5,076 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 â hybrid modelling â 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
Quantifying and managing uncertainty in piecewise-deterministic Markov processes
In piecewise-deterministic Markov processes (PDMP) the state of a
finite-dimensional system evolves dynamically, but the evolutive equation may
change randomly as a result of discrete switches. A running cost is integrated
along the corresponding piecewise-deterministic trajectory up to the
termination to produce the cumulative cost of the process. We address three
natural questions related to uncertainty in cumulative cost of PDMP models: (1)
how to compute the Cumulative Distribution Function (CDF) when the switching
rates are fully known; (2) how to accurately bound the CDF when the switching
rates are uncertain; and (3) assuming the PDMP is controlled, how to select a
control to optimize that CDF. In all three cases, our approach requires posing
a (weakly-coupled) system of suitable hyperbolic partial differential
equations, which are then solved numerically on an augmented state space. We
illustrate our method using simple examples of trajectory planning under
uncertainty.Comment: submitted to SIAM/ASA Journal on Uncertainty Quantificatio
Particle Swarm Optimization Based Source Seeking
Signal source seeking using autonomous vehicles is a complex problem. The
complexity increases manifold when signal intensities captured by physical
sensors onboard are noisy and unreliable. Added to the fact that signal
strength decays with distance, noisy environments make it extremely difficult
to describe and model a decay function. This paper addresses our work with
seeking maximum signal strength in a continuous electromagnetic signal source
with mobile robots, using Particle Swarm Optimization (PSO). A one to one
correspondence with swarm members in a PSO and physical Mobile robots is
established and the positions of the robots are iteratively updated as the PSO
algorithm proceeds forward. Since physical robots are responsive to swarm
position updates, modifications were required to implement the interaction
between real robots and the PSO algorithm. The development of modifications
necessary to implement PSO on mobile robots, and strategies to adapt to real
life environments such as obstacles and collision objects are presented in this
paper. Our findings are also validated using experimental testbeds.Comment: 13 pages, 12 figure
A brief network analysis of Artificial Intelligence publication
In this paper, we present an illustration to the history of Artificial
Intelligence(AI) with a statistical analysis of publish since 1940. We
collected and mined through the IEEE publish data base to analysis the
geological and chronological variance of the activeness of research in AI. The
connections between different institutes are showed. The result shows that the
leading community of AI research are mainly in the USA, China, the Europe and
Japan. The key institutes, authors and the research hotspots are revealed. It
is found that the research institutes in the fields like Data Mining, Computer
Vision, Pattern Recognition and some other fields of Machine Learning are quite
consistent, implying a strong interaction between the community of each field.
It is also showed that the research of Electronic Engineering and Industrial or
Commercial applications are very active in California. Japan is also publishing
a lot of papers in robotics. Due to the limitation of data source, the result
might be overly influenced by the number of published articles, which is to our
best improved by applying network keynode analysis on the research community
instead of merely count the number of publish.Comment: 18 pages, 7 figure
Control theoretic models of pointing
This article presents an empirical comparison of four models from manual control theory on their ability to model targeting behaviour by human users using a mouse: McRuerâs Crossover, Costelloâs Surge, second-order lag (2OL), and the Bang-bang model. Such dynamic models are generative, estimating not only movement time, but also pointer position, velocity, and acceleration on a moment-to-moment basis. We describe an experimental framework for acquiring pointing actions and automatically fitting the parameters of mathematical models to the empirical data. We present the use of time-series, phase space, and Hooke plot visualisations of the experimental data, to gain insight into human pointing dynamics. We find that the identified control models can generate a range of dynamic behaviours that captures aspects of human pointing behaviour to varying degrees. Conditions with a low index of difficulty (ID) showed poorer fit because their unconstrained nature leads naturally to more behavioural variability. We report on characteristics of human surge behaviour (the initial, ballistic sub-movement) in pointing, as well as differences in a number of controller performance measures, including overshoot, settling time, peak time, and rise time. We describe trade-offs among the models. We conclude that control theory offers a promising complement to Fittsâ law based approaches in HCI, with models providing representations and predictions of human pointing dynamics, which can improve our understanding of pointing and inform design
Stability and Diversity in Collective Adaptation
We derive a class of macroscopic differential equations that describe
collective adaptation, starting from a discrete-time stochastic microscopic
model. The behavior of each agent is a dynamic balance between adaptation that
locally achieves the best action and memory loss that leads to randomized
behavior. We show that, although individual agents interact with their
environment and other agents in a purely self-interested way, macroscopic
behavior can be interpreted as game dynamics. Application to several familiar,
explicit game interactions shows that the adaptation dynamics exhibits a
diversity of collective behaviors. The simplicity of the assumptions underlying
the macroscopic equations suggests that these behaviors should be expected
broadly in collective adaptation. We also analyze the adaptation dynamics from
an information-theoretic viewpoint and discuss self-organization induced by
information flux between agents, giving a novel view of collective adaptation.Comment: 22 pages, 23 figures; updated references, corrected typos, changed
conten
A Decentralized Control Framework for Energy-Optimal Goal Assignment and Trajectory Generation
This paper proposes a decentralized approach for solving the problem of
moving a swarm of agents into a desired formation. We propose a decentralized
assignment algorithm which prescribes goals to each agent using only local
information. The assignment results are then used to generate energy-optimal
trajectories for each agent which have guaranteed collision avoidance through
safety constraints. We present the conditions for optimality and discuss the
robustness of the solution. The efficacy of the proposed approach is validated
through a numerical case study to characterize the framework's performance on a
set of dynamic goals.Comment: 6 pages, 3 figures, to appear at the 2019 Conference on Decision and
Control, Nice, F
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