Related papers: Identifying Shapes Using Self-Assembly (extended a…
We initiate the computability-theoretic study of ringed spaces and schemes. In particular, we show that any Turing degree may occur as the least degree of an isomorphic copy of a structure of these kinds. We also show that these structures…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
The automatic assembly problem has attracted increasing interest due to its complex challenges that involve 3D representation. This paper introduces Jigsaw++, a novel generative method designed to tackle the multifaceted challenges of…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
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…
Understanding the shape and structure of objects is undoubtedly extremely important for object recognition, but the most common pattern recognition method currently used is machine learning, which often requires a large number of training…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
In this paper, we propose a machine learning approach to recognise engineering shape features such as holes, slots, etc. in a CAD mesh model. With the advent of digital archiving, newer manufacturing techniques such as 3D printing, scanning…
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…
Shape recognition is the main challenging problem in computer vision. Different approaches and tools are used to solve this problem. Most existing approaches to object recognition are based on pixels. Pixel-based methods are dependent on…
Actions as simple as grasping an object or navigating around it require a rich understanding of that object's 3D shape from a given viewpoint. In this paper we repurpose powerful learning machinery, originally developed for object…
We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We present a method for the automatic assembly of apictorial jigsaw puzzles. This method relies on integral area invariants for shape matching and an optimization process to aggregate shape matches into a final puzzle assembly. Assumptions…
A method for quantitative analysis of local pattern strength and defects in surface self-assembly imaging is presented and applied to images of stripe and hexagonal ordered domains. The presented method uses "shapelet" functions which were…
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 analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…
We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Of particular practical importance is to find tile…
Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for all $N \in \mathbb{N}$, there is a tile set that uniquely self-assembles into an $N \times N$ square shape at temperature 1 with optimal…
The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…