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We present an active tile assembly model which extends Winfree's abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. In addition, we introduce a mathematical framework to…
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…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
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…
Molecular assembly offers a promising path to detect life beyond Earth, while minimizing assumptions based on terrestrial life. As mass spectrometers will be central to upcoming Solar System missions, predicting molecular assembly from…
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…
We present the stellar resolution, a "flexible" tile system based on Robinson's first-order resolution. After establishing formal definitions and basic properties of the stellar resolution, we show its Turing-completeness and to illustrate…
In this work, we propose a framework called Auto-Assembly for automated robotic assembly from design files and demonstrate a practical implementation on modular parts joined by fastening using a robotic cell consisting of two robots. We…
In this paper we explore the power of tile self-assembly models that extend the well-studied abstract Tile Assembly Model (aTAM) by permitting tiles of shapes beyond unit squares. Our main result shows the surprising fact that any aTAM…
As a mathematical model of self-assembling systems, Winfree's abstract Tile Assembly Model (aTAM) is a remarkable platform for studying the behaviors and powers of self-assembling systems. Capable of Turing universal computation, the aTAM…
In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in some sense, uniquely identify whether…
At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…
Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…
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…
Deep learning has demonstrated its strengths in numerous binary analysis tasks, including function boundary detection, binary code search, function prototype inference, value set analysis, etc. When applying deep learning to binary analysis…
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…
Building structures with hierarchical order through the self-assembly of smaller blocks is not only a prerogative of nature, but also a strategy to design artificial materials with tailored functions. We explore in simulation the…
Theory of splicing is an abstract model of the recombinant behaviour of DNAs. In a splicing system, two strings to be spliced are taken from the same set and the splicing rule is from another set. Here we propose a generalised splicing (GS)…
The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of…
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…