Higher Order Cellular Automata

Baas, Nils A.; Helvik, Torbjørn

doi:10.1142/s0219525905000403

Cited by 15 publications

(8 citation statements)

References 18 publications

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“…The system we analyzed is an example of a Higher Order Cellular Automata Baas and Helvik (2005), or even more general, a higher order network being that groups of agents can act together as an entity. This hierarchy is modeled by creating a new agent on the next higher level, as illustrated in Fig.…”

Section: Beyond Three Levelsmentioning

confidence: 99%

Higher order Boolean networks as models of cell state dynamics

Markert

Baas

Levine

et al. 2010

Journal of Theoretical Biology

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The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them. Boolean models have been introduced both as specific examples and as ensemble or distribution network models. However, current ensemble Boolean network models do not make a systematic distinction between different cell components such as epigenetic factors, gene and transcription factors. Consequently, we still do not understand their relative contributions in controlling the cell fate. In this work we introduce and study higher order Boolean networks, which feature an explicit distinction between the different cell components and the types of interactions between them. We show that the stability of the cell state dynamics can be determined solving * Corresponding author Preprint submitted to Journal of Theoretical Biology February 17, 2018 the eigenvalue problem of a matrix representing the regulatory interactions and their strengths. The qualitative analysis of this problem indicates that, in addition to the classification into stable and chaotic regimes, the cell state can be simple or complex depending on whether it can be deduced from the independent study of its components or not. Finally, we illustrate how the model can be expanded considering higher levels and higher order dynamics.

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Section: Beyond Three Levelsmentioning

confidence: 99%

Higher order Boolean networks as models of cell state dynamics

Markert

Baas

Levine

et al. 2010

Journal of Theoretical Biology

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“…In our previous notion of hyperstructures the set X 0 represents the systems or agents ðS i Þ; X 0 the observables (Obs), B 0 the interactions (Int) and a specific choice of b 0 ðS 0 Þ 2 B 0 ðS 0 Þ represents the resultant ''bond'' system giving rise to the next level of objects-called R in previous papers, like S i , Obs, Int, see Baas (1994aBaas ( , b, 1995Baas ( , 1996aBaas ( , b, c, 1997Baas ( , 2004Baas ( , 2005. Now let us form the next level and define:…”

Section: Hyperstructuresmentioning

confidence: 99%

Hyperstructures, Topology and Datasets

Baas¹

2009

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In the natural sciences higher order structures often occur. There seems to be a need for good methods of describing what we mean by higher order structures in various contexts. This is what hyperstructures are intended to do. We motivate and introduce this new concept. Next we illustrate how it can be applied in various types of genomic analysis-particular the correlations between single nucleotide polymorphisms and diseases. The suggested structure is quite general and may be applied to a variety of situations. Finally we discuss how data sets (f. ex. genomic) may lead to topological spaces, giving new invariants and lead to the prediction of hyperstructures.

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“…In our previous notion of hyperstructures the set X 0 represents the systems or agents (S i ), X 0 the observables (Obs), B 0 the interactions (Int) and a specific choice of b 0 (S 0 ) [ B 0 (S 0 ) represents the resultant ''bond'' system giving rise to the next level of objects-called R in previous papers, like S i , Obs, Int, see Baas (1994aBaas ( , b, 1995Baas ( , 1996aBaas ( , b, c, 1997Baas et al 2004;Baas and Helvik 2005). Now let us form the next level and define:…”

Section: Hyperstructuresmentioning

confidence: 99%

Extended Memory Evolutive Systems in a Hyperstructure Context

Baas¹

2009

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This paper is just a comment to the impressive work by A. C. Ehresmann and J.-P. Vanbremeersch on the theory of Memory Evolutive Systems (MES). MES are truly higher order systems. Hyperstructures represent a new concept which I introduced in order to capture the essence of what a higher order structure isencompassing hierarchies and emergence. Hyperstructures are motivated by cobordism theory in topology and higher category theory. The morphism concept is replaced by the concept of a bond. In the paper I briefly introduce hyperstructures motivated geometrically and suggest further developments of the MESs along these lines, which could widen up new areas of applications.

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Higher Order Cellular Automata

Cited by 15 publications

References 18 publications

Higher order Boolean networks as models of cell state dynamics

Higher order Boolean networks as models of cell state dynamics

Hyperstructures, Topology and Datasets

Extended Memory Evolutive Systems in a Hyperstructure Context

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