| EPSRC Reference: |
EP/D03292X/1 |
| Title: |
Discrete stochastic processes in complex systems |
| Principal Investigator: |
Hopcraft, Dr K |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
University of Nottingham |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2005 |
Ends: |
28 February 2009 |
Value (£): |
209,592
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Non-linear Systems Mathematics |
| Statistics & Appl. Probability |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
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Summary on Grant Application Form |
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'Complexity Theory' covers a wide spectrum of scientific investigations of a inter- and multi-disciplinary nature that aims to inform how interactions within large multi-component systems produce collective, correlated and self-organising behaviours. These emergent behaviours arise in spite of the simplicity of the interactions between the component parts, which are inherently random in nature. This intrinsic randomness often drives the evolution and behaviour that emerges. The fluctuations produced by complex systems frequently have no characteristic scale size, length or time associated with them. Consequently, phenomena attracting attention has broadened from the continuous scale-free fluctuations to encompass discrete scale-free fluctuations too. This has prompted the development of stochastic processes capable of generating such discrete scale-free distributions in a stationary state, and these led to the class of discrete-stable distributions, being the discrete analogue of the continuous Levy stable densities. This proposal will explore the properties of these distributions and examine situations when they can be produced or emerge naturally.The discrete-stable distributions differ from their continuous counterparts and the project will explore some of the ramifications of these differences, especially to scale-free networks which are known to describe self-organising systems such as the WWW and genome/proteome interactions. We will capitalise upon our new found potential to construct models of nonlinearly interacting populations that can produce scale-free behaviour and investigate how these systems can be characterised through their being monitored in time. We will explore how the predictions of discrete population models differ from their continuum analogues, with application, for example, to the times to extinction in small or scale-free populations.These developments will provide fresh applications and emphasis for point processes to be deployed in both a descriptive role and as analytical models for probing the fluctuation properties of complex systems.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.nottingham.ac.uk |