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Producing reliable nanoscale self-as...
~
Luhrs, Chris.
Producing reliable nanoscale self-assembly.
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Producing reliable nanoscale self-assembly.
作者:
Luhrs, Chris.
面頁冊數:
79 p.
附註:
Adviser: Ashish Goel.
附註:
Source: Dissertation Abstracts International, Volume: 69-05, Section: B, page: 3099.
Contained By:
Dissertation Abstracts International69-05B.
標題:
Computer Science.
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3313612
ISBN:
9780549620525
Producing reliable nanoscale self-assembly.
Luhrs, Chris.
Producing reliable nanoscale self-assembly.
- 79 p.
Adviser: Ashish Goel.
Thesis (Ph.D.)--Stanford University, 2008.
During DNA self-assembly, tiles may attach to each other forming structures called polyominoes and then attach to the assembly using bonds from multiple tiles. As a result, polyominoes may cause errors in systems designed with only aTAM in mind. We present a block replacement scheme for making any system that admits non-trivial block replacement polyomino-safe. In addition, we present a smaller block replacement scheme that makes the Chinese Remainder counter polyomino-safe and prove that the question of whether a system is polyomino-safe (or other similar properties) is undecidable. Finally, we show that applying our polyomino-safe system produces self-healing systems when applied to most self-healing systems.
ISBN: 9780549620525Subjects--Topical Terms:
212513
Computer Science.
Producing reliable nanoscale self-assembly.
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During DNA self-assembly, tiles may attach to each other forming structures called polyominoes and then attach to the assembly using bonds from multiple tiles. As a result, polyominoes may cause errors in systems designed with only aTAM in mind. We present a block replacement scheme for making any system that admits non-trivial block replacement polyomino-safe. In addition, we present a smaller block replacement scheme that makes the Chinese Remainder counter polyomino-safe and prove that the question of whether a system is polyomino-safe (or other similar properties) is undecidable. Finally, we show that applying our polyomino-safe system produces self-healing systems when applied to most self-healing systems.
520
$a
Finally, we turn to carbon nanotube circuits. Novel technologies for fabricating circuits at smaller scales than currently possible are of obvious significance. One such technology is based on laying out circuits on top of a layer of parallel carbon nanotubes. While similar to standard circuit fabrication, this technology introduces new design problems arising from the underlying directionality of the nanotube substrate and the failure of a percentage of the nanotubes to grow as expected. We address the theoretical aspects of these design questions, which naturally correspond to optimizing representations of boolean functions under certain metrics. In general, we show that it is NP-hard to approximate any of several natural optimization problems (circuit area, number of etched out regions, etc.) relating to these circuits. On the other hand, we are able to present non-trivial designs that improve significantly over naive implementations for several functions of interest such as XOR and plurality.
520
$a
In previous work, self-healing tile systems were only guaranteed to regenerate provided the seed tile remained. In a reasonable probabilistic model fire tile loss, such an assembly will eventually decay though. We present improved self-healing tile systems for the self-assembly of several interesting classes of shapes, including counters, squares, and Turing-computable shapes. Our tile systems can recover from the loss of arbitrarily many tiles, including the seed, provided that a large enough fragment (logarithmic in the size of the desired assembly for the case of counters and squares) is left intact.
520
$a
Nanotechnology has obvious and immense potential for application. Since it is infeasible to manipulate objects on the nanometer scale explicitly, we must develop self-assembly techniques, in which small objects attach to each other using simple local rules. Unfortunately, such rules tend not to be perfectly reliable, and since we need to apply these rules many times even a small failure percentage can derail assembly. Thus, we need to develop techniques to produce correct assembly reliably in spite of the unreliability of the underlying rules. In this thesis, we present methods for producing robust self-assembly in two regimes: DNA tile assembly, and carbon nanotube circuitry.
520
$a
These and other error-correction mechanisms suffer either from high resolution loss or a large increase in the number of tile-types. Large increases in either of these parameters are quite costly in nanoscale self-assembly. To circumvent these issues, we propose dimension augmented proof-reading, a technique that uses the third dimension to do error-correction in two dimensional self-assembling systems. This involves no resolution loss in the two dimensions of interest, results in a smaller increase in the number of tile-types than previous techniques, and appears to have the same error-correction properties. We then use our combinatorial criteria to prove the correctness of dimension augmented proof-reading applied to a self-assembling system that computes the parity of a string.
520
$a
We next address the issue of tiles in a DNA system attaching at strength less than the temperature of the system. Error-correcting systems for this type of issue need to be analyzed in the kinetic Tile Assembly Model; such analysis involves complicated Markov Chains and is cumbersome. We present a set of completely combinatorial criteria that can be used to prove properties of error-correcting self-assembling systems. We illustrate these criteria by applying them to two known proof-reading systems, one of which was not previously known to work.
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