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Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of…
In this paper, we introduce an innovative application of artificial intelligence in the realm of interior design through the integration of Stable Diffusion and Dreambooth models. This paper explores the potential of these advanced…
We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we…
Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and…
The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
We prove a result which strongly hints at the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile…
We prove the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile Assembly Model, when restricted to…
In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger…
We investigate a fundamental question regarding a benchmark class of shapes in one of the simplest, yet most widely utilized abstract models of algorithmic tile self-assembly. Specifically, we study the directed tile complexity of a $k…
We propose a mathematical model of DNA self-assembly using 2D tiles to form 3D nanostructures. This is the first work to combine studies in self-assembly and nanotechnology in 3D, just as Rothemund and Winfree did in the 2D case. Our model…
In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which…
In this paper, we work in a 2D version of the probabilistic variant of Winfree's abstract Tile Assembly Model defined by Chandran, Gopalkrishnan and Reif (SICOMP 2012) in which attaching tiles are sampled uniformly with replacement. First,…
Tile displacement is a newly-recognized mechanism in DNA nanotechnology that exploits principles analogous to toehold-mediated strand displacement but within the context of self-assembled DNA origami tile arrays. Here, we formulate an…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…
Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
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…
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. They are studied both from the…
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…