用线性码构造DNA计算编码的海明距离

最小海明距离是DNA计算编码性能的重要评价标准。利用线性码来构造DNA计算编码的最小海明距离是一种有效的方法,关键在于构造相应的监督矩阵。为了寻找监督矩阵,提出了监督矩阵的搜索算法和优化方法,及两个必要性定理;作为介于最小海明距离上限与下限之间的编码存在性的判断依据,给出了两个关于线性码存在性定理;最后给出了三字母表DNA计算编码相关的监督矩阵搜索算法结果,以及当最小海明距离一定时,接近编码数量上限的部分线性码的存在性结果。根据这些结果和存在性定理,可以推断常用DNA计算编码最小海明距离的存在性。     

DNA chips for species identification and biological phylogenies

The codeword design problem is an important problem in DNA computing and its applications. Several theoretical analyses as well as practical solutions for short oligonucleotides (up to 20-mers) have been generated recently. These solutions have, in turn, suggested new applications to DNA-based indexing and natural language processing, in addition to the obvious applications to the problems of reliability and scalability that generated them. Here we continue the exploration of this type of DNA-based indexing for biological applications and show that DNA noncrosshybridizing (nxh) sets can be successfully applied to infer ab initio phylogenetic trees by providing a way to measure distances among different genomes indexed by sets of short oligonucleotides selected so as to minimize crosshybridization. These phylogenies are solidly established and well accepted in biology. The new technique is much more effective in terms of signal-to-noise ratio, cost and time than current methods. Second, it is demonstrated that DNA indexing does provide novel and principled insights into the phylogenesis of organisms hitherto inaccessible by current methods, such as a prediction of the origin of the Salmonella plasmid 50 as being acquired horizontally, likely from some bacteria somewhat related to Yesinia. Finally, DNA indexing can be scaled up to newly available universal DNA chips readily available both in vitro and in silico. In particular, we show how a recently obtained such set of nxh 16-mers can be used as a universal coordinate system in DNA spaces to characterize very large groups (families, genera, and even phylla) of organisms on a uniform biomarker reference system, a veritable and comprehensive “Atlas of Life”, as it is or as it could be on earth.     

Sticky-free and overhang-free DNA languages

An essential step of any DNA computation is encoding the input data on single or double DNA strands. Due to the biochemical properties of DNA, complementary single strands can bind to one another forming double-stranded DNA. Consequently, data-encoding DNA strands can sometimes interact in undesirable ways when used in computations. It is crucial thus to analyze properties that guard against such phenomena and study sets of sequences that ensure that no unwanted bindings occur during any computation. This paper formalizes and investigates properties of DNA languages that guarantee their robusteness during computations. After defining and investigating several types of DNA languages possessing good encoding properties, such as sticky-free and overhang-free languages, we give algorithms for deciding whether regular DNA languages are invariant under bio-operations. We also give a method for constructing DNA languages that, in addition to being invariant and sticky-free, possess error-detecting properties. Finally, we present the results of running tests that check whether several known gene languages (the set of genes of a given organism) as well as the input DNA languages used in Adlemans DNA computing experiment, have the defined properties.Received: 6 February 2003, Published online: 2 September 2003Research partially supported by Grants R2824A01 and R220259 of the Natural Sciences and Engineering Research Council of Canada.     

Non-Pauli observables for CWS codes

It is known that nonadditive quantum codes can have higher code dimensions than stabilizer codes for the same length and minimum distance. The class of codeword stabilized codes (CWS) provides tools to obtain new nonadditive quantum codes by reducing the problem to finding nonlinear classical codes. In this work, we establish some results on the kind of non-Pauli operators that can be used as observables in the decoding scheme of CWS codes and propose a procedure to obtain those observables.     

图的最大团与最大独立集粘贴DNA计算模型

粘贴模型(stickermodel)是DNA计算中一个很重要的模型.其主要原理就是采用单双链混合型DNA分子进行编码,其优点在于在生物操作过程中不需要DNA链的延伸,不需要生物酶的作用以及DNA链可重复使用等,因此引起了来自不同学科的学者们的广泛关注与兴趣.文中提出了一种求解图的最大团问题的DNA计算模型,该模型采用了两种基本并行计算处理思想,一种是将图分解成小的子图来处理的并行思想;另一种是进行并行生物操作.     

Search methods for tile sets in patterned DNA self-assembly

The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory of structured DNA self-assembly, is to determine a set of coloured tiles that, starting from a bordering seed structure, self-assembles to a given rectangular colour pattern. The task of finding minimum-size tile sets is known to be NP-hard. We explore several complete and incomplete search techniques for finding minimal, or at least small, tile sets and also assess the reliability of the solutions obtained according to the kinetic Tile Assembly Model.     

