CYCLIC OPERATORS FOR COLUMNS OF THE MATRICES OF DISCRETE TRANSFORMS

M. S. Bespalov

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CYCLIC OPERATORS FOR COLUMNS OF THE MATRICES OF DISCRETE TRANSFORMS

机译：离散变换矩阵列的循环算子

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We study the structure and properties of a cyclic operator whose orbits are discrete Walsh functions. We propose an algorithm for constructing such an operator and analyze the Hadamard and Paley enumerations. Bibliography: 14 titles.

机译：我们研究轨道为离散沃尔什函数的循环算子的结构和性质。我们提出了一种构造此类算子的算法，并分析了Hadamard和Paley枚举。参考书目：14种。

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《Journal of Mathematical Sciences 》 |2015年第1期| 36-48| 共13页
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M. S. Bespalov;
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A. G. and N. G. Stoletov Vladimir State University 87, Gor'kogo St., Vladimir 600000, Russia;

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1. Linear operators that preserve maximal column ranks of nonnegative integer matrices [J] . Song SZ. Proceedings of the American Mathematical Society . 1998 ,第8期

机译：保留非负整数矩阵的最大列等级的线性运算符
2. Linear operators that preserve spanning column ranks of nonnegative matrices [J] . Suk-Geun Hwang, Si-Ju Kim, Seok-Zun Song Journal of the Korean Mathematical Society . 1994 ,第4期

机译：保留非负矩阵的跨列等级的线性运算符
3. A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals [J] . PabloSoto-Quiros ScientificWorldJournal . 2015 ,第3期

机译：具有用于矢量值离散时间信号的离散傅里叶变换的块矩阵的并行框架
4. Hardware implementation of a series of transform matrices based on discrete hirschman transform [C] . Peng Xi, Victor DeBrunner Asilomar Conference on Signals, Systems and Computers . 2016

机译：基于离散希尔斯曼变换的一系列变换矩阵的硬件实现
5. Eigenfunctions and eigenoperators of cyclic integral transforms with application to Gaussian beam propagation [D] . McCallum, Matthew S. 2008

机译：循环积分变换的本征函数和本征算子在高斯光束传播中的应用
6. A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals [O] . Pablo Soto-Quiros 2015

机译：矢量值离散时间信号的具有离散傅立叶变换的块矩阵的并行框架
7. Figure 4: (A) One conserved sequence, which occurs 79 times in 46,264 binding site peaks from the ChIP-seq data-set. The mutation profile of this conserved sequence is illustrated, where ’_ ’ indicates this base is unchanged; DEL indicates this base is lost; INS X indicates a new base X is inserted in front of this base. (B) Several repeated elements patterns are listed. (C) In the first column, the top five DNA motifs, mined by meme-chip tools (Machanick Bailey, 2011) are illustrated. The resemblant conserved sequences, found by the CFSP algorithm are listed in the second column. In the third column, the position-specific scoring matrices, which are transformed from mutational information are listed. The similarity between meme motif and resemblant conserved sequence with PSSM format was calculated via a stamp motif comparison tool (Mahony Benos, 2007). The E-values for the similarity of those pairs is displayed in the fourth column. (D) One motif is selected in each group clustered by gkmsvm descriptors, and the corresponding motif found by the CFSP algorithm is listed below. (E) There are additional datasets (File No: ENCFF100GRL, ENCFF616IRT, ENCFF870CER, Target: SREBF1) collected from https://www.encodeproject.org. The top two motifs are selected in each file using meme tools, and the corresponding motifs found by our algorithm are listed below. [O] . -1

机译：图4：（a）一种保守序列，其发生在芯片-SEQ数据集中的46,264个结合位点峰值中的79倍。说明了这种保守序列的突变分布，其中'_'表示该碱度不变; del表示此基础丢失; INS X表示新的基础X插入此基础前面。（b）列出了几种重复的元素模式。（c）在第一栏中，示出了由MEME芯片工具（Machanick＆Bailey，2011）开采的前五个DNA主题。由CFSP算法发现的相应保守序列列于第二列中。在第三列中，列出了从突变信息转换的特定位置的评分矩阵。 MEME主题与PSSM格式的相似性与PSSM格式之间的相似性通过邮票图章比较工具（Mahony＆Benos，2007）计算。这些对相似性的电子值显示在第四列中。（d）在由GKMSVM描述符聚集的每个组中选择了一个图案，下面列出了CFSP算法的相应主题。（e）从https://www.encodeproject.org收集的，有附加数据集（文件no：cernff100grl，cenf616irl，conf8.20cer，target：srebf1）。使用MEME工具在每个文件中选择前两个图案，并且我们的算法发现的相应主题如下所示。
8. Discrete Fourier transform of vector sets and perturbations of circulant matrices [R] . Najfeld, Igor 1981

机译：矢量集的离散傅里叶变换和循环矩阵的扰动

CYCLIC OPERATORS FOR COLUMNS OF THE MATRICES OF DISCRETE TRANSFORMS

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