We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. Contrary to intuition, we show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a square tile assembly ...

In this appendix, we prove the undecidability of the following problems: the constrained domino problem (proved undecidable by Wang): give a tile set and a tile as input, ask whether it is possible to form a tiling of the plane containing the given tile; the unconstrained domino problem (Berger's Theorem): the input is a tile set and the question is whether one can tile the plane with it; the p...

A discourse is more than a random set of sentences, because it is coherent (e.g. Hobbs, 1990) Discourse coheres -among other thingsbecause coherence relations hold between the segments, or rather between the representation people make of the segments. A coherence relation is an aspect of tile meaning of two or more discourse segments that cannot be described in terms of tile meaning of tile seg...

In this paper we explore the power of tile self-assembly models that extend the well-studied abstract Tile Assembly Model (aTAM) by permitting tiles of shapes beyond unit squares. Our main result shows the surprising fact that any aTAM system, consisting of many different tile types, can be simulated by a single tile type of a general shape. As a consequence, we obtain a single universal tile t...

DNA tiles provide a promising technique for assembling structures with nanoscale resolution through self-assembly by basic interactions rather than top-down assembly of individual structures. Tile systems can be programmed to grow based on logical rules, allowing for a small number of tile types to assemble large, complex assemblies that can retain nanoscale resolution. Such algorithmic systems...

At the high resolutions attainable with the new generation space-borne sensors, the focus moves increasingly from spectral characteristics to geometric features. This trend is even more evident for urban areas which tend to show an unpaired concentration of linear features with respect to any other land cover. This naturally applies to both optical and radar images, and suggests one may use loc...

Improving terrain tile data selection efficiency, real-time loading of visible tile data and building GPU-based continuous Level of Details (LOD) are the key technologies for large scale terrain rendering on GPU. In this article, in order to reduce terrain tile data selection time, we build double layers tile quad tree for massive terrain data and organize tile data by designing Z-order space f...

The gradual and painstaking determination of the CKM matrix over a long period of time is a remarkable accomplishment of our field, and hopefully it will attain a level of completion from the B-factory studies to come. The emphasis of B-factories will be on the physics of b quarks and deservedly so. Already, there is discovery of a ∆B = 2 process (Bd−Bd mixing) and an EW-penguin decay (B → K γ)...

We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. We show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a deterministic square (hexagonal) tile assemb...