Geometric State Sum Models from Quasicrystals

Amaral, Marcelo M.; Fang, Fang; Hammock, Dugan; Irwin, Klee

doi:10.20944/preprints202104.0033.v1

“…As a final note, we refer to the paper [30,31] in the domain of quantum gravity where the ordering rules with syntactical freedom are those of quasicrystals instead of those of the biological crystal structures.…”

Section: Discussionmentioning

confidence: 99%

Group Theory of Syntactical Freedom in DNA Transcription and Genome Decoding

Planat¹,

Amaral²,

Fang³

et al. 2021

Preprint

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Transcription factors (TFs) are proteins that recognize specific DNA fragments in order to decode the genome and ensure its optimal functioning. TFs work at the local and global scales by specifying cell type, cell growth and death, cell migration, organization and timely tasks. We investigate the structure of DNA-binding motifs with the theory of finitely generated groups. The DNA ‘word’ in the binding domain -the motif- may be seen as the generator of a finitely generated group Fdna on four letters, the bases A, T, G and C. It is shown that, most of the time, the DNA-binding motifs have subgroup structure close to free groups of rank three or less, a property that we call ‘syntactical freedom’. Such a property is associated to the aperiodicity of the motif when it is seen as a substitution sequence. Examples are provided for the major families of TFs such as leucine zipper factors, zinc finger factors, homeo-domain factors, etc. We also discuss the exceptions to the existence of such a DNA syntactical rule and their functional role. This includes the TATA box in the promoter region of some genes, the single nucleotide markers (SNP) and the motifs of some genes of ubiquitous role in transcription and regulation.

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“…where the pair of vertex types (i j) consider the connectivity of space-filling tilings and in the case of non-space-filling tilings we consider a ball of radius R (as in Appendix A, Remark A1) with respect to the subset T k . 3-Geometric realism: the symmetry of the local weights should reflect the symmetry of the underlying geometry [20,23]. Implementing the symmetry at the level of the weight itself has the bonus that the superposition of local configurations is under the admissible geometric configurations of the tiling configuration space.…”

Section: Geometric State Sum Models From Model Sets and Expected Valuesmentioning

confidence: 99%

“…4-Principle of efficient language (PEL) [24][25][26]: This aims to implement a notion of efficiency in discrete systems, which are codes or languages. The random walks with its auxiliary animations sets A t κ i above can be interpreted as a form of a look-ahead algorithm (so-called look-savings-ahead algorithm in [20]) that allows us to define two computational functions that can be coupled to the geometric state sum model. First we consider the so-called hit potential, Y, which takes values on the natural numbers including zero, Y : T k → N. At each tiling position κ j of T , that has κ i at origin, the hit potential Y j can be defined in two ways, first by the number of animations that uses that position κ j as part of its path…”

Section: Dynamicsmentioning

confidence: 99%

“…Here we consider the same mathematical structures on much smaller scales. Using the notion of geometric state sums, [20] we define a scale invariant probabilistic measure, which allows us to compute the expected values of observables. Then, the model sets background structure works as a fundamental clock [21,22] for relational evolution of emergent quantum matter.…”

Section: Introductionmentioning

confidence: 99%

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On the Emergence of Spacetime and Matter from Model Sets

Amaral¹,

Fang²,

Aschheim³

et al. 2021

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Group Theory of Syntactical Freedom in DNA Transcription and Genome Decoding

Planat¹,

Amaral²,

Fang³

et al. 2022

Preprint

Self Cite

1

0

View full text Add to dashboard Cite

Transcription factors (TFs) are proteins that recognize specific DNA fragments in order to decode the genome and ensure its optimal functioning. TFs work at the local and global scales by specifying cell type, cell growth and death, cell migration, organization and timely tasks. We investigate the structure of DNA-binding motifs with the theory of finitely generated groups. The DNA ‘word’ in the binding domain -the motif- may be seen as the generator of a finitely generated group Fdna on four letters, the bases A, T, G and C. It is shown that, most of the time, the DNA-binding motifs have subgroup structure close to free groups of rank three or less, a property that we call ‘syntactical freedom’. Such a property is associated to the aperiodicity of the motif when it is seen as a substitution sequence. Examples are provided for the major families of TFs such as leucine zipper factors, zinc finger factors, homeo-domain factors, etc. We also discuss the exceptions to the existence of such a DNA syntactical rule and their functional role. This includes the TATA box in the promoter region of some genes, the single nucleotide markers (SNP) and the motifs of some genes of ubiquitous role in transcription and regulation.

show abstract

Geometric State Sum Models from Quasicrystals

Abstract: In light of the self-simulation hypothesis, a simple form implementation of the principle of efficient language is discussed in a self-referential geometric quasicrystalline state sum model in three dimensions. Emergence is discussed in context of geometric state sum models.

Cited by 3 publications

References 24 publications

Group Theory of Syntactical Freedom in DNA Transcription and Genome Decoding

Group Theory of Syntactical Freedom in DNA Transcription and Genome Decoding

On the Emergence of Spacetime and Matter from Model Sets

Group Theory of Syntactical Freedom in DNA Transcription and Genome Decoding

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