MediaWiki API result

{
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        "gapcontinue": "Reflexive_Tile_Assembly_Model_(RTAM)",
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    "warnings": {
        "main": {
            "*": "Subscribe to the mediawiki-api-announce mailing list at <https://lists.wikimedia.org/mailman/listinfo/mediawiki-api-announce> for notice of API deprecations and breaking changes."
        },
        "revisions": {
            "*": "Because \"rvslots\" was not specified, a legacy format has been used for the output. This format is deprecated, and in the future the new format will always be used."
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    "query": {
        "pages": {
            "112": {
                "pageid": 112,
                "ns": 0,
                "title": "Reducing Tile Complexity for Self-Assembly Through Temperature Programming",
                "revisions": [
                    {
                        "contentformat": "text/x-wiki",
                        "contentmodel": "wikitext",
                        "*": "{{PaperTemplate\n|date=2006/01/09\n|abstract=We consider the tile self-assembly model and how tile complexity can be eliminated by permitting the temperature of the self-assembly system to be adjusted throughout the assembly process. To do this, we propose novel techniques for designing tile sets that permit an arbitrary length $m$ binary number to be encoded into a sequence of $O(m)$ temperature changes such that the tile set uniquely assembles a supertile that precisely encodes the corresponding binary number. As an application, we show how this provides a general tile set of size $O(1)$ that is capable of uniquely assembling essentially any $n \\times n$ square, where the assembled square is determined by a temperature sequence of length $O(\\log n)$ that encodes a binary description of $n$. This yields an important decrease in tile complexity from the required  $\\Omega( \\frac{\\log n} {\\log \\log n})$ for almost all $n$ when the temperature of the system is fixed. We further show that for almost all $n$, no tile system can simultaneously achieve both $o(\\log n)$ temperature complexity and $o( \\frac{\\log n} {\\log \\log n})$ tile complexity, showing that both versions of an optimal square building scheme have been discovered. This work suggests that temperature change can constitute a natural, dynamic method for providing input to self-assembly systems that is potentially superior to the current technique of designing large tile sets with specific inputs hardwired into the tileset.\n|authors=Ming-Yang Kao, Robert Schweller\n|file=[[media:ReducingTileComplexityForSelf-AssemblyThroughTemperatureProgramming.pdf | Reducing Tile Complexity for Self-Assembly Through Temperature Programming.pdf]]\n}}"
                    }
                ]
            },
            "339": {
                "pageid": 339,
                "ns": 0,
                "title": "Reflections on Tiles (in Self-Assembly)",
                "revisions": [
                    {
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                        "*": "{{PaperTemplate\n|date=2015/05/11\n|abstract=We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1 RTAM systems is not computationally universal, which is conjectured but unproven for the aTAM, and like the aTAM, the RTAM is computationally universal at temperature 2. We then show that at temperature 1, when starting from a single tile seed, the RTAM is capable of assembling $n$ x $n$ squares for $n$ odd using only $n$ tile types, but incapable of assembling $n$ x $n$ squares for $n$ even. Moreover, we show that $n$ is a lower bound on the number of tile types needed to assemble $n$ x $n$ squares for $n$ odd in the temperature-1 RTAM. The conjectured lower bound for $temperature-1$ aTAM systems is $2n-1$. Finally, we give preliminary results toward the classification of which finite connected shapes in $Z^2$ can be assembled (strictly or weakly) by a singly seeded (i.e. seed of size 1) RTAM system, including a complete classification of which finite connected shapes be strictly assembled by a \"mismatch-free\" singly seeded RTAM system.\n|authors=Jacob Hendricks, Matthew J. Patitz, Trent A. Rogers\n|file=[http://arxiv.org/abs/1404.5985 Reflections on Tiles (in Self-Assembly)]\n}}"
                    }
                ]
            }
        }
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}