1,956 research outputs found
Hybrid modelling of individual movement and collective behaviour
Mathematical models of dispersal in biological systems are often written in terms of partial differential equations (PDEs) which describe the time evolution of population-level variables (concentrations, densities). A more detailed modelling approach is given by individual-based (agent-based) models which describe the behaviour of each organism. In recent years, an intermediate modelling methodology – hybrid modelling – has been applied to a number of biological systems. These hybrid models couple an individual-based description of cells/animals with a PDEmodel of their environment. In this chapter, we overview hybrid models in the literature with the focus on the mathematical challenges of this modelling approach. The detailed analysis is presented using the example of chemotaxis, where cells move according to extracellular chemicals that can be altered by the cells themselves. In this case, individual-based models of cells are coupled with PDEs for extracellular chemical signals. Travelling waves in these hybrid models are investigated. In particular, we show that in contrary to the PDEs, hybrid chemotaxis models only develop a transient travelling wave
Statistical fluctuations in pedestrian evacuation times and the effect of social contagion
Mathematical models of pedestrian evacuation and the associated simulation
software have become essential tools for the assessment of the safety of public
facilities and buildings. While a variety of models are now available, their
calibration and test against empirical data are generally restricted to global,
averaged quantities, the statistics compiled from the time series of individual
escapes (" microscopic " statistics) measured in recent experiments are thus
overlooked. In the same spirit, much research has primarily focused on the
average global evacuation time, whereas the whole distribution of evacuation
times over some set of realizations should matter. In the present paper we
propose and discuss the validity of a simple relation between this distribution
and the " microscopic " statistics, which is theoretically valid in the absence
of correlations. To this purpose, we develop a minimal cellular automaton, with
novel features that afford a semi-quantitative reproduction of the experimental
" microscopic " statistics. We then introduce a process of social contagion of
impatient behavior in the model and show that the simple relation under test
may dramatically fail at high contagion strengths, the latter being responsible
for the emergence of strong correlations in the system. We conclude with
comments on the potential practical relevance for safety science of
calculations based on " microscopic " statistics
Multiagent System Applied to the Modeling and Simulation of Pedestrian Traffic in Counterflow
An agent-based model to simulate a pedestrian crowd in a corridor is presented. Pedestrian crowd models are valuable tools to gain insight into the behavior of human crowds in both, everyday and crisis situations. The main contribution of this work is the definition of a pedestrian crowd model by applying ideas from the field of the kinetic theory of living systems on the one hand, and ideas from the field of computational agents on the other hand. Such combination supported a quantitative characterization of the performance of our agents, a neglected issue in agent-based models, through well-known kinetic parameters. Fundamental diagrams of flow and activity are presented for both, groups of homogeneous pedestrians, and groups of heterogeneous pedestrians in terms of their willingness to reach their goals.Agent-Based Modeling, Pedestrian Crowd, Activity Measurement
The Evolution of Reaction-diffusion Controllers for Minimally Cognitive Agents
No description supplie
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Distributed anonymous function computation in information fusion and multiagent systems
We propose a model for deterministic distributed function computation by a
network of identical and anonymous nodes, with bounded computation and storage
capabilities that do not scale with the network size. Our goal is to
characterize the class of functions that can be computed within this model. In
our main result, we exhibit a class of non-computable functions, and prove that
every function outside this class can at least be approximated. The problem of
computing averages in a distributed manner plays a central role in our
development
System Issues in Multi-agent Simulation of Large Crowds
Crowd simulation is a complex and challenging domain. Crowds demonstrate many complex behaviours and are consequently difficult to model for realistic simulation systems. Analyzing crowd dynamics has been an active area of research and efforts have been made to develop models to explain crowd behaviour. In this paper we describe an agent based simulation of crowds, based on a continuous field force model. Our simulation can handle movement of crowds over complex terrains and we have been able to simulate scenarios like clogging of exits during emergency evacuation situations. The focus of this paper, however, is on the scalability issues for such a multi-agent based crowd simulation system. We believe that scalability is an important criterion for rescue simulation systems. To realistically model a disaster scenario for a large city, the system should ideally scale up to accommodate hundreds of thousands of agents. We discuss the attempts made so far to meet this challenge, and try to identify the architectural and system constraints that limit scalability. Thereafter we propose a novel technique which could be used to richly simulate huge crowds
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
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