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Self-assembling graphs

2006
*
Natural Computing
*

A

doi:10.1007/s11047-006-9013-9
fatcat:inbsvtdombdtznajc5panmog3y
*self*-*assembly*algorithm for synchronising agents and have them arrange according to a particular*graph*is given. ... In: Proceedings of the International Conference on Robotics and Automation), in that it relies only on point-topoint communication, and can deal with any*assembly**graph*whereas Klavins' method dealt only ... The*self*-*assembly*protocol was inspired by*self**assembly*questions in biological systems. ...##
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Self Assembling Graphs
[chapter]

2005
*
Lecture Notes in Computer Science
*

A

doi:10.1007/11499220_51
fatcat:lk32dnzf2rb2xbuuawf7kefsfy
*self*-*assembly*algorithm for synchronising agents and have them arrange according to a particular*graph*is given. ... In: Proceedings of the International Conference on Robotics and Automation), in that it relies only on point-topoint communication, and can deal with any*assembly**graph*whereas Klavins' method dealt only ... The*self*-*assembly*protocol was inspired by*self**assembly*questions in biological systems. ...##
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Robust self-assembly of graphs

2009
*
Natural Computing
*

A recently studied model of

doi:10.1007/s11047-009-9149-5
fatcat:itn6qcrxcjgmlgwwg6ehxtvn5y
*self*-*assembly*is the Accretive*Graph**Assembly*Model whereby an edge-weighted*graph*is*assembled*one vertex at a time starting from a designated seed vertex. ... We then examine the tractability of the robust*self*-*assembly*problem on a natural subclass of planar*graphs*, namely grid*graphs*. ... In the end, we show that the*graph*robustly*self*-*assembles*iffφ is a tautology. ...##
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Robust Self-assembly of Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

A recently studied model of

doi:10.1007/978-3-642-03076-5_11
fatcat:yuoqntqlifh2rcb5wcwhwmev6e
*self*-*assembly*is the Accretive*Graph**Assembly*Model whereby an edge-weighted*graph*is*assembled*one vertex at a time starting from a designated seed vertex. ... We then examine the tractability of the robust*self*-*assembly*problem on a natural subclass of planar*graphs*, namely grid*graphs*. ... In the end, we show that the*graph*robustly*self*-*assembles*iffφ is a tautology. ...##
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Self-Assembly as Graph Grammar as Distributed System
[article]

2011
*
arXiv
*
pre-print

In 2004, Klavins et al. introduced the use of

arXiv:0902.2420v3
fatcat:fb32cbxx6ndjfcrhvr7weaazfe
*graph*grammars to describe -- and to program -- systems of*self*-*assembly*. ... of Soloveichik and Winfree's theorem on local determinism, and we also present a canonical method to simulate asynchronous constant-size-message-passing models of distributed computing with systems of*self*-*assembly*...*Graph*grammars can represent both types of*self*-*assembly*system. ...##
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Self-assembly of geometric space from random graphs

2019
*
Classical and quantum gravity
*

We present a Euclidean quantum gravity model in which random

doi:10.1088/1361-6382/ab1c7d
fatcat:gt5mubinhjfvdprvzrxt7xats4
*graphs*dynamically*self*-*assemble*into discrete manifold structures. ... contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic*graphs*... However it failed to show the full*self*-*assembly*of discrete manifolds from random regular*graphs*, and no direct evidence for the continuous nature of the transition was presented. ...##
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Graph grammars for self assembling robotic systems

2004
*
IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004
*

We conclude the paper with a discussion of how

doi:10.1109/robot.2004.1302558
dblp:conf/icra/KlavinsGL04
fatcat:72qlx3do25cn7knm7thniul2dy
*graph*grammars can be used to direct the synthesis of parts floating in a fluid or for*self*-motive robotic parts. ... In this paper we define a class of*graph*grammars that can be used to model and direct distributed robotic*assembly*or formation forming processes. ... One hypothesis for how this occurs is that simple small components*self**assemble*into more complex aggregates which, in turn,*self**assemble*into larger aggregates. ...##
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Complexity of Graph Self-assembly in Accretive Systems and Self-destructible Systems
[chapter]

2006
*
Lecture Notes in Computer Science
*

of a given

doi:10.1007/11753681_21
fatcat:tdwpryh3gjgkrbyoavuoynonbu
*graph*, referred to as Accretive*Graph**Assembly*Problem (AGAP) and*Self*-Destructible*Graph**Assembly*Problem (DGAP), respectively. ... We define two novel*assembly*models, namely the accretive*graph**assembly*model and the*self*-destructible*graph**assembly*model, and identify one fundamental problem in them: the sequential construction ... We next extend the accretive*graph**self*-*assembly*model to stochastic accretive*graph**self*-*assembly*model. gets*assembled*if anytime any unassembled vertex can be picked with equal probability? ...##
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Complexity of graph self-assembly in accretive systems and self-destructible systems

