Related papers: Small tile sets that compute while solving mazes

Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles…

DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…

The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…

Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions…

The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal…

Since its introduction by Erik Winfree in 1998, the abstract Tile Assembly Model (aTAM) has inspired a wealth of research. As an abstract model for tile based self-assembly, it has proven to be remarkably powerful and expressive in terms of…

DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile…

We present a modular DNA origami design approach to address the challenges of assembling geometrically complex nanoscale structures, including those with nonuniform Gaussian curvature. This approach features a core structure that completely…

Recent advancements in microbiology have motivated the study of the production of nanostructures with applications such as biomedical computing and molecular robotics. One way to construct these structures is to construct branched DNA…

In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles…

Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model…

In this paper, we explore relationships between two models of systems which are governed by only the local interactions of large collections of simple components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM). While…

We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…

We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…

We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are…

There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…

We prove that the number of tile types required to build squares of size n x n, in Winfree's abstract Tile Assembly Model, when restricted to using only non-cooperative tile bindings, is at least 2n-1, which is also the best known upper…

A limitation to molecular implementations of tile-based self-assembly systems is the high rate of mismatch errors which has been observed to be between 1% and 10%. Controlling the physical conditions of the system to reduce this intrinsic…

Nearly thirty years after its inception, the field of DNA-programmed colloidal self-assembly has begun to realize its initial promise. In this review, we summarize recent developments in designing effective interactions and understanding…