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Self-supervised learning is popular method because of its ability to learn features in images without using its labels and is able to overcome limited labeled datasets used in supervised learning. Self-supervised learning works by using a…
This paper introduces the theory and practice of formal verification of self-assembling systems. We interpret a well-studied abstraction of nanomolecular self assembly, the Abstract Tile Assembly Model (aTAM), into Computation Tree Logic…
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…
The purpose of this paper is to provide a construction to model shared-variable systems using higher-dimensional automata which is compositional in the sense that the parallel composition of completely independent systems is modeled by the…
Engelfriet and Vereijken have shown that linear graph grammars based on hyperedge replacement generate graph languages that can be considered as interpretations of regular string languages over typed symbols. In this paper we show that…
In this work we propose a generalization of Winfree's abstract Tile Assembly Model (aTAM) in which tile types are assigned rigid shapes, or geometries, along each tile face. We examine the number of distinct tile types needed to assemble…
Self-assembly plays an essential role in many natural processes, involving the formation and evolution of living or non-living structures, and shows potential applications in many emerging domains. In existing research and practice, there…
The human brain exhibits a strong ability to spontaneously associate different visual attributes of the same or similar visual scene, such as associating sketches and graffiti with real-world visual objects, usually without supervising…
Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correction. We address both questions,…
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…
We consider weighted tree automata over strong bimonoids (for short: wta). A wta $\mathcal{A}$ has the finite-image property if its recognized weighted tree language $[\![\mathcal{A}]\!]$ has finite image; moreover, $\mathcal{A}$ has the…
Recent trends in AIGC effectively boosted the application of visual inspection. However, most of the available systems work in a human-in-the-loop manner and can not provide long-term support to the online application. To make a step…
We prove a Kleene theorem for higher-dimensional automata. It states that the languages they recognise are precisely the rational subsumption-closed sets of finite interval pomsets. The rational operations on these languages include a…
We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…
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…
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…
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…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior…
Colorizing grayscale images offers an engaging visual experience. Existing automatic colorization methods often fail to generate satisfactory results due to incorrect semantic colors and unsaturated colors. In this work, we propose an…