Doubles and negatives are positive (in self-assembly)

In the abstract Tile Assembly Model (aTAM), the phenomenon of cooperation occurs when the attachment of a new tile to a growing assembly requires it to bind to more than one tile already in the assembly. Often referred to as “temperature-2” systems, those which employ cooperation are known to be quite powerful (i.e. they are computationally universal and can build an enormous variety of shapes and structures). Conversely, aTAM systems which do not enforce cooperative behavior, a.k.a. “temperature-1” systems, are conjectured to be relatively very weak, likely to be unable to perform complex computations or algorithmically direct the process of self-assembly. Nonetheless, a variety of models based on slight modifications to the aTAM have been developed in which temperature-1 systems are in fact capable of Turing universal computation through a restricted notion of cooperation. Despite that power, though, several of those models have previously been proven to be unable to perform or simulate the stronger form of cooperation exhibited by temperature-2 aTAM systems. In this paper, we first prove that another model in which temperature-1 systems are computationally universal, namely the restricted glue TAM (rgTAM) in which tiles are allowed to have edges which exhibit repulsive forces, is also unable to simulate the strongly cooperative behavior of the temperature-2 aTAM. We then show that by combining the properties of two such models, the Dupled Tile Assembly Model (DTAM) and the rgTAM into the DrgTAM, we derive a model which is actually more powerful at temperature-1 than the aTAM at temperature-2. Specifically, the DrgTAM, at temperature-1, can simulate any aTAM system of any temperature, and it also contains systems which cannot be simulated by any system in the aTAM.     

Polyomino-safe DNA self-assembly via block replacement

The standard abstract model for analyzing DNA self-assembly, aTAM, assumes that single tiles attach one by one to a larger structure. In practice, tiles may attach to each other forming structures called polyominoes and then attach to the assembly using bonds from multiple tiles. Such polyominoes may cause errors in systems designed with only aTAM in mind. In this paper, we first present a formal definition of when one tile system is a “block replacement” of another. Then 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.     

Activatable tiles for compact robust programmable molecular assembly and other applications

Algorithmic DNA self-assembly is capable of forming complex patterns and shapes, that have been shown theoretically, and experimentally. Its experimental demonstrations, although improving over recent years, have been limited by significant assembly errors. Since 2003 there have been several designs of error-resilient tile sets but all of these existing error-resilient tile systems assumed directional growth of the tiling assembly. This is a very strong assumption because experiments show that tile self-assembly does not necessarily behave in such a fashion, since they may also grow in the reverse of the intended direction. The assumption of directional growth of the tiling assembly also underlies the growth model in theoretical assembly models such as the TAM. What is needed is a means for enforce this directionality constraint, which will allow us to reduce assembly errors. In this paper we describe a protection/deprotection strategy to strictly enforce the direction of tiling assembly growth so that the assembly process is robust against errors. Initially, we start with (1) a single “activated” tile with output pads that can bind with other tiles, along with (2) a set of “deactivated” tiles, meaning that the tile’s output pads are protected and cannot bind with other tiles. After other tiles bind to a “deactivated” tile’s input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. When these are activated in a desired order, we can enforce a directional assembly at the same scale as the original one. Such a system can be built with minimal modifications of existing DNA tile nanostructures. We propose a new type of tiles called activatable tiles and its role in compact proofreading. Activatable tiles can be thought of as a particular case of the more recent signal tile assembly model, where signals transmit binding/unbinding instructions across tiles on binding to one or more input sites. We describe abstract and kinetic models of activatable tile assembly and show that the error rate can be decreased significantly with respect to Winfree’s original kinetic tile assembly model without considerable decrease in assembly growth speed. We prove that an activatable tile set is an instance of a compact, error-resilient and self-healing tile-set. We describe a DNA design of activatable tiles and a mechanism of deprotection using DNA polymerization and strand displacement. We also perform detailed stepwise simulations using a DNA Tile simulator Xgrow, and show that the activatable tiles mechanism can reduce error rates in self assembly. We conclude with a brief discussion on some applications of activatable tiles beyond computational tiling, both as (1) a novel system for concentration of molecules, and (2) a catalyst in sequentially triggered chemical reactions.     

