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- Görnerup, Olof, 1977, et al.
(author)
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A method for finding aggregated representations of linear dynamical systems
- 2010
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In: Advances in Complex Systems. - 0219-5259. ; 13:2, s. 199-215
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Journal article (peer-reviewed)abstract
- A central problem in the study of complex systems is to identify hierarchical and intertwined dynamics. A hierarchical level is defined as an aggregation of the system's variables such that the aggregation induces its own closed dynamics. In this paper, we present an algorithm that finds aggregations of linear dynamical systems, e. g. including Markov chains and diffusion processes on weighted and directed networks. The algorithm utilizes that a valid aggregation with n states correspond to a set of n eigenvectors of the dynamics matrix such that these respect the same permutation symmetry with n orbits. We exemplify the applicability of the algorithm by employing it to identify coarse grained representations of cellular automata.
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| 2. |
- Görnerup, Olof, 1977, et al.
(author)
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A model-independent approach to infer hierarchical codon substitution dynamics
- 2010
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In: BMC Bioinformatics. - : Springer Science and Business Media LLC. - 1471-2105. ; 11
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Journal article (peer-reviewed)abstract
- Background: Codon substitution constitutes a fundamental process in molecular biology that has been studied extensively. However, prior studies rely on various assumptions, e. g. regarding the relevance of specific biochemical properties, or on conservation criteria for defining substitution groups. Ideally, one would instead like to analyze the substitution process in terms of raw dynamics, independently of underlying system specifics. In this paper we propose a method for doing this by identifying groups of codons and amino acids such that these groups imply closed dynamics. The approach relies on recently developed spectral and agglomerative techniques for identifying hierarchical organization in dynamical systems. Results: We have applied the techniques on an empirically derived Markov model of the codon substitution process that is provided in the literature. Without system specific knowledge of the substitution process, the techniques manage to "blindly" identify multiple levels of dynamics; from amino acid substitutions (via the standard genetic code) to higher order dynamics on the level of amino acid groups. We hypothesize that the acquired groups reflect earlier versions of the genetic code. Conclusions: The results demonstrate the applicability of the techniques. Due to their generality, we believe that they can be used to coarse grain and identify hierarchical organization in a broad range of other biological systems and processes, such as protein interaction networks, genetic regulatory networks and food webs.
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| 3. |
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| 4. |
- Nilsson Jacobi, Martin, 1972, et al.
(author)
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A Method For Inferring Hierarchical Dynamics In Stochastic Processes
- 2008
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In: Advances in Complex Systems. - 0219-5259. ; 11:1, s. 1-16
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Journal article (peer-reviewed)abstract
- Complex systems may often be characterized by their hierarchical dynamics. In this paper we present a method and an operational algorithm that automatically infer this property in a broad range of systems discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections impose Markovian dynamics on the coarser level. These projections, which we call Markov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, so a priori knowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes a finite state automaton and an iterated map.
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