Mean-field approximations for dynamical processes on networks are widely used, but existing derivations often rely either on moment closures or on idealised assumptions about network structure, leaving the nature of the underlying averaging unclear. Here we present a mathematically principled framework for deriving edge-based mean-field approximations for a broad class of Markov processes on networks using approximate lumping. We consider models in which each vertex is in one of a finite number of vertex states and transitions depend on the number of neighbours in each state. Our approach partitions the full Markov chain state space according to the number of vertices and edges in each possible state, and averages transition rates between partitions. This yields density-dependent population processes that, in the limit of large system size, reduce to a low-dimensional system of ordinary differential equations. We demonstrate the method on single graphs and graph ensembles, such as Erdős-Rényi random networks, and show that well-known edge-based mean-field approximations arise as special cases of our approach. Our approximate lumping framework clarifies the nature of the averaging underlying mean-field approximations, providing a basis for future work on assessing their accuracy.

Many real-world phenomena can be modeled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyze such dynamical processes on networks, but these are typically derived using plausible probabilistic reasoning, introducing uncontrolled errors that may lead to invalid mathematical conclusions. In this paper, we present a rigorous approach to derive mean-field approximations from the exact description of Markov chain dynamics on networks through a process of averaging called approximate lumping. We consider a general class of Markov chain dynamics on networks in which each vertex can adopt a finite number of "vertex-states"" (e.g. susceptible, infected, recovered), and transition rates depend on the number of neighbors of each type. Our approximate lumping is based on counting the number of each type of vertex-state in subsets of vertices, and this results in a density dependent population process. In the large graph limit, this reduces to a low dimensional system of ordinary differential equations, special cases of which are well known mean-field approximations. Our approach provides a general framework for the derivation of mean-field approximations of dynamics on networks that unifies previously disconnected approaches and highlights the sources of error.

Agent-based modelling has emerged as a powerful tool for modelling systems that are driven by discrete, heterogeneous individuals and has proven particularly popular in the realm of pedestrian simulation. However, real-time agent-based simulations face the challenge that they will diverge from the real system over time. This paper addresses this challenge by integrating the ensemble Kalman filter (EnKF) with an agent-based crowd model to enhance its accuracy in real time. Using the example of Grand Central Station in New York, we demonstrate how our approach can update the state of an agent-based model in real time, aligning it with the evolution of the actual system. The findings reveal that the EnKF can substantially improve the accuracy of agent-based pedestrian simulations by assimilating data as they evolve. This approach not only offers efficiency advantages over existing methods but also presents a more realistic representation of a complex environment than most previous attempts. The potential applications of this method span the management of public spaces under ‘normality’ to exceptional circumstances such as disaster response, marking a significant advancement for real-time agent-based modelling applications.

The use of Agent-Based Models (ABMs) to make predictions in real-time is hindered by their high computation cost and the lack of detailed individual data. This paper proposes a new framework to enable the use of emulators, also referred to as surrogate models or meta-models, coupled with ABMs, to allow for real-time predictions of the behaviour of a complex system. The case study is that of pedestrian movements through an environment. We evaluate two different types of emulators: a regression emulator based on a Random Forest and a time-series emulator using a Long Short-Term Memory neural network. Both emulators perform well, but the time-series emulator proves to generalise better to cases where the number of agents in the system is not known a priori. The results have implications for the real-time modelling of human crowds, suggesting that emulation is a feasible approach to modelling crowds in real-time, where computational complexity prohibits the use of an ABM directly.

: Agent-based models (ABMs) can be found across a number of diverse application areas ranging from simulating consumer behaviour to infectious disease modelling. Part of their popularity is due to their ability to simulateindividualbehavioursanddecisionsoverspaceandtime. However, whilstthereareplentifulexamples within the academic literature, these models are only beginning to make an impact within policy areas. Whilst frameworks such as NetLogo make the creation of ABMs relatively easy, a number of key methodological issues, including the quantification of uncertainty, remain. In this paper we draw on state-of-the-art approaches from the fields of uncertainty quantification and model optimisation to describe a novel framework for the calibration of ABMs using History Matching and Approximate Bayesian Computation. The utility of the framework is demonstrated on three example models of increasing complexity: (i) Sugarscape to illustrate the approach on a toy example; (ii) a model of the movement of birds to explore the efficacy of our framework and compare it to alternative calibration approaches and; (iii) the RISC model of farmer decision making to demonstrate its value in a real application. The results highlight the efficiency and accuracy with which this approach can be used to calibrate ABMs. This method can readily be applied to local or national-scale ABMs, such as those linked to the creation or tailoring of key policy decisions.

