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Self-assembling graphs

Vincent Danos, Fabien Tarissan
2006 Natural Computing  
A 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.  ... 
doi:10.1007/s11047-006-9013-9 fatcat:inbsvtdombdtznajc5panmog3y

Self Assembling Graphs [chapter]

Vincent Danos, Fabien Tarissan
2005 Lecture Notes in Computer Science  
A 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.  ... 
doi:10.1007/11499220_51 fatcat:lk32dnzf2rb2xbuuawf7kefsfy

Robust self-assembly of graphs

Stanislav Angelov, Sanjeev Khanna, Mirkó Visontai
2009 Natural Computing  
A recently studied model of 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.  ... 
doi:10.1007/s11047-009-9149-5 fatcat:itn6qcrxcjgmlgwwg6ehxtvn5y

Robust Self-assembly of Graphs [chapter]

Stanislav Angelov, Sanjeev Khanna, Mirkó Visontai
2009 Lecture Notes in Computer Science  
A recently studied model of 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.  ... 
doi:10.1007/978-3-642-03076-5_11 fatcat:yuoqntqlifh2rcb5wcwhwmev6e

Self-Assembly as Graph Grammar as Distributed System [article]

Aaron Sterling
2011 arXiv   pre-print
In 2004, Klavins et al. introduced the use of 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.  ... 
arXiv:0902.2420v3 fatcat:fb32cbxx6ndjfcrhvr7weaazfe

Self-assembly of geometric space from random graphs

Christy Kelly, Carlo Trugenberger, Fabio Biancalana
2019 Classical and quantum gravity  
We present a Euclidean quantum gravity model in which random 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.  ... 
doi:10.1088/1361-6382/ab1c7d fatcat:gt5mubinhjfvdprvzrxt7xats4

Graph grammars for self assembling robotic systems

E. Klavins, R. Ghrist, D. Lipsky
2004 IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004  
We conclude the paper with a discussion of how 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.  ... 
doi:10.1109/robot.2004.1302558 dblp:conf/icra/KlavinsGL04 fatcat:72qlx3do25cn7knm7thniul2dy

Complexity of Graph Self-assembly in Accretive Systems and Self-destructible Systems [chapter]

John H. Reif, Sudheer Sahu, Peng Yin
2006 Lecture Notes in Computer Science  
of a given 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?  ... 
doi:10.1007/11753681_21 fatcat:tdwpryh3gjgkrbyoavuoynonbu

Complexity of graph self-assembly in accretive systems and self-destructible systems

John H. Reif, Sudheer Sahu, Peng Yin
2011 Theoretical Computer Science  
of a given 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?  ... 
doi:10.1016/j.tcs.2010.10.034 fatcat:xqt5bctp6febxaqfd4ghkz55fe

Tile Based Modeling of DNA Self-Assembly for Two Graph Families with Appended Paths [article]

D. Chloe Griffin, Jessica Sorrells
2022 arXiv   pre-print
Branched molecules of deoxyribonucleic acid (DNA) can 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.  ... 
arXiv:2203.07343v1 fatcat:hyphzhmu6fbmhjhdyus32vt6z4

On the complexity of graph self-assembly in accretive systems

Stanislav Angelov, Sanjeev Khanna, Mirkó Visontai
2007 Natural Computing  
We study the complexity of the Accretive 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.  ... 
doi:10.1007/s11047-007-9048-6 fatcat:typigir6qnawvf3fat2r4yka2a

On the Complexity of Graph Self-assembly in Accretive Systems [chapter]

Stanislav Angelov, Sanjeev Khanna, Mirkó Visontai
2006 Lecture Notes in Computer Science  
We study the complexity of the Accretive 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.  ... 
doi:10.1007/11925903_8 fatcat:2mrlvm4kxzbr5ab6psswpggtwy

Using DNA Self-assembly Design Strategies to Motivate Graph Theory Concepts

J. Ellis-Monaghan, G. Pangborn
2011 Mathematical Modelling of Natural Phenomena  
For all of these methods, an essential step in building the 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  ... 
doi:10.1051/mmnp/20116606 fatcat:dli7svwr4vauplb3vaea2spsee

Models of fullerene and nanoparticle graphs from Classification of self-assembling protein nanoparticle architectures for applications in vaccine design

G. Indelicato, P. Burkhard, R. Twarock
2017 Figshare  
Figures of a fullerene 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  ... 
doi:10.6084/m9.figshare.4872815.v1 fatcat:tqid7qixz5gpvofxfkikbxyjv4

Self-assembly of modular robots from finite number of modules using graph grammars

Vijeth Rai, Anne van Rossum, Nikolaus Correll
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.  ... 
doi:10.1109/iros.2011.6095038 dblp:conf/iros/RaiRC11 fatcat:ngj3kdvqbjbijab664qatvuaky
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