Entanglement-assisted operator codeword stabilized quantum codes

In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes (QECCs), including additive and nonadditive codes, based on the codeword stabilized (CWS) framework on subsystems. The CWS framework is a scheme to construct QECCs, including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct QECCs. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes     

Bio-soft computing with fixed-length DNA to a group control optimization problem

A bio-soft computing method with fixed-length DNA to solve a group control optimization problem is presented in this paper. In the example of a multi-elevator dispatching problem, fixed-length DNA strands are used in representing the nodes and costs, where the costs are varied by the melting temperature of DNA strands. The optimal solution to a 6-story 2-elevator dispatching problem is searched by biochemical techniques based on the thermodynamic properties of designed DNA strands. This research has shown the potential of bio-soft computing solving the engineering applications, and could be implemented in the future bio-systems.     

Is DNA computing viable for 3-SAT problems?

Adleman reported how to solve a 7-vertex instance of the Hamiltonian path problem by means of DNA manipulations. After that a major goal of subsequent research is how to use DNA manipulations to solve NP-hard problems, especially 3-SAT problems. Lipton proposed DNA experiments on test tubes to solve 3-SAT problems. Liu et al. reported how to solve a simple case of 3-SAT using DNA computing on surfaces. Lipton's model of DNA computing is simple and intuitive for 3-SAT problems. The separate (or extract) operation, which is a key manipulation of DNA computing, only extracts some of the required DNA strands and Lipton thinks that a typical percentage might be 90. But it is unknown what would happen due to imperfect extract operation. Let p be the rate, where 0<p<1. Assume that for each distinct string s in a test tube, there are 10^l (l=13 proposed by Adleman) copies of s and that extracting each of the required DNA strands is equally likely. Here, the present paper will report, no matter how large l is and no matter how close to 1 p is, there always exists a class of 3-SAT problems such that DNA computing error must occur. Therefore, DNA computing is not viable for 3-SAT.     

Detecting subgraph isomorphism with MapReduce

In recent years, the MapReduce framework has become one of the most popular parallel computing platforms for processing big data. MapReduce is used by companies such as Facebook, IBM, and Google to process or analyze massive data sets. Since the approach is frequently used for industrial solutions, the algorithms based on the MapReduce framework gained significant attention within the scientific community. The subgraph isomorphism is a fundamental graph theory problem. Finding small patterns in large graphs is a core challenge in the analysis of applications with big data sets. This paper introduces two novel algorithms, which are capable of finding matching patterns in arbitrary large graphs. The algorithms are designed for utilizing the easy parallelization technique offered by the MapReduce framework. The approaches are evaluated regarding their space and memory requirements. The paper also provides the applied data structure and presents formal analysis of the algorithms.     

Evolvable computing by means of evolvable components

Encoding of information in DNA-, RNA- and other biomolecules is animportant area of research in fields such as DNA computing,bioinformatics, and, conceivably, microbiology and genetics. This surveyfocuses on two fundamental problems, the codeword design problemand the representation problem of abiotic information, formassively parallel processing with DNA molecules. The first problemrequires libraries of DNA sequences to be designed so that specificduplexes are formed during annealing while simultaneously preventingother undesirable hybridizations from occurring in the course of acomputation in the tube. The second involves a search for efficient andcost-effective methods of representing non-biological information in DNAsequences for storage and retrieval of large amouns of data (tera- andpeta-byte scales). Two approaches are treated, namely thermodynamic andcombinatoric-computational. Both experimental and theoretical resultsare described. A reference list of major works in the area is given.Finally, some open problems deemed important for their possible impacton encoding of abiotic information representation and processing arediscussed.     

环F2+uF2+u2F2上线性码的深度分布

记R=F₂+uF₂+u²F₂,定义了环R上码字的深度以及R上线性码的深度分布,研究了环R上码字深度的性质,给出了计算环[R]上码字深度的递归算法。利用环R上的线性码C及其生成矩阵,得到了域F2上的线性码C1,Cu,Cu2及相应的生成矩阵。通过域F2上的线性码C1,Cu,Cu2之间的关系,讨论了环R上的线性码的深度谱和深度分布,进而得到R上一类线性码的深度分布。     