This paper explores the use of a particle filter—a data assimilation method—to incorporate real-time data into an agent-based model. We apply the method to a simulation of real pedestrians moving through the concourse of Grand Central Terminal in New York City (USA). The results show that the particle filter does not perform well due to (i) the unpredictable behaviour of some pedestrians and (ii) because the filter does not optimise the categorical agent parameters that are characteristic of this type of model. This problem only arises because the experiments use real-world pedestrian movement data, rather than simulated, hypothetical data, as is more common. We point to a potential solution that involves resampling some of the variables in a particle, such as the locations of the agents in space, but keeps other variables such as the agents’ choice of destination. This research illustrates the importance of including real-world data and provides a proof of concept for the application of an improved particle filter to an agent-based model. The obstacles and solutions discussed have important implications for future work that is focused on building large-scale real-time agent-based models.

Epidemics, voting behaviour and cascading failures in power grids are examples of natural, social and technological phenomena that can be modelled as dynamical processes on networks. The study of such important complex systems requires approximation, but the assumptions that underpin the standard mean-field approaches are routinely violated by dynamics on real-world networks, leading to uncontrolled errors and even controversial results. Consequently, determining the approximation precision has been recognised as a key challenge. We present a micro-scale foundation for mean-field approximation of a wide range of dynamics on networks that facilitates quantification of approximation error, elucidating its connection to network structure and model dynamics. We show that our coarse-graining approach minimises approximation error and we obtain an upper bound on this uncertainty. We illustrate our approach using epidemic dynamics on real-world networks. Mean-field approximations in complex networks, while useful, often vary in accuracy and can be particularly problematic in the case of dynamical correlations. Here, the authors report the use of approximate lumping to derive low-dimensional mean-field equations and estimate the overall approximation error for real-world networks.

The Internet and the services delivered via it are increasingly centralised on a few monopolistic platforms. Today's web frameworks are conceived to cater for increasing returns to scale and winner-takes-all business models with a built-in asymmetry between users and services. Existing multi-agent and agent architectures have seen no significant adoption outside niche applications. We propose a novel agent framework which is designed to allow for a decentralised digital economy to manifest where each individual and organisation is represented by an autonomous economic entity with its own agency. The framework bridges the old and new web and employs distributed ledger technologies as core parts of its construction. We introduce the framework, discuss the performance characteristics of its current implementation and demonstrate several application areas.

Reliable and secure communication between heterogeneously resourced autonomous agents controlled by competing stakeholders in a decentralized environment is a challenge. Agents require a means to find each other and communicate without reliance on a centralized party and participation in the system must be permissionless. We present the Agent Communication Network (ACN), a peer-to-peer lookup system that provides a distributed overlay to the Internet and addresses this problem. The ACN enables agents to find each other and to communicate safely. It achieves this by leveraging a distributed hash table for agent lookup, maintained by participating peers and through the use of public-key cryptography. The paper discusses the properties of the system and its guarantees as well as its integration with a novel multi-agent system. Preliminary benchmark results demonstrate the feasibility of the system, its performance, and its scalability.

Estimates of the resident population fail to account for human mobility, which significantly impacts the numbers of people in urban areas. Employing the ambient population provides a more nuanced approach to small-area population estimation. This paper utilises statistical modelling and novel data to estimate the size of the ambient population in an urban area. Models of the daytime and night-time ambient populations are produced for the city of Leeds, West Yorkshire, UK. Interestingly, the presence of cash machines and hospitality venues were found to be statistically significant and were identified as the most important predictors of the ambient population. In contrast to the literature, the number of retail hubs, transport hubs, and the density of mobile phone cell towers were not found to have statistically significant relationships with footfall camera counts. Footfall camera data and the results of the predictive model were validated through comparison with manually collected pedestrian counts. The results of this validation process demonstrated that at five out of the six locations in Leeds city centre, the model produced expected estimates of the size of the ambient population. The results suggest that the approach of this study can be used as a tool to inform decision-making within local government and studies in which small area estimates of ambient populations are required.

This paper will critically assess the utility of conventional and novel data sources for building fine-scale spatio-temporal estimates of the ambient population. It begins with a review of data sources employed in existing studies of the ambient population, followed by preliminary analysis to further explore the utility of each dataset. The identification and critiquing of data sources which may be useful for building estimates of the ambient population are novel contributions to the literature. This paper will provide a framework of reference for researchers within urban analytics and other areas where an accurate measurement of the ambient population is required. This work has implications for national and international applications where accurate small area estimates of the ambient population are crucial in the planning and management of urban areas, the development of realistic models and informing policy. This research highlights workday population estimates, in conjunction with footfall camera and Wi-Fi sensors data as potentially valuable for building estimates of the ambient population.

We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a large-scale study of such symmetry-induced lumping in real-world networks, from which we identify specific networks for which lumping enables exact analysis that could not have been done on the full state-space. For most networks, lumping gives a state-space compression ratio of up to 10 7 , but the largest compression ratio identified is nearly 10 12 . Many of the highest compression ratios occur in animal social networks. We also present examples of types of symmetry found in real-world networks that have not been previously reported.