Hierarchical growth is necessary and (sometimes) sufficient to self-assemble discrete self-similar fractals

Natural Computing - In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each...     

The effect of malformed tiles on tile assemblies within the kinetic tile assembly model

Many different constructions of proofreading tile sets have been proposed in the literature to reduce the effect of deviations from ideal behaviour of the dynamics of the molecular tile self-assembly process. In this paper, we consider the effect on the tile assembly process of a different kind of non-ideality, namely, imperfections in the tiles themselves. We assume a scenario in which some small proportion of the tiles in a tile set are “malformed”. We study, through simulations, the effect of such malformed tiles on the self-assembly process within the kinetic Tile Assembly Model (kTAM). Our simulation results show that some tile set constructions show greater error-resilience in the presence of malformed tiles than others. For example, the 2- and 3-way overlay compact proofreading tile sets of Reif et al. (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) are able to handle malformed tiles quite well. On the other hand, the snaked proofreading tile set of Chen and Goel (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) fails to form even moderately sized tile assemblies when malformed tiles are present. We show how the Chen–Goel construction may be modified to yield new snaked proofreading tile sets that are resilient not only to errors intrinsic to the assembly process, but also to errors caused by malformed tiles.     

瓷砖图像的纹理特征分类研究

在已有的瓷砖图像分类系统中,仅靠颜色特征和简单的纹理边缘信息只能对无花纹的单色砖或简单花纹的瓷砖进行有效分类,对复杂图案的瓷砖存在识别率低的问题。针对此种情况,结合瓷砖图像的灰度共生矩阵和统计几何特征,将这些特征输入支持向量机进行特征分层分类。采用基于径向基核函数和[K]交叉验证法所得到的最优参数构造支持向量机,解决瓷砖纹理特征具有非线性的分类问题。用瓷砖生产线上采集的大量图像进行实验表明,该方法准确率高,分类效果好。     

基于DNA计算自组装模型的Diffie-Hellman算法破译(英文)

DNA自组装计算模型是近年来引人关注的计算模型,已有基于自组装模型的二进制加法、乘法以及有限域中的加法和乘法的讨论．文中利用DNA自组装模型设计的模乘系统,实现了素数P的本原根g连续乘方后模p的数的排列,从而可以在线性时间内求解离散对数,为破译Diffie—Hellman密钥交换算法提供了新的生物方法．该模乘系统使用了Θ（p）种自组装类型,组装的时间复杂度为Θ（p-1）．系统最后组装结果提取出报告链后,经过PCR和凝胶电泳读取离散对数结果．该模型扩展了DNA自组装计算模型的应用,为求取离散对数提供了新思路．     

多特征融合的瓷砖表面缺陷检测算法研究

鉴于单一特征在瓷砖种类较多的情况下,存在对瓷砖表面缺陷内容表达不明显,导致复杂瓷砖识别率较低。针对这个问题,在词袋模型（BoF）框架的基础上,提出一种有效的多特征融合算法用于瓷砖缺陷检测。该算法采用改进后的SIFT和颜色矩融合特征作为瓷砖图像的区域特征描述;根据每种特征对瓷砖被分类的准确率大小,给提取到的两种区域特征分配各自的权重系数实现特征的加权融合;形成综合特征向量送入SVM分类器达到瓷砖缺陷分类的目的。通过不同类型的瓷砖样本进行实验表明,该算法识别率高,对复杂瓷砖能实现较好的分类。     

Tile-based level of detail for the parallel age

Today's PCs incorporate multiple CPUs and GPUs and are easily arranged in clusters for high-performance, interactive graphics. We present an approach based on hierarchical, screen-space tiles to parallelizing rendering with level of detail. Adapttiles, render tiles, and machine tiles are associated with CPUs, GPUs, and PCs, respectively, to efficiently parallelize the workload with good resource utilization. Adaptive tile sizes provide load balancing while our level of detail system allows total and independent management of the load on CPUs and GPUs. We demonstrate our approach on parallel configurations consisting of both single PCs and a cluster of PCs     