2011
*
Theoretical Computer Science
*

of a given

doi:10.1016/j.tcs.2010.10.034
fatcat:xqt5bctp6febxaqfd4ghkz55fe
*graph*, referred to as Accretive*Graph**Assembly*Problem (AGAP) and*Self*-Destructible*Graph**Assembly*Problem (DGAP), respectively. ... We define two novel*assembly*models, namely the accretive*graph**assembly*model and the*self*-destructible*graph**assembly*model, and identify one fundamental problem in them: the sequential construction ... We next extend the accretive*graph**self*-*assembly*model to stochastic accretive*graph**self*-*assembly*model. gets*assembled*if anytime any unassembled vertex can be picked with equal probability? ...##
###
Tile Based Modeling of DNA Self-Assembly for Two Graph Families with Appended Paths
[article]

2022
*
arXiv
*
pre-print

Branched molecules of deoxyribonucleic acid (DNA) can

arXiv:2203.07343v1
fatcat:hyphzhmu6fbmhjhdyus32vt6z4
*self*-*assemble*into nanostructures through complementary cohesive strand base pairing. ... With theoretical efficiency of laboratory processes in mind, we use a flexible tile model for DNA*assembly*. ... Our results give insight into general rules for*self*-*assembly*when appending a path onto a*graph*. ...##
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On the complexity of graph self-assembly in accretive systems

2007
*
Natural Computing
*

We study the complexity of the Accretive

doi:10.1007/s11047-007-9048-6
fatcat:typigir6qnawvf3fat2r4yka2a
*Graph**Assembly*Problem (AGAP). An instance of AGAP consists of an edge-weighted*graph*G, a seed vertex in G, and a temperature τ . ... The edge weights model the forces of attraction and repulsion, and determine which vertices can be added to a partially*assembled**graph*at the given temperature. ... The*self*-*assembly*process in the Accretive*Graph**Self*-*Assembly*Model proceeds as follows. The*graph*G serves as a template of construction and initially only the seed vertex v s of G is built. ...##
###
On the Complexity of Graph Self-assembly in Accretive Systems
[chapter]

2006
*
Lecture Notes in Computer Science
*

We study the complexity of the Accretive

doi:10.1007/11925903_8
fatcat:2mrlvm4kxzbr5ab6psswpggtwy
*Graph**Assembly*Problem (AGAP). An instance of AGAP consists of an edge-weighted*graph*G, a seed vertex in G, and a temperature τ . ... The edge weights model the forces of attraction and repulsion, and determine which vertices can be added to a partially*assembled**graph*at the given temperature. ... The*self*-*assembly*process in the Accretive*Graph**Self*-*Assembly*Model proceeds as follows. The*graph*G serves as a template of construction and initially only the seed vertex v s of G is built. ...##
###
Using DNA Self-assembly Design Strategies to Motivate Graph Theory Concepts

2011
*
Mathematical Modelling of Natural Phenomena
*

For all of these methods, an essential step in building the

doi:10.1051/mmnp/20116606
fatcat:dli7svwr4vauplb3vaea2spsee
*self*-*assembling*nanostructure is designing the component molecular building blocks. ... A number of exciting new laboratory techniques have been developed using the Watson-Crick complementarity properties of DNA strands to achieve the*self*-*assembly*of graphical complexes. ... Acknowledgements We thank the many students who have worked with us on projects related to*self*-assembing nanostructures including Laura Beaudin, Nick Bruno, Thomas Dickerson, Andrew Gilbert, Jacob Girard ...##
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Models of fullerene and nanoparticle graphs from Classification of self-assembling protein nanoparticle architectures for applications in vaccine design

2017
*
Figshare
*

Figures of a fullerene

doi:10.6084/m9.figshare.4872815.v1
fatcat:tqid7qixz5gpvofxfkikbxyjv4
*graph*and the associated nanoparticle*graph*that can be cut and fold. ... Figure S2 : S2 the full planar net of the nanoparticle*graph*with T d symmetry, corresponding to the fullerene*graph*C 68 inFig. S1. ... By the vertex coloring rule the fullerene*graph*can be decorated by coloring exactly one vertex for each hexagonal face and none for the pentagonal faces, which corresponds to tiling the fullerene*graph*...##
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Self-assembly of modular robots from finite number of modules using graph grammars

2011
*
2011 IEEE/RSJ International Conference on Intelligent Robots and Systems
*

*Assembly*of Modular Robots with Finite Number of Modules Using

*Graph*Grammar Thesis directed by Prof. ... In contrast to

*self*-

*assembly*at the nano and micro scales where abundant building blocks are available, modular robotic systems need to

*self*-

*assemble*from a limited number of modules. ...

*Graph*-Grammars

*Graph*grammars, or

*graph*rewriting systems, are rule sets that transform one

*graph*into another. In a

*self*-

*assembly*context, a desired

*assembly*can be represented as a

*graph*. ...

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