective best-of-n decision process involving asymmetric options, i.e., different costs and/or benefits for each option. We propose and study a novel model capturing those different factors, i) the error in processing social information, ii) the number of zealots (i.e., asocial agents who never change their opinion), iii) the option qualities, iv) the social connectivity structure, and v) the degree centrality of the asocial agents. By using the HMF approach, we study the impact of the above-mentioned factors in the decision dynamics. Our findings indicate that when susceptible agents use the voter model as a mechanism to update their opinion, both the number and the degree of connectivity of the zealots can lead the population to converge towards the lowest quality option. Instead, when susceptible agents use methods more cognitively demanding, the group is marginally impacted by the presence of zealots. The results of the analytical model are complemented and extended by agent-based simulations. Our analysis also shows that the network topology can modulate the influence of zealots on group dynamics

A quantitative micro-macro link for collective decisions: the shortest path discovery/selection example

In this paper, we study how to obtain a quantitative correspondence between the dynamics of the microscopic implementation of a robot swarm and the dynamics of a macroscopic model of nest-site selection in honeybees. We do so by considering a collec- tive decision-making case study: the shortest path discovery/selection problem. In this case study, obtaining a quantitative correspondence between the microscopic and macroscopic dynamics-the so-called micro-macro link problem-is particularly challenging because the macroscopic model does not take into account the spatial factors inherent to the path discovery/selection problem. We frame this study in the context of a general engineering methodology that prescribes the inclusion of available theoretical knowledge about target macroscopic models into design patterns for the microscopic implementation. The attain- ment of the micro-macro link presented in this paper represents a necessary step towards the formalisation of a design pattern for collective decision making in distributed systems

Controlling Robot Swarm Aggregation through a Minority of Informed Robots

Self-organised aggregation is a well studied behaviour in swarm robotics as it is the pre-condition for the development of more advanced group-level responses. In this paper, we investigate the design of decentralised algorithms for a swarm of heterogeneous robots that self-aggregate over distinct target sites. A previous study has shown that including as part of the swarm a number of informed robots can steer the dynamic of the aggregation process to a desirable distribution of the swarm between the available aggregation sites. We have replicated the results of the previous study using a simplified approach, we removed constraints related to the communication protocol of the robots and simplified the control mechanisms regulating the transitions between states of the probabilistic controller. The results show that the performances obtained with the previous, more complex, controller can be replicated with our simplified approach which offers clear advantages in terms of portability to the physical robots and in terms of flexibility. That is, our simplified approach can generate self-organised aggregation responses in a larger set of operating conditions than what can be achieved with the complex controller.Comment: Submitted to ANTS 202

Cross-inhibition leads to group consensus despite the presence of strongly opinionated minorities and asocial behaviour

Strongly opinionated minorities can have a dramatic impact on the opinion dynamics of a large population. Two factions of inflexible minorities, polarised into two competing opinions, could lead the entire population to persistent indecision. Equivalently, populations can remain undecided when individuals sporadically change their opinion based on individual information rather than social information. Our analysis compares the cross-inhibition model with the voter model for decisions between equally good alternatives, and with the weighted voter model for decisions among alternatives characterised by different qualities. Here we show that cross-inhibition, differently from the other two models, is a simple mechanism, ubiquitous in collective biological systems, that allows the population to reach a stable majority for one alternative even in the presence of asocial behaviour. The results predicted by the mean-field models are confirmed by experiments with swarms of 100 locally interacting robots. This work suggests an answer to the longstanding question of why inhibitory signals are widespread in natural systems of collective decision making, and, at the same time, it proposes an efficient mechanism for designing resilient swarms of minimalistic robots

Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making

Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity