21,070 research outputs found
The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly
No full textAlgorithmic self-assembly occurs when components in a disorganized collection autonomously combine to form structures and, by their design and the dynamics of the system, are forced to intrinsically follow the execution of algorithms. Motivated by applications in DNA-nanotechnology, theoretical investigations in algorithmic tile-based self-assembly have blossomed into a mature theory with research strongly leveraging tools from computability theory, complexity theory, information theory, and graph theory to develop a wide range of models and to show that many are computationally universal, while also exposing a wide variety of powers and limitations of each. In addition to computational universality, the abstract Tile-Assembly Model (aTAM) was shown to be intrinsically universal (FOCS 2012), a strong notion of completeness where a single tile set is capable of simulating the full dynamics of all systems within the model; however, this result fundamentally required non-deterministic tile attachments. This was later confirmed necessary when it was shown that the class of directed aTAM systems, those in which all possible sequences of tile attachments eventually result in the same terminal assembly, is not intrinsically universal (FOCS 2016). Furthermore, it was shown that the non-cooperative aTAM, where tiles only need to match on 1 side to bind rather than 2 or more, is not intrinsically universal (SODA 2014) nor computationally universal (STOC 2017). Building on these results to further investigate the impacts of other dynamics, Hader et al. examined several tile-assembly models which varied across (1) the numbers of dimensions used, (2) restrictions imposed on the diffusion of tiles through space, and (3) whether each system is directed, and determined which models exhibited intrinsic universality (SODA 2020). Such results have shed much light on the roles of various aspects of the dynamics of tile-assembly and their effects on the universality of each model. In this paper we extend that previous work to provide direct comparisons of the various models against each other by considering intrinsic simulations between models. Our results show that in some cases, one model is strictly more powerful than another, and in others, pairs of models have mutually exclusive capabilities. This direct comparison of models helps expose the impacts of these three important aspects of self-assembling systems, and further helps to define a hierarchy of tile-assembly models analogous to the hierarchies studied in traditional models of computation
Self-Replication via Tile Self-Assembly (Extended Abstract)
No full textIn this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modifications consist of an extension to 3D, the ability of tiles to form "flexible" bonds that allow bound tiles to rotate relative to each other, and allowing tiles of multiple shapes within the same system. We call this new model the STAM*, and we present a series of constructions within it that are capable of self-replicating behavior. Namely, the input seed assemblies to our STAM* systems can encode either "genomes" specifying the instructions for building a target shape, or can be copies of the target shape with instructions built in. A universal tile set exists for any target shape (at scale factor 2), and from a genome assembly creates infinite copies of the genome as well as the target shape. An input target structure, on the other hand, can be "deconstructed" by the universal tile set to form a genome encoding it, which will then replicate and also initiate the growth of copies of assemblies of the target shape. Since the lengths of the genomes for these constructions are proportional to the number of points in the target shape, we also present a replicator which utilizes hierarchical self-assembly to greatly reduce the size of the genomes required. The main goals of this work are to examine minimal requirements of self-assembling systems capable of self-replicating behavior, with the aim of better understanding self-replication in nature as well as understanding the complexity of mimicking it
Simulation of the Abstract Tile Assembly Model Using Crisscross Slats
No full textThe abstract Tile Assembly Model (aTAM) provides an excellent foundation for the mathematical study of DNA-tile-based self-assembling systems, especially those wherein logic is embedded within the designs of the tiles so that they follow prescribed algorithms. While such algorithmic self-assembling systems are theoretically powerful, being computationally universal and capable of building complex shapes using information-theoretically optimal numbers of tiles, physical DNA-based implementations of these systems still encounter formidable error rates and undesired nucleation that hinder this theoretical potential. Slat-based self-assembly is a recent development wherein DNA forms long slats that combine together in 2 layers, rather than square tiles in a plane. In this approach, the length of the slats is key; while tiles typically only bind to 2 neighboring tiles at a time, slats may bind to dozens of other slats. This increased coordination between slats means that several mismatched slats must coincidentally meet in just the right way for errors to persist, unlike tiles where only a few are required. Consequently, while still a novel technology, large slat-based DNA constructions have been successfully implemented in the lab with resilience to many tile-based construction problems. These improved error characteristics come at a cost however, as slat-based systems are often more difficult to design and simulate than tile-based ones. Moreover, it has not been clear whether slats, with their larger sizes and different geometries, have the same theoretical capabilities as tiles. In this paper, we show that slats are capable of doing anything that tiles can, at least at scale. We demonstrate that any aTAM system may be converted to and simulated by an effectively equivalent system of slats. Furthermore, we show that these simulating slat systems can be made more efficiently, using shorter slats and a smaller scale factor, if the simulated tile system avoids certain uncommon growth patterns. Specifically, we consider 5 classes of aTAM systems with increasing complexity, from zig-zag systems which grow in a rigid pattern to the full class of all aTAM systems, and show how they may be converted to equivalent slat systems. We show that the simplest class may be simulated by slats at only a 2c × 2c scale, where c is the freely chosen coordination number of the slats, and further show that the full class of aTAM systems can be simulated at only a 5c × 5c scale. These results prove that slats have the full theoretical power of aTAM tiles while also providing constructions that are compact enough for potential DNA-based implementations of slat systems that are both capable of powerful algorithmic self-assembly and possessing of the strong error resilience of slats
Universal Shape Replication via Self-Assembly with Signal-Passing Tiles (Extended Abstract)
No full textIn this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of other glues via "signals". In fact, we prove our positive results in a version of the model in which it is slightly more difficult to work (where tiles are allowed to rotate) but show that they also hold in the standard STAM. Specifically, the problem we investigate is "shape replication" wherein, given a set of input assemblies of arbitrary shape, a system must construct an arbitrary number of assemblies with the same shapes and, with the exception of size-bounded junk assemblies that result from the process, no others. We provide the first fully universal shape replication result, namely a single tile set capable of performing shape replication on arbitrary sets of any 3-dimensional shapes without requiring any scaling or pre-encoded information in the input assemblies. Our result requires the input assemblies to be composed of signal-passing tiles whose glues can be deactivated to allow deconstruction of those assemblies, which we also prove is necessary by showing that there are shapes whose geometry cannot be replicated without deconstruction. Additionally, we modularize our construction to create systems capable of creating binary encodings of arbitrary shapes, and building arbitrary shapes from their encodings. Because the STAM is capable of universal computation, this then allows for arbitrary programs to be run within an STAM system, using the shape encodings as input, so that any computable transformation can be performed on the shapes
Report on Meteorological Research March 1, 1935 (m-1)
No full textThe object of the report was to elucidate in detail the various features of the research program in meteorology being carried on at the Daniel Guggenheim Airship Institute in Akron, Ohio. Mr. L. J. Fangman, of the U.S. Weather Bureau, was collaborating with the author in carrying out work such as a study of autographic records of the various meteorological elements during frontal passages with a view to the possible prediction of the intensity of the accompanying disturbance as it may affect the operation of aircraft and a study of atmospheric gustiness with a view to finding the dependence between frequency end amplitude of velocity fluctuations and the vertical temperature and velocity gradients
(Fourth) Report on Meteorological Activities at the DGAI (8-1-36)(Weather Bureau Copy)
No full textThis report is on the investigations of frontal phenomena at the Daniel Guggenheim Airship Institute in Akron, Ohio from January 1, 1935 through August 1, 1936. The investigation was carried out with the cooperation of the U.S. Bureau of Aeronautics, the U.S. Weather Bureau, the California Institute of Technology, and the Guggenheim Airship Institute. Mr. R.C. Robinson of the Weather Bureau cooperated with the author in carrying out the investigation. The object of the investigation was to determine the intensity of the atmospheric disturbances (i.e. rapidity of wind shift and gustiness) accompanying the passage of cold fronts, along with a study of the characteristics of the air masses involved and other features which might affect the intensity of the disturbance. The report treated thirty cold fronts which passed the station during 1935 to 1936
Archives and Images as Repositories of Time, Language, and Forms from the Past: A Conversation with Daniel Eisenberg
No full textDaniel Akech
No full textabstract: Daniel was a little boy when the war came to his village. He witnessed people being shot and running for shelter. There was no food or water so he drank urine and ate tree leaves.
“Lost Boys Found” is an ongoing, interdisciplinary project that is collecting, recording and archiving the oral histories of the Lost Boys/Girls of Sudan. The collection is a work-in-progress, seeking to record the oral history of as many Lost Boys/Girls as are willing, and will be used in a future book.Age: 24Region: Upper NileThis picture and bio was donated to the "Lost Boys Found" oral history project from The Arizona Lost Boys Cente
Daniel Emmett postcard
No full textPostcard of Daniel Emmett and his home in Mount Vernon, Ohio. Emmett is considered to be the author of the antebellum song "Dixie," written in 1859, which became the unofficial song of the Confederate soldiers during the American Civil War. He was born in Mount Vernon in 1815 and taught himself the fiddle, and later became associated with minstrel shows and helped to define that genre. Minstrel shows traveled around the United States, presenting skits and musical performances. Emmett also composed many other songs, including "Old Dan Tucker," "Turkey in the Straw," and "The Blue Tail Fly." He died in 1904
Daniel Jau Maper
No full textabstract: Daniel Jau Maper was herding cattle when Arabs attacked his village.
“Lost Boys Found” is an ongoing, interdisciplinary project that is collecting, recording and archiving the oral histories of the Lost Boys/Girls of Sudan. The collection is a work-in-progress, seeking to record the oral history of as many Lost Boys/Girls as are willing, and will be used in a future book.Age: 27Region: Upper NileThis picture and bio was donated to the "Lost Boys Found" oral history project from The Arizona Lost Boys Cente
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