Zobrazeno 1 - 10
of 158
pro vyhledávání: '"Patitz, Matthew J."'
This paper answers a long-standing open question in tile-assembly theory, namely that it is possible to strictly assemble discrete self-similar fractals (DSSFs) in the abstract Tile-Assembly Model (aTAM). We prove this in 2 separate ways, each taking
Externí odkaz:
http://arxiv.org/abs/2406.19595
Tile assembly systems in the abstract Tile Assembly Model (aTAM) are computationally universal and capable of building complex shapes, but DNA-based implementations encounter formidable error rates that stifle this theoretical potential. Slat-based s
Externí odkaz:
http://arxiv.org/abs/2405.06205
In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types required, of a
Externí odkaz:
http://arxiv.org/abs/2402.16284
Autor:
Hader, Daniel, Patitz, Matthew J.
Algorithmic self-assembly occurs when disorganized components autonomously combine to form structures and, by their design and the dynamics of the system, are forced to follow the execution of algorithms. Motivated by applications in DNA-nanotechnolo
Externí odkaz:
http://arxiv.org/abs/2305.01877
Autor:
Alseth, Andrew, Patitz, Matthew J.
In the abstract Tile Assembly Model (aTAM) square tiles self-assemble, autonomously binding via glues on their edges, to form structures. Algorithmic aTAM systems can be designed in which the patterns of tile attachments are forced to follow the exec
Externí odkaz:
http://arxiv.org/abs/2211.03877
In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of oth
Externí odkaz:
http://arxiv.org/abs/2206.03908
In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modif
Externí odkaz:
http://arxiv.org/abs/2105.02914
We present a series of results related to mathematical models of self-assembling tiles and the impacts that three diverse properties have on their dynamics. We expand upon a series of prior results which showed that (1) the abstract Tile Assembly Mod
Externí odkaz:
http://arxiv.org/abs/1910.03950
Autor:
Alumbaugh, John Calvin, Daymude, Joshua J., Demaine, Erik D., Patitz, Matthew J., Richa, Andrea W.
Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA) model was
Externí odkaz:
http://arxiv.org/abs/1906.01773