Related papers: Small tile sets that compute while solving mazes

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…

Patchy colloids are promising candidates for building blocks in directed self-assembly. To be successful the surface patterns need to both be simple enough to be synthesized, while feature-rich enough to cause the colloids to self-assemble…

The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…

We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…

We propose a new kind of collective motion where swarms of simple agents are able to find and fix the solution of two-dimensional mazes. The model consists of active memoryless particles interacting exclusively via short-ranged perception…

In recent years, a standard computational pathology workflow has emerged where whole slide images are cropped into tiles, these tiles are processed using a foundation model, and task-specific models are built using the resulting…

Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…

In a mosaic, a tessera is a single stone. We introduce tesserae for the co-simulation framework mosaik, where they are sets of entities. They allow for a visual, intuitive, and yet systematic description of simulation scenarios by allowing…

Consecutive matrix multiplications are commonly used in graph neural networks and sparse linear solvers. These operations frequently access the same matrices for both reading and writing. While reusing these matrices improves data locality,…

There has been significant research interest in Procedural Level Generation via Machine Learning (PLGML), applying ML techniques to automated level generation. One recent trend is in the direction of learning representations for level…

Ensembling can improve the performance of Neural Networks, but existing approaches struggle when the architecture likelihood surface has dispersed, narrow peaks. Furthermore, existing methods construct equally weighted ensembles, and this…

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence -- the number of inter-particle bonds -- is a prerequisite for the assembly of…

A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated solution, which then could be simplified. We discuss some…

By exploiting the exquisite selectivity of DNA hybridization, DNA-Coated Colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the…

Pattern self-assembly tile set synthesis (PATS) is a combinatorial optimization problem which aim at minimizing a rectilinear tile assembly system (RTAS) that uniquely self-assembles a given rectangular pattern, and is known to be NP-hard.…

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…

We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems -- we give an example of…

The Calisson puzzle is a tiling puzzle in which one must tile a triangular grid inside a hexagon with lozenges, under the constraint that certain prescribed edges remain tile boundaries and that adjacent lozenges along these edges have…

Inspection of infrastructure using static sensor nodes has become a well established approach in recent decades. In this work, we present an experimental setup to address a binary inspection task using mobile sensor nodes. The objective is…

In areas as diverse as contemporary art, play structures, climbing equipment, and modular construction toys, we see the presence of building block-like polyhedral complexes, which are generalizations of the pieces in the game Tetris. We…