基于Hadoop平台的LDA算法的并行化实现

随着互联网的飞速发展,需要处理的数据量不断增加,在互联网数据挖掘领域中传统的单机文本聚类算法无法满足海量数据处理的要求,针对在单机情况下,传统LDA算法无法分析处理大规模语料集的问题,提出基于MapReduce计算框架,采用Gibbs抽样方法的并行化LDA主题模型的建立方法。利用分布式计算框架MapReduce研究了LDA主题模型的并行化实现,并且考察了该并行计算程序的计算性能。通过对Hadoop并行计算与单机计算进行实验对比,发现该方法在处理大规模语料时,能够较大地提升算法的运行速度,并且随着集群节点数的增加,在加速比方面也有较好的表现。基于Hadoop平台并行化地实现LDA算法具有可行性,解决了单机无法分析大规模语料集中潜藏主题信息的问题。     

On Solutions of Linear Ordinary Difference Equations in their Coefficient Field

We extend the notion of monomial extensions of differential fields, i.e. simple transcendental extensions in which the polynomials are closed under differentiation, to difference fields. The structure of such extensions provides an algebraic framework for solving generalized linear difference equations with coefficients in such fields. We then describe algorithms for finding the denominator of any solution of those equations in an important subclass of monomial extensions that includes transcendental indefinite sums and products. This reduces the general problem of finding the solutions of such equations in their coefficient fields to bounding their degrees. In the base case, this yields in particular a new algorithm for computing the rational solutions of q -difference equations with polynomial coefficients.     

Hardness of Approximating the Closest Vector Problem with Pre-Processing

We show that the pre-processing versions of the closest vector problem and the nearest codeword problem are NP{\mathsf {NP}} -hard to approximate within any constant factor.     

Period distribution for error-correcting codes

The period distribution of an error-correcting code tells how many codewords in the code have a specific minimum period, where the minimum period of a codeword is the minimum number of cyclic shifts necessary to obtain the same codeword. The period distributions of R-S codes, extended R-S codes, and cyclic codes, in general, will be calculated in this paper. The period di stribution problem for the other noncyclic codes still remains unknown.     

一种基于MPEG音频编码的隐写算法

为了解决在压缩音频中实现高透明性、大容量信息隐藏的问题,提出了一种新的基于MPEG音频编码的盲检测隐写算法,首先通过对可变长码字(VLC)配对,实现对原始码字空间的扩展,然后利用码字映射规则完成秘密信息的嵌入.该算法能够保持隐写前后的压缩音频文件大小不变,隐写过程中不需要对MPEG音频进行完全解码.实验结果表明,所提出算法计算复杂度低,同时可获得较高的隐藏容量和良好的不可感知性.     

基于自组装DNA计算的NTRU密码系统破译方案(英文)

自组装DNA计算在解决NP问题,尤其在破译密码系统方面,具有传统计算机无法比拟的优势．文中提出了一种用自组装DNA计算破译NTRU公钥密码系统的方法．针对NTRU密码系统的特点,采用DNA瓦片编码信息,借助于瓦片间的粘性末端进行自组装,给出了求解多项式卷积运算的实现方案．在此基础上,通过引入非确定性的指派瓦片,提出了一种破译NTRU系统的非确定性算法．通过创建数以亿计的参与计算的DNA瓦片,该算法可以并行地测试每个可能的密钥,以高概率地输出正确密钥．该方法最大的优点是充分利用了DNA瓦片具有的海量存储能力、生化反应的巨大并行性以及组装的自发有序性．理论分析表明,该方法具有一定的可行性．     

The syntactic monoid of hairpin-free languages

The study of hairpin-free words has been initiated in the context of DNA computing. DNA strands that, theoretically speaking, are finite strings over the alphabet {A, G, C, T} are used in DNA computing to encode information. Due to the fact that A is complementary to T and G to C, DNA single strands that are complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: if some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper continues the theoretical study of hairpin-free languages. We study algebraic properties of hairpin-free words and hairpins. We also give a complete characterization of the syntactic monoid of the language consisting of all hairpin-free words over a given alphabet and illustrate it with an example using the DNA alphabet.     

基于DNA Tiles自组装的布尔逻辑运算

大量研究工作表明,DNA tiles自组装现象是分子生物计算过程中一个很重要的计算方式.分子自组装的基本特点在于由许多小分子在一定机理的作用下,自动形成更大规模的超级分子结构的过程.自组装用于计算,在于这种组装模式可以抽象成一个自动化的系统,只需根据问题的需要设计好输入,再将其输入到运算系统,经过分子自组装过程,最后能生成问题的解.文中基于这样的运算机理,在DNA tiles自组装这个计算平台上,尝试做布尔逻辑运算,针对4变量4句子的布尔逻辑问题,提出一个DNA tiles自组装自动化运算系统.