A molecular solution for minimum vertex cover problem in tile assembly model

Self-assembly is a generalization of the crystal growth, which has been proposed as a mechanism for the bottom-up fabrication of autonomous DNA computation. In the same context, tile assembly model is a highly distributed parallel model of natural self-assembly. In this paper, we propose a tile assembly system to tackle a well-known NP-complete problem known as Minimum Vertex Cover problem. The proposed algorithm requires Θ(n×m) types of tiles, and each parallel assembly executes in a linear time, where n is the number of vertices and m is the number of edges. Furthermore, the experimental results proved the simplicity and the efficiency of the proposed algorithm to solve the Minimum Vertex Cover, and reduce the overall complexity to find the solution.     

Toward minimum size self-assembled counters

DNA self-assembly is a promising paradigm for nanotechnology. In this paper we study the problem of finding tile systems of minimum size that assemble a given shape in the Tile Assembly Model, defined by Rothemund and Winfree (Proceedings of the thirty-second annual ACM symposium on theory of computing, 2000). We present a tile system that assembles an rectangle in asymptotically optimal time. This tile system has only 7 tiles. Earlier constructions need at least 8 tiles (Chen et al. Proceedings of symposium on discrete algorithms, 2004). We managed to reduce the number of tiles without increasing the assembly time. The new tile system works at temperature 3. The new construction was found by the combination of exhaustive computerized search of the design space and manual adjustment of the search output.     

On runtime adaptive tile defragmentation for resource management in many-core systems

Before an application can be actually launched in a many-core system, the first thing that needs to be done is to get the application mapped to a number of tiles (cores). Such online application mapping process may unfortunately lead to a serious resource leak problem, referred as tile fragmentation, that free (uncommitted) tiles from any single contiguous region are just inadequate to accommodate the performance needs of an incoming application, although the total number of free tiles may still exceed what is required to service this application. When applications have to be mapped to noncontiguous tiles due to fragmentation, there will be obvious performance penalty due to increased communication distances. As a result, defragmentation that consolidates fragmented tiles needs to be routinely exercised, and this defragmentation process must not introduce high computation overhead that otherwise can adversely impact the system performance. In this paper, we propose a task migration-based adaptive tile defragmentation algorithm that helps consolidate running applications through online task migration. This algorithm relocates the applications’ tile regions so that a contiguous free tile region is formed and maintained. By doing so, future applications can be mapped to a region with low communication distance. Both the computation overhead and quality of defragmentation result of the proposed algorithm are adaptively set in response to the system workloads. Enabled by its low overhead, the proposed defragmentation algorithm is an effective resource management enhancement to the existing runtime task-to-tile mapping methods, with as much as 3× system throughput improvement observed in some experiments.     

Automatic partitioning of parallel loops with parallelepiped-shapedtiles

In this paper, an efficient algorithm to implement loop partitioning is introduced and evaluated. We start from results of Agarwal et al. (1995) whose aim is to minimize the number of accessed data throughout the computation of a tile; this number is called the cumulative footprint of the tile. We improve these results along several directions. First, we derive a new formulation of the cumulative footprint, allowing for an analytical solution of the optimization problem stated by Agarwal et al.. Second, we deal with arbitrary parallelepiped-shaped tiles, as opposed to rectangular tiles. We design an efficient heuristic to determine the optimal tile shape in this general setting and we show its usefulness using both examples of Agarwal et al. and a large collection of randomly generated data     

基于边界特征配准的墙地砖缺陷检测研究

该文结合radon变换和几何推理,研究了基于墙地砖边界的用于规则图案表面缺陷检测的图像配准方法。实验证明该算法简单快捷,能检测出墙地砖的一般常见缺陷。     

Generating Stochastic Wall Patterns On‐the‐fly with Wang Tiles

The game and movie industries always face the challenge of reproducing materials. This problem is tackled by combining illumination models and various textures (painted or procedural patterns). Generating stochastic wall patterns is crucial in the creation of a wide range of backgrounds (castles, temples, ruins…). A specific Wang tile set was introduced previously to tackle this problem, in an iterative fashion. However, long lines may appear as visual artifacts. We use this tile set in a new on‐the‐fly procedure to generate stochastic wall patterns. For this purpose, we introduce specific hash functions implementing a constrained Wang tiling. This technique makes possible the generation of boundless textures while giving control over the maximum line length. The algorithm is simple and easy to implement, and the wall structure we get from the tiles allows to achieve visuals that reproduce all the small details of artist painted walls.     

Robust tile-based texture synthesis using artificial immune system

One significant problem in tile-based texture synthesis is the presence of conspicuous seams in the tiles. The reason is that sample patches employed as primary patterns of the tile set may not be well stitched if carelessly picked. In this paper, we introduce a robust approach that can stably generate an ω-tile set of high quality and pattern diversity. First, an extendable rule is introduced to increase the number of sample patches to vary the patterns in an ω-tile set. Second, in contrast to other concurrent techniques that randomly choose sample patches for tile construction, ours uses artificial immune system (AIS) to select the feasible patches from the input example. This operation ensures the quality of the whole tile set. Experimental results verify the high quality and efficiency of the proposed algorithm.     

Staged self-assembly: nanomanufacture of arbitrary shapes with <Emphasis Type="Italic">O</Emphasis>(1) glues

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through the traditional lower bounds in tile self-assembly by encoding the shape in the staging algorithm instead of the tiles. All of our results are based on the practical assumption that only a constant number of glues, and thus only a constant number of tiles, can be engineered. Under this assumption, traditional tile self-assembly cannot even manufacture an n × n square; in contrast, we show how staged assembly in theory enables manufacture of arbitrary shapes in a variety of precise formulations of the model.

Step-wise tile assembly with a constant number of tile types

In this paper, we study the step-wise tile assembly model introduced by Reif (in: Based computers III, vol 48 of DIMACS, 1999) in which shape is assembled in multiple steps. In each step the partially built structure is exposed to a new set of tiles. We show that an N?×?N square can be assembled in N steps using a constant number of tile types. In general, we show that a constant number of tile types (24) is sufficient to assemble a large class of shapes in n steps, where n is the number of tiles of the shape. This class includes all shapes obtained from any shape by scaling by a factor of 2, in which case only 14 tile types suffices. For general shapes, we show that the tile complexity of this model is related to the monotone connected node search number of a spanning tree of the shape assuming the number of steps is n.     

Efficient texture synthesis using strict Wang Tiles

Wang Tiles are constructed from four texture samples, arranged so they can always match a choice of other tiles at two edges. Because they are precomputed, Wang Tiles are a very efficient way to generate textures on the fly. But matching problems occur within tiles and at the corners of adjacent tiles. By replacing the edge-matching texture samples with a new sample in the center of the tile, and using the graph cut path-finding algorithm, we overcome these problems and introduce additional texture diversity. Our s-Wang Tiles are a stricter interpretation of the original Wang Tile design, and our tile set is also smaller than that required by ω-Tiles: only eight different tiles are required for a non-repetitive titling.     

Generating Tile Maps

Tile maps are an important tool in thematic cartography with distinct qualities (and limitations) that distinguish them from better‐known techniques such as choropleths, cartograms and symbol maps. Specifically, tile maps display geographic regions as a grid of identical tiles so large regions do not dominate the viewer's attention and small regions are easily seen. Furthermore, complex data such as time series can be shown on each tile in a consistent format, and the grid layout facilitates comparisons across tiles. Whilst a small number of handcrafted tile maps have become popular, the time‐consuming process of creating new tile maps limits their wider use. To address this issue, we present an algorithm that generates a tile map of the specified type (e.g. square, hexagon, triangle) from raw shape data. Since the ‘best’ tile map depends on the specific geography visualized and the task to be performed, the algorithm generates and ranks multiple tile maps and allows the user to choose the most appropriate. The approach is demonstrated on a range of examples using a prototype browser‐based application.