Related papers: Improved lower and upper bounds on the tile comple…
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…
In this paper we explore the power of geometry to overcome the limitations of non-cooperative self-assembly. We define a generalization of the abstract Tile Assembly Model (aTAM), such that a tile system consists of a collection of…
The abstract tile assembly model (aTam) is a model of DNA self-assembly. Most of the studies focus on cooperative aTAM where a form of synchronization between the tiles is possible. Simulating Turing machines is achievable in this context.…
We develop a new technique for constructing sparse graphs that allow us to prove near-linear lower bounds on the round complexity of computing distances in the CONGEST model. Specifically, we show an $\widetilde{\Omega}(n)$ lower bound for…
The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We consider non-cooperative binding, so-called 'temperature 1', in deterministic or directed (called here confluent) tile self-assembly systems in two dimensions and show a necessary and sufficient condition for such system to have an…
We study the problems of testing and learning high-dimensional discrete convex sets. The simplest high-dimensional discrete domain where convexity is a non-trivial property is the ternary hypercube, $\{-1,0,1\}^n$. The goal of this work is…
This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through…
In this paper we investigate the computational power of the polygonal tile assembly model (polygonal TAM) at temperature 1, i.e. in non-cooperative systems. The polygonal TAM is an extension of Winfree's abstract tile assembly model (aTAM)…
We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield…
The 2-Handed Assembly Model (2HAM) is a tile-based self-assembly model in which, typically beginning from single tiles, arbitrarily large aggregations of static tiles combine in pairs to form structures. The Signal-passing Tile Assembly…
Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the…
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…
The miniaturization of electronic devices has led to the prominence, in technological applications, of ultra-thin films with a thickness ranging from a few tens of nanometers to just about 1-2 nanometers. While these materials are still…
Autonomous assembly is a crucial capability for robots in many applications. For this task, several problems such as obstacle avoidance, motion planning, and actuator control have been extensively studied in robotics. However, when it comes…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence…
Self-assembled nano and micro-structures, particularly those capable of responsive erasure and regeneration, have garnered significant interest for their applications in smart photonics and electronics. However, current techniques for…
A major research area in discrete geometry is to consider the best way to partition the $d$-dimensional Euclidean space $\mathbb{R}^d$ under various quality criteria. In this paper we introduce a new type of space partitioning that is…