Commonly-used data assimilation methods are being adapted for use with agent-based models with the aim of allowing optimisation in response to new data in real-time. However, existing methods face difficulties working with categorical parameters, which are common in agent-based models. This paper presents a new method, the RJUKF, that combines the Unscented Kalman Filter (UKF) data assimilation algorithm with elements of the Reversible Jump (RJ) Markov chain Monte Carlo method. The proposed method is able to conduct data assimilation on both continuous and categorical parameters simultaneously. Compared to similar techniques for mixed state estimation, the RJUKF has the advantage of being efficient enough for online (i.e. real-time) application. The new method is demonstrated on the simulation of a crowd of people traversing a train station and is able to estimate both their current position (a continuous, Gaussian variable) and their chosen destination (a categorical parameter). This method makes a valuable contribution towards the use of agent-based models as tools for the management of crowds in busy places such as public transport hubs, shopping centres, or high streets.

In this demonstration, we introduce a system that facilitates trading agent competitions. Competitions mirror a Walrasian Exchange Economy. Each agent is endowed with a set of digital assets and preferences over them. Agents then trade these assets with each other to increase their respective utilities. They negotiate one-on-one to arrive at an optimal trade, and if successful, settle their transaction trustlessly on an emulated permissionless blockchain. This system is a precursor to a trading platform for digital assets and crypto-tokens in which agents trade on behalf of their users.

The problem of real-time autonomous energy management is an application area that is receiving unprecedented attention from consumers, governments, academia, and industry. This paper showcases the first application of deep reinforcement learning (DRL) to real-time autonomous energy management for a multi-carrier energy system. The proposed approach is tailored to align with the nature of the energy management problem by posing it in multi-dimensional continuous state and action spaces, in order to coordinate power flows between different energy devices, and to adequately capture the synergistic effect of couplings between different energy carriers. This fundamental contribution is a significant step forward from earlier approaches that only sought to control the power output of a single device and neglected the demand-supply coupling of different energy carriers. Case studies on a real-world scenario demonstrate that the proposed method significantly outperforms existing DRL methods as well as model-based control approaches in achieving the lowest energy cost and yielding a representation of energy management policies that adapt to system uncertainties.

We propose a novel consensus protocol based on a hybrid approach, that combines a directed acyclic graph (DAG) and a classical chain of blocks. This architecture allows us to enforce collective block construction, minimising the monopolistic power of the round-leader. In this way, we decrease the possibility for collusion among senders and miners, as well as miners themselves, allowing the use of more incentive compatible and fair pricing strategies. We investigate these possibilities alongside the ability to use the DAG structure to minimise the risk of transaction censoring. We conclude by providing preliminary benchmarks of our protocol and by exploring further research directions.

Agent-based modelling is a valuable approach for systems whose behaviour is driven by the interactions between distinct entities. They have shown particular promise as a means of modelling crowds of people in streets, public transport terminals, stadiums, etc. However, the methodology faces a fundamental difficulty: there are no established mechanisms for dynamically incorporating real-time data into models. This limits simulations that are inherently dynamic, such as pedestrian movements, to scenario testing of, for example, the potential impacts of new architectural configurations on movements. This paper begins to address this fundamental gap by demonstrating how a particle filter could be used to incorporate real data into an agent-based model of pedestrian movements at run time. The experiments show that it is indeed possible to use a particle filter to perform online (real time) model optimisation. However, as the number of agents increases, the number of individual particles (and hence the computational complexity) required increases exponentially. By laying the groundwork for the real-time simulation of crowd movements, this paper has implications for the management of complex environments (both nationally and internationally) such as transportation hubs, hospitals, shopping centres, etc.

The user experience of interacting with distributed ledger technologies (DLT) is fraught with excessive complexity, high risk and unintuitive processes. Moreover, smart contracts deployed in these systems are restricted to being reactive. These limitations have negative implications on user adoption and prevent DLTs from being general purpose. We introduce a framework for the development of Autonomous Economic Agents (AEAs), software agents that act autonomously and pursue an economic goal, and demonstrate how AEAs complement existing decentralised ledgers as a second layer technology. In particular, the framework enables a simplified user experience through automation, supports modularisation and reuse of complex decision making and machine learning capabilities, and allows for proactive behaviour facilitating autonomy. We demonstrate these gains in the context of a specific use-case, a multi-agent trading system modelling a Walrasian Exchange Economy populated by a number of agents trading a basket of tokens.

In this paper, we present a pricing mechanism that aligns incentives of agents who exchange resources on a decentralized ledger with the goal of maximizing transaction throughput. Subdividing a blockchain ledger into shards promises to greatly increase transaction throughput with minimal loss of security. However, the organization and type of the transactions also affects the ledger's efficiency, which is increased by wallet agents transacting in a single shard whenever possible while collectively distributing their transactions uniformly across the available shards. Since there is no central authority to enforce these properties, the only means of achieving them is to design the system such that it is in agents' interest to act in a way that benefits overall throughput. We show that our proposed pricing policy does exactly this by inducing a potential game for the agents, where the potential function relates directly to ledger throughput. Simulations demonstrate that this policy leads to near-optimal throughput under a variety of conditions.